time synchronization and low complexity detection...
TRANSCRIPT
TIME SYNCHRONIZATION AND LOW COMPLEXITY DETECTION FOR HIGH SPEED WIRELESS LOCAL
AREA NETWORKS
A THESIS
Submitted by SATHISH. V
in partial fulfillment for the award of the degree
of
MASTER OF SCIENCE (BY RESEARCH)
FACULTY OF INFO
ANNA UNIV
RMATION AND COMMUNICATION
ENGINEERING
ERSITY: CHENNAI 600 025
APRIL 2006
ANNA UNIVERSITY: CHENNAI 600 025
BONAFIDE CERTIFICATE
Certified that this thesis titled “TIME SYNCHRONIZATION AND LOW
COMPLEXITY DETECTION FOR HIGH SPEED WIRELESS LOCAL
AREA NETWORKS” is the bonafide work of Mr.V.SATHISH who carried out
the research under my supervision. Certified further that to the best of my
knowledge the work reported herein does not form part of any other thesis or
dissertation on the basis of which a degree or award was conferred on an earlier
occasion of this or any other candidate.
SIGNATURE Dr. S. Srikanth SUPERVISOR Member research staff AU-KBC Research centre, MIT, Anna University, Chromepet, Chennai - 600044
iii
ABSTRACT
In this thesis, we propose a low complexity time synchronization
algorithm and a low complexity spatial detection technique for high-speed WLANs
based on the 802.11n standard. The two major goals of the 802.11n standard are
achieving a higher data rate and providing backward compatibility with the existing
legacy 802.11a/g systems. To achieve the first goal, the proposals for the 802.11n
standard use multiple-input multiple-output orthogonal frequency division
multiplexing (MIMO-OFDM) technology. This necessitates the use of spatial
detection techniques at the receiver. The conventional spatial detection techniques
exhibit a tradeoff between their complexity and their performance. Since the
802.11n system uses forward error correcting (FEC) codes at the transmitter and the
viterbi decoder is typically used at the receiver which further increases the
complexity of the system.
To achieve the backward compatibility goal, we have to address two
issues. They are the design of a new preamble and the use of protection mechanism
to avoid interference from the legacy systems. The new preamble should be
understandable by the legacy stations and it should work well for the MIMO-
OFDM systems. The protection mechanism can be provided either in the physical
(PHY) layer level or in the medium access control (MAC) layer level. At the PHY
layer, the header which carries the length and rate field is decoded by the non-
iv
transmitting stations and they defer the channel access for that duration. To decode
the header information of the new preamble successfully, the legacy system should
be able to use its existing initial receiver algorithms. In addition, the new receiver
algorithms have to be proposed for MIMO-OFDM systems which use this new
preamble.
In the first part of the thesis, we propose a low complexity time
synchronization algorithm for the legacy stations and for the MIMO-OFDM stations
in a typical 802.11n network. We first study the different ways of extending the
legacy 802.11a preamble to the MIMO-OFDM systems because using the legacy
preamble in some form for the MIMO systems can help in achieving the backward
compatibility. We study the performance of automatic gain control (AGC)
algorithm using these preambles in the MIMO stations. We show that sending the
cyclically shifted versions of the legacy preamble from the 802.11n transmitter
provides better power measurements at the receiver compared to simply repeating
the legacy preamble at the transmitters. As a first receiver task, we review the
method of simply extending the single-input single-output OFDM (SISO-OFDM)
start of packet detection (SOP) algorithm to MIMO-OFDM systems. We study the
performance of MIMO-OFDM SOP detection algorithm under the spatially
correlated and uncorrelated channels. We propose a new coarse timing estimation
algorithm that can be used in legacy systems and in MIMO-OFDM systems. We
study the performance of the different preambles in the legacy systems and in the
MIMO-OFDM systems. We show that the proposed coarse timing estimation
v
algorithm in SISO systems performs well for legacy preamble and for the new
preambles as compared to the threshold based algorithm. Since the proposed coarse
timing estimation algorithm works well even in lower SNRs, we propose a low
complexity fine timing estimation algorithm for the SISO-OFDM and MIMO-
OFDM systems. We compare the performance of this algorithm with the popular
correlation based techniques. We evaluate the performance of the proposed fine
timing estimation algorithm for all the preamble types under all the channel models.
From the simulation results, we have shown that the cyclically shifted preamble
with cyclic shift of 8 samples for a 2x2 system seems to be good choice for mixed
mode and green field operations.
In the second part of the thesis, we propose a low complexity spatial
detection technique for bit interleaved coded modulated (BICM) MIMO-OFDM
system. We first review the different spatial detection techniques, their performance,
and their complexity requirements. Based on the moderately complex and
moderately performing ordered successive interference cancellation (OSIC)
technique, we propose a new grouping and detection technique. The grouping can
be done in a fixed manner or in an adaptive manner. We study the performance of
the proposed techniques in the uncoded and coded systems. We show that the
performance in the coded system matches with the performance of the OSIC
technique and has lesser complexity compared with the OSIC technique. We also
study the performance of the proposed system under various channel models. For
the simulation, we have considered the BICM MIMO-OFDM system proposed in
vi
draft 802.11n standard. The results show a 40% reduction in complexity can be
achieved by using the proposed technique as compared to complexity requirement
of OSIC technique and achieves similar performance.
v
ACKNOWLEDGEMENTS
I wish to express my deep, sincere gratitude to my guide, Dr. S Srikanth, for his
excellent guidance, encouragement, support, and insightful comments throughout
the period of my master’s degree. He is more than a guide for me. Whatever
knowledge and experience I have gained during my study here, I owe it to him.
I am very grateful to Dr. C N Krishnan of AU-KBC research center for creating an
excellent infrastructure and environment for carrying this research work. I thank Mr.
M. Sethuraman and Mr. Ganges Morekonda for sharing their valuable
experience and knowledge during the technical discussions. They are the sources of
inspiration for my thirst to learn new things. I also thank Prof. S.J.Thiruvengadam
for his continuous encouragement to carry out the research work successfully.
I thank my friends in AUKBC, Muthuraja, Jackson, Vasu, K.Karthik, Selvam,
Arulmozhi, Vijay, Pattabi, Madhav, and Murugu for helping me out with both
technical as well as non-technical inputs at critical situations. I thank my seniors
Rajesh, Bio-Rajesh, Masood, Viji, Anand, Rajamannar and Sujith for helping me in
various aspects to carry out my master’s studies.
I am indebted to my parents for all their prayers, support and encouragement to help
me work on the thesis. I thank my brother, Sakthi, brother-in-law, Bala, sister,
Sangeetha, and beloved Subha for their care and being with me under all
circumstances. I would like to acknowledge my friends Karthik, Vipin, Bama,
Ashok, Renga, Thiagu and Jeyaradha for their support and invaluable
encouragement. Above all, I thank God for giving me all the people and facilities I
needed.
V. SATHISH
viii
TABLE OF CONTENTS
CHAPTER NO TITLE PAGE NO. ABSTRACT iii
LIST OF TABLES xi
LIST OF FIGURES xii
1 INTRODUCTION 1
1.1 OVERVIEW OF WLAN STANDARDS 1
1.2 WIRELESS CHANNELS AND MIMO-OFMD SYSTEMS 3
1.3 GOALS AND CHALLENGES OF IEEE 802.11n SYSTEMS 6
1.3.1 Implementation issues 7
1.3.2 Backward compatibility 7
1.3.3 Protection mechanism 8
1.4 TIME SYNCRHONIZATION IN 802.11n 9
1.4.1 Previous Work 9
1.4.2 Contribution to this thesis 10
1.5 SPATIAL DETECTION TECHNIQUES FOR BICM MIMO-
OFDM SYSTEMS 10
1.5.1 Previous Work 11
1.5.2 Contribution to this thesis 12
1.6 ORGANIZATION OF THESIS 12
2 TIMING SYNCHRONIZATION FOR MIMO-OFDM SYSTEMS 14
2.1 INTRODUCTION 14
2.2 OVERVIEW OF IEEE 802.11a PREAMBLE 14
ix
2.3 EXTENSION OF SISO-OFDM SYSTEM TO MIMO-OFDM
SYSTEM 16
2.3.1 Legacy mode 16
2.3.2 Mixed mode 16
2.3.3 Green field mode 17
2.3.4 MIMO-OFDM packet structure 17
2.3.5 Signal model for receiver operating in different modes 18
2.4 METHODS OF EXTENDING OF SISO PREAMBLE TO
MIMO-OFDM SYSTEM 20
2.4.1 Repetition method 20
2.4.2 Cyclic shift method 24
2.5 INITIAL RECEIVER TASKS FOR MIMO-OFDM SYSTEMS 27
2.5.1 Start of the packet detection 28
2.5.2 Coarse frequency offset estimation 30
2.5.3 Proposed coarse timing estimation 32
2.5.4 Proposed fine timing estimation 40
2.6 SIMULATION SETUP AND RESULTS DISCUSSION 43
2.6.1 Performance of SOP detection 44
2.6.2 Performance of proposed coarse timing estimation 53
2.6.3 Performance of proposed fine timing estimation 60
2.7 CONCLUSION 66
3 LOW COMPLEXITY MIMO-OFDM RECEIVER 67
3.1 INTRODUCTION 67
3.2 SYSTEM MODEL 67
3.2.1 Transmitter model 68
3.2.2 Receiver model 69
3.3 SPATIAL DETECTION TECHNIQUES 71
3.3.1 Non-Linear detection technique 71
3.3.1.1 Maximum Likelihood detection 72
x
3.3.2 Linear detection techniques 72
3.3.2.1 Zero forcing technique 73
3.3.2.2 Minimum mean square error technique 73
3.3.3 Embedded detection techniques 74
3.3.3.1 Ordered successive interference cancellation
technique 74
3.4 PROPOSED GO MMSE V-BLAST 76
3.4.1 Fixed GO MMSE V-BLAST 77
3.4.2 Adaptive GO MMSE V-BLAST 79
3.5 SIMULATION SETUP AND RESULTS DISCUSSION 80
3.5.1 Performance of uncoded system 81
3.5.2 Performance of coded system 84
3.5.3 Complexity comparison 88
3.6 CONCLUSION 88
4 CONCLUSION AND FUTURE WORK 90
APPENDIX
1 PUBLICATION FROM THIS THESIS 93
xi
LIST OF TABLES
TABLE NO TABLE NAME PAGE NO.
2.1 The RMS delay spread for different TGn channel 44
3.1 Complex computations for various spatial detection schemes 88
xi
xii
LIST OF FIGURES
FIGURE NO FIGURE NAME PAGE NO.
1.1.1 OFDM transmitter 4
1.1.2 OFDM receiver 4
1.2 Diagram of a MIMO system 5
1.3.1 MIMO-OFDM transmitter 5
1.3.2 MIMO-OFDM receiver 6
2.1 PLCP preamble of the IEEE 802.11a burst 15
2.2.1 Mixed mode packet 17
2.2.2 Green field mode packet 18
2.3 Repetition of the same preamble in all the transmit antennas of
a MIMO-OFDM system
21
2.4 Cross correlation at the legacy receiver for repetition preamble. 23
2.5 CS versions of legacy preamble in the transmit antennas. tN 25
2.6 Cross correlation at the thp receive antenna for cyclically
shifted preamble with 2 400csT n= s
26
2.7 Averaged auto correlation metric for a 2x2 MIMO-OFDM
system at SNR=10dB
29
2.8 Falling edge of the plateau calculated for a 2x2 system 33
2.9 Falling edge and rising edge of the metrics calculated for a 2x2
system.
36
2.10 Plot of ( )nΛ , ( )nθ and 1/ ( )D n 37
2.11 Probability distribution CTO estimate of a 2x2 MIMO-OFDM
system in an AWGN channel with SNR=10dB
38
2.12 Block diagram of proposed coarse timing estimation 39
xiii
2.13 failP versus SNR at the legacy receiver in mixed mode under the
spatially uncorrelated channel model D.
45
2.14 SNR needed versus channel models at the legacy receiver
under various spatially uncorrelated channels
46
2.15 failP versus SNR at the MIMO receiver in green field mode
under the spatially uncorrelated channel model D.
47
2.16 SNR needed versus channel models at the MIMO receiver in
green field mode under various spatially uncorrelated channels.
48
2.17 Condition number versus taps for different channel modes
measured in the time domain
49
2.18 failP versus SNR at the legacy receiver in mixed mode under the
spatially correlated channel model D.
50
2.19 SNR needed versus channel models at the legacy receiver in
mixed mode under various spatially correlated channels
51
2.20 failP versus SNR at the MIMO receiver in green field mode
under the spatially correlated channel model D
52
2.21 SNR needed versus channel models at the MIMO receiver in
green field mode under various spatially correlated channels.
53
2.22 Comparison of distribution of proposed and threshold based
CTO estimate technique at legacy receivers for different
preambles
55
2.23 Comparison of distribution of proposed and threshold based
CTO estimate technique at MIMO receivers for different
preambles
57
2.24 Percentage of CTO estimates versus channel models: legacy
receiver in mixed mode for different preamble under different
channel models.
58
xiv
2.25 Percentage of CTO estimates versus channel models: MIMO
receiver in green field mode for different preamble under
different channel models.
59
2.26 Comparison of distribution of proposed fine timing estimate
and cross correlation based technique at legacy receivers for
different preambles.
61
2.27 Comparison of distribution of proposed fine timing estimate
and cross correlation based technique at MIMO receivers for
different preambles.
63
2.28 Percentage of fine timing estimates within estimation accuracy
versus channel models: Legacy receiver for different preamble.
64
2.29 Percentage of fine timing estimates within estimation accuracy
versus channel models: MIMO receiver for different preamble.
65
3.1 802.11n MIMO-OFDM baseband transmitter 69
3.2 802.11n MIMO OFDM baseband receiver 70
3.3 Traditional linear detector 73
3.4 Ordered successive interference canceller 76
3.5 Proposed Group ordered MMSE VBLAST detector 79
3.6 Comparison of BER versus SNR: MMSE, MMSE V-BLAST
and proposed fixed GO MMSE V-BLAST for an uncoded 4x4
system.
81
3.7 Comparison of BER versus SNR: MMSE, MMSE V-BLAST
and proposed adaptive GO MMSE V-BLAST with
and .
1.75thres =
2thres =
82
3.8 Comparison of BER versus SNR; Fixed and adaptive GO
MMSE V-BLAST with 1.75thres = and 2thres = .
83
3.9 Comparison of SNR needed versus channel models for a BER
= 10-4; 4x4 uncoded MIMO-OFDM system, Fixed and
adaptive schemes.
84
3.10 Comparison of BER versus EbN0: MMSE, MMSE V-BLAST 85
xv
and proposed fixed GO MMSE V-BLAST for a coded 4x4
system.
3.11 Comparison of BER versus EbN0: MMSE, MMSE V-BLAST
and proposed adaptive GOMMSE V-BLAST with
and 2.
1.75thres =
86
3.12 Comparison of BER versus EbN0: Fixed and adaptive GO
MMSE V-BLAST with 1.75thres = and 2thres = .
86
3.13 Comparison of EbN0 needed versus channel models for a BER
= 10-4; 4x4 coded MIMO-OFDM system, Fixed and adaptive
schemes
87
1
CHAPTER 1
INTRODUCTION
Over the last few years, Wi-Fi is usually deployed as the last hop of the
internet or wireline telephone network, thereby working in conjunction with the
wireline networks. The biggest advantage of Wi-Fi is that it provides mobility and
coverage. At the same time Wi-Fi is the bottleneck for the internet users or people
connected through wireless local area network (WLAN) because it restricts the
maximum utilization of the wireline network. The data rate achieved is not in par
with the wireline network. Recent advancements in wireless research and smart
antenna technology has resulted in an upgrade to the Wi-Fi networks and removed
the bottleneck thereby providing access to the users with extended range and
increased throughput.
1.1 OVERVIEW OF WLAN STANDARDS
The IEEE 802.11 WLAN standard was first defined in 1997 for indoor
communication between computers and the mobile devices within a range of 150
meters. The standard consists of physical layer (PHY) and medium access channel
layer (MAC) specifications (IEEE 802.11 1999). The 802.11 complaint devices use
the 2.4 GHz ISM band for its operation. The PHY layer techniques used in this
standard are frequency hopping spread spectrum (FHSS), direct sequence spread
spectrum (DSSS) and infrared (IR) communication. The maximum data rate that
can be achieved using these techniques is 2 Mbps. The MAC mechanism used is
carrier sense multiple access with collision avoidance (CSMA/CA). This is
achieved by physical carrier sensing and virtual carrier sensing techniques.
2
With the motivation to increase the data rate of WLANs, an enhancement
to the PHY specification of 802.11 was standardized as IEEE 802.11b. In this
standard, the PHY layer uses DSSS and achieves a maximum data rate of 11 Mbps
(IEEE 802.11b 1999). The modulation scheme used is complementary code keying
(CCK). The approximate bandwidth used in this standard is 22 MHz and the
frequency of operation is 2.4 GHz. There is no significant change in the MAC as
compared to the basic 802.11 standard. In 1999, another PHY specification for
enhancing the data rate of the system was also standardized and is called as IEEE
802.11a. Since the 2.4 GHz is crowded with microwave ovens, Bluetooth and other
devices, the 802.11a standard uses 5 GHz for its operation. This standard uses a
spectrally efficient transmission scheme called as orthogonal frequency division
multiplexing (OFDM). The maximum data rate obtained is 54 Mbps with a rough
bandwidth of 20 MHz (IEEE 802.11a 1999). In 2003, another PHY specification
was arrived to collectively provide the PHY features of 802.11b and 802.11a in the
2.4 GHz. This is standardized as IEEE 802.11g. In this standard, there are 2 modes
of operation. They are extended PHY (ERP) rate and the non extended PHY rate
(non-ERP) modes. In the ERP mode, the 802.11g compliant stations provide data
rates from 1 Mbps to 54 Mbps with a backward compatibility to legacy 802.11b
stations whereas in the non-ERP mode, the station can provide only 11b PHY rates
(IEEE 802.11g 2003).
Eventhough the maximum PHY layer rate is around 50 Mbps, the net
throughput obtained is only 60 percent of it in the indoor applications. To increase
the net throughput on par with Ethernet, the task group ‘n’ was formed in January
2004. Many proposals were reviewed to achieve this goal. The three main proposals
are WWiSE, TGnsync and EWC (WWISE 2005, TGnsync 2005 and EWC 2006).
All the 3 proposals utilize multiple transmit and multiple receive antennas called as
multiple-input multiple-output (MIMO) technology. This allows one to transmit
multiple independent data streams simultaneously to increase the spectral efficiency.
This is also known as spatial multiplexing. To encounter the multipath nature of the
3
channel, OFDM is used along with the MIMO technology. Hence, the final system
is categorized as a MIMO-OFDM system. The 3 proposals mandate the 20 MHz
operation and support for 40 MHz operation. They also mandate the interoperability
with the legacy 802.11a/g systems. The maximum PHY data rate that can be
achieved with 4 transmit antennas in 40 MHz is around 500 Mbps. On the MAC
side, all the proposals support frame aggregation, block acknowledge (BACK) and
MAC header compression. In January 2006, the EWC proposal has been finalized
as the draft for the 802.11n standard. Apart from the above features, this supports
advanced techniques for optional modes. They are adaptive beamforming, space
time block coding (STBC), and low density parity coding (LDPC) for increased
range and reliable communications.
1.2 WIRELESS CHANNELS AND MIMO-OFDM SYSTEMS
In recent years, there has been an increase in demand on the data rate
capabilities of wireless systems. This has necessitated an increase in bandwidth and
signaling rate. As the bandwidth increases, the multipath distortion or frequency-
selective fading caused by the physical medium becomes worse. The multipath
channel causes a time dispersion of the transmitted signal resulting in the overlap of
the various transmitted symbols at the receiver (David Tse and Pramod Viswanath,
2005). This is referred to as intersymbol interference (ISI), which, if left
uncompensated, causes high error rates. One of the solutions to the ISI problem is
the use of the OFDM technique (Bingham J.A.C. 1990). In OFDM systems, the
high rate transmit signal is divided into many lower rate sub streams and each sub
stream is modulated by orthogonal carriers. Then all are added to obtain a serial
stream and transmitted. Due to this division, the bandwidth occupied by each sub
stream will be less compare to the total bandwidth. This converts the frequency
selective fading channel to flat fading channel (Jeffrey G. Andrews and Andrea J.
Goldmsith 2004). Hence, an ISI free scenario is obtained. Moreover, the signal of
duration equal to delay spread of the channel is taken from the last part of
modulated signal and appended in front to the modulated signal. This is called
4
Serial to
parallel
Data bits Constellation
mapper
IFFT
Parallel to
serial
Cyclic prefix
Figure 1.1.1: OFDM transmitter
cyclic prefix. Therefore the ISI between the OFDM symbols can be completely
eliminated through the use of a cyclic prefix. Cyclic prefix also helps in maintaining
the orthogonality between the carriers at the receiver in multipath channel. The
whole system can be realized using an IFFT block at the transmitter and FFT at the
receiver. At the receiver, FFT reduces the multipath channel impulse response into a
multiplicative constant with the transmit signal on a tone-by-tone basis. So each
tone can be equalized independently and the complexity of equalizer is eliminated.
A typical OFDM transmitter and OFDM receiver is shown in the figure 1.1.1 and
1.1.2. As mentioned in section 1.2, OFDM has been adopted as the modulation
scheme in 802.11a and 802.11g systems to achieve the maximum rate of 54 Mbps.
Decoded data bits
Serial to
parallel
FFT
Parallel to
serial
Remove Cyclic prefix
Equalizer
Constellation Demapper
To increase the data rate further in the multipath channel MIMO
technology is continued with OFDM (Paulraj A, et al 2003). This is called as
MIMO-OFDM technology and is used in 802.11n system. The expected data rate
can go up to 500 Mbps. In MIMO systems multiple independent streams are
transmitted simultaneously to increase the data rate. A typical MIMO system is
shown figure 1.2.
Figure 1.1.2: OFDM receiver
5
Channel Transmitter
Receiver
Figure 1.2: Diagram of a MIMO system
In a MIMO-OFDM transmitter, a vector is transmitted in each tone with
multiple transmit antennas. At the receiver, the signal at each RX antenna will have
signal from all the transmit signal coming from different channels. After FFT, the
channel frequency response will be a matrix in each tone. The receive vector in each
tone vector will be the matrix multiplied by the transmit vector. Then spatial
detection is performed on the receive vector of each tone to equalize for the channel
and separate the transmit signals.
Multipath remains an advantage for a MIMO-OFDM system since
frequency selectivity caused by multipath improves the rank distribution of the
channel matrices across frequency tones, thereby increasing capacity. A typical
Transmit antennas
OFDM
Modulator
OFDM
Modulator
Spatial Demultiplex
Information bits
Figure 1.3.1: MIMO-OFDM transmitter
6
MIMO-OFDM transmitter and receiver are shown in figures 1.3.1 and 1.3.2,
respectively.
Remove CP &
FFT
Remove CP &
FFT
Receive antennas Constellation
Demapper
Constellation Demapper
Spatial multiplexer
Decoded bits
Spatial detection (ML, ZF, MMSE
and SIC)
Figure 1.3.2: MIMO-OFDM receiver
1.3 GOALS AND CHALLENGES OF 802.11n SYSTEMS
In this section, a brief explanation of the goals of the 802.11n system and
the challenges in attaining the goals is presented. One of the main objectives of the
802.11n system is to achieve higher data rates in a multipath fading channel. One of
the ways suggested in the 802.1ln standard is the use of MIMO-OFDM technology.
Ultimately, the increase in number of antennas in the transmitter and at the receiver
creates many system implementation issues. The other objective is to provide
backward compatibility with the existing legacy 802.11a/b/g systems. This
requirement in turn creates 2 more challenges. First is the design of preamble which
should be understandable by the legacy stations as well and be a good one for
MIMO systems. Second is the protection mechanism from the interference, i.e.,
when the traffic is ongoing between 2 MIMO-OFDM stations, the legacy stations in
the network should understand the duration of the transmission and defer the
channel access. Similarly, a MIMO-OFDM system should understand the
transmission from the legacy stations.
7
1.3.1 Implementation issues
In the system implementation side, the use of MIMO-OFDM technology
in 802.11n system requires multiple radio frequency (RF) and baseband (BB) chains.
There must be at least as many chains as independent data steams at the transmitter
and at the receiver (Jeffrey M. Gilbert, et al 2005). The introduction of parallelism
in the data streams to increase the data rate requires parallel blocks in each BB and
RF for each stream to be processed. This complexity in turn increases the power
consumption and area. Apart from these hardware and cost complexities, there is a
need for low complexity and robust receivers tasks due to the introduction of the
new preamble which operates for both the legacy and MIMO stations. This is
because the initial receiver tasks such as estimation of the receive power for
automatic gain control (AGC), start of packet (SOP) detection, coarse time offset,
coarse frequency offset, and fine time offset depends on the structure of the
preamble. The other implementation issue in MIMO-OFDM systems is the spatial
detection algorithm to be used at the receiver. The receive signal in each RX
antenna is a superposition of signals coming from all the transmit antennas. To
separate them at the receiver, a spatial detector is employed. The spatial detection is
done in subcarriers and the complexity increases as the number of subcarrier
increase. There are different types of spatial detectors with different computational
complexity and performance. There exists a tradeoff between the complexity of the
detection technique and its performance.
1.3.2 Backward compatibility
When a MIMO station intends to transmit a packet to a legacy station,
the MIMO station uses only 1 transmit antenna and transmits the frame in the
legacy format. This enables the existing legacy station to decode the packet and
follow the MAC rules. The other MIMO stations receiving this packet through
multiple receive antennas can use them efficiently and decode the packet and defer
the channel for the MIMO-legacy transmission to progress without collisions. When
the intended receiver is a MIMO station, then the transmitted signal should be in
8
such a way that the legacy stations should understand and defer the channel. To
achieve this objective, either the same legacy frame format can be used for MIMO
transmission or a special preamble structure can be used. The issue here is that a
simple extension of the legacy preambles to MIMO system may be helpful in
achieving backward compatibility but may not provide good performance because
of the beamforming effects. Similarly, the use of special preambles designed for
MIMO systems can work well for MIMO stations but fails with respect to backward
compatibility. Hence, preamble design is an important challenge to achieve
interoperability with legacy stations and better performance in MIMO stations.
1.3.3 Protection mechanism
Since the typical 802.11n network has legacy stations and new MIMO
stations, and CSMA/CA MAC is used, there should be certain ways for these
stations to understand each other and protect themselves from the interference
created by each other. The 3 main proposals for the 802.11n standard had specified
different protection mechanisms at the PHY and MAC level. In the PHY layer level,
a special preamble and header is sent when MIMO-OFDM transmission happens in
the presence of the legacy stations. This makes the legacy station to defer the
medium for MIMO-OFDM traffic. In the MAC layer, protection is done in two
ways. One way is to provide protection using conventional network allocation
vector (NAV) mechanism and the other way is to provide protection using spoofing
wherein the PHY layer convergence function (PLCP) header part of the frame is
modified. The length field which gives the length of the payload in octets and the
rate field which specifies the rate at which the payload is transmitted are changed
suitably. One can use the rate and length field to calculate the duration of the packet.
To provide protection, the rate field is kept at the lowest rate (say 6 Mbps in OFDM
mode). The legacy stations receiving this packet calculate the duration field and
tunes the RF to receiver mode and receives till this duration. So there will be no
interference from the legacy stations for the MIMO-OFDM traffic. When legacy
9
stations transmit, the MIMO stations can receive the signal through different receive
antennas and can easily decode the header to defer the channel access.
From the above discussions, we see that to provide backward
compatibility and protection with the use of new preamble, new receiver algorithms
have to be defined. Also, the receiver algorithms should be robust and simple to
implement. In this thesis, we propose a low complexity time synchronization
technique which works for legacy stations as well as for MIMO stations. A low
complexity spatial detection technique is also proposed for 802.11n systems.
1.4 TIMING SYNCHRONIZATION IN 802.11n
As mentioned earlier, the main focus of the work is to develop a simple
and robust timing synchronization algorithm for the legacy stations and MIMO
stations when the new preamble is used. In a typical 802.11a system, timing
synchronization is done in two stages. First, a rough estimate of the starting position
of the packet is obtained through a coarse timing estimator. In the second stage, the
starting of the OFDM symbol window is obtained by a fine timing estimator. The
non-optimal locking of the symbol starting results in intersymbol interference (ISI)
and intercarrier interference (ICI). Similarly, one can follow the same approach for
timing synchronization in MIMO-OFDM systems.
1.4.1 Previous work
Many time synchronization algorithms have been proposed for SISO-
OFDM systems (Sridhar and K. Giridhar 2003, Victor P. Gil et al 2004 and Yik-
Chung Wu et al 2005). In 2001, Mody A.N and Stuber G. L proposed a new
preamble using a pseudo noise (PN) sequence for MIMO-OFDM systems which
cannot be extended to 802.11n based WLAN systems as interoperability constraints
are not addressed. In 2003, Schenk T.C.W. and Allert Van Zelst defined a time
multiplexed preamble for MIMO-OFDM systems and proposed a new technique for
time and frequency synchronization using that preamble. The drawback of this
10
algorithm is its complexity and the algorithm is proposed only for MIMO-OFDM
systems. Jianhua Liu and Jian Li (2004) has proposed a simple method to extend the
legacy preamble for MIMO-OFDM systems where backward compatibility is
addressed and a new technique for time synchronization has also been proposed.
The proposed preamble and proposed techniques performs better in terms of
synchronization, but performs poorly in AGC convergence due to beam forming
effects
1.4.2 Contribution to the thesis
In this thesis, we first analyze the different modes of operation in a
typical 802.11n network and the various ways of extending the legacy preamble to
MIMO-OFDM systems keeping interoperability in mind. The effect of the new
preamble in different modes is discussed and their performance in the initial
receiver tasks like AGC and time synchronization is discussed. We studied the
performance of the SOP detection in independent and identically distributed
channel and in spatially correlated channels with the different preamble types. A
new coarse timing and fine timing estimation algorithm has been proposed for the
SISO and MIMO systems. The performance of the proposed coarse timing
algorithm is compared with the performance of threshold based technique. The
simulations results show that the proposed technique performs better and simplifies
the complexity of doing fine timing estimation. The low complexity fine timing
estimation algorithm is compared with performance of the cross correlation based
technique. Simulation results show similar performance for both the techniques,
however, the proposed technique requires less complexity.
1.5 SPATIAL DETECTION FOR BICM MIMO-OFDM SYSTEMS
In all the 3 main proposals for the 802.11n standard bit interleaved coded
modulated (BICM) system is proposed. The forward error correction (FEC) encoder
used in the transmitter is the convolutional encoder. Then, typical viterbi decoder is
used at the receiver which takes more time for decoding. Apart from this, the use of
11
MIMO-OFDM technique requires a spatial detector in all the subcarriers. This adds
a significant computation requirement to the total computations required for the
system. The conventional spatial detection techniques are the maximum like hood
(ML), zero forcing, minimum mean square error (MMSE), and the ordered
successive interference cancellation (OSIC) method. The ML method is the optimal
method for detecting the transmit stream and it operates by searching for the most
likely transmitted vector. Thus the complexity will grow exponentially as the size of
the constellation increases. The ZF and MMSE techniques are called as linear
detection techniques, where an equalizing matrix is formed from the channel
estimates and multiplied with the received signal vector. The computations required
to do this will be in the order of cube of the matrix dimension. The OSIC technique
is an intermediate scheme between the ML and linear receivers which has moderate
performance and moderate complexity. The vertical–bell labs layered space time
(V-BLAST) scheme was proposed by (Wolniansky P.W et al 1998) and is one of
the OSIC techniques which can be used either with ZF or with the MMSE canceling
solution.
1.5.1 Previous work
In the literature, several low complexity spatial detection techniques for
BICM MIMO-OFDM systems have been reported. Michael R. G. Butler et al
proposed a low complexity approximate log likelihood receivers using zero forcing
and MMSE as equalizing matrices (Michael R. G. Butler et al, 2004). They
developed a receiver which calculates the MMSE or the zero forcing matrix first
and equalized for the channel. Then, the resultant signal is detected and decoded
using a log likelihood receiver. Similar to the above work, M. K. Abdul Aziz et al
proposed a low complexity and suboptimal ML detection via ZF and MMSE
solution for 802.11n systems (Abdul Aziz M.K et al, 2004). In 2004, Van Zelst and
Schenk proposed 2 detection techniques. They are per-antenna-coded soft output
maximum like hood detector (PAC SOMLD) and Per-antenna-coded V-BLAST
(PAC V-BLAST). These techniques cannot be used in 802.11n based systems
12
because the concept of per antenna coding is not used here. In 2004, Jianhua Liu
and Jian Li proposed a simple MIMO soft detector for a 2x2 system.
1.5.2 Contribution to this thesis
With a motivation of providing a low complexity receiver design for
802.11n systems, we modified the grouping strategy of conventional MMSE V-
BLAST method and called it as group ordered MMSE V-BLAST (GO MMSE V-
BLAST). This scheme can be implemented using a fixed grouping technique or
using a threshold based adaptive grouping method. The performance of the new
method is compared with the performance of the conventional techniques and
extensive simulation results show that the performance of this method is similar to
that of the MMSE V-BLAST method. The complexity of the proposed system is
compared with the complexity of the MMSE V-BLAST technique. It takes only
60% of the computations as in the MMSE V-BLAST method. The performance of
the fixed scheme and the adaptive scheme is also compared for all the channel
conditions.
1.6 ORGANIZATION OF THE THESIS
The remaining chapters are as follows. In chapter 2, we have analyzed
the different modes of operation that is possible in a typical 802.11n network. We
have discussed the various methods for extending the SISO preamble to MIMO
systems that can be used to achieve backward compatibility. In addition comments
on the performance of AGC technique with the new preamble are presented. A
review of the SOP detection and its performance is studied in spatially correlated
and uncorrelated channel models. A new coarse timing technique is proposed and
the performance is analysed for different modes of operation in the legacy receivers
and in the MIMO receivers. Using this coarse timing estimate, a robust low
complexity fine timing estimator is proposed and its performance is compared with
the conventional crosscorrelation based methods. The above time synchronization
13
techniques perform better for the new preamble in legacy systems as well as in the
MIMO systems.
In chapter 3, a low complexity spatial detection technique for BICM
MIMO-OFDM system is proposed. A short review of existing conventional
schemes is presented and the new technique is explained. The performance is
compared with the existing scheme for an uncoded system as well as for a coded
system. In chapter 4, conclusions are presented and summary of robust, low
complexity techniques are presented.
14
CHAPTER 2
TIMING SYNCHORNIZATION FOR MIMO-OFDM SYSTEMS
2.1 INTRODUCTION
In this chapter, we discuss the different modes of operation in a typical
802.11n network and various ways of extending the legacy preamble to MIMO-
OFDM systems for interoperability reasons. The effect of the new preamble in
different modes is discussed and their performance in the initial receiver tasks like
AGC and time synchronization is discussed. We studied the performance of the start
of packet detection in spatially correlated and uncorrelated channels for different the
preamble types. A new coarse timing algorithm has been proposed for the SISO
systems and MIMO systems. The simulations results show that the proposed
technique performs better and simplifies the complexity of doing fine timing
estimation. Based on the coarse timing estimation, a low complex fine timing
estimation algorithm is proposed in this chapter. We also show that the performance
of the proposed time synchronization algorithm performs well for new preamble
and for the legacy preamble.
2.2 OVERVIEW OF IEEE 802.11a PREAMBLE
In the IEEE 802.11a standard the physical layer burst consists of a
preamble part, signal field, and the data part. The preamble consists of two parts.
The first part contains 10 identical short symbols (SS) each of duration 0.8 sµ called
as the short training field (STF). The second part consists of an extended cyclic
prefix (GI) of duration1.6 sµ which is followed by 2 identical long symbols (LS)
15
each of duration 3.2 sµ called as the long training field (LTF). The signal field (SIG)
carries the rate and length information and is of duration 4 sµ
0.8 sµ 1.6 sµ 3.2 sµ
S S S GI LS1 LS SIG
Short training field Long training field Signal Field
Figure 2.1: PLCP preamble of the IEEE 802.11a burst
. The rough bandwidth
of the 802.11a OFDM signal is 20 MHz which implies that the Nyquist sampling
period of 50 ns.
Hence, the SS and LS consists of 16SSN = and samples,
respectively and the GI is 32 samp les. The maximum data rate that can be achieved
in the 802.11a system is 54 Mbps when 64 QAM symbols are used. The preamble
used in 802.11a is shown below in figure 2.1
64LSN =
A typical 802.11a receiver operates in various modes during the
reception of a packet (Victor P. Gil et al 2004). Initially, the system is in acquisition
mode, where the system calculates the normalized received power and when this
exceeds a given threshold the start of packet (SOP) is detected and the automatic
gain control (AGC) algorithm is activated. In this state, the received signal is
attenuated by using the calculated received signal power to maintain the signal
within a range of values. Next, the system enters to the synchronization mode,
where the coarse timing and coarse frequency synchronization is accomplished. All
the above operations are done by using the correlation property of the received STF.
Then by using the LTF, fine timing and fine frequency synchronization is done.
Sometimes the fine timing synchronization is also done by the STF. After this the
channel estimation is accomplished using the LTF. The receiver starts estimating
the transmitted data and also employs tracking algorithms for overcoming residual
offsets. The system moves back to the acquisition mode to detect the next packet
after the current burst is over. Out of 10 sµ allocated for the first 2 modes, 4 sµ is
16
the typical time taken by the AGC to converge and the remaining time is shared
among the other tasks.
2.3 EXTENSION OF SISO SYSTEM TO MIMO-OFDM SYSTEMS
The MIMO-OFDM technique has been proposed as the physical (PHY)
layer technique for the IEEE 802.11n standard as seen in the 3 important proposals.
This standard is an enhancement of the IEEE802.11a/g standard to achieve higher
throughputs. The maximum data rate that can be achieved by this system will be
around 500 Mbps. The WLAN employing 802.11n based systems will have to be
backward compatible with the legacy 802.11a/g systems. Based on this constraint,
the high throughput system should be able to operate in the modes given below.
Since, the main focus of the work is to develop the time synchronization algorithm
for the final converged EWC proposal, most of the discussion is relevant to the
system described in this proposal and for comparisons the preambles from the other
proposals are considered then and there.
2.5.1 Legacy mode
In this mode of operation, the MIMO-OFDM system will act as a SISO
legacy system. The transmission happens between 802.11n stations and the legacy
stations. The MIMO system will effectively use only one antenna for its
transmission and can use multiple antennas for reception in order to gain spatial
diversity. Since the packets are intended for the legacy stations, it should be in
legacy format. The MIMO receivers receiving this packet, decodes the SIG part and
follows the 802.11 MAC protocol rules.
2.5.2 Mixed mode
In this mode, the network consists of MIMO-OFDM stations and legacy
stations. The packets transmitted by the MIMO-OFDM stations are called the
MIMO-OFDM packets. The initial preamble part of this packet should be in legacy
17
format (STF, LTF and SIG) so that legacy stations in the network can decode it and
allows the MIMO-OFDM transmissions to progress without collisions. The MIMO-
OFDM packet also consists of the preamble that is specific to MIMO systems. The
MIMO-OFDM receivers in this mode should be able to decode the MIMO-OFDM
packets and the legacy packets.
2.5.3 Green field mode
This mode is similar to mixed mode where the transmission happens
only between the MIMO-OFDM systems in the presence of legacy receivers.
However, the MIMO-OFDM packets transmitted in this mode will have only
MIMO specific preambles and no legacy format preambles are present. So there is
no protection for the MIMO-OFDM systems from the legacy systems. The MIMO-
OFDM receivers should be able to decode the green field mode packets as well as
legacy format packets.
Legacy format Preamble
High throughput Preamble
L-STF L-LTF L-SIG HT-preamble Pay load
Figure 2.2.1: Mixed mode packet
2.5.4 MIMO-OFDM packet structure
In this section, the structure of the MIMO-OFDM packet also called as
high throughput packet is discussed. Since, the legacy stations are considered in
mixed mode, the MIMO-OFDM packet in this mode has legacy format preamble
and high throughput preamble. In case of green field mode, the MIMO-OFDM
packet consists of only high throughput preamble. This is shown in the figures 2.2.1
and 2.2.2.
18
L-STF HT-preamble Pay load
High throughput preamble
Figure 2.2.2: Green field mode packet
e
prea
field
prea
prea
dete
(Jia
algo
field
rece
2.5.
the
ope
withthp r
L-STF – Legacy short training field
L-LTF – Legacy long training field
L-SIG – Legacy signal field
HT-preamble – High throughput preambl
The figure shows that the mixed mode packet is made up of the legacy
mble (L-STF, L-LTF and L-SIG), HT-preamble and payload. Similarly in green
mode, the packet is made up of HT-preamble and payload. In turn, the HT-
mble is made up of L-STF and HT-preamble. The common field of the
mbles used in both the modes is L-STF. The initial receiver operations like SOP
ction, coarse time and coarse frequency estimation are dependent on the L-STF
nhua Liu et al 2004). The objective of our work is to develop the above receiver
rithms for the receivers operating in the mixed mode as well as in the green
mode. Hence, the discussions from now will focus on the development of these
iver algorithms using the L-STF.
5 Signal model for receivers operating in different modes
In this section, the signal model for a MIMO-OFDM system operating in
green field mode is discussed first and then the signal models for the receivers
rating in other modes are derived from it. Consider a MIMO-OFDM system
transmit (TX) and receive (RX) antennas. The received signal at the tN rN
eceive antenna is given as
19
21
1 0( ) ( ) ( ) ( )
−
= =
⎛ ⎞= − +⎜⎝ ⎠∑∑
t j nN LN
p pq q pq l
r n h l x n l v n e⎟πε
(2.1)
where ( )qx n is the transmitted signal from the TX antenna and is defined as
, where is the representation for the 802.11a/g legacy preamble, is
the impulse response of the channel between the TX and the
thq
( ( ))f s n ( )s n ( )pqh n
thq thp RX antenna, L is
the channel length, is the AWGN at the ( )pv n thp RX antenna with zero mean and
variance 2vσ and ε is the normalized frequency offset caused due to the mismatch in
the frequency of the local oscillators present at the transmitter and at the receiver.
The total power transmitted is normalized across the transmit antennas and is
given as
tN
2
1
( ) 1tN
E x n=
⎡ ⎤ =⎢ ⎥⎣ ⎦∑ . From equation (2.1), one can easily derive the received
signal model for the other modes.
Case.1. In the legacy mode, the MIMO transmitters will use only one antenna for
transmission. Then the received signal at the legacy receiver with and1tN = 1rN =
can be written as
21
0
( ) ( ) ( ) ( )−
=
⎛= − +⎜⎝ ⎠∑
j nLN
l
r n h l x n l v n e⎞⎟πε
(2.2)
where is the SISO channel impulse response. ( )h n
Case.2. In the mixed mode and, the MIMO transmitter uses all the TX antennas.
Then the received signal at the legacy receiver with
tN
1rN = is given as
21
1 0( ) ( ) ( ) ( )
t j nN LN
q qq l
r n h l x n l v n eπε−
= =
⎛ ⎞= − +⎜⎝ ⎠∑∑ ⎟ (2.3)
The received signal model of the MIMO-OFDM receivers operating in mixed mode
will be similar to the one given in equation (2.1).
20
2.4 METHODS OF EXTENDING SISO-OFDM PREAMBLE TO
MIMO-OFDM SYSTEMS
In this section, the different ways of extending the legacy preamble to
MIMO-OFDM systems is discussed and their effects are analyzed. Due to
compatibility constraints in the mixed mode, the initial preamble part of the high
throughput packet is constructed using the preamble specified in the 802.11a
standard. Here, we discuss the methods of extending the SISO OFDM preamble to
MIMO-OFDM system based on the methods suggested in the literature (Jianhua Liu
et al 2004) and the drafts proposed for 802.11n standard (WWISE 2005, TGnsync
2005 and EWC 2006). They are
1. Repeating the legacy preamble in all the transmit antennas.
2. Transmitting cyclically shifted version of the legacy preamble.
Since only one transmit antenna is used in the legacy mode, the MIMO-OFDM
system will always transmit the legacy preamble. But in the other operating modes,
different preambles will have their pros and cons. The following discussions are
relevant only to the mixed and green field modes.
2.4.1 Repetition method
In this method, all the TX antennas of the MIMO transmitter are
mapped with the legacy preamble (Jianhua Liu et al 2004). Then, the resultant
transmitted signal in all the transmit antennas is given as
tN
1( ) ( )t
x n sN
= n (2.4)
where the power of is normalized across the transmit antennas. The preamble
for a TX antenna system is shown below in figure 2.3. Since the initial receiver
tasks such as estimation of the receive power for AGC, coarse time offset, coarse
frequency offset, and fine time offset are dependent on the correlation property of
the STF, the cross correlation of the received signal with the L-STF is studied for
various modes of operation.
( )s n
tN
21
Figure 2.3: Repetition of the same preamble in all the transmit antennas of a MIMO-OFDM system
1
2
tN
STF
STF
STF
SIGLTF MIMO Preamble
MIMO Preamble SIGLTF
MIMO Preamble SIGLTF
In mixed mode deployments, the signal received by the legacy stations is
obtained using (2.3) and (2.4) and is given by
21
1 0( ) ( ) ( ) ( )
t j nN LN
qq l
r n h l x n l v n eπε−
= =
⎛ ⎞= − +⎜⎝ ⎠∑∑ ⎟ (2.5)
To study the correlation property of the received signal only with the type of the
preamble, the effects due to channel impairments and normalized frequency offset
are suppressed in (2.5) and the resulting received signal can be written as
(2.6) 1
( ) ( )tN
q
r n x n=
= ∑
The cross correlation between the received signal and the locally generated STF at
the legacy receivers operating in mixed mode is defined as 1
*
0
( ) ( ) ( )ssN
rxm
R n r n m x−
=
+∑ n
)
1
*
0 1
( ) (ss tN N
m q
x n m x m−
= =
= +∑ ∑ (2.7)
From the above equation, it is evident that the correlator output ( )rxR n will
be similar to cross correlation measured in the SISO system as shown in figure 2.4.
In addition, since the same signals are transmitted in all the TX antennas, one
cannot leverage the diversity advantage due to multiple TX antennas (Paulraj A, et
al 2003). This can be illustrated using a simple example. Let 1L = and 2tN = , then
using equation (2.4), the received signal at the legacy receiver can be written as
22
2
1 2( )( ) { ( ) ( )} ( )2
j nNs nr n h n h n v n eπε⎛= + +⎜
⎝ ⎠
⎞⎟ (2.8)
where 11 1( ) jh n e θα= and 2
2 2( ) jh n e θα= are complex Gaussian channel coefficients with
zero mean and unit variance. 1α , 2α are the attenuations and 1θ , 2θ are the random
phases of the channel coefficients. Since the channel coefficients and are
complex Gaussian random variables, then their sum
1( )h n 2 ( )h n
1 2( ) ( )( )2
h n h nh n += is also a
complex Gaussian random variable with zero mean and unit variance (A Papoulis
1984). Then the received signal in (2.8) becomes ( ) ( ) ( ) ( )r n h n s n v n= + and it is
similar to the received signal in SISO systems. Hence, the performance of the initial
receiver tasks of the mixed mode legacy receivers that are dependent on the
correlation property of the STF will be similar to the performance of SISO systems.
In the green field mode, the received signal at each of the RX antennas of
a MIMO-OFDM station will be similar to the one in equation (2.5). So the cross
correlation between the received stream and the SS at all the RX antennas will be
similar to the one in figure 2.4. But the RX antennas of the MIMO-OFDM system
receive the same signal coming through different channels and different WGN. This
motivates one to use the spatial diversity advantages as seen in the following
example.
Let 1L = , and2tN = 2rN = , then using equation (2.8), the received signal
at the thp RX antenna can be written as
2
1 2( )( ) { ( ) ( )} ( )2
j nN
p p p ps nr n h n h n v n e
πε⎛= + +⎜⎝ ⎠
⎞⎟ (2.9)
where . Since each RX antenna faces different channel and noise, one can do
proper processing and can achieve maximal ratio combining (MRC) kind of
performance (T C Schenk and Allert Van Zelst 2003).
1, 2p =
23
Figure 2.4: Cross correlation at the legacy receiver for
repetition preamble
Apart from these advantages, there are other impairments caused by this
method that affects the performance of the system. First, the repetition of the same
preamble in all the transmit antennas can cause multipath fading resulting in
constructive and destructive addition at the receiver. In effect, the received signal
will be maximized at certain instants and totally nullified at other instants. This
effect is called the beamforming effect (TGnsync 2005). Using the example given
earlier, this effect can be illustrated as follows. If the attenuation factors in equation
(2.8) are equal ( 1 2α α= ), and the phase difference 1 2−θ θ is / 2mπ where is an
integer, then the resultant signal in (2.8) goes to zero. This effect is common in both
the mixed mode and in the green field mode operations. The preamble repetition
affects the receive power estimation which is used by the AGC. The received power
in the
m
thp antenna is given by
(2.10) *
1
_ _tN
p q pq pqq
Pow rx Pow tx h h=
⎛ ⎞= ⎜ ⎟
⎝ ⎠∑
24
where is the transmitted power from the transmit antenna and is given
as
_ qPow tx thq
{ }2( )qE x n . The fluctuation in the received power estimate with respect to data
power measured at one of the RX antenna in a 2x2 MIMO-OFDM varies from -
9.680 dB to +8.200 dB. This measurement is done under the TGn channel model D
with SNR=30dB. This range of variation is severe because apart from this, the
received signal power will also be affected by path loss and shadowing. The analog-
to-digital converter (ADC) which converts the incoming analog signal to digital
signal will operate in a fixed range of amplitude levels. If the amplitude of the
incoming signal crosses this range, then the ADC will be saturated and distortion is
introduced by clipping. To avoid this distortion, an AGC algorithm is used to adjust
the input amplitude levels. For proper AGC operation a good power estimate is
necessary. Based on the received signal power estimate the incoming signal is
scaled to obtain the required adjustment. If the calculated power using (2.10) is
inaccurate, then the AGC performs poorly due to inaccurate power scaling. Hence,
sending similar preambles from all the TX antennas requires the AGC to operate in
large range. In case of legacy receivers in mixed mode, the range of AGC is already
fixed. Hence, if the incoming signal exceeds the AGC range, then the AGC fails.
Similar kind of effect is seen in the green field mode receivers if the range is not
properly fixed.
2.4.2 Cyclic shift method
In this method, the legacy preamble is sent in the first transmit and
cyclically shifted versions of the legacy preamble are sent on the other antennas. Let
be the cyclic shift applied to the legacy preamble from the transmit antenna,
then the transmitted signal can be represented as
qCST thq
1( ) ( )qq
tCSx n s n T
N= − B (2.11)
where is the legacy preamble, ( )s n B is the nominal bandwidth of the system and
the number of samples corresponding to be . For the 1qCST B q
CSN st transmit antenna,
25
Figure 2.5: CS versions of legacy preamble in the transmit antennas. tN
STF LTF MIMO Preamble
MIMO Preamble
MIMO Preamble
1
2
tN
2( )csT
STF
STF ( )tNcsT
LTF 2( )csT
LTF ( )tNcsT
SIG
SIG 2( )csT
SIG ( )tNcsT
1 0CS s= 1 0CSN =the shiftT n and . Figure 2.5 depicts the structure of the preamble with
cyclic shifts at the transmitter.
We shall now discuss the effect of using the cyclically shifted preamble on the
various receiver operations. In mixed mode deployments, the received signal at the
legacy receivers is given as
21
1 0
( ) ( ) ( ) ( )t j nN L
Nq q
q l
r n h l x n l v n eπε−
= =
⎛ ⎞= − +⎜⎝ ⎠∑∑ ⎟ (2.12)
The simplified received signal model with CS preambles as in equation (2.6) is
given as
(2.13) 1
( ) ( )tN
r n x n=
=∑
Then the cross correlation between the received signal and the locally generated
STF is given as 1
*
0 1
( ) ( ) ( )ss tN N
rx qm q
R n x n m x−
= =
= +∑ ∑ m
( )
(2.14) 1
*
1 0
( )t ssN N
qcs
q m
s n m N s m−
= =
= + −∑ ∑
From the expressions (2.11) and (2.14), it is clear that for every N samples, the
correlator output
qcs
( )rxR n will have a peak.
26
Figure 2.6: Cross correlation at the thp receive antenna for cyclically shifted preamble with T n 2 400CS s=
Since the there are shifts within the tN ssN samples, there will be peaks
within this duration. In figure 2.6 the correlation function
tN
( )rxR n for a 2x1 system
with is shown. The figure shows that there are 2 peaks within 16samples
at the output of the correlator. Due to this, the legacy receivers with synchronization
algorithm based on cross correlation will suffer. This is because the algorithm in the
legacy receivers is implemented for the legacy preambles with an assumption that
there will be only one peak for
2 400CST n= s
ssN samples (Yik-Chung Wu et al 2005). But
reception of this CS preamble results in more peaks within in ssN samples and the
timing estimator can give wrong timing estimates resulting in more synchronization
errors.
27
In the green field mode, the received signal at the thp RX antenna will be
similar to the one in equation (2.1). Then the cross correlation between the signal at
the thp antenna and the SS transmitted at the TX antenna is given as thq
1
*
0 1
( ) ( ) ( )ss tN N
prx q q
m q
R n x n m x−
= =
= +∑ ∑ m
= 1 ( )rx
(2.15)
For a 2x2 system with , 2 400CST ns R n and 2 ( )rxR n will be the same as shown in
figure 2.6. Hence, in the green field mode, the synchronization algorithm should be
robust enough to estimate the time offset using this preamble structure. As given in
equation (2.9) the received signal at the thp antenna can be given as
22
1 2( )( )( ) ( ) ( ) ( )
2 2
j ncs N
p p p ps n Ns nr n h n h n v n e
πε⎛ ⎞−= + +⎜⎝ ⎠
⎟
ns
s
(2.16)
where . It is clear from the above equation that one can also effectively use
the multiple signals available at the receiver and exploit the diversity advantages.
Since all the transmit antennas are sending different signals, there is no
beamforming effect as in the repeated preamble case. Regarding to the received
signal power estimation, one can get good estimate of the MIMO channel power
using (2.10) because of the CS preamble structure. Similar to the power estimate for
repetition preambles, the fluctuations in the receive power estimate with respect to
data power is measured for a 2x2 system under the channel model D with
SNR=30 dB. For CS preambles with , the fluctuation is from -9.370 dB
to +7.000 dB and for CS preambles with , the fluctuation is from
-7.560 dB to +4.200 dB. Hence, sending cyclically shifted versions of the legacy
preamble on the multiple transmit antennas will have an improvement in the AGC
power estimation when compared to repetition preambles but there will be
synchronization failure in the mixed mode receivers that are based on cross
correlation of STF.
1, 2p =
2 50CST =
2 400CST n=
28
2.5 INITIAL RECEIVER TASK FOR MIMO-OFDM SYSTEMS
In this section, a review of the initial receiver tasks like SOP detection
and coarse frequency offset estimations for MIMO-OFDM systems is presented. A
simple and robust coarse timing and fine timing synchronization algorithm is
proposed. The performance of the proposed time synchronization technique is
compared with the performance of the existing techniques. The performance due to
different preamble types used in the receivers operating in different modes is also
discussed.
2.5.1 Start of the packet detection
Typically, the first task of the receiver is frame detection which is used to
identify the preamble in order to detect the arrival of the packet. This is done by
using the correlation property of the repeated symbols constituting the preamble.
The technique explained below is the simple MIMO extension of the existing SISO
technique (Schmidl, 1997). Let be the received signal at the ( )pr n thp RX antenna
which is given in equation (2.1). The thp RX chain collects 2 ssN samples and a
sliding correlation is performed between the first ssN and the second ssN samples.
The correlator output is normalized by the energy of the second ssN samples and is
represented as
1*
01 2
0
( ) (( )
( )
ss
ss
N
p pm
p N
p ssm
r m n r m n Nn
r m n N
−
=−
=
+ + +Λ =
+ +
∑
∑
)ss
(2.17)
where is the normalized autocorrelation function of the received signal at the ( )p nΛ
thp RX antenna. Here, n is some arbitrary position from where the SOP algorithm
starts. The multiple signals at the MIMO-OFDM receiver are used efficiently by
calculating the metric for all the RX antennas and averaging the values as given
by
rN
29
1
1( ) ( )rN
ppr
nN =
Λ = Λ∑ n (2.18)
The above combining technique is equivalent to maximal ratio combining which is
given in Van Zelst and Schenk (2004). As the index n approaches the start of the
frame, the metric ( )nΛ increases and forms a plateau. In figure 2.7 shown below the
plateau obtained for a 2x2 MIMO-OFDM system for the CS preamble with
R=10 dB under the channel model D. In noise free conditions, the
maximum value of the plateau goes to unity due to normalization. In multipath
fading and noisy channel, the plateau will be noisy and detecting the start of the
frame is difficult. Hence, a threshold is used to detect the start of the frame. The
rough start of the packet
2 400csT n= s at SN
1c
1M can be obtained by satisfying the criterion
1 1( ) { ,...... }n c for n M M QΛ ≥ = +1 1 (2.19)
1M
Start of packet
Threshold
Metric
Figure 2.7: Averaged auto correlation metric for a 2x2 MIMO-OFDM system at SNR=10 dB
where is the number of samples for which the criterion has to get satisfied
continuously. By doing so the stability of the frame detection algorithm is increased
1Q
30
when noise produces false peaks. The effect of frequency offset as we are
calculating the absolute value of the autocorrelation of the received signal.
The performance of the SOP detection algorithm is measured using the
probability of false alarm and probability of missed detection. Let the actual start
time of the packet be M . The probability of false alarm is defined as
1(( ) 2 )f ssP P M M N= − > (2.20)
and the probability of missed detection is defined as 1(mP P M M )= > . The metrics
fP and are influenced by the threshold . If the threshold is too high, then the
probability of missing the packet will increase especially in low SNR cases and if
the threshold is too low, then the false alarm probability or will increase. A
collective measure of these two metrics is called probability of synchronization
failure (Kun –Wah Yip et al 2002) and is defined as
mP 1c
fail f mP P P= + (2.21)
Since the events false alarm and missed detection are mutually exclusive, they can
be added to get the probability of synchronization failure.
2.5.2 Coarse frequency offset estimation
After the arrival of packet is detected, the AGC algorithm is triggered. A
typical WLAN AGC designed for OFDM systems takes 5 to 6 SS’ for its
convergence (Victor P.Gil et al 2004). Usually a counter is run to count the number
of samples used by AGC. When the counter crosses the preset threshold (samples
corresponding to 6 SS) number of samples, the next task of frequency offset
estimation is initiated. This is done in 2 steps. In the first step, the coarse frequency
offset (CFO) is estimated using the STF and this estimate is used for coarse time
offset (CTO) estimation. In the second step, the LTF is used for estimating the
residual fine frequency offset. The CFO estimation algorithm takes samples from
the position k after which the AGC counter exceeds the threshold. Rather than
estimating the CFO on every receiver branch separately and averaging over the
31
different estimates, the receive streams can be vectorized and used effectively to
achieve a receive diversity kind of performance. This is given by Schenk and A.
Van Zelst (2003). Collect and ( samples from all the receive antennas
and stack them in two vectors
thn )thssn N+ rN
r(n) and ssr(n+ N ) each with dimension 1rN × . The
index starts from the position . Define a correlation metric n k
1
0( ) ( ) ( )
ssNH
ssm
n r n m r n m Nψ−
=
= + + +∑ (2.22)
where H is the hermetian operator. Since only 4 short symbols are left for CFO and
CTO estimation after AGC, the metric ( )nψ is averaged over the next 3 ssN samples
and is given by 13
1 0
1 (( 1) )3
ssN
i mss
P iN
ψ−
= =
Nss m= − +∑ ∑
2 ssj N
NsP e
π ε−
= (2.23)
where s rP P e= + p . Here is the average received signal power and is the noise
term. The coarse frequency offset can be estimated as
rP pe
1ˆ arg( )2c
c
PN
επ
= (2.24)
where arg( )x is the argument of . The above estimate gives MRC like performance
as the contribution of the receive branches is directly proportional to the total
received signal power on all the receive antennas. The maximum range of frequency
offset that can be estimated using the STF is given by
x
0ss
NN
ε≤ ≤ (2.25)
For the 802.11a system with 64N = and 16ssN = , the maximum normalized
frequency offset that can be detected using STF is 4. Using the estimate cε , the
received signal at the thp receive antenna is corrected for the CFO and is given by
ˆ2
( ) ( )cj n
Npr n r n
π ε−
′ = (2.26)
For further processing, the CFO corrected signal is used. Due to the arbitrary
position there will be a constant phase and is given by k
32
ˆ2 (( 6 ) )r ss cM N kθ π ε ε= + − (2.27)
where rθ is the residual frequency offset.
The performance of the CFO estimate is measured by using the mean
square error (MSE) between the original frequency offset and the estimated value.
The cramer-rao bound (CRB) for the frequency offset estimation is the error
variance and is given by
2
2 3ˆvar( ( ))
(2 )cr ss
NerrorN N
επ ρ
≥ (2.28)
where 2 /t x vN 2ρ σ σ= denotes the signal to noise ratio, is the number of samples in
one OFDM symbol duration, and is the number of receive antennas.
N
rN
2.5.3 Proposed coarse timing estimation
The objective of coarse time offset (CTO) estimator is to find the rough
starting position of the STF. The SOP estimate 1M is not a reliable value because
from (2.19) it is clear that its estimation accuracy is 2 ssN samples. The estimation
accuracy is defined as the number samples within which the system can adjust to
operate without synchronization errors. Therefore, a robust rough estimate of coarse
time is found by using the correlation property of the STF. An easy way is to find
the end of the STF from where the rough start of the packet can be determined. In
Schenk and Van Zelst (2004), a simple technique has been proposed for the MIMO-
OFDM systems where the metric ( )p nΛ is calculated as given in equation (2.16) for
the received signal . The CTO estimation algorithm takes samples starting from
the position . Similar to equation (2.17) the metric
( )pr n
k ( )p nΛ is averaged over
receive antennas to achieve a MRC kind of diversity performance. As n
increases, a plateau is formed with a constant value till the first sample of 9
rNth SS and
starts falling after that. This is due to the fact that the calculation of the metric
( )nΛ after the first sample of 9th SS takes samples outside the STF. A plot of the
33
metric ( )nΛ is shown in the figure 2.8. This is obtained for a 2x2 MIMO-OFDM
system with the CS preamble of SNR=10 dB under the most
representative channel model D.
2 400csT n= s at an
The objective is to detect the exact position at which the falling edge
occurs in the presence of multipath and noise. The value of ( )nΛ is compared with a
preset threshold and is continuously checked as follows.
2( )n cΛ ≤ , 2 2{ ,...... }2for n M M Q= + (2.29)
where is a threshold, Q is the number of consecutive samples for which the
criterion should be satisfied and
2c 2
2M is the rough estimate of the start of the 9th SS.
This method ensures that the end of 8th SS is detected accurately. The accuracy of
this estimation method will have different effects with different types of preamble.
Metric
Noisy
Figure 2.8: Falling edge of the plateau calculated for a
2x2 system
Case.1 Repetition preamble
If the preamble type is a simple repetition of 802.11a preamble in all the
TX antennas andtN 28 9ssN M N≤ ≤ ss , then the estimate 2M is reliable in mixed mode
34
and green field mode operations. This is because the CTO estimator has an
estimation accuracy of ssN samples. Hence, a simple cross correlation based fine
timing synchronizer is enough to find the optimum position from where the FFT
window of an OFDM symbol should start (Van Zelst and Schenk 2004).
Case.2 Cyclically shifted preamble
If the preamble type is CS and 28 9ssN M Nss≤ ≤ , then the CTO estimation
performance depends on the shift value . If max( , then from
equation (2.14), it is clear that there will be peaks within ma for every
qcsN ) / 2q
csN Nss≤
tN x( )qcsN ssN .
Any legacy receiver which uses a cross correlation based fine timing synchronizer
performs poorly because of peaks withintN ssN samples. This issue will be solved if
the CTO estimate falls within 28 8 min q( )ss ssN M N N≤ ≤ + cs . In Van Zelst and Schenk
(2004), the problem has been addressed by setting the threshold to relatively
higher value so that the coarse time estimate
2c
2M will be near to the end of the 8th SS.
But setting a high threshold may cause problems at lower SNRs as the plateau
shown in figure 2.8 exhibits fluctuations. Hence, the probability that the maximum
value of the plateau is less than the threshold is high. Note that the falling edge of
the plateau in figure 2.8 is noisy and can affect the detection of end of the 8th SS.
However, the number of correlated terms contributing to the metric ( )nΛ decreases
as increases after the 1n st sample of 9th SS. So the mid part of the transition region
between 8 ssN and 9 ssN will be steadily decreasing as shown in figure 2.8.
To get a stable point for CTO estimation in figure 2.8, let us define a new
metric ( )p nθ which calculates the average power of a difference signal over a
window of 2 ssN and is given by
2ˆ ˆ2 ( ) 2 ( )1
0
1( ) ( ) ( )c sss j n m j n m NN
N Np p p ss
mss
n r n m e r n m N eN
π ε π ε
θ− + − + +−
=
⎧ ⎫⎪ ⎪= + − + +⎨ ⎬⎪ ⎪⎩ ⎭∑
s c
(2.30)
35
where is the received signal which is corrected for frequency offset with the
CFO estimate
( )pr n
cε obtained from equation (2.24). If the frequency offset is assumed to
be zero then the term ( )p nθ contains the average power of the noise within the
window of 2 ssN till the first sample of 9th the SS. This is because the signal parts in
the terms (pr n m)+ and are nullified due to their similarity. Hence, the
metric
(pr n m N+ + )ss
( )p nθ will be lesser and close to twice the noise variance till the first sample
of 9th SS and is given as
1 2
0
1( ) ( ) ( )−
=
⎧ ⎫= + − + +⎨ ⎬
⎩ ⎭∑
ssN
p p pmss
n v n m v n m NN
θ ss (2.31)
2 2vσ
After this point, the metric will increase steadily because the calculation of ( )p nθ
after the first sample of the 9th SS takes samples outside the STF. Then, the metric
can be written as
21 1 1
1 1
1( ) 2 ( ) ( ) ( ) ( )− − −
= = =
⎧ ⎫⎪ ⎪+ + ∗ − + + ∗⎨ ⎬⎪ ⎪⎩ ⎭∑ ∑ ∑
ss t tN N N2
p v p pq p ss pqm j q qss
n σ x n m h n x n m N h nN
θ (2.32)
In the above equation, the first term corresponds to twice the noise variance and the
second term corresponds to the average power of the uncorrelated signal terms
when2, 3,..,0− −ss ssj = N N 8 1,8 2,......,9 1+ +ss ss ssn = N N N − . From equation (2.32),
the metric increases steadily as n increases. The received signals from the multiple
antennas can be effectively used by calculating this metric in all the receive
antennas and averaging them. This is given by
1
1( ) ( )rN
ppr
nN
θ=
= ∑ nθ (2.33)
The metrics ( )nΛ and ( )nθ can be used to get a reliable estimate of the
CTO. A combined plot of ( )nΛ and ( )nθ is shown in figure 2.9. It is clear from the
figure that, steady increase in metric ( )nθ and steady decrease in the metric
( )nΛ can be used optimistically to get the coarse timing estimate. As shown in the
36
above figure, eventhough the falling edge and rising edge of ( )nΛ and ( )nθ
respectively are noisy, their intersection point in the mid region of ( )nΛ and ( )nθ is
stable with less variation. Define a metric
(2.34) ( ) ( ) ( )D n n nθΛ −
The position where there is a sign change in is taken as the CTO estimate. As
increases after the 1
( )D n
n st sample of 9th SS, the number of noise terms and the
uncorrelated signal terms contributing to the metric ( )nθ increases.
Metric1 ( )nΛ
Intersecting point
Metric 2 ( )nθ
Figure 2.9: Falling edge and rising edge of the 2
metrics calculated for a 2x2 system.
Hence, there will be a steady increase in the value of ( )nθ with increasing as given
in equation (2.33). Similarly, the number of correlated terms contributing to the
metric
n
( )nΛ decreases as n increases after the 1st sample of the 9th SS. Hence, the
there will be a steady decrease in the metric ( )nΛ till the end of the 9th SS as shown
in figure 2.9. However, there will be spikes in ( )nΛ after the end of 9th SS due to
long symbol’s contribution to the metric. Thus there will be one intersection point
37
between these two metrics as shown in figure 2.9. This ensures that the there will be
one sign change in between( )D n 8 ssN 9and ssN . From an implementation perspective,
the position where there is a sign change can be obtained using a criterion given
below as
3 arg max{1 ( )}n
M D n= (2.35)
where 3M is the coarse timing estimate. This is because the position where there is
sign change in will also have small value. The combined plot of( )D n ( )nΛ , ( )nθ
and 1/ ( )D n for a 2x2 system under channel model D at 10 dB SNR is shown in
figure 2.10.
Figure 2.10: Plot of ( )nΛ , ( )nθ and 1/ ( )D n
( )D n
( )nθ( )nΛ
Intersecting point
1/ ( )D n
Metric2 ( )nθ
Intersecting point
( )nΛMetric1
From (2.35) it is clear that the estimate 3M will be around the intersecting point of
( )nΛ and ( )nθ . The CTO estimate is the offset that can be obtained by subtracting
the reference position of the 8th SS’ end point from the coarse timing estimate. This
is given by
3 ( 128cM M M )= − + (2.36)
38
where ( is the end point of the 8128)M + th SS. The CTO estimate gives the number
of samples the coarse timing estimate 3M differs from the reference end of 8th SS.
In an AWGN channel with SNR=10dB, the distribution of the CTO
estimate for a 2x2 system transmitting CS preamble with is shown in figure
2.11.
2 8csN =
Figure 2.11: Probability distribution of CTO estimates of a 2x2 MIMO-OFDM system in an AWGN channel with SNR=10dB
From the figure one can see that 99% of the estimate is in the range 5 to 8. As SNR
increases, say at 20 dB all the estimates are with in the range [5, 6]. The
performance of this technique in multipath fading channel will be different as
compared to the performance in a AWGN channel. However, it has been found
from simulations, the range over which the estimates vary are less than in case
of CS preamble with . These estimates are good enough for the CS preamble
with for a simple cross correlation based fine timing estimator which can
give the optimum position from where the FFT window of an OFDM symbol
should start. The simulation performance of different preamble types operating
under various channel models is discussed in the simulation and results section.
2csN
2 8csN =
2 8csN =
39
The proposed coarse timing synchronization procedure can be
summarized as follows.
Step 1)
Collect 2 ssN samples from the thp receive stream starting from the
position k and calculate the metrics ( )p nΛ and ( )p nθ . Similarly, the metrics for all
the receive antennas are obtained and averaged to get ( )nΛ and ( )nθ as given in
equations (2.18) and (2.33) respectively. These metrics are calculated till the
criterion given in (2.29) gets satisfied.
Dela ssN
Normalized Autocorrelation
Average Average
Difference Power
1( )r n
1( )nθ
1( )nΛ
2 ( )r n
( )rNr n
( )rN nΛ ( )
rN nθ
( )nΛ + - ( )nθ
1/ ( )D n ( )D n
argmax{.}n
Coarse timing
estimate
Figure 2.12: Block diagram of proposed coarse timing estimation
Step 2)
Find the difference between ( )nΛ and ( )nθ to obtain . The position
where there is a maximum occurs in 1/ is the coarse timing estimate. From this
( )D n
( )D n
40
the CTO estimate is obtained as given equation (2.36). The block diagram of the
coarse timing estimation algorithm is illustrated in figure 2.12.
2.5.4 Proposed fine timing estimation
The objective of the fine timing synchronizer or symbol timing
synchronizer is to estimate the position from where the FFT window within the
OFDM symbol should start. Although the OFDM systems provide cyclic prefix for
the robustness against symbol timing offsets, a non-optimal fine timing offset will
cause intersymbol interference (ISI) and intercarrier interference (ICI) in multipath
environments (Michael Speth, Stefan A. Fechtel, et al 1999). The fine timing
estimation can be done using long symbols or short symbols. Most of the fine
timing estimation techniques use knowledge of the energy of the channel impulse
response (CIR). The technique proposed in Jianhua Liu et al (2004) transforms the
received signal vector to frequency domain, equalizes for the data and estimates the
CIR power. When this estimate crosses a prefixed threshold, then that position is
taken as fine timing estimate. The disadvantage of this technique is the
computational complexity of the FFT and matrix multiplications. In Van Zelst and
Schenk (2004), a cross correlation technique is proposed. Let the crosscorrelation
between the thp received signal and the TX signal bethq ( )pq nη . Then, the fine timing
estimate is given as
(2.37) ∑∑tr NN
est pqn p=1 q=1
M = argmax η (n)
where estM is the fine timing estimate. From the above expression, it is clear that the
estimation requires more computations because the cross correlation is done across
the RX and across the TX signals. Apart from this, both these two techniques use
long symbols for fine timing estimation which requires more computations. The
coarse timing estimates used in these techniques is uniformly distributed with an
estimation accuracy of ssN samples, i.e., the preamble assumed is the repetition
preamble. However, for the CS preambles these assumptions are not valid.
41
Based on the method proposed by Paolo Priotti (2004) to find the CIR
power, we propose a low complex and efficient fine timing estimation technique
using short symbols. Short symbols are chosen for fine timing estimation with two
motivations. First, the CTO estimation accuracy obtained from the proposed
technique is well within the range. Say for CS preamble with the CTO
estimation accuracy is 95% within the range at the SNR=10 dB. Second, the use of
short symbol for fine timing estimation requires less computations compared to the
use of long symbols. The symbol timing proposed here is a simple cross correlation
technique with fewer computations. For doing fine timing estimation, samples
starting from position are taken and it will be in between 6
min( ) 8qcsN =
3( 32)thM − ssN and 7 ssN . A
window of ssN received samples at the thp RX antenna is correlated with the locally
generated short symbol and is given as
21
*3 1
0( ) ( 32) ( 1)
ssN
p pm
n r m M x n mη−
=
= + − + +∑ (2.38)
where is the received signal at ( )pr m thp receive antenna and the samples are
considered from , 3 32M − 1( )x m is the locally generated signal that would be
transmitted in the 1st transmit antenna and 0,...., 1ssn N= − . Unlike in Van Zelst and
Schenk (2004), here each RX signal is correlated with the signal sent from the
1st transmit antenna to calculate the CIR power within ssN . The steps of this method
can be explained by using a simple 2x2 MIMO-OFDM system. For simplicity,
frequency offset is ignored and the term 3 32M − is dropped from (2.38). Expanding
(2.38) for the 1st RX antenna,
1 2
21 1 1
*1 11 1 1 1 12 2 2 2 1 1
0 0 0
( ) ( ) ( ) ( ) ( ) ( ) ( 1)ssN L L
m l l
n h l x m l h l x m l v m x n mη− − −
= = =
⎛ ⎞= − + − +⎜ ⎟
⎝ ⎠∑ ∑ ∑ + +
+
(2.39)
The term inside the modulus can be further can be expanded as
(2.40) 1 2
1 11 1* *
11 1 1 1 1 12 2 2 2 10 0 0 0
1*
1 10
( ) ( ) ( 1) ( ) ( ) ( 1)
( ) ( 1)
ss ss
ss
N NL L
m l m l
N
m
h l x m l x n m h l x m l x n m
v m x n m
− −− −
= = = =
−
=
− + + + − +
+ + +
∑ ∑ ∑ ∑
∑
42
where 22 1( ) ( )
sscs Nx n x n N= − , and are the respective channel impulse responses.
Assume the optimum starting point that has to be detected is , then, the
estimate of this position for different preamble types is discussed below.
11h 12h
3 32M −
Case.1 Repeated preamble
For this preamble type, the modulus value of the first two terms in (2.40)
are expected to get maximized when 2= −ssn N .This is because only at this position
the preamble part in these terms will get matched exactly with the locally generated
copy of the preamble. However, this position will vary around due to the
occurrence of maximum tap gains in the non-zero position of the CIR and due to
residual frequency offset.
2−ssN
Case.2 Cyclically shifted preamble
In this preamble, the modulus of term1 in equation (2.40) is expected to
get maximized when and this corresponds to power of . Similarly
the modulus of the term2 that corresponds to CIR is expected to get maximized
at .
2 2= − −ss csn N N 12h
11h
2= −ssn N
Generally, for a tN Nr× system, the maximum value of ( )p nη at
corresponds to the power of the CIR between the TX and the
qcsN
thq thp RX antenna.
Hence, cross correlation as in equation (2.38) at each RX antenna will give the CIR
power estimates for that thp RX antenna. The fine timing estimate at the thp RX
antenna is given as
( )( )
1
1
0 arg max ( )
arg max ( )
p csnp
est j jcs cs p cs
n
n if n NM
n N if N n N
η
η +
⎧ ≤ ≤⎪= ⎨
− ≤⎪⎩
j≤ (2.41)
where pestM is the fine timing estimate for the thp RX chain and . The
position corresponding to the maximum CIR power is chosen because the
contribution by that CIR to the received signal is dominant compared to other
2,..., 1tj N= −
43
channels. Then the final symbol timing estimate is obtained by taking the minimum
of all the estimates obtained from all the receive antennas. This is given as rN
1 min( ) 1= − pest cs estM N M − (2.42)
where estM is the final symbol timing estimate. The minimum position is chosen to
make sure that the starting position of the FFT window of an OFDM symbol is in
the starting or inside the CP region. This reduces the ISI and ICI that occurs due to
synchronization errors. The performance of the fine timing estimator is measured in
terms of the probability distribution of the fine timing estimates.
2.6 SIMULATION MODELS AND RESULTS
In this section, the simulation model for the initial receiver tasks like
SOP detection, CTO estimation, and fine timing estimation is explained, and the
performances are discussed later. Simulations are run for legacy receivers that
operate in mixed mode and for the MIMO receivers that operate in the green field
mode. In both the operating modes, a multi antenna transmitter with is used.
However, in the mixed mode, the receiver is assumed to be a SISO legacy receiver
with and in the green field mode a multi antenna receiver with is used.
The performance is studied with different preamble types. For the repetition
preamble, the 2 transmit antennas are loaded with the 802.11a preamble. In the case
of a cyclically shifted preamble type, the legacy preamble is sent and a cyclic shift
of it is transmitted in the other antenna. For our simulations, the shifts specified in
TGn sync and EWC for a 2x2 system is considered. In the first case, the
shift and in the later case, . The total power transmitted is
normalized to unity and is distributed equally across the transmit antennas. The
MIMO channel is simulated by using the details given in TGn channel modeling
(TGn channel model 2003). The RMS delay spread for different channel models is
given in Table 2.1.
2tN =
1=rN 2rN =
2 50csT = ns ns2 400csT =
44
Simulations are performed under the spatially correlated and
uncorrelated channels. For spatially correlated channels, the antenna elements
spacing is kept as 0.5λ in the transmitter and in the receiver array. In case of
uncorrelated channel, the distance between the antenna elements is more than 0.5λ .
The AWGN is simulated using a circularly symmetric complex Gaussian random
variable with zero mean and 2vσ as variance. The normalized frequency offset
introduced is typically uniformly distributed in the range -2 to +2. The received
signal model for the legacy receiver is given by equation (2.2) and for the MIMO
receivers it is given by equation (2.1). The simulations are done for independent
MIMO channel realizations.
610
2.6.1 P
equatio
1 0.4c =
doing e
metric
versus
measur
Table 2.1: The RMS delay spread for different TGn channel
Channel model RMS Delay spread
in nanoseconds
B 15
C 30
D 50
E 100
erformance of SOP detection
For the SOP detection algorithm, the values for the parameters in
n (2.18) are fixed as 1 0.55c = and 1 15=Q for legacy receivers, and
and5 1 25=Q for MIMO-OFDM receivers. These values are chosen after
xtensive simulations under various channel conditions. The performance
for the arrival of the packet is the probability of synchronization failure failP
signal to noise ratio (SNR). In figure 2.13, we present failP versus SNR
ed at the legacy receiver operating in mixed mode in channel model D with
45
nsns
Figure 2.13: P versus SNR at the legacy receiver in mixed mode; Repetition preamble, CS preamble with T and CS preamble withT , spatially uncorrelated channel model D
fail
2 50=cs2 400=cs
no spatial correlation for different preambles types. The results show that the
repetition preamble performs poorly when compared to the CS preambles with
andT . This is because the repetition preamble when used in the
multipath channel creates beamforming effect. The metric calculation is affected by
the beamformed signal which has nulls in many instants whereas the CS preamble
with T has better performance because the input to the metric calculation is
a superposition of different signals coming through different channels. Eventhough
the
2 50csT ns= ns=
ns=
2 400cs
2 400cs
failP decrease with SNR, there is an error floor at higher SNRs. This is seen for
all the preamble types. It is due to the presence of channel dispersion, which results
in ISI and leads to the occurrence of irreducible probabilities of synchronization
failure.
In figure 2.14, the performance of SOP detection algorithm under various
channel models measured for the legacy receiver is shown. We consider the failP of
46
10-3 and the corresponding SNR required to achieve this point is measured. In the
figure 2.14, we plotted the SNR needed to achieve the
10-3 and the corresponding SNR required to achieve this point is measured. In the
figure 2.14, we plotted the SNR needed to achieve the failP of 10-3 for different
preambles under different channel models. One can see that as the SNR required
decreases and we move from channel B to E. It is due to following reason. The
term in equation (16) can be expanded as *( ) ( )p p ssr n r n N+
1 1 1 1 2 2
1 1 1 1 2 2 1 2 1 2
1 1 12 2 * *1 1 1 1 2
1 0 1 0 1; 0;
( ) ( ) ( ) ( ) ( ) ( ) _− − −
= = = = = ≠ = ≠
− + − − +∑∑ ∑∑ ∑ ∑t t tN N NL L L
pq pq pq pq pq pqq l q l q q q l l l
h l x n l h l x n l h l x n l noise term
Figure 2.14: SNR needed versus channel models at the legacy receiver in mixed mode; Repetition preamble, CS preamble with T and CS preamble withT ; spatially uncorrelated channels ; spatially uncorrelated channels
2 50=cs nsnss2 400=cs
As L increases, the number 2( )h l term increases. Then the expected
value of the first term provides multipath diversity performance as explained in
Kun-Wah Yip (2002). Similarly the expected value of the cross terms and noise
terms approaches zero as L increases. Hence, the system operating in rich frequency
47
selective fading channels has improved performance compared to multipath
channels which have lesser number of taps. Since channel model E has more
number of taps, the performance of system under this channel model is better
compared to other channel models. Comparing the performance at P 310fail−=
2 50cs s= 2 400cs ns=
under
channel E, the repetition preamble attains this value at SNR=17 dB, CS preamble
with T n at SNR =16 dB and CS preamble with T at SNR = 15 dB.
From these numbers, one can infer that the repetition preamble performs poorly
compared to the other preamble performances.
Figure 2.15: failP versus SNR at the MIMO receiver in the green field mode; Repetition preamble, CS preamble with T and CS preamble withT , spatially uncorrelated channel model D
2 50=cs ns
2 400=cs ns
In figure 2.15, the failP versus SNR for MIMO-OFDM receiver is plotted.
The simulation is performed under the most representative channel model D for
different preambles and the channel is assumed to be spatially uncorrelated. The
result shows that there is no irreducible error floor in the failP as in legacy receiver
48
performance. It is due to fact that the metric calculation in each RX antenna and
combining them together will give MRC type of performance. Hence, as the SNR
increases the failP goes to zero. Comparing the failP versus SNR of different
preambles, the CS preamble with shows good performance. 2 400=csT ns
Figure 2.16: SNR needed versus channel models at the MIMO receiver in green field mode; Repetition preamble, CS preamble with T n and CS preamble withT ; spatially uncorrelated channels
2 50=cs sns2 400=cs
The performance of the SOP detection algorithm in MIMO receiver is
studied for different preamble types under different channel models. The SNR
required to achieve failP of 10-4 is measured for different preambles under different
channel models and plotted in figure 2.16. The results show that the multipath
diversity provides gain for rich multipath channels rather that the multipath
channels with lesser channel taps. So the system under channel E achieves this point
at lower SNR. Comparing the performance under channel E, the repetition preamble
attains the failP of 10-4 at SNR=15.6 dB, CS preamble with 2 50csT n= s at
49
SNR =16.2 dB and CS preamble with T n at SNR = 12.3 dB. These number
shows that the CS preamble with performs better.
2 400cs s=
2 400csT ns=
Channel C
Channel B
Channel D
Channel E
2.6.1.1 Impact of spatial correlation
To study the effect of spatial correlation in failP versus SNR, the
condition number for different channels is studied first. Figure 2.17 shows the
condition number versus tap number measured in time domain. The condition
number for the tap positions where there is no channel coefficient is zero. This is
measured for the spatial distance of 0.5λ between the antennas elements in the TX
array, and between the antenna elements in RX array. In spatially correlated
channels, the performance of the system varies according to the amount of spatial
correlation introduced.
Figure 2.17: Condition number versus taps for different channel modes measured in the time domain
50
Figure 2.18: P versus SNR at the legacy receiver in mixed mode; Repetition preamble, CS preamble with T and CS preamble withT , spatially correlated channel model D
fail
2 50=cs nsns2 400=cs
oiThe channel model C has highest condition number in most of the taps,
and then channel B is the next and so on. The impact of spatial correlation in the
SOP detection algorithm is studied for legacy receivers in mixed mode and MIMO
receivers in green field mode. For mixed mode operation, the spatial correlation is
introduced at the transmitter side whereas for the green field mode the spatial
correlation is introduced at the transmitter and at the receiver side. Figure 2.18
shows the failP versus SNR of a legacy receiver in mixed mode under the channel
model D which is spatially correlated. This figure compares the performance of
various preamble types. As mentioned in uncorrelated channel case, there will be
irreducible error floor in the value of failP as SNR increases. Comparing the
51
Figure 2.19: SNR needed versus channel models at the legacy receiver in mixed mode; Repetition preamble, CS preamble with T and CS preamble withT ;
2 50=cs nsns
2 400cs ns=performance of different preambles, the CS preamble with T performs
better when compared to the performance of other preamble types.
The impact of different multipath channels on the SOP detection
performance is plotted in the figure 2.19. The SNR required to achieve the failP of
10-3 is plotted for different preambles under different channels is shown in figure
2.19. Since channel B and C has higher condition number and lesser number of taps,
the performance under these channels is poor compared to other channel models.
2 400=cs Spatially correlated channels
For MIMO-OFDM receivers, the failP versus SNR is plotted in figure
2.20. The CS preamble with T performs better compared to other preamble
types. One can see from the figure that, a MRC kind of diversity is achieved due to
2 400cs ns=
52
Figure 2.20: failP versus SNR at the MIMO receiver in green field mode; Repetition preamble, CS preamble with T and CS preamble withT , spatially correlated channel model D
2 50=cs nsns
2 400cs ns=
2 400=cs
the multiple received signals at the receiver. Even in the presence of heavy spatial
correlation, similar diversity performance as in uncorrelated case is obtained. In
figure 2.21 the impact of multipath channel on the SOP algorithm under the
correlated channel is measured. From the SOP detection simulation study, we infer
that the repetition preamble has poor performance compared to the other preamble
types. Regarding the channel effect, the algorithm gives better performance when
there is rich multipath channel. If the spatial correlation is introduced in the channel,
then the SOP detection algorithm performance degrades significantly under those
channels. Comparing the performance of different preambles, we see that the CS
preamble with T performs better.
53
Figure 2.21: SNR needed versus channel models at the MIMO receiver in green field mode; Repetition preamble, CS preamble with T n and CS preamble withT ; Spatially correlated channels
2 50=cs sns2 400=cs
2.6.2 Performance of proposed coarse timing estimation
The performance of a coarse timing estimation algorithm is measured by
plotting the probability distribution of the CTO estimates obtained by that algorithm.
In our simulations, the probability distribution of the proposed CTO estimation
algorithm is compared with the performance of already existing threshold based
CTO estimation algorithm. The threshold based algorithm is chosen for comparison
with two motivations. First, this technique is efficient in estimating the end of STF
in terms of complexity and speed. Second, most of the symbol time synchronizer
proposed in J-J. Van de Beek et al (1997), A.J.Coulson (2001), and Yik-Chunk Wu
et al (2005) for SISO systems use this technique for coarse timing estimation. The
variation in these techniques exists only in the fine timing estimation algorithm
using LTF. The CTO estimate for the threshold based algorithm can be obtained
54
Figure 2.22.1 Repetition preamble Figure2.22.2 CS preamble with 2csT = 50ns
from the criterion given in equation (2.28). The parameters are
and2 0.6c = 2 15=Q for mixed mode receivers and 2 0.55c = and for green field
receivers. These values are chosen based on the simulation experiments. The CTO
estimate for the threshold based system is defined as the difference between the
reference time and estimated time
2 10Q =
2M . Similarly, for the proposed system, the
parameters used in the equation (2.28) are given as 2 0.55c = , for mixed
mode receivers and ,
2 15M =
2 0.45c = 2 10M = for green field receivers. The CTO estimates
are obtained using the equation (2.36). The MIMO channel models used for the
simulations are spatially correlated multipath channels. Figure 2.22 shows
comparison of the performance between the proposed technique and the threshold
based technique measured at the legacy receivers. The results are obtained for
different preamble types under the most representative channel model D with
SNR=10 dB. Figure 2.22.1 shows the results for the system with repetition
preamble. One can see from the figure that, the CTO estimates of the proposed
technique are well within the estimation accuracy of 16 samples whereas the
threshold based technique has CTO estimates outside the estimation accuracy. The
performance of the CS preamble with is shown in figure 2.22.2. 2 50csT = ns
55
Figure 2.22.3 CS preamble with T 2cs = 400ns
ns s=
s=
ns
Figure 2.22: Comparison of probability distribution threshold based CTO estimate and the proposed CTO estimate measured at legacy receivers in mixed mode for different preambles under the channel model D with SNR=10 dB. 1. Repetition, 2. CS with T , and 3. CS with T n
2 50=cs
2 400cs
The range of the estimates obtained using the proposed technique is
within the desired range of 15 samples whereas the threshold based technique has
the estimates outside the desired range. Similarly, for CS preamble withT n ,
the probability distributions are plotted in figure 2.22.3. One can see from the figure
that the CTO estimates obtained by using the proposed technique are well within the
estimation accuracy of 8 samples. In case of threshold based technique only 74% of
CTO estimates are within the estimation accuracy.
2 400cs
From the above results, it is clear that the threshold based technique
performs poorly in lower SNRs compared to the proposed technique. Since the
estimation accuracy for the first two preambles types is better, one can use the
threshold based coarse timing estimation technique and can do better in fine timing
synchronization. However, for the CS preamble with , the threshold
based technique cannot be used because of its poor performance. Therefore, for the
2 400csT =
56
Figure 2.23.2: CS preamble with 2Figure 2.23.1: Repetition preamble csT = 50ns
legacy receivers operating in mixed mode, the proposed coarse timing
synchronization algorithm performs better. The results obtained from proposed
technique have similar distribution shape for all the preamble types and the mean
value is around 5. Even though the proposed estimator performs well even in the
lower SNRs like 10 dB, at higher SNRs, say at 35 dB, both the proposed and
threshold based techniques performs similarly. This is because the metric ( )nΛ is
less noisy and the estimate obtained from the threshold based technique itself is
robust at these SNRs.
Figure 2.23 shows the distribution of the CTO estimates measured in
MIMO-OFDM receivers operating in green field mode for different preamble types
under the most representative channel model D at SNR =10 dB. The comparison
between the proposed technique and threshold based technique shows similar
performance trend like the mixed receivers in context to various preamble types.
Due to the MRC type of operation at the receiver, the proposed scheme performs
better compared to the mixed mode receivers. From all the three figures 2.23.1,
2.23.2 and 2.23.3, it is clear that about 99% of the estimates are within the range [3,
9] and its mean is around 5. Even though the threshold based technique performs
57
Figure 2.23.3: CS preamble withT 2cs
Figure 2.23: Comparison of probability distribution of the proposed CTO estimate and threshold based CTO estimate measured at MIMO receivers in green field mode for different preambles under the channel model D with SNR=10dB. 1. Repetition, 2. CS with T , and 3. CS with ns s2 400csT n=2 50=cs
= 400ns
s ns=
poorly at lower SNRs, this technique performs similar to the proposed technique at
higher SNRs.
2.6.2.1 Impact of multipath profile
Since each channel model has different channel dispersion, the mean
value of the distribution obtained from the proposed technique varies with different
channel models. To compare the performance of the proposed scheme under all
these channel models, we find the percentage of CTO estimates with in the
estimation accuracy of each preamble type. As mentioned in the above section, the
estimation accuracy for repetition preamble is 16 samples, for CS preamble with
it is 15 samples and for CS preamble with T it is 8 samples. 2 50csT n= 2 400cs
In Figure 2.24, we plotted the percentage of CTO estimates obtained
with in the estimation range for each preamble under all the channel models. The
channel considered here are spatially correlated channels and SNR is 10 dB. The
58
Figure 2.24: Percentage of CTO estimates versus channel models: legacy receiver in mixed mode for different preamble under different channel models. SNR=10 dB and spatially correlated channels
figure shows that channel model C and channel B shows poor performance
compared to channel D and E. This is because, the spatial correlation of channel C
and B is high when compared other channel models. Also, the repetition preamble
exhibits a poorer performance when compared to the other preamble types.
This is due to the beamforming effect which creates nulls in certain
instances. The performance of channel C for the repetition preamble is very poor
because of the combined effect of highest spatial correlation and the beamforming
effect. In effect the repetition preamble under channel C has poorer performance
compared to other channel models. One can also see that even in legacy receivers,
one can achieve 90% CTO estimates within the estimation range for CS preambles.
In figure 2.25, the performance of a MIMO receiver operating in a green
field receiver is measured for various preamble types under various channel models.
59
Figure 2.25: Percentage of CTO estimates versus channel models: MIMO receiver in green field mode for different preamble under different channel models. SNR=10 dB and spatially correlated channels
The simulation conditions to measure the MIMO performance is similar to the
mixed mode conditions. Compared with the legacy receiver performance which is
operating mixed mode, MIMO receivers have more percentage of CTO estimates
within the estimation range. This is because of exploiting the multiple received
signals available at the receiver. Similar to mixed mode performance, the repetition
preamble has poorer performance as compared to the other preambles.
From the above results, we see that for CS preamble with has
good performance in terms of AGC convergence, SOP detection and coarse timing
estimation. The proposed CTO estimation algorithm performs well even in the
lower SNRs. Especially, in the legacy receivers, the same algorithm can be used for
performing coarse timing estimation with the legacy preamble when stations are in
legacy mode and with the CS preambles when they are in mixed mode. So, the
legacy systems in the 802.11n network can have better time synchronization for
both the legacy mode and in the mixed mode. The proposed technique also
2 400csT n= s
60
performs well for the MIMO-OFDM receivers. Since, the CTO estimates obtained
from the proposed technique for different preambles are within their estimation
ranges, one can use a simple cross correlation technique to get the fine timing
estimate.
2.6.3 Performance of fine timing estimation
The fine timing estimation is done by using the coarse timing estimate
obtained from the proposed algorithm. The proposed coarse timing estimation
algorithm is efficient in finding the timing within the estimation range for all the
preamble types even in lower SNRs. This motivates us to use the short symbols to
find the fine timing estimate with lesser computations. From the results of CTO
estimation algorithm, we have shown that eventhough the mean value of the CTO
estimate varies with channel models, the range over which the estimates are
distributed is almost the same for all the channel models. Hence, one can shift the
appropriate number of samples backward and can do the fine timing estimate. For
the repetition preamble and the CS preamble with , one has to do 16
samples and 15 samples shift respectively, i.e., the fine timing estimation starts
from
csT = 50 ns
163M - for repetition preamble and 153M - for CS preamble with . In
case the of CS with , the range is between 2 and 10, so the fine timing
estimation starts from
csT = 50 ns
csT = 400 ns
103M - . The probability distribution of the fine timing
estimate obtained from the proposed technique is compared probability distribution
of the fine timing estimate obtained from the cross correlation based technique.
To isolate the performance of the fine timing estimator, we use the same
coarse timing estimate in both the techniques. In figure 2.26, the performance of the
proposed technique is measured in the legacy receivers with various preamble types.
The simulation is done for a 2x2 system under the most representative channel
model D with SNR=10 dB. The results show that both the fine timing estimation
techniques perform similarly. The advantage of the proposed system is that it
61
requires lesser computations compared to the correlation based technique. The
performance for various preambles is shown in figures 2.26.1, 2.26.2 and 2.26.3.
Figure 2.26.1: Repetition preamble Figure 2.26.2: CS preamble withT 2cs = 50ns
Figure 2.26.3: CS preamble withT = 400ns2cs
Figure 2.26: Comparison of probability distribution of proposed fine timing estimate and cross correlation based estimate measured at legacy receivers in mixed mode for different preambles under the channel model D with SNR=10dB. 1. Repetition, 2. CS with T , and 3. CS with 2 50=cs ns s2 400csT n=
62
In the figures 2.27.1, 2.27.2 and 2.27.3, the performance of the proposed
fine timing estimation algorithm is compared with the performance of the cross
correlation based technique for MIMO-OFDM receivers. The simulation conditions
are similar to the mixed mode. The performance of all the preambles using the
proposed technique in MIMO receivers is similar to the performance of the cross
correlation based technique.
In the figures 2.27.1, 2.27.2 and 2.27.3, the performance of the proposed
fine timing estimation algorithm is compared with the performance of the cross
correlation based technique for MIMO-OFDM receivers. The simulation conditions
are similar to the mixed mode. The performance of all the preambles using the
proposed technique in MIMO receivers is similar to the performance of the cross
correlation based technique. One can see from the figure that, the percentage of
estimates with in the estimation range is large when compared to the estimates of
the mixed mode system. This is because, the multiple receive signals are used
efficiently to obtain the fine timing estimates. Apart from this advantage, the usage
of short symbols also reduces the computational complexity require for the fine
timing synchronization.
Figure 2.27.1: Repetition preamble Figure 2.27.2: CS preamble with T 2cs = 50ns
63
Figure 2.27.3: CS preamble with T 2cs = 400ns
ns s
Figure 2.27: Comparison of probability distribution of proposed fine timing estimate and cross correlation based estimate measured at MIMO receivers in green field mode for different preambles under the channel model D with SNR=10dB. 1. Repetition, 2. CS with T , and 3. CS with 2 50=cs
2 400csT n=
2.6.3.1 Effect of multipath profile
The impact of the multipath profile is studied and shown in figures 2.28
and 2.28. From the results obtained for channel D, one can see that the range over
which the fine timing estimates are distributed is 0 to 5. This is due to fact that the
occurrence of maximum tap gain in non-zero taps or due to the occurrence of
maximum gain in two or more taps. From simulation results, we obtained that for
channel model E, the range is [0, 5]. To compare the performance of the proposed
technique for all the preambles under all the channel models, we measured the
percentage of fine timing estimates within the estimation accuracy. Here the
estimation accuracy is 0 to 5.
The simulations are performed at SNR=10 dB. The results the legacy
receivers operating in mixed mode for different preamble types under different
channel modes are shown in figures 2.28. The repetition preamble shows poorer
performs in all the channel models. The performance of the fine timing estimation
64
Figure 2.28: Percentage of estimates within estimation accuracy versus channel models: Legacy receiver in mixed mode for different preamble under different spatially correlated channel models. SNR=10 dB
algorithm for different preambles under different channel models is measured for
MIMO-OFDM receiver. This is shown in the figure 2.29. Similar to mixed mode
performance, the repetition preamble exhibits poorer performance when compared
to other preambles. One can also see that more than 95% of fine timing
synchronization is obtained even at lower SNR=10 dB using this technique at less
complexity compared to the cross correlation technique. Since the maximum
estimation accuracy is 5 samples, one can shift 5 samples backwards and start the
FFT windowing. This ensures that the system will operate in the ISI free region.
From the results obtained for AGC, SOP detection, coarse timing
estimate and fine timing estimate, one can infer that the simply repeating the legacy
preamble in all the transmit antennas of the MIMO transmitter performs poorly
65
Figure 2.29: Percentage of fine timing estimates within estimation accuracy versus channel models: MIMO receiver in green field mode for different preamble under different channel models. SNR=10 dB and spatially correlated channels
compared to sending the cyclically shifted versions of the legacy preamble in all the
transmit antennas.
The CS preamble with seems to be better preamble that can
achieve backward compatibility and performs well in MIMO receivers. The
proposed coarse timing estimation algorithm and fine timing estimation algorithm
can be implemented in the legacy station that operate in the mixed mode and in the
MIMO station that operate in the green filed mode. The other advantage is that the
legacy stations can use the proposed algorithms for legacy preambles.
2csT = 400 ns
66
2.7 CONCLUSION
In this chapter, we analyzed the different ways of extending the SISO
preamble to MIMO-OFDM systems for backward compatibility reasons and its
effects on the performance of the initial receiver tasks like AGC and time
synchronization. We showed that the CS preamble with has better
receive power estimate for AGC compared to the other techniques. We studied the
performance of the SOP detection in spatially correlated and in spatially
uncorrelated channels with all the preamble types where repetition type performs
poorer compared to CS preambles. We proposed a new coarse timing estimation
technique for CS preambles in both the modes of operation. From the simulation
results, it can be seen that the proposed CTO estimation method performs better
even in lower SNRs compared to the performance of threshold based technique.
Based on this performance, a simple technique for finding the fine timing estimate
is proposed using short symbols and its performance is compared with the
performance of a complex cross correlation technique. From the simulation results,
the proposed technique shows similar performance to the cross correlation based
technique.
2 400csT = ns
67
CHAPTER 3
LOW COMPLEXITY MIMO OFDM RECEIVER
3.1 INTRODUCTION
The IEEE 802.11n standard is an enhancement to the existing IEEE
802.11a/g WLAN standards. The PHY layer technique uses multiple antennas both
at the transmitter and at the receiver to achieve the higher data rates. The maximum
PHY layer data rate that can be achieved is around 400 Mbps. The operating
bandwidth of this system is 20MHz and it also has support for 40MHz operation.
The PHY layer and the MAC layer specifications given by the EWC group (2006)
is the draft proposal which has been accepted by all the parties. As mentioned in
section 2.2, the MIMO-OFDM system operates in all the 3 modes. The main
objective of this chapter is to provide a low complexity spatial detection technique
for MIMO-OFDM receivers operating in the mixed mode and green field mode.
3.2 SYSTEM MODEL
In this section, the MIMO-OFDM transmitter model proposed in EWC
proposal (2006), for the IEEE 802.11n standard has been discussed. A typical
receiver structure for the proposed transmitter has been analysed and discussed, and
the signal model at each receive antenna is also derived. The MIMO transmitter and
the corresponding receiver will be similar in the mixed and in the green field mode
of operation.
68
3.2.1 Transmitter model
The MIMO-OFDM baseband architecture with TX antennas is shown
in figure 3.1. The incoming data bits are randomized using a scrambler in order to
avoid the occurrence of long zeros and ones. The output of the scrambler block
ensures that the bits are equally likely to satisfy the theoretical assumptions. The
scrambled bits are passed into an encoder sparser where it is demultiplexed across
the forward error correction (FEC) encoders in a round robin fashion. Here,
is the number of encoding streams and in EWC (2006), for 1
tN
ESN
ESN 1ESN = 1× and
systems and for 2 2× 2ESN = 3 3× and 4 4× systems. The last six scrambled zero bits
in each FEC input is replaced by the unscrambled zero bits. This is done to make
the FEC encoder to an all zero state after the encoding is done. The FEC block
encodes the data to enable channel error correction capabilities. The FEC block is
made up of binary CE followed by a puncturing block. The basic block achieves the
coding rate of ½ and the other coding rates like 3/4, 2/3 and 5/6 are achieved with
the help of puncturing pattern defined in EWC (2006). The output of the 2 FEC
units is interleaved and is done in 3 stages. In the first stage, a stream parser is used
wherein the output of the encoders are divided into block of s bits where
is the number of bits assigned to a single axis (real of imaginary)
in a constellation point. From each encoder,
max{1, / 2}BPSCs N=
ssN consecutive blocks of the bits are
taken and fed across the
s
ssN spatial stream. In the second stage, the bits at each
spatial stream are divided into blocks of and interleaved using the technique
given in EWC (2006). Then, the interleaved bits from each stream are grouped into
bits and mapped to the constellation points. In the final stage, the output of the
CBPSN
CBPSN
ssN streams is passed through a spatial mapper. The spatial mapper distributes the
complex symbols to the transmit chains. In each chain, out of 64 subcarriers in
20MHz operation, data symbols are mapped on the subcarriers -28 to -1 and +1 to
28. The remaining subcarriers are loaded with guard subcarriers and pilot symbols.
Then in each chain, a N-point IFFT is taken and the cyclic prefix of length is
taken from the end of IFFT output is appended in front of it. The signals are then
tN
/ 4N
69
upconverted to radio frequency and transmitted through the TX antennas. The
total power transmitted is normalized across the transmit antennas and is given
as
tN
tN
2
1
( ) 1tN
E x n=
⎡ ⎤ =⎢ ⎥⎣ ⎦∑ , where ( )qx n is the transmitted signal from the TX antenna. thq
1 IFFT & CP
IFFT & CP
tN
Stre
am P
arse
r
Enco
der P
arse
r
FEC
Enc
oder
FE
C E
ncod
er
1
ssN
Interleave QAM Mapper
Interleave QAM Mapper
Spat
ial m
appi
ng
1
ESN
Scra
mbl
er
Figure 3.1: The 802.11n MIMO-OFDM baseband transmitter
3.2.2 Receiver model
At the receiver, antennas are used to receive the signal. The signals in
each RX antenna are down converted to baseband and sampled with a maximum
sampling duration of 50ns. Assuming that the receiver is perfect time and frequency
synchronized, and the exact channel knowledge is available at the receiver, the
remaining processing is performed. The received signal at the
rN
thp RX antenna is
given as
70
(3.1) 1
1 0
( ) ( ) ( ) ( )tN L
p pq qq l
r n h l x n l v n−
= =
= −∑∑ p+
where is the impulse response of the channel between the q TX and
the
( )pqh n th
thp RX antenna, L is the channel length and v is the AWGN at the ( )p n thp RX
antenna with zero mean and variance 2vσ . A standard OFDM receiver is used in
each RX chain to obtain the frequency domain estimates.
Figure 3.2: 802.11n MIMO OFDM baseband receiver
M
ultip
lexe
r ESN
Vite
rbi d
ecod
er
Vite
rbi d
ecod
er
CP & FFT
CP & FFT
rN
1
DeinterleaveQAM De-Mapper
DeinterleaveQAM De-Mapper
SSN
1
Stre
am D
e-pa
rser
Spat
ial D
etec
tor a
nd d
emap
ping
(Z
ero
forc
ing,
MM
SE, S
IC, e
tc)
Des
cram
bler
1
The complex estimates corresponding to a particular subcarrier from all
the RX chains are grouped together to form a vector. Then, spatial detection is done
jointly on this vector of complex symbols corresponding to this subcarrier. Similar
processing is done in all the subcarriers and the received signals are spatially
separated into ssN signals. Using a QAM demodulator, the complex symbols are
demodulated and deinterleaved in the case of hard decision decoding. However, in
soft decision decoding, the soft information from the OFDM receivers are
deinterleaved and decoded. A spatial demapper collects the deinterleaved signals
from the ssN paths and multiplexes them to the viterbi decoders. After decoding, ESN
71
descrambling is done to rearrange the bits in a similar fashion to the input of the
transmitter. This is shown in figure 3.2
3.3 SPATIAL DETECTION
The key technique behind the MIMO-OFDM receiver is the spatial
detection done in each subcarrier. After removing the cyclic prefix, FFT is taken on
all the received signals. Then, the components corresponding to the subcarrier
from all the streams are stacked in a vector and is represented as
thk
( ) ( ) ( ) ( )k k k k= +Y H X V (3.2)
where is the vector containing elements of the subcarrier, is the
channel matrix in the subcarrier domain, is the transmit signal
vector at the subcarrier and is the noise vector at the subcarrier. The
elements in the noise vector are independent and identically distributed (i.i.d)
circularly symmetric complex Gaussian random variables with zero mean and
( )kY 1tN × thk ( )kH
tN N× r ( )kX 1tN ×
thk ( )kV thk
2vσ as
variance. Since the spatial detection is performed for all the subcarriers in a similar
way, the index in (3.1) is dropped and the equation is rewritten as k
= +Y HX V (3.3)
The spatial detection techniques can be broadly classified as
i Non-linear detection
ii Linear detection
iii Embedded detection technique
3.3.1 Non-linear detection technique
The main feature of this detection technique is that it achieves better
system performance but with increased cost due to complexity. Usually, it involves
searching of the optimal solution from the all possible solutions set.
72
3.3.1.1 Maximum likelihood detection (ML)
One way to estimate the transmit vector X from (3.2) is by doing an
exhaustive search in a set which contains all possible combinations of the transmit
vectors. If the vector in the set is equal likely, then the estimate obtained is an
optimal solution. The detection technique can be mathematically represented as
2
arg minest ssN∈
= −X A
X Y HX (3.4)
where estX is a vector containing the estimates, 1tN × A is the constellation set which
contains all possible transmit vectors. Minimizing this argument corresponds to
finding the vector which is most likely transmitted. The maximum diversity order
that can be achieved by each stream by using this technique is . The major
disadvantage of the ML detection technique is the exponential increase in its
complexity with the modulation mode. As the size of the constellation increases
(say from BPSK to 16 QAM) the complexity of searching the optimal solution
increases and the complexity measure is given as where
rN
( tNO M∼ ) M is the number
of points in the constellation.
3.3.2 Linear receivers
The main feature in the linear detection technique is the low complexity
approach. However, there will be a loss in the performance of the system compared
to the non-linear receivers. A nulling solution or an equalizer matrix G is calculated
from the channel information H available at the receiver. Then, the received signal
vector Y is linearly transformed by the equalizer matrix to obtain the transmit
signal estimate and is given as
est +X = GHX GV (3.5)
where is the matrix and G tN N× r estX is the transmit signal estimate. The block
diagram of the traditional linear receiver is shown in the figure 3.3. Using the linear
receivers, the maximum diversity order that can be achieved by each stream
is . Depending on the method of calculating the equalization matrixG , the
linear receivers ca be categorized as follows
1r tN N− +
73
estX X Y
V
Equalizer G
Channel Matrix H
Figure 3.3: Traditional linear detector
3.3.2.1 Zero forcing technique (ZF)
The ZF technique is a simple linear decorrelating detector that decouples
the received signal vector into parallel SISO streams. The equalizer matrix used
here is given as
†ssN=G H (3.6)
where †H is the pseudo inverse of the channel matrix H and is defined
as † ( ) 1H H−=H H H H . This solution completely nulls out the inter stream
interference but suffers from the noise enhancement if the channel matrix is rank
deficient or ill-conditioned. The complexity of this scheme is only in the order of
because this operation involves only matrix multiplications and matrix
inverse.
3( tO N∼ )
3.3.2.2 Minimum mean square error detection (MMSE)
The MMSE technique is a simple linear detection technique which
optimally trades off the effect caused by the inter-stream interference and the
background Gaussian noise. The equalizer matrix used here is defined as
1( )H 2ss vN σ −=G H H + I HH
)
(3.7)
In lower SNRs, this receiver acts as a matched filter by optimally balancing the
interference and noise. In higher SNRs, the MMSE detector becomes the ZF
receiver. The complexity of this scheme is in the order of . The major
disadvantage of this scheme is that the MMSE solution calculation requires the
value of noise variance
3( tO N∼
2vσ at the receiver making it computationally inefficient.
74
Apart from the increase in complexity, small errors in the noise variance estimate
results in poor performance of this technique.
3.3. 3 Embedded detection technique
The major feature of this technique is its moderate complexity with
moderate bit error rate (BER) performance. This technique performs a non linear
detection that extracts the streams by using the linear solutions like ZF or MMSE,
with and without ordered successive interference cancellation (OSIC) (D. Rohit
Nabar, 2004). Since the proposed technique is a modification of the OSIC technique,
a review of this technique is given.
3.3.3.1 Ordered successive interference cancellation
Instead of decoupling the received signal vector into parallel SISO
streams and detecting them individually, one detected output stream can aid the
detection of the other streams to achieve a better performance. This is done by
subtracting the interference caused by the detected stream from the received signal
vector and next stream is detected from it. The question of which stream should be
detected first can be addressed by using an optimal detection ordering strategy. The
OSIC technique is summarized as follows. Let i be the iteration index and a stream
detected per iteration. Then, the whole algorithm can be implemented in 4 steps.
Step1. Computing initial nulling solution:
Set 1i = . Obtain the nulling solution given for linear receivers in order
to satisfy the performance related criterion such as ZF or MMSE.
iG
Step2. Find the detection order
Determine the optimal detection order to detect the strongest signals first.
The optimal ordering scheme for the ZF criterion is based on the postdetection SNR
of each signal (P. W. Wolniansky et al 1998). The SNR of the thj stream at the
output of the detector is given as { } ( )22 2ji j v ip E X σ= g j where j
ig is the thj row of
the ZF nulling solution calculated in the iteration andiG thi 1,....., tj N= . Then, the
75
vector containing the output SNRs obtained in the iteration is sorted in a
descending order and their index is stored in another vector . The first value in is
the index of the received signal with large post detection SNR and it corresponds to
row of which has smaller
ip thi
iq iq
iG2j
ig . This is the signal to be detected first. Similarly,
for the MMSE criterion based system, the optimal ordering is based on the post
detection SINR of each received signal. The vector 1( ( )H 2i ss vdiag N σ )−=p H H + I
is sorted in descending order and their indices are stored in . The first value in is
the index of the RX signal with the largest post detection SINR and is detected first.
iq iq
Step3. Nulling and slicing
The received signal vectorY is weighted linearly with the nulling vector
ig to obtain the estimate of the signal corresponding to signal. This is given as (1)iq
{ }(1)iest i iquant=qX g Y (3.8)
Here ig is the 1 tN× vector and is the iY 1tN × vector. The estimated value of the
signal is quantized to the nearest value of the signal constellation.
Step4. Interference cancellation and recursion
The interference caused by the detected signal is cancelled from the
received signal by subtracting the remodulated version of the detected signal from
the received signal. This is given as
(3.9) 1i(1)
i(1)i i e+ = − qqY Y h X st
where is the column of the channel matrix. i(1)qh (1)
thiq
Further, the column in channel matrix (1)iq H is replaced with zeros to obtain i+1H
and . Iterate from the step2 by setting i+1G 1i i= + until all the streams are detected.
The above steps are illustrated in the figure 3.4. The maximum diversity order
obtained by a steam is
tN
(1)th
iq r tN N i− + . The overall performance of the system is
better than that of the linear receivers but close to the ML performance. As the
iterations increase, the numbers of columns of the channel matrix to be replaced
76
with zeros also increase. Hence, the computations required for matrix inverse for
this deflated matrix is less. Thus, the approximate complexity for the technique is
given as3 2
3 2
16 2
2
rNt r
p
N Np p p=
⎛ ⎞++ + +⎜ ⎟
⎝ ⎠∑ . However, this complexity itself makes it
difficult to implement because apart from this the receiver has to implement other
operations like viterbi decoding and so on. For example, let 4rN = ,
and , then 53120 complex multiplications are needed. 4tN = 64N =
Interference cancellation
(1)iqestX
( 1)thi + iteration Obtain 1i+H ,
1i+G and 1i+p
H 2vσ
Detect the stream
corresponding
First value in corresponds to the stream
iq
Sort in descendin
g order and store the index
in q
ip
i
iY
Nulling solution
H
iG (ZF or MMSE) and
Ordering
2vσ
1i+Y
Repeat the steps until all the streams are
detected
Values in r
ipepresents the SINR
Figure 3.4: Ordered successive interference cancellation
3.4 PROPOSED LOW COMPLEXITY TECHNIQUE
In this section, a low complexity spatial detection technique is proposed
for a BICM MIMO-OFDM system which achieves a similar performance as the
MMSE V-BLAST system. In Sana SFAR et al (2003), a low complexity group
ordered SIC technique is proposed for multiuser MIMO CDMA systems. Based on
this concept, a low complex group ordered MMSE VBLAST (GO MMSE
77
VBLAST) technique for MIMO-OFDM systems is proposed. The proposed detector
consists of gN group detectors wherein all the streams in a particular group are
detected by using a single MMSE solution. The group detectors are successively
connected so that a particular group detector in the chain has access to the decisions
made by the previous detector. Inside each group detector, an ordered SIC is done
and the ordering is based on the optimal ordering strategy given in Hassibi (2000).
In spatially correlated MIMO channels, some of the spatial streams can face similar
fading conditions. This can lead to a similar nulling solution for these streams.
Consequently, instead of finding the nulling solution for each stream, the streams
facing similar channel conditions are grouped together and a common nulling
solution is calculated for that group. This reduces the complexity significantly and
still maintains the performance comparable to the performance of MMSE VBLAST.
Grouping of streams can be done in a fixed or in an adaptive manner. In a typical
802.11n system, the TX and RX antennas will face spatially correlated channel
condition because of antenna packing to meet space constraints. So this technique
can be applied the MIMO receivers operating mixed mode and green field mode.
3.4.1 Fixed GO MMSE V-BLAST:
In this technique, for each group tN Ng streams are assigned and 1
MMSE solution is calculated for all the streams in that group. The whole algorithm
can be divided into 4 steps.
Step1. Computing the initial nulling solution and grouping:
Set and obtain the MMSE nulling solution . Calculate the
vector as in step 2 of the SIC technique given in section 3.3.3.1. Sort the elements
of this vector in descending order and store the indices in another vector . The
received signals corresponding to the values in are divided into
1i = iG
p
q
q gN groups.
Step2. Group nulling and detection
Use the rows of corresponding to streams in the group for nulling
and detect the signals in that group. The SIC technique is employed to detect the
iG thi
78
signals inside that group and is similar to the one in the OSIC technique. Decisions
are made on the detected signal by quantizing it to the nearest constellation point
before making it available to the next signal in that group.
Step3. Group interference cancellation
Let iestX be the vector containing the detected streams of the group.
Then, the interference caused by this group is cancelled from the received signal
and is given as
thi
(3.10) / )t gi(N N
mi+1 i m est
m=i(1)= - X∑Y Y h
where tN Ng is the number of streams of the group, is the interference
cancelled received signal available for the next group detection.
thi i+1Y
Step4. Recursion
Move to the ( group and repeat from step2 until all the groups are
detected. Obtain
1)thi +
i+1H and after replacing the columns of the stream
corresponding to the detected stream with zeros. This can be illustrated in the figure
3.5.
i+1G
In the proposed technique, only one MMSE solution is calculated per
group detector. As the iteration increases, the number of columns in the channel
matrix with zeros increases and the computations required for calculating the
deflated matrix inverse decreases. Hence, the approximate complexity for the
technique is given as
/ 3 2
3 2
, / ,..6 2
2
t g
r r t g
N Nt
p N N N N
N Np p p= −
++ + +∑ r (3.11)
For example, let , , and4rN = 4tN = 64N = , then substituting these values in (3.11)
the number of complex multiplications required is 35712. There is a 40 % reduction
in the number of complex multiplications as compared with the MMSE VBLAST
method while still achieving similar performance.
79
(0 )qGroup 1
Interference cancellation
1estX
YSIC
2Y
Values in re
ppresents the SINR
H
Nulling solution
iG (ZF or MMSE) and
Ordering criterion
p
Sort in descendin
g order and store the index
in
p
q
( )1tq N −
Group gN gN
estX gNY
SIC
Figure 3.5: Proposed Group ordered MMSE VBLAST detector
2vσ
3.4.2 Adaptive GO MMSE V-BLAST
The proposed technique can also be implemented in an adaptive manner.
Unlike the fixed technique, the number of group detectors gN in this technique is
not fixed. The initial vector is normalized with its minimum element and grouped
iteratively using a threshold. For each of the iteration, the vector is updated and
grouping is done with the prefixed threshold. The SIC techniques applied inside and
across the group detectors are similar to fixed GO MMSE V-BLAST. In summary,
the whole technique can be categorized into 3 steps.
ip
ip
Step1:
Set and obtain the MMSE nulling solution as given in section
3.3.2.1. Calculate the vector as in OSIC technique and normalize the vector with
its minimum value. This is given as
1i = iG
p
inorm
min
=pp
p (3.12)
80
Step 2:
Store the index of the elements in whose value is less that the threshold
and store it in . The streams corresponding to these indices in are assigned
to group1. Repeat the steps 2 and 3 given for fixed GO MMSE V-BLAST to
estimate the transmit signals corresponding to group.
ip
thres iq iq
thi
Step 3:
Obtain the channel matrix i+1H and the nulling solution for the next
iteration and iterate from step 1 until all the signals are detected. The complexity of
the system is variable because of the threshold based ordering. For simulations, the
threshold value is kept as 1.75 and 2. These values are obtained after doing
extensive simulation studies.
i+1G
thres
3.5 SIMULATION MODEL AND RESULTS DISCUSSION
In this section, the simulation model used for measuring the performance
of the proposed system is discussed. The performance of the proposed algorithm is
analysed for coded and uncoded systems. The MIMO-OFDM system considered
here consists of 4 TX and 4 RX antennas ( 4tN = and 4rN = ). For an uncoded
system simulation, the bit stream is distributed across the ssN signal paths using a
round robin sparser and QPSK modulation is performed in each path( 4=ssN ). A
64-point IFFT is performed in each path and a CP of 16 samples is appended for
combating ISI. The channel models used for simulation are obtained from the
details given in the TGn channel models (2003) and AWGN is added with the
channel corrupted signal and detection is performed. In fixed GOMMSE V-BLAST,
the number of groups is 2( 2=gN ). For the adaptive grouping scheme the threshold
is kept as 1.75 and 2. The bit error rate (BER) versus SNR is measured for different
spatially correlated channel models. The simulation is done for independent
channel realizations.
410
81
For a coded system, the transmitter model used for simulation is taken
from the EWC proposal (2006). Similar to uncoded systems, we considered a 4x4
MIMO-OFDM system for simulations. The generator polynomial for the encoder is
represented as { }1 8133=g and { }2 171=g 8 , and the rate of the encoder is ½. The
payload assumed is 200 bytes and zeros are padded to obtain integer number of
OFDM symbols in all the TX chains. The number of spatial streams 4ssN = and
QPSK modulation is performed in all the signal paths. Only 56 subcarriers are
loaded with data and the remaining subcarriers are loaded with pilot symbols and
zeros. The output of the spatial parser is performed across the transmit chains.
The simulation is done for 5000 independent channel realizations. The performance
is measured in terms of bit error rate (BER) versus Eb/No and a complexity analysis
is performed.
tN
3.5.1 Performance of an uncoded system
In figure 3.6, the BER versus SNR comparison for MMSE based detector,
MMSE V-BLAST and fixed GO MMSE V-BLAST is shown.
Figure 3.6: Comparison of BER versus SNR: MMSE, MMSE V-BLAST and proposed fixed GO MMSE V-BLAST for an uncoded 4x4 system under channel model D
82
The simulation is done for a 4x4 uncoded system under the most
representative channel model D. The result shows that the performance of the
proposed scheme is between the MMSE performance and the MMSE V-BLAST
performance. Comparing the performance at BER = 10-3, MMSE requires more than
40 dB SNR to achieve this BER, SIC attains this BER at SNR=24.5 dB and
proposed scheme requires 28.5 dB. From the above numbers, one can infer that the
proposed scheme performs better than the MMSE receiver and slightly inferior
performance when compared with the OSIC technique. The advantage is that this
performance is achieved with less complexity when compared with MMSE V-
BLAST.
Similarly in the figure 3.7, the results for adaptive based scheme are
presented. The threshold values for the adaptive schemes are kept as and
. Similar to the fixed GO MMSE V-BLAST scheme, the adaptive scheme
1.75thres =
2thres =
Figure 3.7: Comparison of BER versus SNR: MMSE, MMSE V-BLAST and proposed adaptive GO MMSE V-BLAST with
and for an uncoded 4x4 system under channel model D
1.75thres = 2thres =
83
also performs superior to MMSE scheme and performs poor compared to the OSIC
technique. As the threshold value of the adaptive scheme reduces, the performance
of the MMSE V-BLAST and the performance of proposed technique converge.
When , the MMSE V-BLAST and proposed scheme will have similar
performance.
1thres =
From the above results, we infer that the performances of proposed
schemes are approaching the performance of the OSIC technique with lesser
complexity. In figure 3.8, we compare the performance of fixed grouping technique
and adaptive grouping schemes. The fixed scheme performs poor compared to the
adaptive scheme because the detection groups are formed by just dividing the
nulling solution into gN groups. It is not necessary that the post detection SINR for
all the streams inside a group to be same. In the case of an adaptive scheme,
grouping is performed adaptively based on the threshold. Hence, performing SIC
inside the group will give better result compared to the fixed groups.
Figure 3.8: Comparison of BER versus SNR; Fixed and adaptive GO MMSE V-BLAST with thre and for an uncoded 4x4 system under the channel model D
1.75s = 2thres =
84
In figure 3.9 the performance of the proposed schemes are compared
with various channel models. The SNR required to obtain BER of 10-4 is measured
under all the channel models and compared in this figure. From the results, one can
see that the system under channel model C and B requires more SNR to achieve this
BER. This is because, the condition number measured in the time domain for these
channels are high compared to the other channel models. Also the adaptive scheme
with performs better compared to the other schemes. 1.75thres =
Figure 3.9: Comparison of SNR needed versus channel models for a BER = 10-4; 4x4 uncoded MIMO-OFDM system, Fixed and adaptive schemes
3.5.2 Performance of coded system
The performance of the proposed schemes is compared for the BICM
MIMO-OFDM system given in the 802.11n draft. In figure 3.10, the BER
performance of the fixed GO MMSE V-BLAST is compared with the MMSE and
OSIC technique. It can be seen that the performance of the fixed scheme and the
OSCI method are similar. At BER=10-4 point, there is only 1.1 dB difference
85
between these two curves. Comparing the performance of the proposed schemes in
coded and uncoded systems one can see that the proposed scheme performs better in
the coded systems. This is because, the coding and interleaving performed in the
system, exploits the frequency diversity resulting in a better performance.
Figure 3.10: Comparison of BER versus EbN0: MMSE, MMSE V-BLAST and proposed fixed GO MMSE V-BLAST for a coded 4x4 system under channel model D
Similarly, the result for adaptive grouping in a coded system is shown in the figure
3.11. The same trend is seen in this figure as in an uncoded system. One can infer
from the result that both the threshold based grouping performance matches with
the MMSE V-BLAST scheme. The BER versus Eb/No comparison for the fixed
grouping and adaptive grouping is shown in figure 3.12. Unlike the uncoded system,
the performance of fixed grouping, adaptive grouping with and adaptive
grouping with are similar. This is because of the diversity which is
leveraged by coding and interleaving.
1.75thres =
2thres =
86
Figure 3.11: Comparison of BER versus EbN0: MMSE, MMSE V-BLAST and proposed adaptive GO MMSE V-BLAST with 1.75thres = and
4 system under channel model D
2thres = for a coded 4x
Figure 3.12: Comparison of BER versus EbN0: Fixed and adaptive GO MMSE V-BLAST with thre and ; coded system under channel D
1.75s = 2thres =
87
In figure 3.13, the Eb/N required to attain BER of 10o -4 is shown for the proposed
fixed and adaptive scheme under all the channel models. As we discussed in the
uncoded system performance, the channel C and B requires more Eb/No as
compared with other channel models. Also the most representative channel model D
achieves this BER at of 14.5 dB. From all the results that we have seen above,
the performance of the proposed fixed scheme and the adaptive scheme considered
is similar in the BICM systems under all the channel models considered.
Eb/No
Figure 3.13: Comparison of EbN0 needed versus channel models for a BER = 10-4; 4x4 coded MIMO-OFDM system, Fixed and adaptive schemes
We extended the simulation for a 2x2 MIMO-OFDM system where we
found that the performance of the proposed techniques and the OSIC techniques are
similar but there is no significant complexity reduction as in the 4x4 systems. So
this technique is helpful when there more number of antennas used at the transmitter
and at the receiver.
88
3.5.3 Complexity comparisons
In this section, the computations required for the proposed technique and
the other techniques are compared and discussed. We considered only the number
of complex multiplications and complex additions for counting computations. In
table 3.1, a comparison of the computations required by the proposed fixed GO
MMSE V-BLAST and the other schemes is shown. For this computation a 4x4
MIMO-OFDM systems with 56 useful data subcarriers are considered.
only 336
Hence, f
decoding
achieves
3.6 CO
detection
BICM M
low comp
is a mod
performa
method,
adaptive
Table 3.1: Complex computations for various spatial detection schemes
Spatial detection technique No of complex operations
MMSE 22400
MMSE V-BLAST 36400
Fixed GO MMSE V-BLAST 25760
Compared with MMSE scheme, the proposed grouping technique takes
0 computations extra but performs better compared to the MMSE scheme.
or 802.11n systems which requires more complexity due to viterbi
and spatial detection, the proposed scheme reduces some complexity and
the similar performance as MMSE V-BLAST.
NCLUSION
In this chapter, we presented a short review of the conventional spatial
techniques and the computational requirements if they are implemented in
IMO-OFDM systems. To address the complexity concern, we proposed a
lexity spatial detection technique called GO MMSE V-BLAST. Since this
ification of the MMSE V-BLAST, the performance is compared with the
nce of the plain MMSE receiver and the MMSE V-BLAST receiver. In our
grouping of received signals can be performed by fixed method or by
method. The simulation study is performed for the coded and the uncoded
89
systems. The result of the uncoded system shows that the performance of the
proposed technique is in between the performance of MMSE and MMSE V-BLAST
schemes. However, the performance of coded system for the proposed technique is
similar to the performance of the MMSE V-BLAST system. This is achieved with a
very less increase in complexity when compared to plain MMSE technique
complexity. Hence, the proposed techniques can be used as a low complexity spatial
detection technique for the 802.11n MIMO receivers where complexity is a major
concern.
90
CHAPTER 4
CONCLUSION
In this thesis, we have analyzed different methods of extending the
legacy 802.11a preamble to 802.11n systems so as to provide backward
compatibility. We studied the performance of initial receiver tasks such as AGC and
SOP detection which depends on the structure of the preamble. From the simulation
study, we have shown that simply sending the legacy preamble in all the transmit
antennas of MIMO-OFDM system is not a good preamble for backward
compatibility and performance reasons. We showed that sending the cyclically
shifted version of the legacy preamble in all the transmit antennas provides better
AGC convergence and SOP detection. We simulated the performance for 50ns shift
cyclic and 400ns shift for a 2x2 system. We found that preamble with 400ns shift
performs better when compared to the preamble with 50ns shift.
We proposed a low complexity and robust coarse time estimation
algorithm for the legacy stations and MIMO stations. The performance of the
proposed algorithm is compared with the performance of threshold based technique.
From the simulation results, we showed that the coarse time offset estimates are
within the estimation accuracy for CS preamble with 400ns shift. We compared the
performance with repetition preamble and CS preamble with 50ns shift. We found
that the CS preamble with 400ns shift has more percentage of CTO estimates within
estimation accuracy. Based on the coarse time estimates, we proposed a low
complexity fine timing estimation method using short symbols. We have chosen
short symbols for fine timing estimation for two reasons. First, the coarse timing
91
estimates are well within the estimation accuracy. So a simple cross correlation kind
of fine timing synchronizer can be used. Second, the computations required for fine
timing synchronizer using short symbols is less when compared to the fine timing
synchronizer using long symbols. We compared the performance of the proposed
algorithm with the performance of the cross correlation based technique. From the
simulation results, we found that both the techniques perform similarly but the
advantage in the proposed technique is its lesser complexity. Also, the fine timing
estimates obtained for the CS preamble with 400ns shift has more percentage within
the ISI free region when compared to the other preamble types. We have shown that
the proposed synchronization algorithms can be used in the legacy receivers for
both the legacy preamble and for the new preambles. From the simulation results,
we have shown that the legacy stations with the proposed algorithms perform better
when compared to the existing algorithms.
In the second part of the thesis, we proposed a low complexity spatial
detection technique for bit interleaved coded modulated (BICM) MIMO-OFDM
systems. We first reviewed the different spatial detection techniques, their
performance, and their complexity requirements. Based on the moderately complex
and moderately performing ordered successive interference cancellation (OSIC)
technique, we proposed a new grouping and detection technique to reduce the
complexity further. The grouping can be done in the fixed manner or in the adaptive
manner. We studied the performance of the proposed techniques in the uncoded and
coded systems. We showed that the performance in the coded system matches with
the performance of the OSIC technique. Also the complexity of the proposed spatial
detection technique is slightly better than the linear spatial detection techniques. We
also studied the performance of the proposed system under various channel models.
The future scope for the work can be explained as follows. In our work
we have tested the proposed coarse and fine timing estimation algorithm for a 2x2
system which is a mandatory mode of 802.11n. The standard also supports the
92
optional mode of 4x4 system where each transmit the preamble with different cyclic
shifts. The proposed work can be extended to 4x4 system preambles where one has
scope to achieve better performance than preambles for 2x2 system. This is because
of the diversity performance achieved by the use of more number of antennas at the
transmitter and at the receiver. This is possible in the legacy and MIMO receivers.
The low complexity spatial detection technique can be applied to the MIMO-OFDM
system that is proposed in IEEE 802.16d/e standard where complexity is a major
concern.
94
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APPENDIX 1
PUBLICATIONS FROM THIS THESIS V.Sathish, S.Srikanth, “Low complexity MIMO detection technique for high speed
WLANs”, pp. 63-67, Proc. National Conference RF & Baseband systems for
wireless applications, TIFAC core, Madurai, India, Dec 11-12, 2005.