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
propagation 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
receiver 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
antennas
 r1 ( k ) 





 rN ( k ) 
 R 

 h11  hNT 1 


 
  
h1N  hN N 
T R 
 R
 x1 (k ) 





 xN (k )
 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
 n1 (k ) 





nN (k )
 R 
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
joint 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
exploiting
 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

.
B

.
 N
N
e1 T  c1 T
e1l  c1l 

. .
.


. .
.

NT
NT
. . el  cl 
. .
Diversity criterion : Maximize diversity order=rNR
where r is the rank of B
Maximum diversity obtained is NTNR
r 
  i 
 i 1 
NR
Coding gain criterion : Maximize coding gain=
r
where, i i1 =eigenvalues of B
Probability of Error [6]
Rayleigh channel :
 r 
P(c  e | hi, j )    i 
 i 1 
NR
( Es /(4 N 0 ))rN R
Ricean channel :
Es



K



i
,
j
i
N M
4N0
1

P(c  e | hi , j )   
exp(
)


Es
j 1 i 1 (1  ( E s / 4 N 0 )i )
1




i
4N0


where, i ir1
: eigenvalues of code separation matrix B
K i, 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
Output for
Antenna1,Antenna2
00
State 1
Output for
Antenna1,Antenna2
10
State 2
Output for
Antenna1,Antenna2
20
21
22
23
State 3
Output for
Antenna1,Antenna2
30
31
32
32
01
02
03
0
11
12
13
1
2
3
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 :
Tx1
s4 s3
s2 s1
-s1 *
s0
s0 *
s1
s0
Tx2
The received symbols : r0  r (t )  h0 s0  h1s1  n0
 Decoding:
r1  r (t  T )  h0 s1*  h1s0*  n1
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
xˆ  arg
min
x k {x1 ,...,x NT }
C
r  Hxk
2
where C is the constellation size.
 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.
2.
3.
4.
5.
Ordering: choosing the best channel
Nulling: using ZF or MMSE
Slicing: making a symbol decision
Canceling: subtracting the detected symbol
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
to use in practical scenario
MIMO is a promising technology for the next generation
wireless systems
References I
1.
2.
3.
4.
5.
Al-Dhahir, N., Fragouli, C., Stamoulis, A., Younis, W., and Calderbank, R.,
“Space-time processing for broadband wireless access,” IEEE Communications
Magazine, Volume: 40, Issue: 9, pp. 136-142, 2002
Gore, D. A., Heath, R. W. Jr., and Paulraj, A. J., “Performance Analysis of
Spatial Multiplexing in Correlated Channels,” submitted to Communications,
IEEE Transactions March 2002.
Telatar, I. E., “Capacity of multi-antenna Gaussian channels,” Tech. Rep.
#BL0112170-950615-07TM, AT&T Bell Laboratories, 1995
Foschini, G. J. and Gans, M. J., “ On limits of wireless communications in a
fading environment when using multiple antennas,” Wireless Personal
Communications, vol. 6, pp. 311-335, 1998
Erceg, V., Soma, P., Baum, D.S., Paulraj, A.J., “Capacity Obtained from MultiInput-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.
7.
8.
9.
Tarokh, V., Jafarkhani, H., and Calderbank, A. R., “Space-time Codes for High
Data Rate Wireless Communication: Performance Criterion and Code
Construction,” IEEE Trans. Inform. Theory, Vol. 44, No. 2, pp. 744-765, July
1998
Alamouti, S. M., “A simple transmit diversity technique for wireless
communications,”
Selected
Areas
in
Communications,
IEEE
Journal,16(8):1451–1458, 1998
Gore, D. A., Heath, R. W. Jr., and Paulraj, A. J., “Performance Analysis of
Spatial Multiplexing in Correlated Channels,” submitted to Communications,
IEEE Transactions March 2002
Golden, G. D., Foschini, C. J., Valenzuela, R. A., and Wolniansky, P. W.,
“ Detection algorithm and initial laboratory results using V-BLAST space-time
communication architecture,” IEE Lett., Vol. 35, No. 1, pp. 14-16, January 1999
Thank you !