On Multipath Fading Channels at High SNR

TL;DR

This paper analyzes the capacity of noncoherent multipath fading channels at high SNR, revealing conditions under which capacity is bounded or unbounded, and characterizing the growth rate when the number of paths is finite.

Contribution

It provides a detailed characterization of the capacity behavior in multipath fading channels at high SNR, including bounds and growth rates based on path gain decay.

Findings

Capacity is bounded if path gains decay exponentially or slower.

Capacity is unbounded if path gains decay faster than exponentially.

When the number of paths is finite, capacity grows double-logarithmically with SNR.

Abstract

This work studies the capacity of multipath fading channels. A noncoherent channel model is considered, where neither the transmitter nor the receiver is cognizant of the realization of the path gains, but both are cognizant of their statistics. It is shown that if the delay spread is large in the sense that the variances of the path gains decay exponentially or slower, then capacity is bounded in the signal-to-noise ratio (SNR). For such channels, capacity does not tend to infinity as the SNR tends to infinity. In contrast, if the variances of the path gains decay faster than exponentially, then capacity is unbounded in the SNR. It is further demonstrated that if the number of paths is finite, then at high SNR capacity grows double-logarithmically with the SNR, and the capacity pre-loglog, defined as the limiting ratio of capacity to log(log(SNR)) as SNR tends to infinity, is 1 irrespective of the number of paths.