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.

💡 Research Summary

This paper investigates how non‑ideal power amplifiers (PAs) affect the radar performance of OFDM‑based integrated sensing and communications (ISAC) systems, focusing on the two most common modulation families: constant‑modulus phase‑shift keying (PSK) and variable‑amplitude quadrature amplitude modulation (QAM). Because OFDM signals have a high peak‑to‑average power ratio (PAPR), practical transmitters must operate PAs in a region where clipping or saturation occurs, which introduces distortion that can degrade both communication and sensing functions.

System model – A monostatic ISAC transceiver transmits M OFDM symbols, each consisting of N sub‑carriers of duration T. A cyclic prefix (CP) of length L is added to avoid inter‑symbol interference. The time‑domain signal after CP insertion is denoted (\bar{x}m). The PA is modeled as a soft‑envelope limiter (SEL) with a saturation voltage (V{\text{sat}}). The input‑back‑off (IBO) is defined as the ratio between the 1 dB compression point power and the average input power, and the input signal is scaled by a factor (\alpha) to achieve the desired IBO.

Non‑linear modeling – Two complementary approaches are used:

1. Bussgang decomposition – Assuming a large number of sub‑carriers, the time‑domain OFDM waveform is approximated as i.i.d. complex Gaussian. By applying the Bussgang theorem, the PA output can be expressed as
   \