2009/02/19 by Tobias Koch, Koch, Tobias, Amos Lapidoth +1
Computer Science · Mathematics · #FOS: Computer and information sciences #Information Theory (cs.IT) #cs.IT #math.IT
paper · pdf · doi:10.48550/arxiv.0902.3372
12 pages, submitted to the IEEE Transactions on Information Theory
arxiv created 2009/02/19 · arxiv updated 2009/12/01
The capacity of peak-power limited, single-antenna, noncoherent, flat-fading channels with memory is considered. The emphasis is on the capacity pre-log, i.e., on the limiting ratio of channel capacity to the logarithm of the signal-to-noise ratio (SNR), as the SNR tends to infinity. It is shown that, among all stationary & ergodic fading processes of a given spectral distribution function and whose law has no mass point at zero, the Gaussian process gives rise to the smallest pre-log. The assumption that the law of the fading process has no mass point at zero is essential in the sense that there exist stationary & ergodic fading processes whose law has a mass point at zero and that give rise to a smaller pre-log than the Gaussian process of equal spectral distribution function. An extension of our results to multiple-input single-output fading channels with memory is also presented.