2-D Root-MUSIC Approach for Delay-Doppler Parameter Estimation for DFRC-OTFS Modulation

Orthogonal time-frequency space (OTFS) is a modulation scheme with properties that are particularly well-suited for integrated sensing and communications (ISAC). The structure of the scheme enables transmission of a dual-function radar communications (DFRC) OTFS frame consisting of pilot and data symbols, with the flexibility to select the pilot symbols to form a desirable sensing radar waveform. In this article, a 2-D root-multiple signal classification (MUSIC) approach is presented to estimate the delays and Doppler shifts corresponding to multiple scatterers using such an OTFS waveform. First, the MUSIC approach for a single-pilot symbol is presented, along with a discussion highlighting the challenges in extending this method to the multiple-pilot scenario. Such an extension proves to be important in practical scenarios since multiple-pilot symbols can provide coherent integration gain for delay-Doppler (DD) estimation, enabling the transmitted waveform to have a lower peak-to-average power ratio (PAPR). Thus, the proposed method is extended for multiple pilots, and the widely used linear frequency-modulated (LFM) chirp pilot pulse is shown to possess desirable properties for applying the proposed MUSIC approach. Cramér-Rao bounds (CRBs) are derived and used as a benchmark for the performance of the 2-D MUSIC algorithm. The numerical results demonstrate that a DFRC OTFS frame with an LFM pilot sequence can achieve the same estimation accuracy with a lower PAPR as compared to an OTFS frame with a single-pilot symbol.