Design of Multiple ISL-Aware Waveforms With SINR Guarantees for Integrated Sensing and Multi-User Communications

We investigate waveform optimization for integrated sensing and multi-user communications. The key idea is to minimize the integrated sidelobe level of the multiple transmit waveforms while ensuring that the signal-to-interference-plus-noise ratio of each communication user remains above a prescribed threshold. Moreover, by exploiting the available spatial degrees of freedom, we enforce identical effective channel gains for all desired noise-free symbols. This design decouples the signal strength from spatial beamforming and simplifies symbol detection at the users. The main challenge lies in handling a non-convex quartic objective with multiple coupled constraints, where the weight vector appears inside correlation terms, making the problem difficult to solve directly. To address this issue, we resort to the majorization-minimization (MM) technique to convert the objective into a tractable form. We then derive a series of surrogate functions and supporting results for the MM steps, enabling the solution to be obtained iteratively. Simulation results demonstrate the effectiveness of the proposed waveform design.