Waveform design for the radar-communications coexistence with good correlation properties

We deal with the waveform design problem for the radar-communications coexistence (RCC) that ensures low levels of waveform correlations and meanwhile implements efficient information embedding (IE) via the fast-time waveform transmission. To tackle the problem, we propose two unimodular waveform designs, in which the integrated sidelobe level (ISL) is evaluated to find the optimal waveform correlations for the radar transmission and the attributes of waveform phases with large degrees of freedom are exploited to embed communication symbols. The first design is an offline strategy simply using the phase initialization for waveform generation to embed communication symbols. It requires only a predefined database that maps the waveform initialization to the emitted version of it, which gives the lowest ISL of the waveform. The second design serves as an online strategy employing the phase difference between any two waveform elements for the implementation of IE, and its accuracy to approaching desirable phases is elaborately transformed into a quadratic form and jointly designed with the minimization of ISL. We formulate this design as a nonconvex optimization problem, whose compound objective involves the outer product of the waveform vector that is to be designed. Moreover, we apply the majorization-minimization technique to solve the formulated problem, based on which we also devise an efficient algorithm that iterates with a closed-form solution. Simulation results verify the effectiveness of the proposed designs for the RCC.