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## PowerPoint Slideshow about ' Coded Modulation for Orthogonal Transmit Diversity' - dawn-glover

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Presentation Transcript

Motivation

- Wireless Communication Environment
- Noise
- Multipath
- Fading
- MAI
- Demands
- Multimedia applications High rate
- Data communication Reliability

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!)

Data

Channel

Decoder

Data

Channel

Encoder

.

.

.

Multiple-Antenna Systems- Capacity min(nT, nR) Higher rate
- Potential spatial diversity More reliability

[I. E. Telatar]

Code matrix

Space

Recovered

Data

Space-Time

Decoder

Space-Time

Encoder

.

.

Time

.

Space-Time CodingData

- Slowly fading
- Spatial diversity and coding gain
- Fast fading
- Spatial and temporal diversity, and coding gain

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

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

diversity

coding gain

Slowly Fading Channels- Upper bound for pairwise error probability
- No temporal diversity

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)

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

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

diversity

temporal

diversity

coding gain component

Fast Fading Channels- Upper bound for pairwise error probability

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

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)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]

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

Diversity 4

Simulation Results (2)Comparison of simple OTD with concatenated ST code

(Outer code: 4-dimensional MLC)

Generalized OTD

- 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

diversity

coding gain

Slowly Fading Channels- Upper bound for pairwise error probability
- Design criteria
- Maximization of free Euclidean distance

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

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 ResultsSlowly fading channel

Fast fading channel

8-state TCM outer code

optimum for AWGN

MTCM outer code

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

- [email protected]
- [email protected]
- [email protected]
- http://www.ece.rice.edu/~mohammad

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