Joint Transmit and Receive Beamforming for Tri-directional Coil-Based Magnetic Induction Communications

In this paper, we enhance the omnidirectional coverage performance of tri-directional coil-based magnetic induction communication (TC-MIC) and reduce the pathloss with a joint transmit and receive magnetic beamforming method. An iterative optimization algorithm incorporating the transmit current vector and receive weight matrix is developed to minimize the pathloss under constant transmit power constraints. We formulate the mathematical models for the mutual inductance of tri-directional coils, receive power, and pathloss. The optimization problem is decomposed into Rayleigh quotient extremum optimization for transmit currents and Cauchy-Schwarz inequality-constrained optimization for receive weights, with an alternating iterative algorithm to approach the global optimum. Numerical results demonstrate that the proposed algorithm converges within an average of 13.6 iterations, achieving up to 54% pathloss reduction compared with equal power allocation schemes. The joint optimization approach exhibits superior angular robustness, maintaining pathloss fluctuation smaller than 2 dB, and reducing fluctuation of pathloss by approximately 45% compared with single-parameter optimization methods.