Coded modulation for orthogonal transmit diversity
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Coded Modulation for Orthogonal Transmit Diversity. Motivation. Wireless Communication Environment Noise Multipath Fading MAI Demands Multimedia applications  High rate Data communication  Reliability. Challenges. Problems

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Presentation Transcript

Motivation
Motivation

  • Wireless Communication Environment

    • Noise

    • Multipath

    • Fading

    • MAI

  • Demands

    • Multimedia applications  High rate

    • Data communication  Reliability


Challenges
Challenges

  • Problems

    • Low achievable rates if single transmit and receive antenna systems are used

    • Less reliability due to low SNR and fading

  • Some Possible Solutions

    • Use more bandwidth (limited resource!)

    • Use strong codes (computational complexity!)

    • Use multiple antennas (hardware complexity!)


Multiple antenna systems

Recovered

Data

Channel

Decoder

Data

Channel

Encoder

.

.

.

Multiple-Antenna Systems

  • Capacity   min(nT, nR) Higher rate

  • Potential spatial diversity  More reliability

[I. E. Telatar]


Space time coding

Space-Time

Code matrix

Space

Recovered

Data

Space-Time

Decoder

Space-Time

Encoder

.

.

Time

.

Space-Time Coding

Data

  • Slowly fading

    • Spatial diversity and coding gain

  • Fast fading

    • Spatial and temporal diversity, and coding gain


Space time code design
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
System Model

  • Decouples the problems of maximizing

    • Spatial diversity

    • Temporal diversity and/or coding gain


Orthogonal transmit diversity

OTD

Transmitter

TX antenna 1

Alamouti

Encoder

RX antenna

TX antenna 2

Orthogonal Transmit Diversity

[S. Alamouti]

  • Achieves full diversity (2)

  • Provides full rate (R = 1)

  • No capacity loss

  • Simple ML decoder


Slowly fading channels

spatial

diversity

coding gain

Slowly Fading Channels

  • Upper bound for pairwise error probability

    • No temporal diversity


Design criteria
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

(Standard Euclidean distance)


Simulation results 1

R = 2 b/s/Hz

0

10

0, 2, 4, 6

1 dB gain

1, 3, 5, 7

-1

10

Frame Error Probability

2, 0, 6, 4

-2

10

3, 1, 7, 5

AT&T 4-state space-time trellis code

4-state TCM outer code

optimum for AWGN

Concatenated orthogonal space-time trellis code

Outage Probability

-3

10

9

10

11

12

13

14

15

16

17

18

SNR (dB)

Simulation Results (1)

Better performance with same complexity


Simulation results 2

R = 2 b/s/Hz

0, 2, 4, 6

0

10

1, 3, 5, 7

2 dB gain

2, 0, 6, 4

-1

10

3, 1, 7, 5

Frame Error Probability

4, 6, 0, 2

5, 7, 1, 3

-2

10

6, 4, 2, 0

AT&T 8-state space-time trellis code

7, 5, 3, 1

Concatenated orthogonal space-time trellis code

Outage Probability

-3

10

9

10

11

12

13

14

15

16

17

18

8-state TCM outer code

optimum for AWGN

SNR (dB)

Simulation Results (2)

Better performance with same complexity


Fast fading channels

spatial

diversity

temporal

diversity

coding gain component

Fast Fading Channels

  • Upper bound for pairwise error probability


Design criteria 1
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

Ck=(c2k-1, c2k)

(2D coordinate 2)

c2k

c2k-1

Ck=(c2k-1, c2k)

(4D point)

(2D coordinate 1)

c2k

Original M-ary

constellation

Expanded M2-ary

constellation

Constellation Expansion (1)


Design criteria 2

Expanded

constellation

Ck

OTD

Transmitter

c2k c2k-1

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

[D. Divsalar]


Simulation results 11

R = 1 b/s/Hz

0

0

10

10

-1

10

-1

10

-2

10

Diversity 3

Frame Error Probability

Symbol Error Probability

-3

10

Diversity 4

-2

10

-4

10

AT&T smart-greedy space-time trellis code

AT&T smart-greedy space-time trellis code

Concatenated orthogonal space-time code

Concatenated orthogonal space-time code

-3

-5

10

10

0

2

4

6

8

10

12

14

16

18

20

-2

0

2

4

6

8

10

12

14

16

SNR per Bit (dB)

SNR per Bit (dB)

Slowly fading channel

Fast fading channel

Simulation Results (1)

Comparison with AT&T smart-greedy code

Better performance with same complexity


Simulation results 21

Diversity 2

Diversity 4

Simulation Results (2)

Comparison of simple OTD with concatenated ST code

(Outer code: 4-dimensional MLC)


Generalized otd
Generalized OTD

  • OTD systems with nT>2 and nR1

  • Achieve maximum diversity order (nTnR)

  • Not full rate (R < 1)

    • Full rate, full diversity, complex orthogonal designs exist only if nT=2


Slowly fading channels1

spatial

diversity

coding gain

Slowly Fading Channels

  • Upper bound for pairwise error probability

  • Design criteria

    • Maximization of free Euclidean distance


Fast fading channels1

temporal diversity

coding gain component

Concatenation of RQ points in original signal set

Point in expanded

constellation

Ck = (c(k-1)RQ+1, …, ckRQ)

Fast Fading Channels

  • Upper bound for pairwise error probability

  • Design criteria

    • Maximizing Hamming and product distances in expanded constellation


Simulation results

R = 1.5 b/s/Hz

R = 1 b/s/Hz

-1

10

0

10

3 & 4 transmit,

1 receive

-2

10

-1

10

-3

3 transmit,

Diversity 6

10

Symbol Error Probability

Frame Error Probability

-2

10

-4

10

-3

10

4 transmit,

Diversity 8

-5

3 & 4 transmit,

2 receives

10

-4

-6

10

10

2

4

6

8

10

12

14

16

6

7

8

9

10

11

12

13

14

SNR per Bit (dB)

SNR per Bit (dB)

Simulation Results

Slowly fading channel

Fast fading channel

8-state TCM outer code

optimum for AWGN

MTCM outer code


Summary
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



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