Multi-OFDM Waveform Design for Joint Radar and Communications Via Hybrid Modulations: Achieving Good ISL and PMEPR Performances

In this paper, we investigate the design of multiple orthogonal frequency-division multiplexing (OFDM) waveforms for joint radar and communications applications. The design objectives are to simultaneously minimize the integrated sidelobe level (ISL) and the peak-to-mean envelope power ratio (PMEPR) of the OFDM waveforms, while enabling high-rate data transmission through efficient information embedding (IE). To this end, we propose an adaptive IE scheme that jointly exploits frequency index and phase modulations to embed communication information while preserving sufficient degrees of freedom for radar-oriented optimization. Based on the proposed hybrid modulation framework, multi-OFDM waveforms are designed by optimizing a balanced trade-off between ISL and PMEPR. Unlike conventional approaches that focus solely on peak-to-average power ratio reduction or power allocation, the proposed method jointly optimizes the amplitudes and phases of complex weights across multiple OFDM subcarriers. The resulting design incorporates multiple constraints, including support for hybrid IE, compliance with the total transmit power budget, and enforcement of minimum amplitude levels for OFDM subcarrier weights. We formulate it as a nonconvex optimization problem, which is inherently challenging to solve. To address this challenge, we reformulate the objective function and apply majorization-minimization techniques. Furthermore, to address the complexity arising from multiple constraints, we reformulate the original problem as a joint optimization framework involving two separable variables, namely, the weight amplitude and phase, which is then solved in a cyclic manner. Closed-form iterative update rules are derived using suitable majorization functions, and the amplitude optimization is addressed via Lagrangian analysis and Karush-Kuhn-Tucker conditions. Finally, an efficient algorithm is proposed, and extensive simulation results demonstrate the effectiveness of the proposed approach.