1. Space Time Codes

2. A MIMO SYSTEM

3. System Model

4. System Model Why Space Time coding ?
MIMO system with NT transmit and NR receive antennas
: received vector
: quasi-static channel matrix
: transmitted vector
: white Gaussian noise vector
Why Space Time coding ?

5. Space-Time Coding 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

6. Space-Time Coding Space-Time Block Codes: Space-Time Trellis Codes:
These codes are transmitted using an orthogonal block structure which enables simple decoding at the receiver.
Space-Time Trellis Codes:
These are convolutional codes extended to the case of multiple transmit and receive antennas.

7. Space-Time Coding
Space-Time Block Codes achieve maximum possible diversity advantage but no coding gain and bandwidth expansion
advantage: simplicity
Space-Time Trellis Codes (STTC) joint design of error control coding, Modulation, transmit
and receive diversity
complexity coding gain, spectral efficiency,
and diversity improvement

8. Maximizing diversity with Space-Time Codes
Space–Time Trellis Codes (STTC) offer better performance
at the cost of increased complexity
Complex decoding (vector version of the Viterbi algorithm)
—increases exponentially with the transmission rate
Full diversity. Coding gain
Space–Time Block Codes (STBC)
Simple maximum–likelihood (ML) decoding based on linear processing
Full diversity. Minimal or no coding gain

9. Space-Time Trellis Coding1 2 3
Aim : To realize joint encoding, modulation
and diversity across space and time .
Design : 4-QAM / QPSK
4 – state
2 – Transmit antennas

10. 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
‘0’ 01
‘1’ 10
‘2’ 11
‘3’
State 0
Output for
Antenna1,Antenna2 02 03
State 1 12 13
State 2 20 21 22 23
State 3 30 31 32
State # 1 2 3

11. Example Assume initial state : 00  state 0
Input stream :
Tx. Ant. 1 :
Tx. Ant. 2 :
Delay diversity ?

12. Example - Delay diversity code, QPSK modulation
Example - Delay diversity code, QPSK modulation Code rate ½ , 2 Tx antennas
Input
x ∈ ℤ4
output
antenna 1
antenna 2 D c1 c2
Encoder structure:
Example:
x =
c1 =
c2 =
1 symbol delay

13. Example -Space-time ring TCM code 4-state trellis, code rate ½ (and n=2)
Encoder structure: c1 x D c2 + 3
input seq.
output seq. t0 t1 2 1
input St
St+1 c1 c2 1 3 2 2 1 3

14. Example -Space-time ring TCM code 4-state trellis, code rate ½ (and n=2)

16. Space Time Trellis Decoding
For the 2 Tx antennas system the metric is reduced to:
m (rj ( l ), ci ( l ) / h ij ( l ) )
=   [ rj( l ) - {h 1j ( l ) c1( l ) + h 2j ( l ) c2( l ) } ] 2
l = 1
j = 1 L m

17. Space Time Trellis Decoding

18. 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

19. Space-Time Block Codes

20. Space-Time Block Code Alamouti Codes
Tx1
Tx2
-c2* c1
c1* c2
Encoding and Transmission :
Decoding:
Linearly combine received symbols
Perform Maximum Likelihood (ML) detection
Diversity order of 2NR guaranteed
The received symbols :

22. STBC for Tx. Ant > 2

23. Simulation Results for Alamouti Scheme
Increase in number of receive antennas → increases diversity order

24. Comparison of Alamouti and Trellis
Space–Time Trellis codes perform better than Alamouti scheme.
Alamouti code is lot simpler to decode than trellis codes

25. Capacity increase in MIMO

26. Scope of MIMO
MIMO channels offer multiplexing gain, diversity gain, power gain (array gain) and a co–channel interference cancellation gain
Tradeoff between diversity gain and multiplexing gain: Careful balancing between those gains is required
Space-Time Coding: Space-Time block codes (STBC) and Space-Time Trellis Codes
Easy to combine with error control codes
MIMO systems offer a solution choice for future generation wireless networks
Distributed MIMO: Cooperative wireless networks