In this paper, we investigate a nonconvex fractional quadratically constrained quadratic problem (fractional QCQP), which has a wide application to the resource allocation optimization in wireless communication systems. Different from the state-of-the-art methods needing to solve semidefinite programmings or second-order cone programmings, we propose a fast algorithm for solving fractional QCQP by combining the successive convex approximation method and the consensus alternating direction method of multipliers, which has only simple computations and works very fast in applications with modest accuracy. We also apply the proposed fast algorithm to secure beamforming design for enhancing physical layer security in cognitive nonorthogonal multiple access (NOMA) networks, where secrecy rate optimization problems in both underlay and overly cognitive NOMA networks are typical fractional QCQPs and have not been well studied. Simulation results have shown that our proposed fast algorithm achieves almost the same performance as the state-of-the-art methods, however, the proposed fast algorithm has very low computation complexity.

中文翻译：

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分数阶 QCQP 快速算法及认知非正交多址网络中安全波束形成的应用


在本文中，我们研究了非凸分数二次约束二次问题（分数QCQP），该问题在无线通信系统中的资源分配优化中具有广泛的应用。与需要求解半定规划或二阶锥规划的最先进方法不同，我们提出了一种结合逐次凸逼近法和乘子一致交替方向法来求解分数式QCQP的快速算法，该算法具有仅进行简单的计算，并且在精度适中的应用中运行速度非常快。我们还将所提出的快速算法应用于安全波束成形设计，以增强认知非正交多址（NOMA）网络中的物理层安全性，其中底层和过度认知 NOMA 网络中的保密率优化问题是典型的分数 QCQP 问题，尚未得到充分研究。仿真结果表明，我们提出的快速算法实现了与最先进的方法几乎相同的性能，但是，所提出的快速算法具有非常低的计算复杂度。