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.

中文翻译：

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星地综合网络的保密-能量高效混合波束成形

在本文中，我们研究了卫星-地面集成网络的保密-节能混合波束成形 (BF) 方案，其中多波束卫星系统与蜂窝系统共享毫米波频谱。在窃听信道不完美偏离角的假设下，基站的混合波束成形器和卫星的数字波束成形器联合设计，以最大限度地提高可实现的保密能量效率，同时满足信干噪比地球站 (ES) 和蜂窝用户的约束。由于公式化的优化问题是非凸的并且在数学上难以处理，我们提出了两种鲁棒的 BF 方案来获得低复杂度的近似解。具体来说，对于单个 ES 的情况，我们将 Charnes-Cooper 方法与迭代搜索算法相结合，将原始非凸问题转换为可解问题并获得 BF 权重向量。在多个ES的情况下，利用序列凸逼近方法，将原问题转化为具有多个矩阵不等式和二阶锥约束的线性问题，得到了性能令人满意的解。所提出的稳健 BF 设计方案的有效性和优越性通过使用现实卫星和地面下行链路信道模型的模拟得到验证。我们将原始问题转换为具有多个矩阵不等式和二阶锥约束的线性问题，为此我们获得了性能令人满意的解决方案。所提出的稳健 BF 设计方案的有效性和优越性通过使用现实卫星和地面下行链路信道模型的模拟得到验证。我们将原始问题转换为具有多个矩阵不等式和二阶锥约束的线性问题，为此我们获得了性能令人满意的解决方案。所提出的稳健 BF 设计方案的有效性和优越性通过使用现实卫星和地面下行链路信道模型的模拟得到验证。