Normalized Ambiguity Function Characteristics of OFDM, OTFS, AFDM, and CP-AFDM for ISAC

This paper presents a unified and system-agnostic analysis of the ambiguity function (AF) characteristics of four representative multicarrier waveforms, orthogonal frequency division multiplexing (OFDM), orthogonal time frequency space (OTFS), affine frequency division multiplexing (AFDM), and chirp-permuted AFDM (CP-AFDM), which are considered as key candidates for enabling integrated sensing and communications (ISAC) in future sixth generation (6G) networks. The AF of each waveform is obtained directly from its discrete-time definition and enhanced via ideal fractional interpolation, enabling precise characterization of its continuous-time delay-Doppler response. Two signaling modes are examined: a communication-oriented case with random information symbols suitable only for monostatic scenarios, and a sensing-oriented case with fixed unimodular symbols suitable for general multi-static scenarios. Furthermore, the AFs and the ambiguity metrics including the 3dB mainlobe width, peak-to-sidelobe ratio (PSLR), and integrated sidelobe ratio (ISLR), are evaluated in normalized delay-Doppler units, enabling direct translation to any physical system configuration defined by bandwidth, sampling frequency, or symbol duration, while ensuring straightforward and consistent comparison across waveforms. The results establish a consistent benchmark for comparing waveform sensing capabilities in ISAC design, consolidating known behaviors: OFDM exhibits excellent delay resolution and sidelobe behavior but poor Doppler response, whereas advanced waveforms achieve improved balance between delay and Doppler resolution with varying sidelobe characteristics. The simulation code of the smooth AFs, is openly shared to promote reproducibility and support future ISAC waveform research.