Millimeter wave signals have a higher order of magnitude of path loss than the microwave signals used in most wireless systems today.Therefore,millimeter-wave systems must be combined with large antenna arrays to counteract path losses with beamforming gains.Traditional all digital beamforming methods require one RF chain per antenna unit,which is difficult to be applied to Massive MIMO systems due to the high cost and high power consumption of RF chain components at high frequencies.To address this challenge of hardware limitations,a hybrid beamforming architecture is considered in which the overall beamforming consists of a low-dimensional digital beamforming and a radio frequency beamforming implemented using an analog phase shifter.In this paper,the hybrid beamforming algorithm is analyzed and studied for point-to-point single-user narrowband millimeter-wave Massive MIMO scenario.Based on the existing manifold optimization algorithms,Wolfe criterion is used to replace Armijo-Goldstein criterion to perform line search in the iterative search process of conjugate gradient descending method,aiming at maximizing spectral efficiency.The problem of extreme point omission in the existing manifold optimization algorithm is effectively solved,and the bit error rate performance is improved and the complexity is reduced.The simulation results show that the performance of the improved manifold optimization algorithm is improved in bit error rate and spectral efficiency,which is closer to the performance of the all-digital beamforming algorithm.The hybrid beamforming of narrowband system can also be extended to the wideband system which is more in line with the actual situation of millimeter-wave.The orthogonal frequency division multiplexing(OFDM)system is studied in this paper.Aiming at the high complexity of the existing alternate minimization method in the operation of gradient descent method,a low complexity alternative algorithm,hybrid beamforming algorithm based on matrix orthogonality,was proposed.By using the orthogonal constraints of the simulated beamforming matrix,the problem of minimizing the optimization objective function is transformed into the problem of solving the minimum value of the lower bound of the optimization objective,and the upper bound is used as the replacement of the objective function.Simulation results show that the improved alternate minimization method can greatly reduce the complexity with almost no performance reduction. |