The Optimal Tradeoff Between PAPR and Ambiguity Functions for Generalized OFDM Waveform Set in ISAC Systems

Integrated sensing and communications (ISAC) has been identified as one of the six usage scenarios for IMT-2030. Compared with communication performance, sensing performance is much more vulnerable to interference, and the received backscattered sensing signal with target information is usually too weak to be detected. It is interesting to understand the optimal tradeoff between interference rejection and signal strength improvement for the best sensing performance, but unfortunately it still remains unknown. In this paper, the trinity of auto-ambiguity function (AF), cross-AF and peak-to-average-power ratio (PAPR) is proposed to describe the interference and coverage related aspects for ISAC systems where multi-carrier waveform is usually assumed. We extend the existing orthogonal frequency division multiplexing (OFDM) waveforms in 5G to a generalized OFDM waveform set with some new members and a unified parametric representation. Then the optimal Pareto tradeoff between PAPR, auto-AF and cross-AF (i.e., the union bound) is developed for the generalized OFDM waveform set. To achieve the optimal Pareto union bound with reasonable computational complexity, we further propose a framework to optimize waveform parameters and sequences jointly. Finally, some practical design examples are provided and numerical results reveal that significant improvements can be achieved compared to the state-of-the-art 5G waveforms and sequences.