A Compressive Sensing-Based Colocated MIMO Radar Power Allocation and Waveform Design

Compressive sensing (CS) is a widely used technique for (multiple) target detection in multiple input multiple output (MIMO) radars. In this paper, our goal is to enhance the quality of CS-based detection techniques for a colocated MIMO radar with given location of transmit and receive nodes. Our approach is to design the transmit waveforms based on the given antenna locations and optimally allocate the total power budget among the transmitters. The design criterion in this paper is the coherence of the resulting sensing matrix. Based on this criterion, we derive and solve a convex optimization problem for power allocation. For waveform design, however, the direct method studied is non-convex, and although iterative descent methods could be used to achieve suboptimal solutions, they might be unfeasible waveforms (e.g., waveforms with high peak to average power ratios). Here, we first show that the coherence measure depends only on the covariance matrix of the waveforms (rather than the waveforms themselves). Next, we introduce three different convex programs to achieve the covariance matrix. Finally, we transform the covariance matrix into realistic waveforms; although multiple solutions exist, a closed-form expression for all possible solutions is available. Specifically, we design the waveforms by applying practical constraints such as constant modulus. Simulation results confirm that the introduced designs improve the detection performance of a CS-MIMO radar.