Efficient Waveform Design with Good Correlation and Information Embedding Performances for the Joint MIMO Radar and Communications

This paper focuses on the waveform design that simultaneously supports accurate information embedding (IE) and low integrated sidelobe level (ISL)/weighted ISL (WISL) of waveforms for joint multiple-input multiple-output radar and communications (JMRC). We propose a strategy to embed communication symbols by modulating the fast-time phase values of waveforms and consider practice constraints such as the peak-to-average ratio (PAPR) to provide more degrees of freedom (DOFs) for waveform design. Based on this, we formulate a generalized waveform design that minimizes ISL/WISL into a non-convex problem with PAPR constraints and phase constraints exploited for IE. Then, we reformulate the objective in a quartic form and simplify the constraints. To solve it, we minimize the objective function via gradient descent with the support of a locally adaptive Lipschitz-constant related quantity and use an alternating projection scheme to address the constraints. Our contribution also includes proposing a method of detecting the embedded communication symbols. Simulations verify the effectiveness of our design.