A Robust Design for MISO Physical-Layer Multicasting over Line-of-Sight Channels

TL;DR

This paper presents a robust beamforming design for MISO multicast systems over LOS channels with phase errors, using a Taylor expansion and Bernstein inequality to minimize power while satisfying probabilistic SNR constraints.

Contribution

It introduces a new robust design method that accounts for phase errors in LOS channels, improving power efficiency over existing Gaussian approximation approaches.

Findings

Non-robust design may lead to system collapse under phase errors.

Proposed method requires lower power than Gaussian approximation-based robust designs.

Approach effectively handles probabilistic SNR constraints with phase uncertainties.

Abstract

This paper studies a robust design problem for far-field line-of-sight (LOS) channels where phase errors are present. Compared with the commonly used additive error model, the phase error model is more suitable for capturing the uncertainty in an LOS channel, as the dominant source of uncertainty lies in the phase. We consider a multiple-input single-output (MISO) multicast scenario, in which our goal is to design a beamformer that minimizes the transmit power while satisfying probabilistic signal-to-noise ratio (SNR) constraints. The probabilistic constraints give rise to a new computational challenge, as they involve random trigonometric forms. In this work, we propose to first approximate the random trigonometric form by its second-order Taylor expansion and then tackle the resulting random quadratic form using a Bernstein-type inequality. The advantage of such an approach is that an approximately optimal beamformer can be obtained using the standard semidefinite relaxation technique. In the simulations, we first show that if a non-robust design (i.e., one that does not take phase errors into account) is used, then the whole system may collapse. We then show that our proposed method is less conservative than the existing robust design based on Gaussian approximation and thus requires a lower power budget.