Constant Modulus Frequency- and Phase-Shift Keying Waveforms for ISAC
This paper considers a hybrid frequency- and phase-shift keying (FPK) waveform for integrated sensing and communications (ISAC). Compared to FSK-based ISAC waveforms in the literature, the proposed waveform shows similar local radar estimation accuracy and superior performance both in terms of data rates and radar global accuracy. The ambiguity function (AF) is used as a tool to evaluate the radar performance of the FPK waveform. We show that incorporating phase modulation into the FSK waveform generally has an insignificant effect on the sharpness of the AF main lobe while reducing the values of the peak sidelobe levels (SLs) in the AF. We also derive the Cramer-Rao lower bounds of the delay and Doppler shift estimates for the FPK waveform. Additionally, since the AF SLs vary depending on the data embedded in the waveform, we analyze and provide approximations for the distribution of the AF SLs. Finally, we analyze the error performance of both the optimal and suboptimal communication receivers, and derive the nearest-neighbors approximation for the symbol error probability using the optimal receiver. Numerical examples illustrate the accuracy of our approximations and show the performance improvements of the FPK waveform compared to FSK.