Fundamental overview and simulation

of MIMO systems for Space-Time

coding and Spatial Multiplexing

EE381k-11 Wireless Communication

May 3, 2003

Hoo-Jin Lee, Shailesh Patil, and Raghu G. Raj

Introduction I
 Multiple Input Multiple Output (MIMO)
 Multiple antennas at source and destination.

 Motivation : Current wireless systems [1, 2]

 Capacity constrained networks.
 Issues related to quality and coverage.
Introduction II
 MIMO increases capacity [3]
 MIMO uses independent channel fading due to multipath pro
pagation to increase capacity.
 No extra expen$ive bandwidth required !!

C  NT log2(1 + SNR)

 MIMO gives reliable communication [4]

 Multiple independent samples of the same signal at the receiv
er give rise to “diversity”.
Introduction III
 Diversity exhibited :

 Spatial diversity
 spacing between antennas

 Transmit diversity
 space – time coding

 Receive diversity
 receive antennas
System Model I
 MIMO system with NT transmit and NR receive antenna
s
 r1 (k )   h11  hN 1   x1 (k )   n1 (k ) 
  
   
T

 

        
  
rN (k ) h1N  hN N   xN (k ) nN (k )
 R   R T  R 
R
T

r ( k )  H  x( k )  n ( k )
r (k ) : received vector
H : quasi-static channel matrix
x(k ) : transmitted vector
n(k ) : white Gaussian noise vector
System Model II
 Rayleigh channel model : multi-path

 Channel between any two pair of antennas is independent

 Each hik is complex Gaussian with unit variance

 Ricean channel model : line of sight (K = 0dB) [5]

MIMO LabVIEW demo
 Intuition to MIMO system
 Presented at WNCG open house
 Modified for project presentation
 MIMO demo
Goals
 Study and simulate basic MIMO systems
 Space-Time coding : Better error performance
 Trellis codes
 Alamouti code
 Spatial Multiplexing : Higher data rate
 Maximum likelihood receiver
 Linear receiver
 Successive interference cancellation or V-BLAST
 Ricean channel model (Prof. Rappaport’s suggestion)
 Application of MIMO systems
 Space-Time Coding I

 What is Space-Time coding?

 Coding schemes allow for the adjusting and optimization of j
oint encoding across space and time in order to maximize the
reliability of a wireless link.

 Space-Time codes allow us to achieve this goal by explo

iting
 Spatial diversity in order to provide coding and diversity gains
over an uncoded wireless link
Space-Time Coding II

1. Space-Time Block Codes:

These codes are transmitted using an orthogonal block
structure which enables simple decoding at the receiver.

2. Space-Time Trellis Codes:

These are convolutional codes extended to the case of
multiple transmit and receive antennas.
Design Criteria for Space-Time Codes
Error matrix B for code words c and e:
 e11  c11 . . e1l  c1l 
 
. . . .
B 
 . . . . 
 N N NT NT

e1 T  c1 T . . el  cl 

Diversity criterion : Maximize diversity order=rNR

where r is the rank of B
Maximum diversity obtained is NTNR r 
NR
  i 
Coding gain criterion : Maximizer coding gain=  i 1 
 
where, i i 1=eigenvalues of B
Probability of Error [6]
Rayleigh channel :
NR
 r 
P(c  e | hi , j )    i  ( Es /( 4 N 0 ))  rN R
 i 1 

Ricean channel :
 Es 
N M
  K i , j i 
 1 4N0
P (c  e | hi , j )    exp( )

j 1 i 1 (1  ( E s / 4 N 0 )i )
Es 
 1  i 
 4N0 

where,  i  ir1 : eigenvalues of code separation matrix B

Ki, j : Ricean K factor between antenna i and j
Es : symbol energy
N0 : noise power
Space-Time Trellis Coding
Example of a 2 transmit space-time trellis code with 4 states
(4-PSK constellations, spectral efficiency of 2bps/Hz)
Input Bits 00 01 10 11

State #
State 0 00 01 02 03
Output for
Antenna1,Antenna2 0

State 1 10 11 12 13
Output for 1
Antenna1,Antenna2

State 2 20 21 22 23 2
Output for
Antenna1,Antenna2

3
State 3 30 31 32 32
Output for
Antenna1,Antenna2
Simulation Results for Trellis Codes
2 Tx, 1Rx, 4PSK codes: 2 Tx, 2Rx, 4PSK codes:

Increase in number of states → increases coding gain

Increase in number of receive antennas → increases diversity gain
Space-Time Block Code – Alamouti [7]
 Encoding and Transmission :
-s1 * s0
Tx1

s4 s3 s2 s1 s0 s0 * s1

Tx2

The received symbols : r0  r (t )  h0 s0  h1s1  n0

r1  r (t  T )   h0 s1*  h1s0*  n1
 Decoding:
 Linearly combine received symbols
 Perform Maximum Likelihood (ML) detection

 Diversity order of 2NR guaranteed

Simulation Results for Alamouti Scheme

Increase in number of receive antennas → increases diversity order

 Comparison of Alamouti and Trellis

Space–Time Trellis codes

perform better than Alamouti
scheme.

Alamouti code is much

simpler to decode than trellis
codes
 Ricean Channel Simulations
Alamouti 2Tx, 2Rx Trellis 2Tx, 2Rx

For both Alamouti and Trellis codes the performance improves with
Ricean channel.
 Spatial Multiplexing Overview
 Multiple data streams are transmitted simultaneously
and on the same frequency using a transmit array
 Different data sub-streams are transmitted from
different antennas
 The transmitter does not need channel state information
 No need for fast feedback links.
Spatial Multiplexing Detection I [8]
 Maximum Likelihood (ML): optimum and most
complex detection method
2
xˆ  arg min r  Hx k where C is the constellation size.
x k {x1 ,...,x NT }
C

 Linear detection
 Zero-Forcing (ZF): pseudo inverse of the channel, simplest
xˆ  (H * H ) 1 Hr  H  r
 Minimum mean-squared error (MMSE) : intermediate
complexity and performance
1
xˆ  ( I N R  H H H ) 1 H H  r
SNR
Spatial Multiplexing Detection II [9]
 V-BLAST
 extracts data streams by ZF or MMSE filter with ordered
successive interference cancellation (SIC)

 Steps for V-BLAST detection

1. Ordering: choosing the best channel
2. Nulling: using ZF or MMSE
3. Slicing: making a symbol decision
4. Canceling: subtracting the detected symbol
5. Iteration: going to the first step to detect the next symbol
 Simulation Results of ML Receiver in
Rayleigh and Ricean Channels
4QAM, antenna configurations Rayleigh vs. Ricean

•Increase of the Number of Rx antennas → Increase of the performance

•The Ricean channel: approximately 1dB gain more than in the Rayleigh
channel at SER of 10-4
 Simulation Results of ZF Receiver in
Rayleigh and Ricean Channels
4QAM, antenna configurations Rayleigh vs. Ricean

•Increase of the Number of Rx antennas → Increase of the performance

•The Ricean channel: approximately 1dB gain more than in the Rayleigh
channel at SER of 10-2
 Simulation Results of MMSE Receiver in
Rayleigh and Ricean Channels
4QAM, antenna configurations Rayleigh vs. Ricean

•Increase of the Number of Rx antennas → Increase of the performance

•The Ricean channel: approximately 1dB gain more than in the Rayleigh
channel at SER of 10-2
Simulation Results of ZF V-BLAST Receiver
in Rayleigh and Ricean Channels
4QAM, antenna configurations Rayleigh vs. Ricean

•Increase of the Number of Rx antennas → Increase of the performance

•Performance in the Ricean fading channel > Performance in the Rayleigh
fading channel (approximately 0.5 dB increase in the Ricean fading channel at SER
of 10-2)
Simulation Results of MMSE V-BLAST
Receiver in Rayleigh and Ricean Channels
 MMSE V-BLAST Rayleigh vs. Ricean

•Increase of the Number of Rx antennas → Increase of the performance

•Performance in the Ricean fading channel > Performance in the Rayleigh
fading channel
Comparison among Spatial Multiplexing
Receivers in Rayleigh Channel

• Performance and Complexity:

ML receiver > MMSE V-BLAST (SIC) receiver
> ZF V-BLAST (SIC) receiver > MMSE receiver > ZF receiver
Applications and Conclusions
 Applications
 3G UMTS (optional): 3GPP WCDMA and GSM/EDGE
 Wireless LAN: IEEE 802.11 and HIPERLAN/2
 Strong candidate for 4G along with OFDM

 Conclusions
 Multipath is not enemy but ally.
 Space-time coding scheme: Diversity and Coding gains
→ error performance improvement
 Spatial multiplexing scheme: V-BLAST is the most suitable t
o use in practical scenario
 MIMO is a promising technology for the next generation wire
less systems
References I
1. Al-Dhahir, N., Fragouli, C., Stamoulis, A., Younis, W., and Calderbank, R., “Sp
ace-time processing for broadband wireless access,” IEEE Communications Ma
gazine, Volume: 40, Issue: 9, pp. 136-142, 2002
2. Gore, D. A., Heath, R. W. Jr., and Paulraj, A. J., “Performance Analysis of Spati
al Multiplexing in Correlated Channels,” submitted to Communications, IEEE T
ransactions March 2002.
3. Telatar, I. E., “Capacity of multi-antenna Gaussian channels,” Tech. Rep. #BL0
112170-950615-07TM, AT&T Bell Laboratories, 1995
4. Foschini, G. J. and Gans, M. J., “ On limits of wireless communications in a fadi
ng environment when using multiple antennas,” Wireless Personal Communicati
ons, vol. 6, pp. 311-335, 1998
5. Erceg, V., Soma, P., Baum, D.S., Paulraj, A.J., “Capacity Obtained from Multi-I
nput-Multi-Output Channel Measurements in fixed Wireless Environments at 2.
5GHz,” Communications, 2002. ICC 2002. IEEE International Conference on ,
Volume: 1 , 2002, Page(s): 396 –400
References II
6. Tarokh, V., Jafarkhani, H., and Calderbank, A. R., “Space-time Codes for High
Data Rate Wireless Communication: Performance Criterion and Code Constructi
on,” IEEE Trans. Inform. Theory, Vol. 44, No. 2, pp. 744-765, July 1998
7. Alamouti, S. M., “A simple transmit diversity technique for wireless communica
tions,” Selected Areas in Communications, IEEE Journal,16(8):1451–1458, 199
8
8. Gore, D. A., Heath, R. W. Jr., and Paulraj, A. J., “Performance Analysis of Spati
al Multiplexing in Correlated Channels,” submitted to Communications, IEEE T
ransactions March 2002
9. Golden, G. D., Foschini, C. J., Valenzuela, R. A., and Wolniansky, P. W., “ Det
ection algorithm and initial laboratory results using V-BLAST space-time comm
unication architecture,” IEE Lett., Vol. 35, No. 1, pp. 14-16, January 1999
Thank you !