Waveform design for the joint MIMO radar and communications with low integrated sidelobe levels and accurate information embedding

In this paper, we focus on the multiple-waveform design for the joint multiple-input multiple-output radar and communications system, which aims to simultaneously attain low integrated sidelobe level (ISL) of waveforms and accurate fast-time modulation for information embedding (IE). We propose a novel strategy to exploit the attributes of waveform phases with extremely large degrees of freedom for embedding communication symbols, based on which we formulate the generalized waveform design into a nonconvex optimization problem. Our major contribution lies in converting both the ISL related objective and the fast-time modulation related constraints for IE into tractable quadratic forms. To achieve this, we introduce a novel diagonal matrix with Toeplitz blocks to reformulate and then relax the problem into a form that involves the outer product of the waveform vector in its objective. In order to solve this problem, we exploit the majorization-minimization technique to devise an algorithm that enables a closed-form solution at each iteration. Simulation results verify the effectiveness of our design.