Coded Modulation for Orthogonal Transmit Diversity
Coded Modulation for Orthogonal Transmit Diversity. Motivation. Wireless Communication Environment Noise Multipath Fading MAI Demands Multimedia applications High rate Data communication Reliability. Challenges. Problems
Coded Modulation for Orthogonal Transmit Diversity
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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!)
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 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 • 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
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
spatial 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)
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
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
spatial 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)
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]
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
Diversity 2 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
spatial diversity coding gain Slowly Fading Channels • Upper bound for pairwise error probability • Design criteria • Maximization of free Euclidean distance
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
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 • 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 • mohammad@rice.edu • mahsa@rice.edu • aaz@rice.edu • http://www.ece.rice.edu/~mohammad
