performance of ofdm system with constant amplitude modulation
TRANSCRIPT
Circuits and Systems, 2013, 4, 329-341 http://dx.doi.org/10.4236/cs.2013.44045 Published Online August 2013 (http://www.scirp.org/journal/cs)
Performance of OFDM System with Constant Amplitude Modulation
Waleed Saad, Nawal El-Fishawy, Sayed El-Rabaie, Mona Shokair Department of Electronic and Communication Engineering, Faculty of Electronic Engineering, Minoufiya University, Menouf, Egypt
Email: [email protected], [email protected], [email protected], [email protected]
Received September 8, 2012; revised January 1, 2013; accepted January 9, 2013
Copyright © 2013 Waleed Saad et al. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.
ABSTRACT
The Orthogonal Frequency Division Multiplexing (OFDM) technique has recently received considerable attention for wireless networks. Despite its advantages, it has a major drawback of its high Peak-to-Average Power Ratio (PAPR) value which affects the system efficiency and the cost. In this paper, a proposed system is discussed to achieve 0 dB PAPR value. It depends on a proposed block, called Constant Amplitude (CA) modulation. The whole characteristic mathematical analysis is presented for the proposed system. Additionally, the complexity evolution is explained. Af- terwards, many MATLAB simulation programs are executed. Time and frequency domain behaviors are presented. Furthermore, in-band distortion introduced by the proposed CA modulation is calculated in terms of Error Vector Mag- nitude (EVM). Moreover, the proposed system outperforms the conventional one when compared in terms of PAPR, equalization, and BER under Additive White Gaussian Noise (AWGN) channel and multipath fading channels. In addi- tion, the impact of the proposed scheme design parameter is studied. Keywords: OFDM; Multipath Fading Channels; PAPR; BER; Equalizer; EVM
1. Introduction
Many modern broadcasting wireless systems (such as wireless local area networks, digital audio and digital video broadcasting, WiFi, WiMAX, LTE) use multicar- rier modulations like OFDM [1].
One of the advantages of OFDM modulations is its re- sistance against multipath. Its drawback is the large PAPR value which is a measure of the modulated signal envelope dynamics. This makes the modulated signal very sensitive to the distortions introduced by the non linearity of power amplifiers. Hence, this increases the cost of the RF power amplifier which is one of the most expensive components in the radio hardware. Many strategies are introduced by the researchers to reduce the PAPR value of the OFDM signal [2-5].
In this paper, a proposed scheme is suggested to achieve 0 dB PAPR value. Therefore, it outperforms the previous techniques in terms of PAPR reduction value. It depends on a proposed block, named CA modulation, which is inserted in the conventional system to fix the OFDM signal amplitude. The mathematical model of the proposed scheme is presented. Furthermore, the com- plexity modification is studied. Additionally, many MATLAB simulation programs are executed to compare
the performance of the proposed and the conventional OFDM systems in terms of time and frequency domains, in-band distortion, PAPR, BER for multipath fading channels, and equalization. Moreover, the impact of the proposed scheme design parameter is explained. The simulation showed that the proposed system behaved better performance than the conventional one in all measurement terms.
The paper is organized as follows; Section 2, intro- duces the mathematical model for the conventional OFDM system. The PAPR definition and some of the major existing methods for reducing it are defined in Sections 3 and 4, respectively. Section 5, gives a com- prehensive mathematical analysis for the proposed sys- tem. Section 6, evaluates the complexity proposed by the proposed scheme. Extensive simulation results are dis- cussed in Section 7. Finally, conclusions are extracted in section 8 followed by the relevant references.
2. Conventional OFDM System Model
2.1. The Transmitter
The schematic diagram of the OFDM system is shown in Figure 1. At the transmitter, the encoded data are
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Figure 1. The conventional OFDM system.
transformed to parallel sequence of complex num-bers in one of several possible mapping formats (QPSK, 16-QAM, 64-QAM, etc.). Then, the N-points Inverse Fast Fourier transform (IFFT) is applied to the resulting modulated symbols. After that, a cyclic prefix (CP) is added to the resulting signal and it is converted to a serial sequence. Afterwards, the resulting signal is analogy modulated after the conversion to analog signal. Finally, the resulting signal is transmitted through the wireless channel [2].
N
One sampled baseband OFDM symbol after the IFFT can be expressed as:
N
1
0
2exp
0 1
Ns
k
nTs x k j k
N N
n N
n (1)
where 1j and x k represents the com-plex modulated data symbol of duration
thk
sT . This OFDM symbol can be written in a 1N column vector as [1]:
T
1
1, , , ss
s s s
N TTs iT s iT s iT
N N
S
W X
(2)
where denotes the transpose of and T 0 :i is the OFDM symbol number. and 1W X are the complex points IFFT N N N matrix and the complex OFDM modulated data symbol (column)
thi1N
vector, respectively. X and W can be expressed as follows:
1
T0 , 1 , , 1i i ix x x N X (3)
2 21 1 1 1
1
2 21 1 1 1
1 1 1
1 e e
1 e e
j jN N
j N j N NN N
W
2 T1
212
0
22
1
212
2
1e
ee
ee
ee
j kN
jj k N
N
j kj k n N
N
j Nj k N N
N
(5)
1s PW (6)
where the samples and the subcarriers are re- presented by the rows and the columns of the
N N1W
matrix, respectively. They can be separated as shown by (5), (6) into the two vectors; (the complex samples vector which varies for each subcarrier) and
P 1N
1sW (the N1 complex subcarriers vector). In order
to achieve unitary, 1W should be scaled by 1 N [6].
After CP insertion, the samples variation is modified to 1cpN N n N where is the number of CP cpN
samples which should be 1 1 1 1
, , , or4 8 16 32
N
. There-
fore, vector should be regulated as (7). Consequently, PS and 1W nsions are expanded to 1cpN N dime , NcpN N , s implied in (8). respectively a
1
2
1
0
1
2
e
e
e
e
e
e
e
cp
cp
j k N NN
j k N NN
j k NN
j kN
cp
j kN
j k nN
j k NN
P P
(7)
1 1cp cp cp s
S W X P W X
N
(4)
(8)
2.2. The Energy Loss
ansmitted signal has the disad-The use of a CP in the trvantage of requiring more transmit energy. The loss of transmit energy (or loss of signal-to-noise ratio (SNR)) due to the CP is [7]:
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Losscp
NE
N N
(9)
It is worth mentioned that cpS should be divided by
LossE to compensate the wa energy due to the CP rtion.
2.3. The Wireless
stedinse
Communication Channel
. The The transmitted waveform gets corrupted by noisemultipath fading channel having impulse response h t of length cpL N can be expressed as follows:
1L
0
l ll
h t h t
(10)
where and lh l y
represent the complex fading and the
wn in Figure 1, the received signal
(11)
where is the compl
propagation dela of the thl path, and L is the number of multipaths, respectively
2.4. The Receiver
.
At the receiver as shois analogy demodulated and then it is converted into a digital format. Afterwards, the CP is removed from the resulting signal and it is transformed into N parallel samples. Then, the signal is transformed in the fre- quency domain via the N points FFT. Thereafter, fre- quency domain equalization (FDE) is performed. Finally, the demapping and parallel to serial processes are per- formed. After removing the CP, the received symbol can be written as:
to
noise Y HS N
noiseN by A
1N hich i
ex noise vector con-tributed WGN w s Gaussian distributed with zero mean. H is the NN circulant channel matrix describing th ultipath g channel. It can be diago-nalized by the FFT and IFFT as follows [8]:
0 1 10 0 Lh h h
e m fadin
(12)
(13)
where is
0
1
1
1 0
0
0
0
0 0
L
L
L
h
h
h
h h
H
1W WΛ
Λ th
N diagonal matrix containing the Nulant sFFT of e circ equence of H . W is the com-
plex N points FFT NN matrixAfter the N points FFT, the resultin mbol is:
. g sy
14)
The FDE complex coefficients can be deco ar
fft noise noise Y WY WS WN X WNΛ Λ (
C rived ac- rding to the minimum mean squ e (MMSE) criterion
as follows [9]:
11H HSNR
C Λ Λ Λ (15)
where H designates the complex conjugate transpose- tion of . A major advantage of the equalization in fre- quency domain is the low computational complexity. The price to be paid is a reduction in the data rate caused by the insertion of the CP [10]. The symbol after FDE can be expressed as:
fft noiseX CY C X CWNΛ (16)
After demapping, these noise can bm
e greatly mini-ized and the original symbol X can be recovered.
3. Peak-to-Average Powe Ratio r
ependently in Since OFDM signals are modulated indeach subcarrier, the combined OFDM signals are likely to have large peak powers at certain instances. The peak power is generally evaluated in terms of PAPR.
Accordingly, the PAPR of the OFDM signal which is defined as the ratio of the maximum power divided by the average power of the signal is expressed as:
2
Max snTs
10 210 dBlog
s
NPAPR
nTE s
N
(17)
where snTs
N
returns the magnitude of snTs
N
and
.E denotes the expectation operation [2,11]. ) of the
amThe Cumulative Distribution Function (CDFplitude z of an OFDM signal sample [11] is given by:
1 e zF z (18)
The CDF of the PAPR for an Ofo
FDM data block can be und in [11] as:
1 eNzP PAPR z CDF (19)
where is the number of subcarriers. For DN an oversam-
pled OF M, this last formula should be modified to:
1 eNzCDF
(20)
where the PAPR of an oversampled signal for N sub- carriers is approximated by the distribution f Nor subcarriers without oversampling. For four times over- sampled OFDM signals, 2.3 is a good approxima- tion [12].
Therefore, CCDF of th R for an oversampled e PAP
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OFDM data block is:
1 1 1 eNzCCDF CDF
(21)
4. PAPR Reduction Methods
PR have been ac- coding [14], peak
value. A
FDM sys- te
n. The drawbacks of the DSI m
m using wavelet transform is proposed. It re
idea has be
ibe the structure of a proposed to avoid the OFDM PAPR Many strategies for reducing the PA
complished such as clipping [13], windowing [15] and tone reservation [16]. Unfortunately, most of these schemes are unable to achieve a large re- duction in the PAPR with a low complexity, low coding overhead and without performance degradation.
Partial Transmit Sequence (PTS) method is a well known method which can reduce the OFDM PAPR
major drawback of PTS method is its high computa- tional complexity due to the necessity of large number of Inverse Fast Fourier Transforms (IFFT) [17].
The selective mapping (SLM) scheme is one of the most effective PAPR reduction schemes in O
ms. SLM scheme can achieve several decibels of PAPR reduction and hence significantly improves the transmis- sion power efficiency [18]. One of its major disadvan- tages is the transmission of side information bits in order to enable the receiver to recover the transmitted data blocks. The reduction of PAPR value in SLM scheme is better than obtained in PTS method but a large number of Inverse Discrete Fourier Transform (IDFT) blocks are required. This results in increased computational and hardware complexity [18].
Dummy Sequence Insertion (DSI) scheme is another method for PAPR reductio
ethod is that the length of data is increased which af- fects the bandwidth. This degrades the transmission effi- ciency [19].
Additionally, in [5], an efficient technique for the OFDM syste
duces the PAPR value from 8.8 dB for conventional OFDM system to 1.5 dB. While in [20], a novel multi- carrier spread spectrum watermarking scheme for the application of image error concealment using multicar- rier-code division multiple access with binary phase shift keying transmission in Rayleigh fading channel is pro- posed. This scheme can be used for PAPR reduction. Furthermore, in [21], The reduction of dynamic range or PAPR is made by using a compander in the Space Divi- sion Multiplexing/Companded Orthogonal Frequency Division Multiplexing (SDM/COFDM) system.
In [22-24], A constant envelope paired burst OFDM was proposed to achieve 0 dB PAPR. Its main
en just adding two constant envelope OFDM signals which have been amplified using a single grossly nonlinear amplifier. The constant envelope OFDM signal can also be thought of as a phase transformation of the OFDM signal [25]. In this paper, our proposed technique
uses a different method to achieve the 0 dB PAPR.
5. The Proposed Scheme
5.1. The Transmitter
In this section, we descrefficient OFDM schemeproblem. It is shown in Figure 2. At the transmitter, a new block named by “Constant Amplitude (CA) Modulator” is inserted after the IFFT process. It consists of three sub-blocks as shown in Figure 3. Firstly, a lead-ing zero sample is inserted prior to each OFDM symbol via “Inserting Zero Sub-block”. Secondly, extra samples are inserted between each two adjacent samples of the resulting OFDM symbol via “Inserting Samples Sub- block”. These extra samples are gradually increased or decreased according to the primitive samples. Finally, each sample value of the resulting signal is converted into 0 or 0.5 value via “Comparing Samples Sub- block”. This is based on the comparison between it and a reference ge ted signal.
Therefore, 0 dB PAPR value is expected to be achieved via our proposed
nera
CA modulator. That is be- cause the output of the CA modulator has a constant am- plitude and the randomly amplitude peaks of the OFDM phenomenon is eliminated.
The mathematical analysis of the proposed scheme can be summarized as follows:
1) After IFFT block, the complex OFDM symbol S , expressed by (2), is separated into its real and imaginary parts as follows:
1
1
ReRe
ImRe
S W XS
S W X (22)
where Re and Im donate the real and the imaginary part of . Su quently, our proposed block (CA
tor) rtee
bsemodula is inse d for each part.
2) At th real branch, after “Inserting Zero Sub-block”,
Figure 2. The proposed OFDM system.
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0.8
Inserting Zero
InsertingSamples
Comparing Samples
Removing Residual Samples
Removing Leading
Zero
Samples Generation
SZ SS SO
0.80.8 0.60.6 0.6 0.40.4 0.4 0.20.2 0.2
YO YSYZY
0
-0.2 0
-0.4 -0.6 -0.8
-1 5 10 15 20 25 0
-0.2 -0.2-0.4-0.4 -0.6-0.6
-0.8 -0.8-1
5 10 15 20 25 30 35 -10 5 10 15 20 25 30 35
0 5 10 15 20 25 30 35
S
Figure 3. The CA structure. the resulting real OFDM symbol Re
zS 1
0 1
Re Rez zdiff i i i
i N
S S
has 1N sam-ples. It can be written as:
(23)
blo e re
(25)
where is the extra inserted samples between each
two adjacent samples in
0
1
1
Re
Re
Rez
Re
Re
n
N
S
S
S
S
S
0
insN
symbol. diff iRezS is the
difference between these two adjacent samples. 4) After “Comparing Samples Sub-block”, each sam-
ple value in the ResS symbol is converted into 0 or
3) After “Inserting Samples Sub- ck”, th sulting real OFDM symbol Re
sS leng is in ed to 1 1N N N . It can
th creaswritten as: ins be
0 0
1 00
1
2 00
1
1
1
1
1
1
Rez
ins
ins
ins
Res
Re Rez
Rez
ins
insRez
ins
Rez
Rez
diff
N
diff
N
N
n n
diff in
N
N diff in
N
n
N
S
S
S S
S
S
S
S
(24)
00
1
1 0
ins
Re Rez
N diff
S S
0.5 value. This a) Gener
is executed by the followi steps: ate a reference symbol called accumulated
stepped samples
ng
ACC .
each sam Res iSb) Compare ple value in with
1i ACC , where is the sample numb
c) Produce the resulting OFDM symbol
i er. ReoS and up-
date symbol as follows:
I) If
ACC
1Res i i S ACC , the output 0.5Re
o i S
and 11i i ACC ACC
1insN
.
II) If 1Res i i S ACC , the output 0.5Re
o i S
and 11i i ACC ACC
1insN
.
III) If 1Re i i sS ACC , the output 0Re i oS
and 1i i C ACC . AC
The output ReoS symbol size is not changed from
1N . ReoS and ACC can be represented as follows:
0
0.5sgn 1 0
0.5sgn 2 1
0.5sgn 1 2
Res
Re Reo s
Res N N
S ACC
S S ACC
S ACC
(26)
W. SAAD ET AL. 334
1
0 0
1 0
s
ACC
ACC
1 Re Ren
S
0 1i insN
1
2
2 N
N
N
ACC
ACC
1 si in
S
ACC ACC (27)
sgn 1 0
0 0
x x
(28)
1 0x
x
sgn 1
1
Res
ins
i i
N
S ACC
1
5)devel
1
i
i N
(29)
At the imaginary branch, the same analysis can be oped to derive Im
oS . Therefore, the final modified tra OFDM sym nsmitted obol S can be expressed as:
Re Io o oj mS S S (30)
Finally, the CP is inserted. The resulting symbol can be d as:
6) expresse
p ˆ 1:cp o c oN N N S S S (31)
w
due to e ex resul
5.2. The Energy Loss
The use of a CA modulator in the transmitted signal has the disadvantage of requiring more transmit energy. The loss of transmit energy due to the CA modulalowed by the CP insertion is:
here 1cp insN N is the modified CP length
th tended ting symbol.
cp N
tor fol-
Loss1 1cp ins cp
N NE
N N N N N
(32)
Loss
1
1ins
EN
(33)
It is worth mentioned that oS should be divided by
LossE to compensate the wasted energy.
5.3. The Receiver
At the receiver as shown in Figure 2, the received signal is analogy demodulated and then it is converted into a digital format. Afterwards, CP is removed and our pro-posed “Constant Amplitude (CA) De-modulator” is inserted to reverse the impact of the CA modulator. It
consists of three sub-blocks as shown in Figure 3. Firstly, the OFDM symbol is regention Sub-block”. Secondly, the exremoved from the resulting OFDM symbol via “Remov- ing Residual Samples Sub-block”. Finally, the leading zero sample is removed from the foOFDM symbol via “Removing Leablock”.
ts Fatio
The mathematical analysis calo
erated via “Samples Genera- tra inserted samples are
refront of each ding Zero Sub-
Then, the signal is transformed into the frequency do- main via the N poin FT. Finally, the demapping and parallel to serial processes re performed without any equalization as in the conven nal system.
n be summarized as fol- ws: 1) After CP removal, the resulting symbol is:
ˆ :o cp cp cpN N N N 1 Y Y
he noisy demodulated received syd into its real
(34)
2) T mbol oY is separate Re and imaginary oY Im
oY parts. Subsequently, our proposed block (CA de-m inserted for each part.
, after “Samples Generation
odulator) is
3) At the real branchSub-block”, the OFDM symbol is regenerated. This is executed by the following steps:
a) Generate a reference symbol with a leading zero sample RACC .
b) Update RACC symbol as follows:
I) If 0Reo i Y , then
11
1RinsNR i i
ACC ACC .
II) If 0Re io Y , then
11R Ri i
N
1ins . ACC ACC
III) If 0Reo i Y , then
1R Ri i ACC ACC .
c) Produce the resulting OFDM symbol Res Y
1:R N ACC . It can be written as follows:
0 0
0 0 1
0 1
R
R RRes
R R N
Y
Δ
Δ Δ
Δ Δ
(35)
sgn 1ReR o insN YΔ (36)
4) After “Removing Residual Samples Sub-block”, the resulting real OFDM symbol Re
zY size is 1 1N . it can be exposed as:
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0Res
Y
1Res
Y
Res insN Y
Removed
1Res insN
Y
Y
1
Rez
Res ins
Res ins
N N
N N
Y
Y
37)
Removed
2Res
Re
N
Y
Y
1s N
5) After ov
(
“Rem ing Leading Zero Sub-block”, the re- sulting real OFDM symbol ˆ ReY size is 1N . It can be ex
(38)
6) At the imaginary branch, the same analysis can be developed to derive
posed as:
0
1ˆ
Rez
RezRe
Rez N
Y
YY
Y
ˆ ImY . Therefore, the final modified re DM sy can be expressed as:
(39)
whth Channel n ed due to the
multipath fading channel. These noises are catego- rized into: ◦ In phase noise which does not change the signal
polarity. This noise is eliminated viascheme. That is because only positive or negative levels are used in our proposed CA modulator, while the zero level is very due to the OFDM nature.
ch e signal ionally, the noise which affects the
zero samples values. These types of noise can’t be eliminated by both systems.
System accuracy: This produces errors from the im- perfections of the samples recovery at “samples gen- eration sub-block”. These errors are greatly mini- mized by increasing value but this degrades the system throughput.
7) After the points FFT, the resulting
covered OF mbol Y
ˆ ˆ ˆ noise errorRe Imj Y Y Y Y
ere Y is the OFDM symbol after removing CP in e conventional system. It differs from Y by means of:
oise: Those are mainly produc
our proposed
rarely to be occurred On the contrary, the
conventional system can't eliminate this noise in this stage.
◦ Out of phase noise whi changes th po- larity. Addit
insN
N 1N symbol is X X .
pping
8) After dema , these errors can be greatly
mized and the original symbol
mini-
X can be recovered.
6. Complexity Evaluation
6.1. Complexity Analysis for the Proposed CA Modulator
The complexity added to the conventional OFDMmitter by the CA modulator can be illustrated as In order to delay the input samples one clock to insert
the zero sample prior to each OFDM symbol, only a simple register with the sample width is required for the “Inserting Zero Sub-block”.
Only one simple subtractor used times per OFDM symbol, one simple adder used
trans- follows:
N N 1 times
per OFDM symbol, and one divider by 1insN are
y ademanded by the “Inserting Samples Sub-block”. The divider can be replaced b simple shift registers, if
1insN is a power of 2. le comparator used tim DM
symbol and a simple adder times per OFDM symbol, are the price to bing Samples Sub-block”.
Therefore, the additional operational complexity is two simple adders, one simple subtractor, and one simple co
a d CA De-Modulator
es
tors, and two simple
ders, two simple subtractors, and fo ra
, the mplexity of our proposed technique
A simp N used
es per OF2 1N
e paid for “Compar-
mparator per one CA modulator.
6.2. The Complexity An lysis for the Propose
The exc s in the conventional OFDM receiver complex- ity via the CA de-modulator can be summarized as fol- lows: One simple adder used 1N times per OFDM
symbol, and simple comparator used N times per OFDM symbol are needed by “Samples Generation
bSu -block”. Simple switches are used to eliminate the residual
samples for both “Removing Residual Samples Sub- block” and “Removing Leading Zero Sub-block”.
Therefore, the additional operational complexity is one simple adder and one simple comparator per one CA modulator.
6.3. The Overall Additional Complexity Computation
The overall transmitter additional complexity is four simple adders, two simple subtraccomparators. That is because each transmitter contains two CA modulators. Further, the overall receiver addi- tional complexity is two simple adders and two simple comparators. Therefore, the proposed scheme requires additional six simple ad
ur simple compa tors. Noteworthy co
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isui te-
grator, and grossly look up table “memory storage” at the iver, a huge complexity
ea up
table, two low-pass filters, arc-tan function generator,
e
tiveness heme. WiMAX system has
OFDM systems are studied. The upper part of Figure 4, compares 50 real part samples for
ventional syste system produces a constant ampli-
very low compared to the previous constant envelope technique in [23-25] which req res oversampling, in
transmitter. According to the receis added. It requires a band-pass filter (which is arconsuming), two complex multipliers, a grossly look
phase unwrapper, matched filters, and hard decisions. Additionally, the frequency domain equalizer is needed contrary to our proposed scheme.
6.4. The Complexity Reduction Analysis for the Proposed Scheme
The equalization process is removed in the proposed scheme. That is because of the presence of the “Samples Generation Sub-block”. Therefore, the receiver complex- ity is extremely reduced.
Additionally, hermitian OFDM can be used. Hence, only real outputs are occurred. Therefore, only one CA modulator/ de-modulator is used instead of two. Then, the overall additional complexity is reduced by a factor of 2.
7. Simulation Results and Discussions
7.1. Simulation Setup
Monte Carlo MATLAB simulation experiments havbeen carried out to study the performance and the effec-
of the proposed scbeen used as an example of the conventional OFDM system [26]. The WiMAX and the CA modulation block parameters used for these simulations are illustrated in Table 1. Both AWGN and multipath channels are con- sidered. For the multipath channel, we consider ITU Pe- destrian A and ITU Vehicular A channels [27] with
GN. The deAW lay profiles of the two channels are de- scribed in Table 2.
7.2. Time and Frequency Domains Behaviors
In this subsection, the characteristics of both conven- tional and proposed
both systems output. On the contrary to the conm, our proposed
tude signal. Therefore, 0 dB PAPR value is expected to be achieved.
The lower part of Figure 4, compares the frequency domain for both systems output. It is clear that the fre- quency domain of the proposed system concentrates the power in the DC component and the side bands. There- fore, it suffers from the severe frequency selectivity channels.
Table 1. Simulation parameters.
WiMAX parameters
System bandwidth 20 MHz
Oversampling ratio 144/125
Modulation scheme QPSK
FFT length 256
Data subcarriers 192
Pilot subcarriers 8
CP length 1/16
Pulse shaping None
Equ ZF and MMSE
size
Channel estimation Perfect
alization
Derived parameters
Sampling rate 23.04 MHz
Subcarriers spacing 90 KHz
IFFT symbol period 11.11 μsec
OFDM symbol period 13.89 μsec
CA Modulation parameters
insN 31
Step 1 1insN 1/32
Output values 0, 0.5
Table 2. Channel delay profiles of ITU Pedestrian A and Vehicular A channels [27].
Path
Channel model 1 2 3 4 5 6
Ped. A Delay (nsec) 0 110 190 410 - -
Power (dB) 0 −9.7 −19.2 −22.8 - -
Veh. A Delay (nsec) 0 310 710 1090 1730 2510
Power (dB) 0 −1 −9 −10 −15 −20
frequency/Fs frequency/Fs
Figure 4. Time and frequency domains for both systems.
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7.3. In-Band Distortion Calculation
Error vector gure of merit adopted by tion standards for evaluating in-band distortions introduced muni-c
concept.
magnitude (EVM) is a popular fivarious communica
in a comation system.
Figure 5, illustrates the EVM Denote by kX
-called th nal, its distorted version, and
the erro al (vector). so as [26,
e reference sig kYr sign28]:
k k k
M is definedDEV
Y X The
12
02max
1
EVM % 100%
N
kk
DN
S
(40)
12
k0
10 2max
1
10log
N
k
DN
S
(41)
w maximum amplitude of the constella-ti ine
EVM dB
here maxS is theon points that def kX , and is ber of
p r rrier modulations, high ower nt in the
reference signal constellation. More recently, for multi- ations, is de as reference
The influence of the transmission channel is not con-
on its undesirable effects. 103 OFDM symbols are generated to calculate EVM value. In our calcula ns,
N single ca
est p
fined
the numoints in a measurement.
is, by convention, theFo
max
maxS
caco
poi
rrier modul S the nstellation average power [29].
sidered and the signal distortion is caused only by CA modulation to focus only
tio ˆkY X and max kS X X . The
simu lue r e g1 or
7.4. AP
In t s o P fo he c -vent nal a p d D ys are eval d
lated EVM va fo th iven si ulation area is m4.85% –16.64 dB.
P R Performance
his subsection, the CCDF f the APR r t onio nd the pro ose OF M s tems uate
0
Phase Error ϕk
In-phase
Received Signal Yk
Reference Signal Xk
Error Signal Dk
Magnitude Error Ek
Quadraturel
Figu
a ,
account. It is
lues
oposed blo
7.5. BER Performance
Figure 7 illustrates the BER performance tional and the proposed OFDM systems with different channel types. The Minimum Mean Square Error (MMSE) Equalizer is used for the conventional system, while the proposed system does not need any
re 5. Illustration of the EVM definition.
nd compared. 104 data blocks are generated to calculatethe CCDFs of the PAPR. To have a precise PAPR valuethe oversampling factor should take intochosen to be 4 [11].
In Figure 6, plots of the CCDFs of the PAPR for both systems are shown. It is clear that the conventional Wi-MAX system has PAPR values in the range ~6.5 - 11.5 dB, while the proposed system has 0 dB PAPR va . That is because of the con tant amplitude achieved by the pr ck “CA modulator”. This means that there are no peaks in the transmitted signal.
of the conven-
Equalization
Figure 6. The CCDFs of the PAPR for the conventional and the proposed OFDM systems.
BER Vs Eb/No
E /N (dB) b o
Figure 7. BER vs. Eb/No for the conventional and the proposed OFDM systems.
Copyright © 2013 SciRes. CS
W. SAAD ET AL. 338
processes. It can be observed that the proposed system provides a significant BER performance improvement over the conventional system.
7.5.1. For AWGN Channel The performance of the proposed system is better than that of the conventional system over all b oE N
ity ratio) (the
energy per bit to noise power spectral dens val-ues. At BER = 10–2, the performance gain is about 6.6 dB for the proposed system when compared to that of the conventional system. This is attributed to the use of only positive or negative levels in our proposed CA de- modulator, while the zero level is very rarely to be hap- pened due to the OFDM nature. Therefore, the effect of the In-phase noise can be completely removed. However,
pact of Out-of-phase noise can’t be eliminated. the imThat is because it changes the signal polarity. It is worth mentioned that our proposed system perform- ance is superior to the best case of the previous constant envelope OFDM system [25] by 2 dB gain.
7.5.2. For ITU Pedestrian-A Multipath Fading Channel
The performance of the proposed system is also better than that of the conventional system over all b oE N values. At BER = 10–2, the performance gain is about 8.4 dB for the proposed system when compared to that of the
formance gain is due to the
onsequently, BER performance enhancement can be achieved but, the price to be paid is a reduction in the system transmission throughput.
7.5.3. For ITU Vehicular-A Multipath Fading Channel
The performance of the proposed system outperforms the conventional system for
conventional system. The improvement in the per
multipath fading channel effect. Hence, our CA de- modulator outperforms the equalization process in the conventional system for multipath noise impact removal. In addition, extra samples are inserted in the proposed system. Therefore, the length of the CP is increased. C
20.5 dBb oE N in is about 19 dB
. At BER = 10–2, the performance ga for the pro- posed system when compared to that of the conventional system.
While the conventional system behaves better than the proposed system for 20.5 dBb oE N
dation in the . The perform-
ance significantly degra high b oE Ned syste
re- gime is due to the huge excess in the propos m symbol length. Therefore, the proposed system is a
frequency selectivity is se- . Under using a g coding or channel
adaptive modulation scheme, this limitation can be overcome.
Due to the long proposed system symbol length, the performance is the best under Vehicular-A channel then under Pedestrian-A channel and finally under AWGN channel for low
f- fected by the Doppler spreading in the multipath fading channel. This is more evident in the Vehicular-A channel
mulation results where the sivere ood channel
b oE N regime 6.6 dBb oE N . This order is reversed for high b oE N values.
7.6. Impact of Equalization
In this subsection, the effect of the equalization process for the conventional and the proposed OFDM systems are studied as shown in Figure 8. Both Zero Forcing (ZF) and MMSE equalization process are compared unde
), it behaves as an equal- noise removal. Therefore,
r Vehicular-A channel. It is clear that the equalization processes enhances the performance of the conventional system, while it degrades the proposed system perform- ance. That is because besides, the original function of the CA de-modulator in the proposed system (which is to regenerate the OFDM samplesizer for the In-phase channelthe proposed system does not need any equalization processes. In addition, due to the perfect channel estima- tion used, both ZF and MMSE equalization have the same performance.
7.7. Impact of insN
The main parameter which affects the proposed scheme is insN value. Its effect on the system accuracy, In-band distortion, output symbol length, complexity, and the transmission throughput are studied.
7.7.1. The System Accuracy Under no channel conditions, Figure 9 compares the original real OFDM symbol ReS and the recovered one ˆ ReY . It is clear that the error is reduced and hence,
accuracy high values. the system is increased for ins
N
system
system
Eb/No(dB)
Figure 8. The Equalization effect for both the conventional and the proposed OFDM systems.
Copyright © 2013 SciRes. CS
W. SAAD ET AL. 339
That is because for higher insN values, the less step size 1 1ins is rN educed. T , the CA de-modulator can
ER performanc
performance is achieved. Howevepr
henmore precisely follow the original symbol.
Figure 10 displays the B e of the pro- posed OFDM system under Vehicular-A multipath fad- ing channel environment. It is clear that for higher insN values, better r, the
ice to be paid is the system throughput or the system speed degradation.
7.7.2. In-Band Distortion Under no channel conditions, the EVM values are calcu- lated for different insN values as displayed in Table 3. It is clear that for higher insN values, lower EVM val- ues are obtained. Hence, better performance is achieved.
0 Samples
Error
Original OFDM symbol
Nins = 1
Nins = 3
Nins = 7
Nins = 31
Nins = 63
Samples Recovered symbols
100 200 -1 0 1
0 100 200 -1 0 1
0 100 200 -1 0 1
0 100 200 -1 0 1
0 100 200 -1 0 1
0 100 200 -1 0 1
0 100 200-1 0 1
0 100 200-1 0 1
0 100 200-1 0 1
0 100 200-1 0 1
0 100 200-1 0 1
amplitude
Figure 9. Original vs. recovered OFDM symbols for differ-ent insN values.
Eb/No(dB)
Figure 10. BER for different insN values unde ehicular- r V
multipath fading channel.
Table 3. EVM values vs. different values.
EVM (%) EVM (dB)
A
insN
insN
1 71.02 −2.99
3 32.11 −9.89
7 19.98 −14.02
31 14.85 −16.64
63 14.55 −16.83
7.7.3. The Symbol Length For are inserted, the OFDM symbol length is ininsN creased by
- 1insN N N . T herefore, the processing
xity Due to the
means more pr
t, the OFDM symbol length
time is increased which affects the system speed.
7.7.4. The System Comple serial manner used to perform the proposed
CA modulation, the higher N value ins
ocessing time to produce the output. Therefore, insN values do not affect the system complexity but it affects the system speed.
7.7.5. The Transmission Throughput For insN incremen sT
he sam is
. Consequently, there is no effect on t -dwidth, the IFFT length, and
increasedpling rate, the required banthe subcarrier spacing. However, the transmission
throughput is decreased to
2
1 1cp ins
s
N
N N NT
N
compared to 2
cps
N
N NT
N
in a first case using QPSK
modulation. However, if the OFDM symbol length sT
, the re is kept
fixed, the sampling rate is increased. Hence quired bandwidth is enlarged. Moreover, the IFFT length is de- creased. Consequently, the subcarrier spacing is in- creased. However, there is no degradation in the trans- mission throughput.
8. Conclusion
OFDM is a method of transmitting data simultaneously over multiple equally-spaced carrier frequencies, using Fourier transform processing for modulation and de
osed scheme in this paper (which uses the suggested A modulation block) has achieved 0 dB PAPR value.
Consequently, the power amplifier of the transmitter can
-modulation. High PAPR value is the most serious OFDM drawbacks. On the contrary to traditional techniques, the
roppC
Copyright © 2013 SciRes. CS
W. SAAD ET AL. 340
operate at the optimum (saturation) point. Hence, its effi- ciency and battery life are maximized. The mathematical model for the proposed system has been discussed. Fur- thermore, Extensive simulation programs have been executed to study the behavior of the proposed system compared with the traditional one. The proposed system has outperformed the traditional one in terms of BER under AWGN and multipath fading channels. At BER = 10–2, 6.6 dB, 8.4 dB, and 19 dB performance gains have been achieved for the proposed system over the conven-tional one under AWGN, ITU Pedestrian-A, and ITU Vehicular-A multipath fading channel, respectively. Ad- ditionally, the proposed system has outperformed the previous constant envelope system in terms of hardware complexity and BER perf e. Moreover, CA modu-
14tion parameters. In addition,
the e ired pro-posed scheme. Finally, the impact of has been studied. For highe alues, the s curacy has be increased b h a cost of sy oughput degradation.
R NCES [1] R. Prasad, “Multicarrier Te s for 4G
ch House, Boston, Lon- don, 2003.
and R. Muhamed, “Fundamen-
nications Engineer
[3] H. Y. Sakran, M. Shokair and A. A. Elazm, “Combined for PAPR Reduction in
i:
ormanclation has introduced EVM = .85% for In-band distor-tion under the given simula
qualization process has not requ for the
ins
ystem acN
ster insN v
en ut wit m thr
EFERES. Hara and chniqueMobile Communications,” Arte
[2] J. G. Andrews, A. Ghoshtals of WiMAX: Understanding Broadband Wireless Networking,” In: T. S. Rappaport, Ed., Prentice Hall Commu ing and Emerging Technolo- gies, Prentice Hall, San Francisco, 2007.
Interleaving and CompandingOFDM Systems,” Progress in Electromagnetics Research C, Vol. 6, 2009, pp. 67-78. do 10.2528/PIERC08122211
[4] A. Sayed-Ahmed, M. Shokair and E.-S. El-Ra , “PAPR Reduction for LFDMA Using a Reduced Com- plexity PTS Scheme,” 29th National Radio Science Con- ference (NRSC
baie
), Cairo, 10-12 April 2012, pp. 515-522.
e and M. Shokair, ing D
ctrical Engineering & Applie” CRC Press, Boca Taton, 2000
doi:10.1201/9781420037388
[5] W. Saad, N. El-Fishawy, S. El-Rabia“An Efficient Technique for OFDM System Us is-crete Wavelet Transform,” The 6th International Work-shop on Mobile Commerce and Services (WMCS2010), Hualian, 10-14 May 2010, pp. 533-541.
[6] K. R. Rao and P. Yip, “The Transform and Data Com- pression Handbook (Ele Signal Processing Series), .
d
[7] J. V. de Beek, P. Odling, S. Wilson and P. Borjesson, “Orthogonal Frequency-Division Multiplexing (OFDM),”
of Radio Sciio Science (URSI),
[8] I. Koffman and V. Roman, “Broadband Wireless AccessSolutions Based on OFDM Access in IEEE 802.16,”
mmunications Magazine, Vol. 40, No. 4, 2002,
in Review ence 1996-1999, International Union of Rad 1999.
IEEE Co
pp. 96-103. doi:10.1109/35.995857
[9] Y. Liang, “Block-Iterative GDFE (BI-GDFE) for CPCDMA and MCCDMA,” IEEE Vehicular Technology Confer- ence (VTC), Vol. 5, 2005, pp. 3033-3037.
[10] S. D. Falconer, A. Ariyavisitakul, A. Benyamin-Seeyar and B. Eidson, “Frequency Domain Equalization for Sin- gle-Carrier Broadband Wireless Systems,” IEEE Com-
agazine, Vol. 40, No. 4, 2002, pp. 58-66. .995852
munications Mdoi:10.1109/35
[11] R. Prasad, “OFDM for Wireless Communications Sys-tems,” Artech House, Boston, London, 2004.
[12] S. H. Han and J. H. Lee, “Modified Selected Mapping Scheme for PAPR Reduction of Coded OFDM Signal,” IEEE Transactions on Broadcasting, Vol. 50, No. 3, 2004, pp. 335-341. doi:10.1109/TBC.2004.834200
[13] H. G. Ryu, B. I. Jin and I. B. Kim, “PAPR Reduction Using Soft Clipping and ACI Rejection in OFDM Sys- tem,” IEEE Transactions on Consumer Electronics, Vol. 48, No. 1, 2002, pp. 17-22. doi:10.1109/TCE.2002.1010087
[14] S. Slimane, “Reducing the Peak to Average Power Ratio of OFDM Signals through Precoding,” IEEE Transac- tions on Vehicular Technology, Vol. 56, No. 2, 2007, pp. 686-695. doi:10.1109/TVT.2007.891409
[15] G. G. Chen, R. Ansari and Y. W. Yao, “Improved Peak Windowing for PAPR Reduction in OFDM,” IEEE Ve- hicular Technology Conference (VTC), Barcelona, 26-29 April 2009, pp. 1-5.
[16] K. Park and I. Park, “Low-Complexity Tone Reservation for PAPR Reduction in OFDM Communication Sys- tems,” IEEE Transactions on Very Large Scale Integra- tion (VLSI) Systems, Vol. 20, No. 10, 2012, pp. 1919- 1923.
[17] J. Hou, J. Ge and J. Li, “Peak to Average Power Ratio Reduction of OFDM Signals Using PTS Scheme with Low Computational Complexity,” IEEE Transactions on Broadcasting, Vol. 57, No. 1, 2011, pp. 143-148.
[18] S. Mohammady, R. M. Sidek, P. Va am, M. N. Hamidon and N. Sulaiman, “Study of PAPR Reduction Methods in OFDM Systems,” Advanced Communication Technology (ICACT) Conference, Seoul, 13-16 Febuary 2011, pp. 127-1
rahr
30.
[19] H.-G. Ryu, J. E. Lee and J. S. Park, “Dummy Sequence Insertion (DSI the OFDM Com- munication Sy ons on Consumer
) for PAPR Reduction instem,” IEEE Transacti
Electronics, Vol. 50, No. 1, 2004, pp. 89-94. doi:10.1109/TCE.2004.1277845
[20] S. P. Maity, S. Maity and J. Sil, “Multicarrier Spread Spectrum Watermarking for Secure Error Concealment in Fading Channel,” Telecommunication Systems, Vol. 49, No. 2, 2012, pp. 219-229. doi:10.1007/s11235-010-9369-0
[21] M. Shokair and H. Sakran, “Performance of SDM/ COFDM System in the Presence of Nonlinear Power Amplifier,” Telecommunication Systems, Vol. 50, No. 2, 2012, pp. 89-95. doi:10.1007/s11235-010-9393-0
[22] R. Dinis and A. Gusmáo, “CEPB-OFDM: A New Tech-
Copyright © 2013 SciRes. CS
W. SAAD ET AL.
Copyright © 2013 SciRes. CS
341
th
Conference, Vol.
iley,
ctober-1 November 2006, pp. 1830-
4th ARFTG r 2004, pp. 45-52.
nique for Multicarrier Transmission with Saturated Power Amplifiers,” IEEE ICCS’96 Conference, Singapore City, November 1996.
[23] R. Dinis and A. Gusmáo, “Carrier Synchronization wi
Wire
CEPB-OFDM,” IEEE VTC’97 Conference, Phoenix, 4-7 May 1997, pp. 1370-1374.
[24] R. Dinis and A. Gusmáo, “Performance Evaluation of a Multicarrier Modulation Technique Allowing Strongly Nonlinear Amplification,” IEEE ICC’98
Hobo
2, Atlanta, 7-11 June 1998, pp. 791-796.
[25] S. C. Thompson, “Constant Envelope OFDM Phase Modulation,” Ph.D. Dissertation, University of California, San Diego, 2005.
[26] “Part 16: Air Interface for Fixed and Mobile Broadband
less Access Systems,” IEEE Standard for Local and Metropolitan Area Networks Standard, March 2006.
[27] H. G. Myung and D. Goodman, “Single Carrier FDMA: A New Air Interface for Long Term Evolution,” W
ken, 2008.
[28] C. Zhao and R. J. Baxley, “Error Vector Magnitude Analysis for OFDM Systems,” Fortieth Asilomar Con- ference on Signals, Systems and Computers (ACSSC’06), Pacific Grove, 29 O1834.
[29] M. D. McKinley, K. A. Remley, M. Myslinski, J. S. Kenney, D. Schreurs and B. Nauwelaers, “EVM Calcula-tion for Broadband Modulated Signals,” 6Conference, Orlando, 3 Decembe