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In this paper, we investigate secrecy-energy efficient hybrid beamforming (BF) schemes for a satellite-terrestrial integrated network, wherein a multibeam satellite system shares the millimeter wave spectrum with a cellular system. Under the assumption of imperfect angles of departure for the wiretap channels, the hybrid beamformer at the base station and digital beamformers at the satellite are jointly designed to maximize the achievable secrecy-energy efficiency, while satisfying signal-to-interference-plus-noise ratio constraints of both the earth stations (ESs) and cellular users. Since the formulated optimization problem is nonconvex and mathematically intractable, we propose two robust BF schemes to obtain approximate solutions with low complexity. Specifically, for the case of a single ES, we integrate the Charnes-Cooper approach with an iterative search algorithm to convert the original nonconvex problem into a solvable one and obtain the BF weight vectors. In the case of multiple ESs, by exploiting the sequential convex approximation method, we convert the original problem into a linear one with multiple matrix inequalities and second-order cone constraints, for which we obtain a solution with satisfactory performance. The effectiveness and superiority of the proposed robust BF design schemes are validated via simulations using realistic satellite and terrestrial downlink channel models.
Lin et al. (Mon,) studied this question.