Minimization of Internally Reflected Power Via Waveform Design in Cognitive MIMO Radar

State-of-the-art cognitive multiple-input multiple-output (MIMO) radars maximize the signal-to-interference-plus-noise ratio (SINR) for an extended target of interest by matching the transmitted waveforms to the target impulse response (TIR). Existing methods to match the transmitted waveforms do not consider the problem of internally reflected power due to the mutual coupling between the transmitting antenna array elements, which results in transmitter inefficiency and possible hardware damage. While the mutual coupling problem in MIMO radars has been handled using microwave techniques heretofore, we herein advocate a signal-processing approach to this problem in cognitive MIMO radars. Specifically, we propose an effective waveform design formalism allowing to jointly maximize the SINR and minimize the reflected power from the transmitting antennas under a TIR matching constraint, while achieving waveform orthogonality in the Doppler domain. Minimizing the reflected power is achieved through the incorporation of a regularization term, taking the form of an $\ell _{\infty }$-norm, in the objective function of a minimum variance distortionless response criterion. An efficient proximal gradient method is developed to solve the resulting nonsmooth optimization problem. Simulations with different TIR distributions and transmitting antenna array sizes show that the proposed waveform design algorithm results in lower active reflection coefficients for the antenna elements than selected benchmarks. Furthermore, our algorithm offers a competitive SINR performance compared to these benchmarks and can cope with the fast-varying TIR.