Coded Modulation for Orthogonal Transmit Diversity Mohammad Jaber

Coded Modulation for Orthogonal Transmit Diversity Mohammad Jaber Borran, Mahsa Memarzadeh, and Behnaam Aazhang June 29, 2001

Motivation Ø Wireless Communication Environment ªNoise ªMultipath ªFading ªMAI Ø Demands ªMultimedia applications High rate ªData communication Reliability

Challenges Ø Problems ªLow achievable rates if single transmit and receive antenna systems are used ªLess reliability due to low SNR and fading Ø Some Possible Solutions ªUse more bandwidth (limited resource!) ªUse strong codes (computational complexity!) ªUse multiple antennas (hardware complexity!)

Multiple-Antenna Systems Data Channel Encoder . . Channel Decoder Recovered Data Ø Capacity min(n. T, n. R) Higher rate [I. E. Telatar] Ø Potential spatial diversity More reliability

Space-Time Coding Space-Time Code matrix Data Space-Time Encoder Time . . Space-Time Recovered Data Decoder Ø Slowly fading ªSpatial diversity and coding gain Ø Fast fading ªSpatial and temporal diversity, and coding gain

Space-Time Code Design Ø Previous approaches ª Jointly maximizing spatial and temporal diversity and coding gain ª No systematic code design method, difficult Ø Suggested approach ª Decouples the problem into simpler ones ª Simplifies code design procedure ª Provides systematic code construction method ª Performs better than existing codes

System Model Ø Decouples the problems of maximizing ª Spatial diversity ªTemporal diversity and/or coding gain

Orthogonal Transmit Diversity [S. Alamouti] OTD Transmitter Alamouti Encoder TX antenna 1 RX antenna TX antenna 2 Ø Achieves full diversity (2) Ø Provides full rate (R = 1) Ø No capacity loss Ø Simple ML decoder

Slowly Fading Channels Ø Upper bound for pairwise error probability spatial diversity coding gain ª No temporal diversity

Design Criteria Ø Maximization of coding gain (Standard Euclidean distance) ª Same as design criterion for single antenna systems in AWGN channels ª Codes designed for optimum performance in AWGN channels are optimum outer codes

Simulation Results (1) R = 2 b/s/Hz 0 10 1, 3, 5, 7 2, 0, 6, 4 3, 1, 7, 5 4 -state TCM outer code optimum for AWGN Frame Error Probability 0, 2, 4, 6 1 d. B gain -1 10 -2 10 AT&T 4 -state space-time trellis code Concatenated orthogonal space-time trellis code Outage Probability -3 10 9 10 11 12 13 14 15 16 17 18 SNR (d. B) Better performance with same complexity

Simulation Results (2) R = 2 b/s/Hz 0, 2, 4, 6 0 10 2, 0, 6, 4 3, 1, 7, 5 4, 6, 0, 2 5, 7, 1, 3 6, 4, 2, 0 Frame Error Probability 1, 3, 5, 7 2 d. B gain -1 10 -2 10 AT&T 8 -state space-time trellis code Concatenated orthogonal space-time trellis code Outage Probability 7, 5, 3, 1 -3 10 8 -state TCM outer code optimum for AWGN 9 10 11 12 13 14 15 16 17 18 SNR (d. B) Better performance with same complexity

Fast Fading Channels Ø Upper bound for pairwise error probability spatial diversity temporal diversity coding gain component

Design Criteria (1) Ø Maximization of ª Hamming distance ª Product distance between pairs of consecutive symbols: (c 2 k-1, c 2 k) , (e 2 k-1, e 2 k) Design for an Expanded Constellation

Constellation Expansion (1) Ø In dimension (2 D coordinate 2) c 2 k-1 Ck=(c 2 k-1, c 2 k) Ø In size c 2 k-1 c 2 k Ck=(c 2 k-1, c 2 k) (4 D point) (2 D coordinate 1) c 2 k Original M-ary constellation Expanded M 2 -ary constellation

Design Criteria (2) Ø Design for expanded constellation based on maximizing • Symbol Hamming distance • Product of squared distances ªSame as design criteria for single antenna systems in fast fading channels [D. Divsalar] Expanded constellation Ck c 2 k-1 OTD Transmitter

Simulation Results (1) Comparison with AT&T smart-greedy code R = 1 b/s/Hz 10 10 10 Frame Error Probability Symbol Error Probability 10 -1 -2 Diversity 3 -3 Diversity 4 10 10 -4 AT&T smart-greedy space-time trellis code Concatenated orthogonal space-time code -5 -2 0 2 4 6 8 10 12 SNR per Bit (d. B) Fast fading channel 14 16 10 10 0 -1 -2 AT&T smart-greedy space-time trellis code Concatenated orthogonal space-time code 10 -3 0 2 4 6 8 10 12 14 16 18 SNR per Bit (d. B) Slowly fading channel Better performance with same complexity 20

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

Generalized OTD Ø OTD systems with n. T>2 and n. R 1 Ø Achieve maximum diversity order (n. Tn. R) Ø Not full rate (R < 1) ªFull rate, full diversity, complex orthogonal designs exist only if n. T=2

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

Fast Fading Channels Ø Upper bound for pairwise error probability temporal diversity Ø Design criteria coding gain component ª Maximizing Hamming and product distances in expanded constellation Point in expanded constellation Concatenation of RQ points in original signal set Ck = (c(k-1)RQ+1, …, ck. RQ)

Simulation Results R = 1. 5 b/s/Hz 10 0 3 & 4 transmit, 1 receive -1 10 -2 10 -3 10 3 & 4 transmit, 2 receives -4 10 2 4 6 8 10 12 14 SNR per Bit (d. B) 16 Symbol Error Probability Frame Error Probability 10 10 10 R = 1 b/s/Hz -1 -2 -3 3 transmit, Diversity 6 -4 4 transmit, Diversity 8 -5 -6 6 7 8 9 10 11 12 SNR per Bit (d. B) Slowly fading channel Fast fading channel 8 -state TCM outer code optimum for AWGN MTCM outer code 13 14

Summary Ø Concatenated orthogonal space-time code ª Decouples the problems of maximizing spatial diversity, temporal diversity and/or coding gain ª Simplifies code design procedure and provides a systematic method for code construction ª Has better performance compared to existing space-time codes

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