GMD-Based Hybrid Beamforming for Large Reconfigurable Intelligent Surface Assisted Millimeter-Wave Massive MIMO

Reconfigurable intelligent surface (RIS) is considered to be an energy-efficient approach to reshape the wireless environment for improved throughput. Its passive feature greatly reduces the energy consumption, which makes RIS a promising technique for enabling the future smart city. Existing beamforming designs for RIS mainly focus on optimizing the spectral efficiency for single carrier systems. Meanwhile, complicated bit/power allocation on different spatial domain subchannels needs to be designed for better bit error rate (BER) performance in conventional singular value decomposition-based beamforming. To avoid this, in this paper, we propose a geometric mean decomposition-based beamforming for RIS-assisted millimeter wave (mmWave) hybrid MIMO systems. In this way, multiple parallel data streams in the spatial domain can be considered to have the same channel gain, so that the better BER can be achieved without sophisticated bit/power allocation. Moreover, by exploiting the common angular-domain sparsity of mmWave massive MIMO channels over different subcarriers, a simultaneous orthogonal matching pursuit algorithm is utilized to obtain the optimal multiple beams from an oversampling 2D-DFT codebook. Besides, by only leveraging the angle of arrival and angle of departure associated with the line of sight (LoS) channels, we further design the phase shifters for RIS by maximizing the array gain for LoS channel. Simulation results show that the proposed scheme can achieve better BER performance than conventional approaches. Our work is an initial attempt to discuss the broadband beamforming for RIS-assisted mmWave massive MIMO with the hybrid architecture.