Optimization and Quantization of Multibeam Beamforming Vector for Joint Communication and Radio Sensing

Joint communication and radio sensing (JCAS) in millimeter-wave (mmWave) systems requires the use of a steerable beam. For analog antenna arrays, a single beam is typically used, which limits the sensing area within the direction of the communication. Multibeam technology can overcome this limitation by separately generating package-level direction-varying sensing subbeams and fixed communication subbeams and then combine them coherently. In this paper, we investigate the optimal combination of the two subbeams and the quantization of the beamforming (BF) vector that generates the combined beam. When either the full channel matrix or only the angle of departure (AoD) of the dominating line-of-sight (LOS) path is known at the transmitter, we derive the closed-form expressions for the optimal combining coefficients that maximize the received communication signal power. For the quantization of the BF vector, we focus on the two-phase-shifter array where two phase shifters are used to represent each BF weight. We propose novel joint quantization methods by combining the codebooks of the two phase shifters. The mean squared quantization error is derived for various quantization methods. Extensive simulation results validate the accuracy of the analytical results and the effectiveness of the proposed multibeam optimization and joint quantization methods.