放大转发双向中继系统中降低总功率的波束成形设计

Total Power Minimizing Beamforming Design for Amplify-and-Forward Two-Way Relaying System

本文研究了多天线放大转发双向中继系统中在满足源节点信噪比要求条件下最小化系统总功率的波束成形设计问题。该问题是非凸优化问题,为了有效求解该问题,采用分层优化方法将原问题分解成发送波束成形向量优化、接收波束成形向量优化和中继波束成形矩阵优化三类子问题。发送/接收波束成形向量通过求解Rayleigh商最小化问题来获得。中继波束成形矩阵优化问题通过半正定松弛方法转化成半正定优化问题来求解。在求解这三类优化问题的基础上,提出了一种迭代波束成形算法,并采用单调有界序列定理证明了所提算法的收敛性。计算机仿真表明:所提算法经过若干次迭代即可收敛到稳定点;相比于已有算法,本文算法能显著降低系统总功率。

This paper studied the beamforming design in muhi-antenna amplify-and-forward two-way relaying system. The beamforming design was formulated as an optimization problem with the aim to minimize the total transmitting power, subject to SNR constraints at the two source nodes. Since the primal problem was nonconex, it was decomposed into three types of subproblems, namely transmit beamforming, receive beamforming and relay beamforming. The transmit/ receive beamforming vectors could be obtained via solving the Rayleigh quotient minimization problem. The relay beamforming matrix was obtained by solving the semidefinite programming problem that was formulated by using the semidefinite relaxation method. After solving the above three types of subproblems, an iterative algorithm was pro- posed to solve the primal beamforming design problem. The convergence of the proposed algorithm was proven by using the monotonic boundary sequence theorem. The computer simulation results show that the proposed algorithm conver- ges to the stable point in a reasonable number of iterations and reduces a great amount of power consumption compared to existing algorithm.