Channel Customization for Joint Tx-RISs-Rx Design in Hybrid mmWave Systems

In strong line-of-sight millimeter-wave (mmWave) wireless systems, the rank-deficient channel severely hampers spatial multiplexing. To address this inherent deficiency, multiple reconfigurable-intelligent-surfaces (RISs) are introduced in this study to customize the wireless channel. Utilizing the RIS to reshape electromagnetic waves, we theoretically show that a favorable channel with an arbitrary tunable rank and a minimized truncated condition number can be established by elaborately designing the placement and reflection matrix of RISs. Different from existing works on multi-RISs, the number of elements needed for each RIS to combat the path loss and the limited phase control is also considered. On the basis of the proposed channel customization, a joint transmitter-RISs-receiver (Tx-RISs-Rx) design under a hybrid mmWave system is investigated to maximize the spectral efficiency. Using the proposed scheme, the optimal singular value decomposition-based hybrid beamforming at the Tx and Rx can be obtained without matrix decomposition for the digital and analog beamforming. The bottoms of the sub-channel mode in the water-filling algorithm, which are conventionally uncontrollable, are proven to be independently adjustable by RISs. Moreover, the transmit power required for realizing multi-stream transmission is derived. Numerical results are presented to verify our theoretical analysis and exhibit substantial gains over systems without RISs.