Joint Design of Receiving Filters and Complementary set of Sequences for ISAC With Sidelobe Level Suppression

The integrated sensing and communication (ISAC) waveform with a low sidelobe level on all delay indices is important for probing targets in the ISAC scenario. In this article, we consider the problem of jointly designing receiving filters and unimodular complementary sets of sequences (CSS) by minimizing the weighted sum of complementary integrated sidelobe level (CISL) and ISAC interference term at the communication receiver. We propose an optimization algorithm based on the majorization minimization scheme to solve the formulated nonconvex problem with a promised convergence. Fast Fourier transform (FFT) operations are performed in each iteration to improve the computation efficiency. Simulation results demonstrate that the crosscorrelation between the optimized receiving filters and CSS can achieve very low autocorrelation sidelobe levels on all time delay indices. The proposed algorithm has better convergence performance and the same computation complexity compared to the gradient descent algorithm.