Ambiguity Function Analysis and Improvement of Integrated WFRFT-OTFS Waveform

Integrated sensing and communication (ISAC) is one of the key enabling technologies for future wireless networks, where sensing performance of different waveforms can be typically characterized through the ambiguity function (AF). In this paper, orthogonal time frequency space (OTFS) modulation is spread by the weighted fractional Fourier transform (WFRFT), and the AF performance in different dimensions of integrated WFRFT-OTFS waveform are investigated and deeply analyzed. Firstly, as the linear combination of OTFS and single carrier (SC) systems, the AF of WFRFT-OTFS waveform are derived according to the united feature of WFRFT, and thus AF with any WFRFT order can be obtained through the linear combination of OTFS and SC. In addition, the WFRFT-OTFS achieves the tradeoff AF performance between delay dimension and Doppler dimension, which determines the distance accuracy and speed accuracy respectively. Finally, according to superior autocorrelation properties of P4 sequences, we propose a symbol-embedded P4 (SEP4) phase encoding to further enhance the sensing performance of integrated WFRFT-OTFS waveform based on symbol-level phase precoding. It is revealed that theoretical analyses match well with simulation results in WFRFT-OTFS waveform. The proposed SEP4 precoding improves the sensing AF and introduces negligible impact on the communication performance.