The phase-only null beamforming synthesis via manifold optimization

The phase-only beamforming synthesis is widely applied in millimeter wave communication, radar and sonar. Due to the CMC, the problem is non-convex. The most current methods solve the problem by designing the phase, which either degrades the performance or needs huge complexity. To address this issue, a low-complexity Riemannian Manifold Optimization based Conjugate Gradient (RMOCG) method is proposed. First, the original problem is transformed into an unconstrained prob-lem on a complex circle manifold. Then, a RMOCG algorithm is derived, by deriving the gradient descent direction and the step size for ensuring the cost function non-increasing. Comparing with the existing methods, the proposed method has the following advantages: 1) the null depth is respectively 8 dB deeper than [6] and 3 dB deeper than [12]. 2) The computational cost is 2 magnitude lower than [6] and 1 magnitude lower than [12].