Hybrid digital and analog beamforming is a highly effective technique for implementing beamforming methods in millimeter wave (mmWave) systems. It provides a viable solution to replace the complex fully digital beamforming techniques. However, the current design of precoding and combining matrices in hybrid beamforming solely relies on the channel information, neglecting the crucial consideration of the structure of covariance matrices of the transmit signals. In this paper, we present a novel approach for the joint design of hybrid beamforming matrices at the transmitter and receiver. This approach is centered around the optimization of the covariance matrix of the transmitted signals. Our goal is to maximize the downlink sum rate capacity of the system by achieving an optimal design of the transmit covariance matrix. We tackle the non-convex nature of this problem by leveraging the dual relationship between the broadcast channel (BC) and the multiple access channel (MAC). Through extensive simulations in various scenarios, including point-to-point multi-input multi-output (MIMO), multi-user (MU) multi-input single-output (MISO), and MU-MIMO, we demonstrate the superiority of our proposed method over traditional designs. These results highlight the effectiveness and versatility of our approach in optimizing beamforming for mmWave systems.

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