Massive MIMO secure beamforming design via manifold optimization combined with momentum

Abstract

Secure beamforming with constant modulus has been regarded as a promising solution in enhancing the physical-layer security by intelligently designing the antenna phase of massive multiple-input multiple-output (MIMO) devices. The resulting problem is non-convex and NP-hard due to the constant modulus constraint (CMC). Existing methods mainly solve the problem by relaxing the constraints or the objective function, which inevitably introduces the relaxation error. We notice that the complex circle manifold (CCM), where complex numbers maintain a constant modulus, naturally satisfies the CMC. Further, considering the iteration points as high-dimensional particle points, the optimization process on the CCM can be regarded as the motion of the particle on the high-dimensional plane formed by the manifold. Based on this feature, we propose the manifold optimization method combining momentum (MOCM). Concretely, the original problem is first transformed into an unconstrained problem on the complex circle manifold. Then, the descent direction is derived to solve the problem by incorporating momentum into gradient information, which speeds up the convergence process. Simulation results show that the proposed method is 1 bps/Hz higher than existing works.