Analytical Performance Evaluation of CP-OTFS for ISAC Under High-Doppler and Large-Delay Conditions

Orthogonal time-frequency space (OTFS) modulation is a promising waveform for integrated sensing and communication (ISAC) in high-mobility environments, where both large Doppler shifts and target delays must be accurately handled. Existing CP-OTFS radar analyses often assume CP-preserving target delays, for which the received echo remains inside the protected interval and CP-induced interference is avoided. However, practical sensing scenarios may involve large Doppler shifts and large target delays exceeding the cyclic-prefix duration, leading to CP violation and interference. This paper extends the analytical performance evaluation of cyclic-prefix OTFS (CP-OTFS) to this large-delay regime while also accounting for Doppler shifts. Starting from the CP-OTFS transmit signal, point-target channel, time-frequency demodulation, and delay-Doppler matched filtering, closed-form expressions are derived for the radar matched-filter output statistics, including the mean response, average delay-Doppler energy, main-lobe energy, peak sidelobe level ratio (PSLR), and integrated sidelobe level ratio (ISLR). For the communication function, an analytical error vector magnitude (EVM) expression is derived to quantify the degradation induced by large delays. The analytical expressions are evaluated as functions of target delay and Doppler shift and validated through end-to-end CP-OTFS ISAC simulations. The results demonstrate the accuracy of the analytical expressions and quantify the reduction in useful energy, the increase in interference, the degradation of the PSLR and ISLR, and the increase in EVM.