On Multipath Fading Channels at High SNR

TL;DR

This paper analyzes the capacity of discrete-time multipath fading channels at high SNR, revealing that the capacity pre-loglog is 1 regardless of the number of paths, under a noncoherent model.

Contribution

It establishes that the capacity pre-loglog remains 1 for finite-path multipath channels at high SNR, regardless of the number of paths, in a noncoherent setting.

Findings

Capacity pre-loglog is 1 for all finite paths L.

High SNR capacity growth rate is characterized by the pre-loglog.

Results hold for noncoherent channels with known statistics.

Abstract

This paper studies the capacity of discrete-time multipath fading channels. It is assumed that the number of paths is finite, i.e., that the channel output is influenced by the present and by the L previous channel inputs. A noncoherent channel model is considered where neither transmitter nor receiver are cognizant of the fading's realization, but both are aware of its statistic. The focus is on capacity at high signal-to-noise ratios (SNR). In particular, the capacity pre-loglog - defined as the limiting ratio of the capacity to loglog SNR as SNR tends to infinity - is studied. It is shown that, irrespective of the number paths L, the capacity pre-loglog is 1.