Ultra-High Resolution Method for Multipath Within a Co-Delay-Doppler Bin in DFT-P-OCDM
Communication systems can reuse their transmitted signals for sensing without dedicated radar transmissions. For an established DFT-preprocessed orthogonal chirp division multiplexing (DFT-P-OCDM) waveform, this task becomes difficult when several physical paths in a doubly selective channel fall into the same co-delay-Doppler bin. In this case, the number of resolvable delay classes inferred from the pilot may be smaller than the number of physical paths within the co-bin. This mismatch increases the difficulty of path number determination, fractional Doppler offset estimation, and channel reconstruction. We derive a pointwise relationship between the input and output in the DFT preprocessed Fresnel (DPF) domain for doubly selective channels with multiple paths within the co-delay-Doppler bin. Based on this input and output relation, we propose the two stage ultra high resolution (TSUR) framework. The first stage uses pilots of the phase progression to estimate delay, while the second stage uses the leakage samples to estimate the Doppler and the number of paths within each delay class. Furthermore, we derive CRLBs and analyze how the pilot configuration trades sensing resolution and communication recovery. Simulation results demonstrate that TSUR resolves same delay paths within a co-delay-Doppler bin, remains robust to exist delay offsets, and achieves lower fractional Doppler estimation errors than sequential extraction and off-grid baselines.