On Capacity and Capacity per Unit Cost of Gaussian Multiple Access Channel with Peak Power Constraints

TL;DR

This paper analyzes the capacity and capacity per unit cost of Gaussian multiple access channels with peak power constraints, providing numerical optimization, analytical characterizations, and insights into energy-efficient communication strategies.

Contribution

It introduces a novel approach using Blahut-Arimoto Algorithm for capacity optimization and derives the capacity per unit cost for GMAC with peak power constraints.

Findings

Symmetric antipodal input distribution for users with higher SNR

Capacity per unit cost is independent of user rate ratio

Optimal strategies differ from average-power constraint scenarios

Abstract

This paper investigates the capacity and capacity per unit cost of Gaussian multiple access-channel (GMAC) with peak power constraints. We first devise an approach based on Blahut-Arimoto Algorithm to numerically optimize the sum rate and quantify the corresponding input distributions. The results reveal that in the case with identical peak power constraints, the user with higher SNR is to have a symmetric antipodal input distribution for all values of noise variance. Next, we analytically derive and characterize an achievable rate region for the capacity in cases with small peak power constraints, which coincides with the capacity in a certain scenario. The capacity per unit cost is of interest in low power regimes and is a target performance measure in energy efficient communications. In this work, we derive the capacity per unit cost of additive white Gaussian channel and GMAC with peak power constraints. The results in case of GMAC demonstrate that the capacity per unit cost is obtained using antipodal signaling for both users and is independent of users rate ratio. We characterize the optimized transmission strategies obtained for capacity and capacity per unit cost with peak-power constraint in detail and specifically in contrast to the settings with average-power constraints.