The Sensing Performance Analysis for Single- and Multi-Carrier Modulations

In this paper, we focus on the sensing performance for communication-centric integration of sensing and communication (ISAC) systems, which utilize communication signals for sensing. Specifically, we mainly focus on the sensing capabilities of four representative modulation schemes, corresponding to four fundamental channel representations: single-carrier (SC), orthogonal frequency division multiplexing (OFDM), orthogonal time frequency space (OTFS) modulation and orthogonal Doppler frequency modulation (ODFM) in time-delay, time-frequency, delay-Doppler, and Doppler-frequency domains, respectively. We compute the autocorrelations of these modulation signals and give a general Kronecker-based framework to derive their delay profiles and sidelobe levels. Considering the randomness of communication signals, we derive the expected mainlobe and sidelobe levels for these modulation schemes and define intra-slot and inter-slot transforms for symbols within and across time slots. Theoretical results reveal that the intra-slot transform of modulation schemes determines delay profiles, and waveforms defined in the frequency domain achieve superior ranging performance compared to those in the delay domain. Additionally, we investigate the impact of constellation mapping on sensing performance, demonstrating that frequency-domain modulations achieve optimal ranging performance when using constant-modulus mapping constellations. The simulation results verify the theoretical analysis and provide a sensing performance comparison across these modulation schemes in terms of detection probability P<inf xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">d</inf> and root mean square error (RMSE).