Low Sidelobe Level and PAPR OTFS Waveform Design for ISAC Systems

Orthogonal Time Frequency Space (OTFS) modulation holds significant potential for diverse applications in both sensing and communication fields. This paper mainly investigates waveform optimization for OTFS modulation, aiming to design pilot symbol matrices with low sidelobe levels and data symbol matrices with high communication rates under peak-to-average power ratio constraints. We first formulate the problem of minimizing the weighted integrated sidelobe levels and maximizing the communication rate in the delay-Doppler domain. Subsequently, to address the complicated optimization problem, a Majorization-Minimization based algorithm is proposed to decompose it into a series of subproblems. These subproblems are then reformulated as unconstrained optimization problems on the Stiefel manifold, and the Riemannian conjugate gradient method is employed to solve them efficiently. Moreover, a faster iterative algorithm is proposed based on second-order Taylor approximation to accelerate the convergence speed. Simulation results validate that the proposed algorithms effectively achieve pilot matrices with desirable ambiguity functions and data symbol matrices with high communication rates under various weighting factors.