On Convex Relaxations for Joint Transmit-Receive Design in Radar Systems

This dissertation investigates joint design of transmit and receive resources in radar systems, given prior knowledge of a signal-dependent clutter environment, based on simultaneous convex relaxation. Motivated by waveform-adaptive space-time adaptive processing(WA-STAP), we first analyze traditional approaches to joint trans-receive design, which alternate between optimal signal designs for fixed filters and vice versa to maximize signal-to-interference-plus-noise ratio (SINR). First, we demonstrate that SINR & its variants arenon-convex bi-quadratic programs (BQP). Next, we provide perspectives on current alternating methods used to solve BQPs in terms of linear semidefinite (SDP) & quadratically-constrained quadratic (QCQP) programs. We then develop a novel method of performing thisjoint design based on quadratic semidefinite programming (QSDP). Our proposed relaxation scheme first analyzes the power-constrained problem, and is accompanied by exploration of operator structures for signal-dependent clutter. This technique is then extended to morechallenging waveform constraints -- in particular, constant modulus and similarity constrained designs. A refinement scheme is devised to improve recovery of vector solutions from therelaxed matrix solution for the constant modulus problem. Finally, we apply the techniqueto a system model other than WA-STAP; namely, the reverberant sonar/radar channel. Numerical simulations are provided to show the superior performance of our method for SINR, detection, & resolution across multiple environmental scenarios