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

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!)

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

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

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

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

Slowly Fading Channels  Upper bound for pairwise error probability  No temporal diversity spatial diversity coding gain

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) 4-state TCM outer code optimum for AWGN 0, 2, 4, 6 1, 3, 5, 7 2, 0, 6, 4 3, 1, 7, 5 Better performance with same complexity

Simulation Results (2) 8-state TCM outer code optimum for AWGN 0, 2, 4, 6 1, 3, 5, 7 2, 0, 6, 4 3, 1, 7, 5 4, 6, 0, 2 5, 7, 1, 3 6, 4, 2, 0 7, 5, 3, 1 Better performance with same complexity

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

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

Constellation Expansion (1)  In dimension  In size (2D coordinate 1) (2D coordinate 2) (4D point) c2kc2k c 2k-1 C k =(c 2k-1, c 2k )

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 Expanded constellation C k OTD Transmitter c 2k c 2k-1 [D. Divsalar]

Simulation Results (1) Comparison with AT&T smart-greedy code Better performance with same complexity R = 1 b/s/Hz SNR per Bit (dB) Frame Error Probability AT&T smart-greedy space-time trellis code Concatenated orthogonal space-time code Slowly fading channel SNR per Bit (dB) Symbol Error Probability Fast fading channel Diversity 4 Diversity 3 AT&T smart-greedy space-time trellis code Concatenated orthogonal space-time code

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

 OTD systems with n T >2 and n R  1  Achieve maximum diversity order (n T n R )  Not full rate (R < 1)  Full rate, full diversity, complex orthogonal designs exist only if n T =2 Generalized OTD

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

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

Simulation Results Slowly fading channelFast fading channel MTCM outer code 8-state TCM outer code optimum for AWGN

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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