Gaussian Fading Is the Worst Fading

Details Gaussian Fading Is the Worst Fading Gaussian Fading Is the Worst Fading

2009-02-19

arxiv.org/abs/0902.3372v1

Computer Science

Information Theory

12 pages, submitted to the IEEE Transactions on Information Theory

Scientific paper

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.

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