On the Sensitivity of Noncoherent Capacity to the Channel Model

TL;DR

This paper investigates how the noncoherent capacity of certain fading channels is affected by the channel model details, showing that for practical SNRs, capacity remains close to AWGN capacity under specific channel assumptions.

Contribution

It demonstrates that for underspread WSSUS Rayleigh-fading channels, noncoherent capacity is nearly unaffected by the spectral support of the scattering function at practical SNRs.

Findings

Noncoherent capacity remains close to AWGN capacity for practical SNRs.

Capacity sensitivity depends on the spectral support of the scattering function.

Provides a pulse-design criterion for OFDM systems.

Abstract

The noncoherent capacity of stationary discrete-time fading channels is known to be very sensitive to the fine details of the channel model. More specifically, the measure of the set of harmonics where the power spectral density of the fading process is nonzero determines if capacity grows logarithmically in SNR or slower than logarithmically. An engineering-relevant problem is to characterize the SNR value at which this sensitivity starts to matter. In this paper, we consider the general class of continuous-time Rayleigh-fading channels that satisfy the wide-sense stationary uncorrelated-scattering (WSSUS) assumption and are, in addition, underspread. For this class of channels, we show that the noncoherent capacity is close to the AWGN capacity for all SNR values of practical interest, independently of whether the scattering function is compactly supported or not. As a byproduct of our analysis, we obtain an information-theoretic pulse-design criterion for orthogonal frequency-division multiplexing systems.