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Reconfigurable intelligent surface (RIS) is considered to be anenergy-efficient approach to reshape the wireless environment for improvedthroughput. Its passive feature greatly reduces the energy consumption, whichmakes RIS a promising technique for enabling the future smart city. Existingbeamforming designs for RIS mainly focus on optimizing the spectral efficiencyfor single carrier systems. To avoid the complicated bit allocation ondifferent spatial domain subchannels in MIMO systems, in this paper, we proposea geometric mean decomposition-based beamforming for RIS-assisted millimeterwave (mmWave) hybrid MIMO systems so that multiple parallel data streams in thespatial domain can be considered to have the same channel gain. Specifically,by exploiting the common angular-domain sparsity of mmWave massive MIMOchannels over different subcarriers, a simultaneous orthogonal match pursuitalgorithm is utilized to obtain the optimal multiple beams from an oversampling2D-DFT codebook. Moreover, by only leveraging the angle of arrival and angle ofdeparture associated with the line of sight (LoS) channels, we further designthe phase shifters for RIS by maximizing the array gain for LoS channel.Simulation results show that the proposed scheme can achieve better BERperformance than conventional approaches. Our work is an initial attempt todiscuss the broadband hybrid beamforming for RIS-assisted mmWave hybrid MIMOsystems.

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