On the Mutual Information and Low-SNR Capacity of Memoryless Noncoherent Rayleigh-Fading Channels

The memoryless noncoherent single-input-single-output (SISO) Rayleigh-fading channel is considered. Closed-form expressions are derived for the mutual information between the output and the input of this channel when the input magnitude distribution is discrete and is restricted to having two mass points. It is subsequently shown how these expressions can be used to obtain closed-form expressions for the capacity of this channel for signal to noise ratio (SNR) values of up to approximately 0 dB, and a tight capacity lower bound for SNR values between 0 dB and 10 dB. The expressions for the channel capacity and its lower bound are given as functions of a parameter which can be obtained via numerical root-finding algorithms.

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

[2]  H. Vincent Poor,et al.  Capacity of multiple-antenna systems with both receiver and transmitter channel state information , 2003, IEEE Trans. Inf. Theory.

[3]  Joseph Lipka,et al.  A Table of Integrals , 2010 .

[4]  Amos Lapidoth,et al.  Capacity bounds via duality with applications to multiple-antenna systems on flat-fading channels , 2003, IEEE Trans. Inf. Theory.

[5]  A. A. Inayat‐Hussain.  New properties of hypergeometric series derivable from Feynman integrals. I. Transformation and reduction formulae , 1987 .

[6]  C. W. Clenshaw,et al.  The special functions and their approximations , 1972 .

[7]  Ravi P. Agarwal.  Generalized hypergeometric series , 1963 .

[8]  G. Taricco,et al.  Capacity of fading channel with no side information , 1997 .

[9]  Ibrahim C. Abou-Faycal,et al.  The capacity of discrete-time memoryless Rayleigh-fading channels , 2001, IEEE Trans. Inf. Theory.

[10]  Capacity-Achieving Input Phase Distributions for Noncoherent Rayleigh-Fading Channels with Memory , 2006, 2006 IEEE 7th Workshop on Signal Processing Advances in Wireless Communications.

[11]  G. Pólya,et al.  Functions of One Complex Variable , 1998 .

[12]  Jianqiu Zhang.  On the bounds of the non-coherent capacity of Gauss-Markov fading channels , 2005, Proceedings. (ICASSP '05). IEEE International Conference on Acoustics, Speech, and Signal Processing, 2005..

[13]  J. Conway,et al.  Functions of a Complex Variable , 1964 .

[14]  A. A. Inayat‐Hussain,et al.  New properties of hypergeometric series derivable from Feynman integrals II. A generalisation of the H function , 1987 .

[15]  Robert C. Forrey,et al.  Computing the Hypergeometric Function , 1997 .

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

[17]  Ranjan K. Mallik,et al.  Channel capacity of adaptive transmission with maximal ratio combining in correlated Rayleigh fading , 2004, IEEE Transactions on Wireless Communications.

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

[19]  Nicolas Gama,et al.  Rankin's Constant and Blockwise Lattice Reduction , 2006, CRYPTO.

[20]  Ninoslav Marina.  Rayleigh Fading Multiple Access Channel Without Channel State Information , 2004, ICT.

[21]  Lizhong Zheng,et al.  Communication on the Grassmann manifold: A geometric approach to the noncoherent multiple-antenna channel , 2002, IEEE Trans. Inf. Theory.

[22]  Upamanyu Madhow,et al.  On fixed input distributions for noncoherent communication over high-SNR Rayleigh-fading channels , 2004, IEEE Transactions on Information Theory.