Biquadratic optimization based joint transmit and receive beamforming with sequential rank relaxation

We consider the joint design of transmit and receive beamforming in multiple-input-multiple-output (MIMO) systems by utilizing prior knowledge of the target and interferences. The design problem is to maximize the receiver output signal-to-interference-plus-noise-ratio (SINR) with the transmit power constraint for each element. A conventional SINR maximization is based on the transmit and receive iteration (T-R iteration), which often converges slowly. In contrast, we formulate the problem as a biquadratic optimization by lumping together the transmit and receive beamformers, which allows us to update them at the same time, thus bypassing T-R iteration and initialization. Our approach converges significantly faster and often to a better beamforming solution, especially when strong interferences are present. Simulation results show that the proposed approach reduces the computational complexity by tens to hundreds of times than the T-R iteration method, depending on the interference level, while the latter may exhibit a considerable SINR loss when prematurely terminated or poorly initialized.