Two Stage Beamforming in Massive MIMO: A Combinatorial Multi-Armed Bandit Based Approach

In frequency division duplex (FDD) massive multi-input multi-output (MIMO), the two-stage beamforming (TSB) using channel covariance matrices (CCM) can significantly reduce the downlink training length (DTL) and channel feedback. However, the overhead to estimate the CCM is large. In this paper, a combinatorial multi-armed bandit (CMAB) based TSB scheme is proposed without requirement of CMM. Particularly, the problem of the pre-beamforming matrix design is transformed into a CMAB problem. We consider the pre-beamforming matrix design in each slot as the arm selection in the CMAB, and convert the problem of the arm selection into a 0-1 integer linear programming problem, which can be solved by the branch-and-bound method. During the training process, the maximum likelihood method is used to detect the power of angle spectrum, and the angle range of each user is determined adaptively. We prove that the regret grows logarithmically with time, such that the proposed scheme converges towards the optimal action. Finally, simulation results demonstrate that the proposed scheme can significantly improve the spectral efficiency.