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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