Digital/Hybrid Beamforming via KLMS Algorithm in Presence of Mutual Coupling With Experimental Evaluation for 5G and V2V Communications

—An adaptive kernel-based least mean square algorithm called (KLMS) is proposed for antenna array beamforming. It can be implemented for constant or varying channel situations. The KLMS algorithm convergence is analyzed and the stability condition related to the step size value is obtained. The performance of the KLMS algorithm is evaluated in terms of mean square error (MSE), error vector magnitude (EVM), and beam pattern. The effects of additive white Gaussian noise (AWGN), number of interferences, the difference between the arriving angles of desired and interfering signals, and fading channel on the performance are investigated for an 8-element mutually coupled array antenna. The results are compared with those of the LMS, normalized LMS (NLMS), and constraint stability LMS (CSLMS) algorithms. It is shown that the KLMS algorithm outperforms the other algorithms significantly. We investigate two use-cases including hybrid beamforming and vehicle-to-vehicle (V2V) communications in the 5G communication systems. Instead of maximizing the spectral efficiency (SE), the MSE is used to minimize the estimation error as a performance metric, where the problem is solved by iterative KLMS algorithm in lieu of alternating optimization. The SE of the proposed KLMS hybrid beamforming has superior performance in partially-connected (PC) structure systems and appropriate performance in fully-connected (FC) structure with low computational complexity. Moreover, the packet error rate (PER) and bit error rate (BER) performances of beamforming in V2V communications are evaluated for a link V2V communication with known locations of vehicles and phase errors stemming from Doppler shifts, position error, and beam unlock.