Capacity of The Discrete-Time Non-Coherent Memoryless Gaussian Channels at Low SNR

TL;DR

This paper precisely characterizes the capacity of discrete-time non-coherent Gaussian channels at low SNR, revealing the optimal input distribution, the capacity itself, and bounds on input parameters, enhancing understanding of non-coherent channel limits.

Contribution

It provides an exact capacity expression and optimal input distribution for low SNR non-coherent Gaussian channels, a novel analytical advancement.

Findings

Derived the exact capacity at low SNR.

Characterized the optimal input distribution.

Provided bounds on the input distribution's support.

Abstract

We address the capacity of a discrete-time memoryless Gaussian channel, where the channel state information (CSI) is neither available at the transmitter nor at the receiver. The optimal capacity-achieving input distribution at low signal-to-noise ratio (SNR) is precisely characterized, and the exact capacity of a non-coherent channel is derived. The derived relations allow to better understanding the capacity of non-coherent channels at low SNR. Then, we compute the non-coherence penalty and give a more precise characterization of the sub-linear term in SNR. Finally, in order to get more insight on how the optimal input varies with SNR, upper and lower bounds on the non-zero mass point location of the capacity-achieving input are given.