The Noncoherent Rician Fading Channel -- Part I : Structure of the Capacity-Achieving Input

TL;DR

This paper investigates the structure of capacity-achieving inputs for Rician fading channels without channel state information, revealing discrete amplitude distributions under various constraints and analyzing phase-noise effects.

Contribution

It characterizes the optimal input amplitude distributions for Rician channels under moment and peak constraints, including phase-noise scenarios, showing they are discrete with finite mass points.

Findings

Optimal inputs are discrete with finite mass points in low-power regimes.

Discrete amplitude structure holds across the entire SNR range under peak constraints.

Capacity-achieving inputs in phase-noise models have finite discrete levels.

Abstract

Transmission of information over a discrete-time memoryless Rician fading channel is considered where neither the receiver nor the transmitter knows the fading coefficients. First the structure of the capacity-achieving input signals is investigated when the input is constrained to have limited peakedness by imposing either a fourth moment or a peak constraint. When the input is subject to second and fourth moment limitations, it is shown that the capacity-achieving input amplitude distribution is discrete with a finite number of mass points in the low-power regime. A similar discrete structure for the optimal amplitude is proven over the entire SNR range when there is only a peak power constraint. The Rician fading with phase-noise channel model, where there is phase uncertainty in the specular component, is analyzed. For this model it is shown that, with only an average power constraint, the capacity-achieving input amplitude is discrete with a finite number of levels. For the classical average power limited Rician fading channel, it is proven that the optimal input amplitude distribution has bounded support.