Impact of Insufficient CP on Sensing Performance in OFDM-ISAC Systems

Orthogonal frequency-division multiplexing (OFDM) is widely considered a leading waveform candidate for integrated sensing and communication (ISAC) in 6G networks. However, the cyclic prefix (CP) used to mitigate multipath effects in communication systems also limits the maximum sensing range. Target echoes arriving beyond the CP length cause inter-symbol interference (ISI) and inter-carrier interference (ICI), which degrade the mainlobe level and raise sidelobe levels in the range-Doppler map (RDM). This paper presents a unified analytical framework to characterize the ISI and ICI caused by an insufficient CP length in multi-target scenarios. For the first time, we derive closed-form expressions for the second-order moments of the RDM under both matched filtering (MF) and reciprocal filtering (RF) processing with insufficient CP length. These expressions quantify the effects of CP length, symbol constellation, and inter-target interference (ITI) on the mainlobe and sidelobe levels. Based on these results, we further derive explicit formulas for the peak sidelobe level ratio (PSLR) and integrated sidelobe level ratio (ISLR) of the RDM, revealing a fundamental trade-off between noise amplification in RF and ITI in MF. Numerical results validate our theoretical derivations and illustrate the critical impact of insufficient CP length on sensing performance in OFDM-ISAC systems.