On communication over unknown sparse frequency-selective block-fading channels

The problem of reliable communication over unknown frequency-selective block-fading channels with sparse impulse responses is considered. In particular, discrete-time impulse responses with block-fading interval N, length L < N, and exactly S ≤ L non-zero coefficients are considered, where both the locations and values of non-zero coefficients change independently across blocks and are apriori unknown. Assuming that the non-zero coefficients and noise are both Gaussian, it is first shown that the ergodic noncoherent channel capacity has pre-log factor 1 − S over N for any L. Then, a pilot-aided transmission (PAT) scheme and noncoherent decoder are proposed which are capable of communicating with arbitrarily small error probability using only S pilots per fading block. Furthermore, the achievable rate of this scheme is shown to have the optimal pre-log factor, i.e., 1 − S over N. Finally, a lower complexity PAT scheme is proposed, whose e-achievable rate has the pre-log factor 1 − S+1 over N for any e > 0.1

[1]  G. Deane,et al.  Surface wave focusing and acoustic communications in the surf zone , 2004 .

[2]  R. Gallager Information Theory and Reliable Communication , 1968 .

[3]  P. Stevenhagen,et al.  Chebotarëv and his density theorem , 1996 .

[4]  Andreas F. Molisch,et al.  Ultrawideband propagation channels-theory, measurement, and modeling , 2005, IEEE Transactions on Vehicular Technology.

[5]  Philip Schniter Joint estimation and decoding for sparse channels via relaxed belief propagation , 2010, 2010 Conference Record of the Forty Fourth Asilomar Conference on Signals, Systems and Computers.

[6]  Yingbin Liang,et al.  Capacity of noncoherent time-selective Rayleigh-fading channels , 2004, IEEE Transactions on Information Theory.

[7]  David Tse,et al.  Fundamentals of Wireless Communication , 2005 .

[8]  Moe Z. Win,et al.  Evaluation of an ultra-wide-band propagation channel , 2002 .

[9]  S. Wicker Error Control Systems for Digital Communication and Storage , 1994 .

[10]  Philip Schniter,et al.  On the Spectral Efficiency of Noncoherent Doubly Selective Block-Fading Channels , 2010, IEEE Transactions on Information Theory.

[11]  Thomas Kailath,et al.  On the capacity of frequency- selective channels in training-based transmission schemes , 2004, IEEE Transactions on Signal Processing.

[12]  Shlomo Shamai,et al.  Gaussian codes and weighted nearest neighbor decoding in fading multiple-antenna channels , 2004, IEEE Transactions on Information Theory.

[13]  Philip Schniter,et al.  Belief-propagation-based joint channel estimation and decoding for spectrally efficient communication over unknown sparse channels , 2010, Phys. Commun..

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

[15]  J. Tropp On the conditioning of random subdictionaries , 2008 .

[16]  Robert D. Nowak,et al.  Compressed Channel Sensing: A New Approach to Estimating Sparse Multipath Channels , 2010, Proceedings of the IEEE.

[17]  William G. Cowley,et al.  Blind maximum likelihood sequence detection over fast fading channels , 1996, 1996 8th European Signal Processing Conference (EUSIPCO 1996).

[18]  T. Tao An uncertainty principle for cyclic groups of prime order , 2003, math/0308286.

[19]  Emmanuel J. Candès,et al.  Robust uncertainty principles: exact signal reconstruction from highly incomplete frequency information , 2004, IEEE Transactions on Information Theory.

[20]  Philip Schniter,et al.  A Message-Passing Receiver for BICM-OFDM Over Unknown Clustered-Sparse Channels , 2011, IEEE Journal of Selected Topics in Signal Processing.

[21]  Giuseppe Caire,et al.  The MIMO ARQ Channel: Diversity-Multiplexing-Delay Tradeoff , 2006, IEEE Trans. Inf. Theory.