Coded Modulation for Orthogonal Transmit Diversity

1. Coded Modulation for Orthogonal Transmit Diversity

2. Motivation • Wireless Communication Environment • Noise • Multipath • Fading • MAI • Demands • Multimedia applications  High rate • Data communication  Reliability

3. 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!)

4. Recovered Data Channel Decoder Data Channel Encoder . . . Multiple-Antenna Systems • Capacity   min(nT, nR) Higher rate • Potential spatial diversity  More reliability [I. E. Telatar]

5. 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

6. 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

7. System Model • Decouples the problems of maximizing • Spatial diversity • Temporal diversity and/or coding gain

8. 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

9. spatial diversity coding gain Slowly Fading Channels • Upper bound for pairwise error probability • No temporal diversity

10. 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)

11. 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

12. 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

13. spatial diversity temporal diversity coding gain component Fast Fading Channels • Upper bound for pairwise error probability

14. 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

15. 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)

16. 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]

17. 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

18. Diversity 2 Diversity 4 Simulation Results (2) Comparison of simple OTD with concatenated ST code (Outer code: 4-dimensional MLC)

19. 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

20. spatial diversity coding gain Slowly Fading Channels • Upper bound for pairwise error probability • Design criteria • Maximization of free Euclidean distance

21. 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

22. 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

23. 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

24. Contact Information • mohammad@rice.edu • mahsa@rice.edu • aaz@rice.edu • http://www.ece.rice.edu/~mohammad