Optimized Transmission with Improper Gaussian Signaling in the K-User MISO Interference Channel

TL;DR

This paper explores how improper Gaussian signaling can be optimized in a K-user MISO interference channel to enhance achievable rates, introducing a novel algorithm that leverages pseudo-covariance matrices and semidefinite relaxation techniques.

Contribution

It proposes a separate optimization algorithm for transmit covariance and pseudo-covariance matrices, establishing the optimality of rank-1 pseudo-covariance matrices for improved rate regions.

Findings

Improved achievable rates over proper Gaussian signaling.

Optimality of rank-1 pseudo-covariance matrices.

Efficient semidefinite relaxation-based solution.

Abstract

This paper studies the achievable rate region of the K-user Gaussian multiple-input single-output interference channel (MISO-IC) with the interference treated as noise, when improper or circularly asymmetric complex Gaussian signaling is applied. The transmit optimization with improper Gaussian signaling involves not only the signal covariance matrix as in the conventional proper or circularly symmetric Gaussian signaling, but also the signal pseudo-covariance matrix, which is conventionally set to zero in proper Gaussian signaling. By exploiting the separable rate expression with improper Gaussian signaling, we propose a separate transmit covariance and pseudo-covariance optimization algorithm, which is guaranteed to improve the users' achievable rates over the conventional proper Gaussian signaling. In particular, for the pseudo-covariance optimization, we establish the optimality of rank-1 pseudo-covariance matrices, given the optimal rank-1 transmit covariance matrices for achieving the Pareto boundary of the rate region. Based on this result, we are able to greatly reduce the number of variables in the pseudo-covariance optimization problem and thereby develop an efficient solution by applying the celebrated semidefinite relaxation (SDR) technique. Finally, we extend the result to the Gaussian MISO broadcast channel (MISO-BC) with improper Gaussian signaling or so-called widely linear transmit precoding.