Asymptotic error probability analysis of quadratic receivers in Rayleigh-fading channels with applications to a unified analysis of coherent and noncoherent space-Time receivers

A general, asymptotic (high signal-to-noise (SNR)) error analysis is introduced for quadratic receivers in frequency-flat and multipath Rayleigh-fading channels with multiple transmit and receive antennas. Asymptotically tight expressions for the pairwise error probabilities are obtained for coherent, noncoherent, and differentially coherent space-time receivers. Not only is our unified analysis applicable to more general modulation schemes and/or channel models than previously considered, but it also reveals a hitherto unrecognized eigenvalue structure that is common to all of these problems. In addition to providing an easy recipe for computing the asymptotic pairwise error rates, we make some conclusions regarding criteria for the design of signal constellations and codes such as (a) the same design criteria apply for both correlated and independent and identically distributed (i.i.d.) fading processes and (b) for noncoherent communications, unitary signals are optimal in the sense that they minimize the asymptotic union bound.

[1]  Matthias Brehler,et al.  Signal Constellations for Noncoherent Space-Time Communications , 1910 .

[2]  R. Chang.  Synthesis of band-limited orthogonal signals for multichannel data transmission , 1966 .

[3]  W. C. Jakes,et al.  Microwave Mobile Communications , 1974 .

[4]  J.E. Mazo,et al.  Digital communications , 1985, Proceedings of the IEEE.

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

[6]  Michael J. Barrett,et al.  Error Probablity for Optimal and Suboptimal Quadratic Receivers in Rapid Rayleigh Fading Channels , 1987, IEEE J. Sel. Areas Commun..

[7]  Charles R. Johnson,et al.  Topics in Matrix Analysis , 1991 .

[8]  James K. Cavers,et al.  Analysis of the error performance of trellis-coded modulations in Rayleigh-fading channels , 1992, IEEE Trans. Commun..

[9]  Carl W. Helstrom,et al.  Elements of signal detection and estimation , 1994 .

[10]  M. Schwartz,et al.  Communication Systems and Techniques , 1996, IEEE Communications Magazine.

[11]  Mahesh K. Varanasi.  Parallel group detection for synchronous CDMA communication over frequency-selective Rayleigh fading channels , 1996, IEEE Trans. Inf. Theory.

[12]  Gerard J. Foschini,et al.  Layered space-time architecture for wireless communication in a fading environment when using multi-element antennas , 1996, Bell Labs Technical Journal.

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

[14]  Giuseppe Caire,et al.  Computing error probabilities over fading channels: A unified approach , 1998, Eur. Trans. Telecommun..

[15]  M. J. Gans,et al.  On Limits of Wireless Communications in a Fading Environment when Using Multiple Antennas , 1998, Wirel. Pers. Commun..

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

[17]  M. Varanasi,et al.  A Systematic Approach to Noncoherent Detection for DPSK Modulation in Multiuser Correlated Diversity Rayleigh Fading Channels , 1998 .

[18]  Thomas L. Marzetta,et al.  Capacity of a Mobile Multiple-Antenna Communication Link in Rayleigh Flat Fading , 1999, IEEE Trans. Inf. Theory.

[19]  Mahesh K. Varanasi,et al.  A systematic approach to the design and analysis of optimum DPSK receivers for generalized diversity communications over Rayleigh fading channels , 1999, IEEE Trans. Commun..

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

[21]  Michael P. Fitz,et al.  Signal design for transmitter diversity wireless communication systems over Rayleigh fading channels , 1999, IEEE Trans. Commun..

[22]  Emre Telatar,et al.  Capacity of Multi-antenna Gaussian Channels , 1999, Eur. Trans. Telecommun..

[23]  Michael P. Fitz,et al.  A new view of performance analysis techniques in correlated Rayleigh fading , 1999, WCNC. 1999 IEEE Wireless Communications and Networking Conference (Cat. No.99TH8466).

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

[25]  Brian L. Hughes.  Differential Space-Time modulation , 2000, IEEE Trans. Inf. Theory.

[26]  Bertrand M. Hochwald,et al.  Differential unitary space-time modulation , 2000, IEEE Trans. Commun..

[27]  B. Hughes.  Extensions to the theory of differential space-time modulation , 2000, 2000 IEEE International Symposium on Information Theory (Cat. No.00CH37060).

[28]  Thomas L. Marzetta,et al.  Unitary space-time modulation for multiple-antenna communications in Rayleigh flat fading , 2000, IEEE Trans. Inf. Theory.

[29]  Lizhong Zheng,et al.  Packing Spheres in the Grassmann Manifold: A Geometric Approach to the Non-coherent Multi-Antenna Ch , 2000 .

[30]  Hamid Jafarkhani,et al.  A differential detection scheme for transmit diversity , 2000, IEEE Journal on Selected Areas in Communications.

[31]  Hesham El Gamal,et al.  On the theory of space-time codes for PSK modulation , 2000, IEEE Trans. Inf. Theory.

[32]  Gerhard Bauch,et al.  Turbo processing in transmit antenna diversity systems , 2001, Ann. des Télécommunications.

[33]  Hamid Jafarkhani,et al.  Multiple transmit antenna differential detection from generalized orthogonal designs , 2001, IEEE Trans. Inf. Theory.

[34]  Mahesh K. Varanasi,et al.  Noncoherent multiuser detection for nonlinear modulation over the Rayleigh-fading channel , 2001, IEEE Trans. Inf. Theory.

[35]  Babak Hassibi,et al.  Representation theory for high-rate multiple-antenna code design , 2001, IEEE Trans. Inf. Theory.

[36]  Matthias Brehler,et al.  Signal design and convolutional coding for noncoherent space-time communication on the block-Rayleigh-fading channel , 2002, IEEE Trans. Inf. Theory.

[37]  Brian L. Hughes,et al.  Optimal space-time constellations from groups , 2003, IEEE Trans. Inf. Theory.

[38]  Matthias Brehler,et al.  Optimum multiuser noncoherent DPSK detection in generalized diversity Rayleigh-fading channels , 2003, IEEE Trans. Inf. Theory.