Training-Based Adaptive Transmit–Receive Beamforming for MIMO Radars

The recent advancements in digital control of the waveforms transmitted by radar systems has enabled implementation of multiple-input multiple-output radar systems. In such radars, each element is capable of transmitting a different waveform; in this paper, we focus on modifying a multiplicative weight at each transmitter to improve detection performance. Several authors have considered the problem of optimizing the transmit weights and the receive filter generally to maximize the output signal-to-interference-plus-noise ratio. Crucially, these previous works assumed a priori knowledge of the required second-order statistics. In this regard, we make two key contributions: First, we formulate and solve an optimization problem to estimate these required statistics using only signals received in previous coherent processing intervals (CPIs). Essentially, we estimate the transmit interference covariance matrix using receive data. The estimation does not assume any specific structure for the clutter covariance matrix. By using the most recent CPIs in the design, our approach makes it possible to track changes in the interference environment, and, therefore, adaptively design the transmit code in real time. Second, we introduce reduced-dimension processing for transmit adaptivity. As in the case of receive space-time adaptive processing (STAP), it is crucial to be able to perform filter design with only a limited number of available training samples. While reduced-dimension processing is well established for receive adaptivity, as we will see, transmit reduced-dimension processing requires a completely different formulation. We consider transmit code design for a single look angle-Doppler bin and also for a range of Doppler bins in the case that the target Doppler shift is unknown. Finally, we present simulation results, in the context of phase-perturbed propagation and airborne radars, to illustrate the performance of the proposed methods.