Low SNR Capacity of Fading Channels with Peak and Average Power Constraints

Flat-fading channels that are correlated in time are considered under peak and average power constraints. For discrete-time channels, a new upper bound on the capacity per unit time is derived. A low SNR analysis of a full-scattering vector channel is used to derive a complimentary lower bound. Together, these bounds allow us to identify the exact scaling of channel capacity for a fixed peak to average ratio, as the average power converges to zero. The upper bound is also asymptotically tight as the average power converges to zero for a fixed peak power. For a continuous time infinite bandwidth channel, Viterbi identified the capacity for M-FSK modulation. Recently, Zhang and Laneman showed that the capacity can be achieved with non-bursty signaling (QPSK). An additional contribution of this paper is to obtain similar results under peak and average power constraints

[1]  Bruce E. Hajek,et al.  Capacity per unit energy of fading channels with a peak constraint , 2003, IEEE Transactions on Information Theory.

[2]  J. Nicholas Laneman,et al.  How Good is Phase-Shift Keying for Peak-Limited Fading Channels in the Low-SNR Regime ? , 2005 .

[3]  Shlomo Shamai,et al.  Mutual information and minimum mean-square error in Gaussian channels , 2004, IEEE Transactions on Information Theory.

[4]  Amos Lapidoth,et al.  The fading number and degrees of freedom in non-coherent MIMO fading channels: a peace pipe , 2005, Proceedings. International Symposium on Information Theory, 2005. ISIT 2005..

[5]  Sergio Verdú,et al.  On channel capacity per unit cost , 1990, IEEE Trans. Inf. Theory.

[6]  Bruce E. Hajek,et al.  Broad-band fading channels: Signal burstiness and capacity , 2002, IEEE Trans. Inf. Theory.

[7]  Muriel Médard,et al.  Bandwidth scaling for fading multipath channels , 2002, IEEE Trans. Inf. Theory.

[8]  J. Nicholas Laneman,et al.  How Good is Phase-Shift Keying for Peak-Limited Rayleigh Fading Channels in the Low-SNR Regime? , 2005, ArXiv.

[9]  Amos Lapidoth,et al.  On the asymptotic capacity of stationary Gaussian fading channels , 2005, IEEE Transactions on Information Theory.

[10]  G. Maruyama.  THE HARMONIC ANALYSIS OF STATIONARY STOCHASTIC PROCESSES , 1949 .

[11]  Bruce E. Hajek,et al.  Capacity and reliability function for small peak signal constraints , 2002, IEEE Trans. Inf. Theory.

[12]  A. Viterbi.  Performance of an M -ary orthogonal communication system using stationary stochastic signals , 1967, IEEE Trans. Inf. Theory.

[13]  Bruce E. Hajek,et al.  Capacity bounds for noncoherent fading channels with a peak constraint , 2005, Proceedings. International Symposium on Information Theory, 2005. ISIT 2005..

[14]  Teng Li,et al.  Approaching capacity on correlated fading channels with unknown state , 2005, Proceedings. International Symposium on Information Theory, 2005. ISIT 2005..