Joint Robust Transmit/Receive Adaptive Beamforming for MIMO Radar Using Probability-Constrained Optimization

In this letter, a joint robust transmit/receive adaptive beamforming for multiple-input multiple-output (MIMO) radar based on probability-constrained optimization approach is developed in the case of Gaussian and arbitrary distributed mismatches present in both the transmit and receive signal steering vectors. A tight lower bound of the probability constraint is also derived by using duality theory. The formulated probability-constrained robust beamforming problem is nonconvex and NP-hard. However, we reformulate its cost function into a bi-quadratic function while the probability constraint splits into transmit and receive parts. Then, a block coordinate descent method based on second-order cone programming is developed to address the biconvex problem. Simulation results show an improved robustness of the proposed beamforming method as compared to the worst-case and other existing state-of-the-art joint transmit/receive robust adaptive beamforming methods for MIMO radar.