On the Ambiguity Function of OFDM-based ISAC Signals Under Non-Ideal Power Amplifiers

Integrated Sensing and Communications (ISAC) has garnered significant attention as a promising technology for next-generation wireless and vehicular communications. Among candidate waveforms, Orthogonal Frequency Division Multiplexing (OFDM) has been extensively investigated over the past decade for its robustness against frequency-selective fading and its favorable ranging performance. However, the waveform's sensing and communication (S&C) performance depends strongly on the modulation scheme; while variable-amplitude constellations such as quadrature amplitude (QAM) are more efficient for communication, constant-modulus modulations such as phase shift keying (PSK) are more suitable for sensing. Yet, it remains unclear whether these findings persist under power amplifier (PA) nonlinearity. Because OFDM signals exhibit a high peak-to-average power ratio (PAPR), they require highly linear PAs to avoid distortion, which conflicts with radar requirements, where high transmit power is always beneficial for sensing. In this work, we analyze the effect of PA-induced distortions on the sensing task for PSK and QAM constellations. By introducing the Signal-to-Distortion Ratio (SDR), we examine the extent of the distortion limitation on the ranging task. We complement simulation results with a theoretical characterization of the ambiguity function (AF), thereby explicitly demonstrating how distortion artifacts manifest in the zero-Doppler sidelobes (i.e, ranging sidelobes) and the zero-delay sidelobes. Simulations show that PA distortions impose a palpable performance ceiling for both constellations, reshape the AF, and reduce detection probability, diminishing the theoretical advantage of unimodular signaling and further compromising the OFDM sensing performance with non-uniform envelope signals.