Joint Design of ISAC Waveform under PAPR Constraints

In this paper, we formulate the precoding problem of integrated sensing and communication (ISAC) waveform as a non-convex quadratically constrainted quadratic program (QCQP), in which the weighted sum of communication multi-user interference (MUI) and the gap between dual-use waveform and ideal radar waveform is minimized with peak-to-average power ratio (PAPR) constraints. We propose an efficient algorithm based on alternating direction method of multipliers (ADMM), which is able to decouple multiple variables and provide a closed-form solution for each subproblem. In addition, to improve the sensing performance in both spatial and temporal domains, we propose a new criteria to design the ideal radar waveform, in which the beam pattern is made similar to the ideal one and the integrated sidelobe level of the ambiguity function in each target direction is minimized in the region of interest. The limited memory Broyden-Fletcher-Goldfarb-Shanno (L-BFGS) algorithm is applied to the design of the ideal radar waveform which works as a reference in the design of the dual-function waveform. Numerical results indicate that the designed dual-function waveform is capable of offering good communication quality of service (QoS) and sensing performance.