wireless communication with multiple antennas€¦ · wireless communication with multiple antennas...
TRANSCRIPT
Wireless Communication with
Multiple Antennas
B. Sundar Rajan
Indian Academy of Sciences, Bangalore
Department of Electrical Communication Engineering,
Indian Institute of Science, Bangalore
05 July 2013.
B. Sundar Rajan (ECE) IASc Talk, 05 July 2013 1 / 31
Outline of presentation
1 Information, Uncertainty, and Communication
2 Capacity of multi-antenna systems
3 Codes for multi-antenna systems
4 Well known codes from ECE
5 Recent patents and concluding remarks
B. Sundar Rajan (ECE) IASc Talk, 05 July 2013 2 / 31
Outline
1 Information, Uncertainty, and Communication
2 Capacity of multi-antenna systems
3 Codes for multi-antenna systems
4 Well known codes from ECE
5 Recent patents and concluding remarks
B. Sundar Rajan (ECE) IASc Talk, 05 July 2013 3 / 31
Is ”Information” measurable?
CHANNEL RECEIVERTRANSMITTER
X Y
Figure: A digital communication system transmitting INFORMATION
X can take FINITE values
Y is an observation
Y conveys some information about X ? - How much ?
B. Sundar Rajan (ECE) IASc Talk, 05 July 2013 3 / 31
Is ”Information” measurable?
BEAUTY HEIGHT
TEMPARATURE
STUPIDITY
SMARTNESS
WEIGHT
.....
..........
....................
ANGLE
Figure: ”Information” belongs to which one of the above?
”Information” is MEASURABLE
B. Sundar Rajan (ECE) IASc Talk, 05 July 2013 4 / 31
Information and Uncertainty
”Uncertainty” is MEASURABLE - Claude E. Shannon (1948)
Information = Reduction of Uncertainty
Four Axioms of Uncertainty
If X takes M values with probability distribution p1, p2, · · · , pM , then theuncertainty denoted by H(p1, p2, · · · , pM) is given by
H(p1, p2, · · · , pM) = −
M∑
i=1
pi log2(pi ) bits
There is ONLY ONE function of several variables p1, p2, · · · , pM thatsatisfy all the four axioms.
B. Sundar Rajan (ECE) IASc Talk, 05 July 2013 5 / 31
Capacity of a communication system
CHANNEL RECEIVERTRANSMITTER
X Y
Observation Y at the receiver reduces the uncerainty about X .
Observation Y at the receiver conveys information = the reduction inthe uncertainty.
There is an upper limit on the amount of information that can beconveyed/transmitted.
The maximum amount of information that can be conveyed/transmitted iscalled the Shannon Capacity.
B. Sundar Rajan (ECE) IASc Talk, 05 July 2013 6 / 31
Outline
1 Information, Uncertainty, and Communication
2 Capacity of multi-antenna systems
3 Codes for multi-antenna systems
4 Well known codes from ECE
5 Recent patents and concluding remarks
B. Sundar Rajan (ECE) IASc Talk, 05 July 2013 7 / 31
A multiple antenna wireless system
Tx 1
Tx 2
Tx N Rx M
Rx 1
Rx 2
H =
α11 α12 · · · α1M
α21 α22 · · · α2M...
... · · ·...
αN1 αN2 · · · αNM
Multiple input multiple output (MIMO) channel: N transmitters, M
receivers
αij is the complex channel gain from i–th transmit antenna to j–threceive antenna
H is the N × M channel matrix
B. Sundar Rajan (ECE) IASc Talk, 05 July 2013 7 / 31
A 2x2 Access Point
Allows to share 3G connection within home wirelessly to many usersusing WiFi.
(2x2 802.11n access point)
B. Sundar Rajan (ECE) IASc Talk, 05 July 2013 8 / 31
A 3x3 + 3x3 Access Point
This product has 6 antennas;
3 external dipole antennas for 2GHz and there are 3 internal stampedantennas on the board (inside box) for 5 GHz.
(802.11n compliant access point)
B. Sundar Rajan (ECE) IASc Talk, 05 July 2013 9 / 31
A 4x4 Access Point
4x4 IEEE 802.11n compliant access point- coding in 4 streams.
B. Sundar Rajan (ECE) IASc Talk, 05 July 2013 10 / 31
Another 4x4 Access Point
4x4 IEEE 802.11ac complaint access point - coding in 4 streams.
B. Sundar Rajan (ECE) IASc Talk, 05 July 2013 11 / 31
Wireless Channels: Diversity and Capacity
In many cases Spatial Diversity is needed
Wireless Channels: Capacity
Multipath propagation has historically been regarded as animpairment because it causes signal fading.
Information theory has shown that with multipath propagation,multiple antennas at both transmitter and receiver can establishessentially multiple parallel channels that operate simultaneously, onthe same frequency band at the same total radiated power.
B. Sundar Rajan (ECE) IASc Talk, 05 July 2013 12 / 31
Capacity growth with M=Number of Rx; (N=Number of
Tx=1)
0 2 4 6 8 10 120
2
4
6
8
10
12
Capacity vs. M for 0 dB ≤ P ≤ 35 dB (uppermost curve) in 5 dBincrements.
I.Emre Telatar, “Capacity of Multi-antenna Gaussian Channels,” EuropeanTransactions on Telecommunications, vol.10, No.6, pp.585-595, 1999.
Similar diminishing-return behaviour with M fixed.B. Sundar Rajan (ECE) IASc Talk, 05 July 2013 13 / 31
Capacity growth with N=M
00
20
40
60
80
100
120
140
c
5 10 15 20
35
30
25
20
15
10
50
p (in dB)
N=M=
N = M capacity in natsnumber of receive antennasnumber of transmit antennas
p =total transmit power
c =
B. Sundar Rajan (ECE) IASc Talk, 05 July 2013 14 / 31
Possible gains with 2 antennas
IS − 136 +
IS − 136
0
225
200
175
150
125
100
75
50
25
0 5 10 2015
2 Tx 1 Rx Antennas
1 Tx 1 Rx Antennas
1 Tx 2 Rx Antennas
2 Tx 2 Rx Antennas
Achievable Data Rates with Multiple AntennasAc
hiev
able
Dat
e Ra
te (k
bits
/sec
) per
30
kHz
Chan
nal
SNR per Rx Antenna (dB)
We can be here
We are here now
“It is dangerous to put limit on wireless”Guglielmo Marconi (1932)
B. Sundar Rajan (ECE) IASc Talk, 05 July 2013 15 / 31
Outline
1 Information, Uncertainty, and Communication
2 Capacity of multi-antenna systems
3 Codes for multi-antenna systems
4 Well known codes from ECE
5 Recent patents and concluding remarks
B. Sundar Rajan (ECE) IASc Talk, 05 July 2013 16 / 31
Space-Time Codes and System Impacts
The way to achieve the capacity of a communication channel is byCoding and Signal Processing
Space-Time Codes are coding schemes appropriate to multipleantenna systems.
For various TDMA systems, it was shown that STC codes for 2Transmit chains can increase the capacity by about 60% (Winters,Clark).
Ericsson Researchers have shown that the capacity of WCDMAsystems (UMTS) increases (also by around 60%) using STC and 2Transmit chains.
B. Sundar Rajan (ECE) IASc Talk, 05 July 2013 16 / 31
Space–Time Coded Modulation
Information
Source Receiver
Space–Time Encoder
The overall channel is made up of of N × M slowly varyingsub–channels.
At any time interval, N signals are transmitted simultaneously, onefrom each transmit antenna.
Uncoded SISO system (Scalar transmission)
Coded SISO system (Vector transmission)
MIMO quasi-static channel (Matrix transmission)
B. Sundar Rajan (ECE) IASc Talk, 05 July 2013 17 / 31
Space-Time Codes (STC)Signal 2
Signal 1
ConstellationMapper
Constellation
Mapper
InformationSource
ST Block Code
ˆ
c1 c2˜
=
»
c1 −c∗2c2 c∗1
–
→ Idea: (Alamouti code)
[c1 c2] →
[
c1 −c∗2c2 c∗1
]
B. Sundar Rajan (ECE) IASc Talk, 05 July 2013 18 / 31
The problem of designing STCs
A space-time code is a (large) finite set of complex matrices of appropriatesize.
Obtain a matrix of appropriate size with variable entries such that spacetime codes can be generated by letting the variable take values from asmall set of complex numbers. (Such matrices are called Designs)
The designs are required to satisfy several properties !!!
B. Sundar Rajan (ECE) IASc Talk, 05 July 2013 19 / 31
Mathematical tools in MIMO communication
Diversity Gain/Advantage: Can be studied using Division Algebras usingthe Rank Criterion
Coding Gain/Advantage: Studied using Determinants of the differencecodeword matrices
Information Losslessness: The property which assures zero loss in cpacitydue to use of block codes - Studied using Trace-Orthogonality of thecodeword matrices.
low encoding complexity linear space-time codes: Theory of Orthogonaland quasi-orthogonal designs.
Diversity-Multiplexing Trade-off: Part of this property can be studiedusing Non-vanishing determinants (Sufficient condition for optimal tradeoff)
Low/Reduction in Maximum-Likelihood decoding: Completely given byHurwitz-Radon orthogonality for matrices
Ergodic Capacity Calculations: Essential mathematical tool is RandomMatrix Theory
Precoder Design with partial (finite) feedback Theory of ComplexUnitary Matrices.
Precoder Design with perfect (full) feedback Study of behaviour ofB. Sundar Rajan (ECE) IASc Talk, 05 July 2013 20 / 31
Outline
1 Information, Uncertainty, and Communication
2 Capacity of multi-antenna systems
3 Codes for multi-antenna systems
4 Well known codes from ECE
5 Recent patents and concluding remarks
B. Sundar Rajan (ECE) IASc Talk, 05 July 2013 21 / 31
Well known space-time codes from ECE Department !!
”Full-diversity, high-rate space-time block codes from divisionalgebras,” B.A.Sethuraman, B. Sundar Rajan and V. Shashidhar,2003.
”Explicit Space-time codes achieving the diversity-multiplexing gaintradeoff,” P.Elia, K.R.Kumar, S.A.Pawar, P.Vijay Kumar and H.F.Lu,2006.
”Single-symbol maximum likelihood decodable linear STBCs,” Md.Zafar Ali Khan and B. Sundar Rajan, 2006.
”STBC-schemes with nonvanishing determinant for certain number oftransmit antennas,” T. Kiran and B. Sundar Rajan, 2005.
”Perfect space-time codes for any number of antennas,” P. elia,B.A.Sethuraman and P. Vijay Kumar, 2007.
All the above appeared in IEEE Transactions on Information Theory
B. Sundar Rajan (ECE) IASc Talk, 05 July 2013 21 / 31
Practically Important Codes
The three antenna codes accepted for IEEE 802.16e standard is a variationof the codes from ”Single-symbol maximum likelihood decodable linearSTBCs,” Md. Zafar Ali Khan and B. Sundar Rajan, 2006.
The above code was proposed by Beceem Communications whichsuccessfully brought out WiMax chipsets.
Graduate students from ECE department played a critical role in buildingthe Beceem chips.
B. Sundar Rajan (ECE) IASc Talk, 05 July 2013 22 / 31
Outline
1 Information, Uncertainty, and Communication
2 Capacity of multi-antenna systems
3 Codes for multi-antenna systems
4 Well known codes from ECE
5 Recent patents and concluding remarks
B. Sundar Rajan (ECE) IASc Talk, 05 July 2013 27 / 31
Figure: The best code for 4Tx-2Rx system known so far
B. Sundar Rajan (ECE) IASc Talk, 05 July 2013 27 / 31
Figure: A detection technique for LARGE-MIMO systems
B. Sundar Rajan (ECE) IASc Talk, 05 July 2013 29 / 31
Concluding Remarks
6 more US patents have been filed with IISc as assignee.
A project to build a large multi-antenna wireless system for DEALDehradun is going on (with Prof. Chockalingam (PI) and Prof. VinodSharma and B. Sundar Rajan (Co-PIs)
B. Sundar Rajan (ECE) IASc Talk, 05 July 2013 30 / 31