Full-Diversity Codes for MISO Systems Equipped With Linear or ML Detectors

In this paper, a general criterion for space-time block codes (STBC) to achieve full diversity with a linear receiver is proposed for a wireless communication system having multiple transmitter and single receiver antennas [multiple-input-single-output (MISO)]. Particularly, the STBC with Toeplitz structure satisfies this criterion, and therefore, enables full diversity. Further examination of this Toeplitz STBC reveals the following important properties: (1) the symbol transmission rate can be made to approach unity; (2) applying the Toeplitz code to any signalling scheme having nonzero distance between the nearest constellation points results in a nonvanishing determinant. In addition, if quadratic-amplitude modulation (QAM) is used as the signalling scheme, then for independent MISO flat-fading channels, the Toeplitz codes is proved to approach the optimal diversity-versus-multiplexing tradeoff with a zero-forcing (ZF) receiver when the number of channel uses is large. This is, so far, the first nonorthogonal STBC shown to achieve the optimal tradeoff for such a receiver. On the other hand, when maximum-likelihood (ML) detection is employed in a MISO system, the Toeplitz STBC achieves the maximum coding gain for independent channels. When the channel fading coefficients are correlated, the inherent transmission matrix in the Toeplitz STBC can be designed to minimize the average worst case pairwise error probability.

[1]  Andrew J. Viterbi,et al.  Error bounds for convolutional codes and an asymptotically optimum decoding algorithm , 1967, IEEE Trans. Inf. Theory.

[2]  Peter Lancaster,et al.  The theory of matrices , 1969 .

[3]  Franklin S. Weinstein,et al.  Simplified relationships for the probability distribution of the phase of a sine wave in narrow-band normal noise (Corresp.) , 1974, IEEE Trans. Inf. Theory.

[4]  J. Snyders,et al.  Simplified Relationships for the Prohahijity Distribution of the Phase of a Sine Wave in Narrow-Band Normal Noise , 1974 .

[5]  H. Witsenhausen A Determinant Maximization Problem Occurring in the Theory of Data Communication , 1975 .

[6]  Jennifer Seberry,et al.  Orthogonal Designs: Quadratic Forms and Hadamard Matrices , 1979 .

[7]  S. Rice,et al.  Distribution of the Phase Angle Between Two Vectors Perturbed by Gaussian Noise , 1982, IEEE Trans. Commun..

[8]  John G. Proakis,et al.  Digital Communications , 1983 .

[9]  Gene H. Golub,et al.  Matrix computations , 1983 .

[10]  F. R. Gantmakher The Theory of Matrices , 1984 .

[11]  Charles R. Johnson,et al.  Matrix analysis , 1985, Statistical Inference for Engineers and Data Scientists.

[12]  Thomas M. Cover,et al.  Elements of Information Theory , 2005 .

[13]  J. Craig A new, simple and exact result for calculating the probability of error for two-dimensional signal constellations , 1991, MILCOM 91 - Conference record.

[14]  J. H. Winters,et al.  Two signaling schemes for improving the error performance of frequency-division-duplex (FDD) transmission systems using transmitter antenna diversity , 1993, IEEE 43rd Vehicular Technology Conference.

[15]  J. H. Winters,et al.  The diversity gain of transmit diversity in wireless systems with Rayleigh fading , 1994, Proceedings of ICC/SUPERCOMM'94 - 1994 International Conference on Communications.

[16]  A. Robert Calderbank,et al.  Space-Time Codes for High Data Rate Wireless Communications : Performance criterion and Code Construction , 1998, IEEE Trans. Inf. Theory.

[17]  J. H. Winters The diversity gain of transmit diversity in wireless systems with Rayleigh fading , 1998 .

[18]  Siavash M. Alamouti,et al.  A simple transmit diversity technique for wireless communications , 1998, IEEE J. Sel. Areas Commun..

[19]  Mohamed-Slim Alouini,et al.  A unified approach to the performance analysis of digital communication over generalized fading channels , 1998, Proc. IEEE.

[20]  L. Tong,et al.  Multichannel blind identification: from subspace to maximum likelihood methods , 1998, Proc. IEEE.

[21]  Joseph M. Kahn,et al.  Fading correlation and its effect on the capacity of multi-element antenna systems , 1998, ICUPC '98. IEEE 1998 International Conference on Universal Personal Communications. Conference Proceedings (Cat. No.98TH8384).

[22]  A. Robert Calderbank,et al.  Space-Time block codes from orthogonal designs , 1999, IEEE Trans. Inf. Theory.

[23]  Anna Scaglione,et al.  Redundant filterbank precoders and equalizers. II. Blind channel estimation, synchronization, and direct equalization , 1999, IEEE Trans. Signal Process..

[24]  Joseph M. Kahn,et al.  Fading correlation and its effect on the capacity of multielement antenna systems , 2000, IEEE Trans. Commun..

[25]  Sergio VerdÂ,et al.  Modulation and Coding for Linear Gaussian Channels , 2000 .

[26]  Arogyaswami Paulraj,et al.  Space-time block codes: a capacity perspective , 2000, IEEE Communications Letters.

[27]  Petre Stoica,et al.  Space-Time block codes: A maximum SNR approach , 2001, IEEE Trans. Inf. Theory.

[28]  Arogyaswami Paulraj,et al.  Delay diversity code for frequency selective channels , 2001 .

[29]  Xiang-Gen Xia,et al.  Two generalized complex orthogonal space-time block codes of rates 7/11 and 3/5 for five and six transmit antennas , 2001, SPIE Optics + Photonics.

[30]  Ari Hottinen,et al.  Square-matrix embeddable space-time block codes for complex signal constellations , 2002, IEEE Trans. Inf. Theory.

[31]  Mohamed Oussama Damen,et al.  A construction of a space-time code based on number theory , 2002, IEEE Trans. Inf. Theory.

[32]  Georgios B. Giannakis,et al.  Optimal transmitter eigen-beamforming and space time block coding based on channel mean , 2002, 2002 IEEE International Conference on Acoustics, Speech, and Signal Processing.

[33]  Babak Hassibi,et al.  High-rate codes that are linear in space and time , 2002, IEEE Trans. Inf. Theory.

[34]  Robert W. Heath,et al.  Linear dispersion codes for MIMO systems based on frame theory , 2002, IEEE Trans. Signal Process..

[35]  Jean-Claude Belfiore,et al.  Quaternionic lattices for space-time coding , 2003, Proceedings 2003 IEEE Information Theory Workshop (Cat. No.03EX674).

[36]  Lizhong Zheng,et al.  Diversity and multiplexing: a fundamental tradeoff in multiple-antenna channels , 2003, IEEE Trans. Inf. Theory.

[37]  Xiang-Gen Xia,et al.  Upper bounds of rates of complex orthogonal space-time block code , 2003, IEEE Trans. Inf. Theory.

[38]  Mohamed Oussama Damen,et al.  Universal space-time coding , 2003, IEEE Trans. Inf. Theory.

[39]  Xiang-Gen Xia,et al.  On the nonexistence of rate-one generalized complex orthogonal designs , 2003, IEEE Trans. Inf. Theory.

[40]  Georgios B. Giannakis,et al.  Optimal transmitter eigen-beamforming and space-time block coding based on channel correlations , 2003, IEEE Transactions on Information Theory.

[41]  Georgios B. Giannakis,et al.  Full-diversity full-rate complex-field space-time coding , 2003, IEEE Trans. Signal Process..

[42]  Xue-Bin Liang,et al.  Orthogonal designs with maximal rates , 2003, IEEE Trans. Inf. Theory.

[43]  Xiang-Gen Xia,et al.  Two generalized complex orthogonal space-time block codes of rates 7/11 and 3/5 for 5 and 6 transmit antennas , 2003, IEEE Trans. Inf. Theory.

[44]  Rohit U. Nabar,et al.  Introduction to Space-Time Wireless Communications , 2003 .

[45]  B. Sundar Rajan,et al.  Full-diversity, high-rate space-time block codes from division algebras , 2003, IEEE Trans. Inf. Theory.

[46]  P. Dayal,et al.  An optimal two transmit antenna space-time code and its stacked extensions , 2003, The Thrity-Seventh Asilomar Conference on Signals, Systems & Computers, 2003.

[47]  Constantinos B. Papadias,et al.  Full-Rate Full-Diversity Linear Quasi-Orthogonal Space-Time Codes for Any Number of Transmit Antennas , 2004, EURASIP J. Adv. Signal Process..

[48]  Markus Rupp,et al.  Generalized Alamouti Codes for Trading Quality of Service against Data Rate in MIMO UMTS , 2004, EURASIP J. Adv. Signal Process..

[49]  Giuseppe Caire,et al.  Lattice coding and decoding achieve the optimal diversity-multiplexing tradeoff of MIMO channels , 2004, IEEE Transactions on Information Theory.

[50]  Emanuele Viterbo,et al.  The golden code: a 2 x 2 full-rate space-time code with non-vanishing determinants , 2004, International Symposium onInformation Theory, 2004. ISIT 2004. Proceedings..

[51]  J. Belfiore,et al.  Algebraic 3x3, 4x4, 6x6 Space-Time Codes with non-vanishing Determinants , 2004 .

[52]  Signal constellations for quasi-orthogonal space-time block codes with full diversity , 2004, IEEE Transactions on Information Theory.

[53]  Xiang-Gen Xia,et al.  On optimal cyclotomic lattices and diagonal-single-layer space-time block codes , 2004, International Symposium onInformation Theory, 2004. ISIT 2004. Proceedings..

[54]  X. Xia,et al.  Closed Form Designs of Complex Orthogonal Space-Time Block Codes of Rates for or Transmit Antennas , 2004 .

[55]  Jian-Kang Zhang,et al.  Information lossless full rate full diversity cyclotomic linear dispersion codes , 2004, 2004 IEEE International Conference on Acoustics, Speech, and Signal Processing.

[56]  Xiang-Gen Xia,et al.  Closed form designs of complex orthogonal space-time block codes of rates (k+1)/(2k) for 2k_1 or 2k transmit antennas , 2005, International Symposium onInformation Theory, 2004. ISIT 2004. Proceedings..

[57]  Christopher Holden,et al.  Perfect Space-Time Block Codes , 2004 .

[58]  J. Belfiore,et al.  Algebraic 3 × 3 , 4 × 4 and 6 × 6 Space-Time Codes with non-vanishing Determinants , 2004 .

[59]  J. Belfiore,et al.  The golden code: a 2×2 full-rate space-time code with nonvanishing determinants , 2004, IEEE Trans. Inf. Theory.

[60]  Kon Max Wong,et al.  Trace-orthonormal full diversity cyclotomic linear dispersion codes , 2004, International Symposium onInformation Theory, 2004. ISIT 2004. Proceedings..

[61]  Robert Schober,et al.  Optimized delay diversity for frequency-selective fading channels , 2005, IEEE Transactions on Wireless Communications.

[62]  Genyuan Wang,et al.  On optimal multilayer cyclotomic space-time code designs , 2005, IEEE Transactions on Information Theory.

[63]  Camilla Hollanti,et al.  Dense full-diversity matrix lattices for four transmit antenna MISO channel , 2005, Proceedings. International Symposium on Information Theory, 2005. ISIT 2005..

[64]  Pranav Dayal,et al.  An optimal two transmit antenna space-time code and its stacked extensions , 2005, IEEE Transactions on Information Theory.

[65]  Jian-Kang Zhang,et al.  Optimal norm form integer space-time codes for two antenna MIMO systems , 2005, Proceedings. (ICASSP '05). IEEE International Conference on Acoustics, Speech, and Signal Processing, 2005..

[66]  Xiang-Gen Xia,et al.  Closed-form designs of complex orthogonal space-time block codes of rates (k+1)/(2k) for 2k-1 or 2k transmit antennas , 2005, IEEE Transactions on Information Theory.

[67]  B. Sundar Rajan,et al.  STBC-schemes with nonvanishing determinant for certain number of transmit antennas , 2005, IEEE Transactions on Information Theory.

[68]  Chintha Tellambura,et al.  Optimal rotations for quasi-orthogonal STBC with two-dimensional constellations , 2005, GLOBECOM '05. IEEE Global Telecommunications Conference, 2005..

[69]  Jian-Kang Zhang,et al.  Linear toeplitz space time block codes , 2005, Proceedings. International Symposium on Information Theory, 2005. ISIT 2005..

[70]  P. Vijay Kumar,et al.  Explicit Space–Time Codes Achieving the Diversity–Multiplexing Gain Tradeoff , 2006, IEEE Transactions on Information Theory.

[71]  Frédérique E. Oggier,et al.  Perfect Space–Time Block Codes , 2006, IEEE Transactions on Information Theory.

[72]  Stephen P. Boyd,et al.  Convex Optimization , 2004, Algorithms and Theory of Computation Handbook.

[73]  B. S. Rajan,et al.  Multigroup-Decodable STBCs from Clifford Algebras , 2006, ITW 2006.

[74]  B. Sundar Rajan,et al.  Multigroup Decodable STBCs From Clifford Algebras , 2009, IEEE Transactions on Information Theory.