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

This letter studies a robust design problem for far-field line-of-sight (LOS) propagation 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 propagation channel, as the dominant source of uncertainty lies in the phase. We consider a multiple-input single-output multicast scenario, in which our goal is to design a beamformer that minimizes the transmit power while satisfying probabilistic signal-to-noise ratio constraints. In particular, the probabilistic constraints give rise to a new computational challenge, as they involve random trigonometric forms. In this study, 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. It follows that an approximately optimal beamformer can be obtained using the standard semidefinite relaxation technique. Such a design approach is applicable to both independent and correlated phase errors. In the simulations, we first show that if a nonrobust 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.