Mohammad Jaber Borran, Mahsa Memarzadeh, and Behnaam Aazhang

June 29, 2001

Coded Modulation for Orthogonal Transmit Diversity

Motivation

Wireless Communication EnvironmentNoise

Multipath

Fading

MAI

DemandsMultimedia applications High rate

Data communication Reliability

Challenges

ProblemsLow achievable rates if single transmit and

receive antenna systems are used

Less reliability due to low SNR and fading

Some Possible SolutionsUse more bandwidth (limited resource!)

Use strong codes (computational complexity!)

Use multiple antennas (hardware complexity!)

Multiple-Antenna Systems

Capacity min(nT, nR) Higher rate

Potential spatial diversity More reliability

Data ChannelEncoder ...

ChannelDecoder

RecoveredData

[I. E. Telatar]

Space-Time Coding

Slowly fadingSpatial diversity and coding gain

Fast fadingSpatial and temporal diversity, and coding gain

DataSpace-TimeEncoder ...

Space-TimeCode matrix

Spac

eTime

Space-TimeDecoder

RecoveredData

Space-Time Code Design

Previous approaches Jointly maximizing spatial and temporal

diversity and coding gain No systematic code design method, difficult

Suggested approach Decouples the problem into simpler ones Simplifies code design procedure Provides systematic code construction method Performs better than existing codes

System Model

Decouples the problems of maximizing

Spatial diversity

Temporal diversity and/or coding gain

[S. Alamouti]

*

*

cc

-cc

12

21

c

OTDTransmitter TX antenna 1

TX antenna 2

RX antenna

1*2 cc

2*1 cc

12 cc

AlamoutiEncoder

Orthogonal Transmit Diversity

Achieves full diversity (2) Provides full rate (R = 1) No capacity loss Simple ML decoder

Slowly Fading Channels

Upper bound for pairwise error probability

No temporal diversity

2

01

2

4)(

N

EecP s

L

lllec

spatialdiversit

y

coding gain

Design Criteria

Maximization of coding gain

Same as design criterion for single antenna systems in AWGN channels

Codes designed for optimum performance in AWGN channels are optimum outer codes

L

llle ecd

1

2)e,c(

(Standard Euclidean distance)

Simulation Results (1)

9 10 11 12 13 14 15 16 17 1810

-3

10-2

10-1

100

SNR (dB)

Fra

me

Err

or P

roba

bilit

y

AT&T 4-state space-time trellis code Concatenated orthogonal space-time trellis codeOutage Probability

R = 2 b/s/Hz

1 dB gain

4-state TCM outer code optimum for AWGN

0, 2, 4, 6

1, 3, 5, 7

2, 0, 6, 4

3, 1, 7, 5

Better performance with same complexity

Simulation Results (2)

9 10 11 12 13 14 15 16 17 1810

-3

10-2

10-1

100

SNR (dB)

Fra

me

Err

or P

roba

bilit

y

AT&T 8-state space-time trellis code Concatenated orthogonal space-time trellis codeOutage Probability

R = 2 b/s/Hz

2 dB gain

8-state TCM outer codeoptimum for AWGN

0, 2, 4, 6

1, 3, 5, 7

2, 0, 6, 4

3, 1, 7, 5

4, 6, 0, 2

5, 7, 1, 3

6, 4, 2, 0

7, 5, 3, 1

Better performance with same complexity

Fast Fading Channels

Upper bound for pairwise error probability

),(),(;

2

0

2

22

2

1212

2122124

)(kkkk eecck

skkkk N

EececP ec

spatialdiversit

y

coding gain

component

temporaldiversity

Design Criteria (1)

Maximization of

Hamming distance Product distance

between pairs of consecutive symbols:

(c2k-1, c2k) , (e2k-1, e2k)

Design for an Expanded Constellation

Constellation Expansion (1)

In dimension In size

c2k-1

c2k

Ck=(c2k-1, c2k)

Original M-aryconstellation

Expanded M2-aryconstellation

(2D coordinate 1)

(2D coordinate 2)

(4D point)

c2k

c2k-1 Ck=(c2k-1, c2k)

Design Criteria (2)

Design for expanded constellation based on maximizing

• Symbol Hamming distance• Product of squared distances

Same as design criteria for single antenna systems in fast fading channels

Expanded constellation

Ck

OTDTransmitter

c2k c2k-1

122 k*

k cc

k*

k cc 212

[D. Divsalar]

Simulation Results (1)

Comparison with AT&T smart-greedy code

Better performance with same complexity

R = 1 b/s/Hz

0 2 4 6 8 10 12 14 16 18 2010

-3

10-2

10-1

100

SNR per Bit (dB)

Fra

me

Err

or P

roba

bilit

yAT&T smart-greedy space-time trellis code

Concatenated orthogonal space-time code

Slowly fading channel

-2 0 2 4 6 8 10 12 14 1610

-5

10-4

10-3

10-2

10-1

100

SNR per Bit (dB)

Sym

bol E

rror

Pro

babi

lity

Fast fading channel

Diversity 4

Diversity 3

AT&T smart-greedy space-time trellis codeConcatenated orthogonal space-time code

Simulation Results (2)

8 10 12 14 16 18 2010

-5

10-4

10-3

10-2

10-1

SNR per Bit

Sym

bol E

rror

Pro

babi

lity

Uncoded Orthogonal Transmission (R = 3 bits/s/Hz)MLC for Orthogonal Transmission (R = 3 bits/s/Hz)

Diversity 4

Diversity 2

Comparison of simple OTD with concatenated ST code(Outer code: 4-dimensional MLC)

OTD systems with nT>2 and nR1

Achieve maximum diversity order (nTnR)

Not full rate (R < 1)Full rate, full diversity, complex orthogonal

designs exist only if nT=2

Generalized OTD

Slowly Fading Channels

Upper bound for pairwise error probability

Design criteria

Maximization of free Euclidean distance

RT nn

sRL

lll N

EecP

01

2

4)( ec

spatialdiversit

y

coding gain

Fast Fading Channels

Upper bound for pairwise error probability

Design criteria Maximizing Hamming and product distances

in expanded constellation

Concatenation of RQ points in original signal

setCk = (c(k-1)RQ+1, …, ckRQ)

Point in expanded

constellation

),...,(),...,(; 01

2

)1()1(

1)1(1)1(4

)(kRQRQkkRQRQk

RT

eecck

nn

sRQ

qqRQkqRQk N

EecP ec

coding gain component

temporal diversity

Simulation Results

Slowly fading channel Fast fading channel

2 4 6 8 10 12 14 1610

-4

10-3

10-2

10-1

100

SNR per Bit (dB)

Fra

me

Err

or P

roba

bilit

y

6 7 8 9 10 11 12 13 1410

-6

10-5

10-4

10-3

10-2

10-1

SNR per Bit (dB)

Sym

bol E

rror

Pro

babi

lity

R = 1.5 b/s/Hz R = 1 b/s/Hz

3 & 4 transmit,1 receive

3 & 4 transmit,2 receives

3 transmit,Diversity 6

4 transmit,Diversity 8

MTCM outer code8-state TCM outer code optimum for AWGN

Summary

Concatenated orthogonal space-time code

Decouples the problems of maximizing spatial diversity, temporal diversity and/or coding gain

Simplifies code design procedure and provides a systematic method for code construction

Has better performance compared to existing space-time codes

Contact Information

mohammad@rice.edumahsa@rice.eduaaz@rice.edu

http://www.ece.rice.edu/~mohammad