Design of Multiple Binary Waveforms for the Joint MIMO Radar and Communications

In this paper, we focus on the multi-waveform design for the joint radar and communications, wherein the elements of waveforms are required to take binary values and to support both good integrated sidelobe level (ISL) and information embedding (IE) performances simultaneously. Since the binary waveform attribute enables limited degrees of freedom for the design, we partially choose to exploit both the phase and index modulations (PIM) of waveform elements to embed communication symbols in the fast-time domain, while we reserve a portion of them to improve the overall ISL of waveforms without PIM. To this end, we divide the fast-time waveforms to be designed into multiple blocks, each of which contains multiple uniform segments. We further develop a rule to instruct the elaboration of segments for IE via PIM within each block, and we leave the remaining segments among blocks unconstrained for the reduction on overall ISL of the binary waveforms. Based on the above, we formulate the design into a non-convex optimization problem that incorporates both the ISL minimization of waveforms and constraints on the fast-time IE. To tackle this problem, we reformulate it into a solvable integer optimization form, for which we employ the coordinate descent framework to find solutions. To make the work complete, we propose an associated method to determine the proper number of IE segments in the waveform design. Simulation results verify the effectiveness of our proposed design.