Space Time Codes

2

A MIMO SYSTEM

3

System Model

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System Model MIMO system with NT transmit and NR receive antennas

: received vector

: quasi-static channel matrix

: transmitted vector

: white Gaussian noise vector

RTR

T

NNN

N

hh

hh

1

111

)(

)(1

kr

kr

RN

)(

)(1

kx

kx

TN

)(

)(1

kn

kn

RN

)()()( kkk nxHr H

)(kr

)(kn)(kx Why Space Time coding ?

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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

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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.

Space-Time Coding

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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

Space-Time Coding

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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

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Space-Time Trellis Coding

0

1

2

3

Aim : To realize joint encoding, modulation and diversity across space and time .

Design : 4-QAM / QPSK4 – state2 – Transmit antennas

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Example of a 2 transmit space-time trellis code with 4 states

(4-PSK constellations, spectral efficiency of 2bps/Hz)

Space-Time Trellis Coding

Input Bits 00‘0’

01‘1’

10‘2’

11‘3’

State 0Output forAntenna1,Antenna2

00 01 02 03

State 1Output forAntenna1,Antenna2

10 11 12 13

State 2Output forAntenna1,Antenna2

20 21 22 23

State 3Output forAntenna1,Antenna2

30 31 32 32

State #

0

1

2

3

11

Example Assume initial state : 00 state 0

Input stream : 0 3 0 1 2 0 3 2 0 1 0 0

Tx. Ant. 1 : 0 0 3 0 1 2 0 3 2 0 1 0 Tx. Ant. 2 : 0 3 0 1 2 0 3 2 0 1 0 0

Delay diversity ?

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Example - Delay diversity code, QPSK modulation

Code rate ½ , 2 Tx antennas

Encoder structure:Example: x = 1 3 2 0 1 c1 = 1 3 2 0 1

c2 = 0 1 3 2 0

Input x ∈ ℤ4

outputantenna 1

outputantenna 2D

c1

c2

1 symbol delayState

0 0

1

2

0/00

1/10

2/20

3/30

0/00

1/10

2/20

3

3/30

0/01

1/11

2/21

3/31

0/02

1/12

2/22

3/32

0/03

1/13

2/23

3/33

transition label: x /c 1c2

3

2

1

0

3

2

1

0

3

2

1

0

3

2

1

0

2/23

0/02

1/10

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Example -Space-time ring TCM code4-state trellis, code rate ½ (and n=2)

Encoder structure:

c1x

D c2+ +

3

1 2 3 1 1

input seq.

output seq.

1 2 3 1 1

1 3 0 3 0

t0 t1

2 1

0 0 0 0 0

0 1 3 0 1

0 2 2 0 2

0 3 1 0 3

1 0 1 1 1

1 1 0 1 2

1 2 3 1 3

1 3 2 1 0

2 0 2 2 2

2 1 1 2 3

2 2 0 2 0

2 3 3 2 1

3 0 3 3 3

3 1 2 3 0

3 2 1 3 1

3 3 0 3 2

input

St St+1

c1 c2

input

St St+1

c1 c2

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Example -Space-time ring TCM code4-state trellis, code rate ½ (and n=2)

0 0

1

2

0/00

1/11

2/22

3/33

0/00

1/11

2/22

3

3/33

1/12

2/23

3/30

0/01

2/20

3/31

0/02

1/13

3/32

0/03

1/10

2/21 3

2

1

0

3

2

1

0

3

2

1

0

3

2

1

0

3/30

1/13 1/10

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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 = 1j = 1

L m

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Space Time Trellis Decoding

State

survivor path

0 0

1

2

3

0/00

1/11

2/22

3/33

22.378

1.0917

21.437

41.135

0/00

1/12

0

1

2

Transitionmetrics

12.071+22.378=34.449

22.952+1.0917=24.044

Accumulatedmetrics

2/23

3

7.8235+21.437=29.2602

4.5824+41.137=45.7176

1.0917+10.1054=11.1971 survivor

222211222

2211111 )1()1()1()1()1()1()1()1()1()1( cgcgrcgcgr

received1st antenna

CSItransition

signals

received2nd antenna

CSI transitionsignals =

branchlabels

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Simulation Results for Trellis Codes2 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

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Space-Time Block Codes

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Encoding and Transmission :

Decoding: Linearly combine received symbols Perform Maximum Likelihood (ML) detection

Diversity order of 2NR guaranteed

Space-Time Block Code Alamouti Codes

c1c2c3c4c5

Tx1

Tx2

-c2* c1

c1* c2

The received symbols : 021100 )( nchchtrr

1*11

*201 )( nchchTtrr

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22

STBC for Tx. Ant > 2

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Simulation Results for Alamouti Scheme

Increase in number of receive antennas → increases diversity order

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Comparison of Alamouti and Trellis

Space–Time Trellis codes perform better than Alamouti scheme.

Alamouti code is lot simpler to decode than trellis codes

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Capacity increase in MIMO

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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