Communication over non-Gaussian channels - Part I: Mutual information and optimum signal detection

Abstract

Gaussian distribution as a source of additive noise is a wellknown modeling assumption, which lead to important and insightful results on the channel capacity, detection reliability, and estimation accuracy. It is also well-recognized that in many practical settings the Gaussian distribution may not be adequate to model the underlying noise phenomenon, and various non-Gaussian noise models are employed for the design and performance analysis of communication systems. However, existing non-Gaussian noise models can be cumbersome to use as it is difficult to prescribe the model parameters and estimate them prior to signal detection, and hard to perform analysis and optimization of communication systems with realistic channel estimation. With the above challenges in mind, in the first part of our work, we introduce a model for the additive non-Gaussian channel (ANGC) with a focus on simplicity, robustness, and ease of analytical tractability. Specifically, we consider a compound noise distribution that is composed of a conditionally additive white Gaussian noise (AWGN) and a Gamma distributed noise variance. This model reduces to the traditional AWGN model when the shape parameter of the Gamma distribution tends to infinity, and the detection and estimation performances on ANGC can easily be reduced to their counterparts on the AWGN channel. With this model, we first present the average mutual information when multiple antennas are employed at the transmitter and the receiver. Next, we derive closed-form expressions for the average probability of error for binary and higher-order modulations when the receiver has perfect channel state information. In the second part of our work, we consider noise variance estimation, pilot-assisted channel estimation (PACE), signal detection with PACE, and coded sequence detection with a mismatched decoding metric.