Communication-Centric ISAC Based on Zak-OTFS: A Novel Backpropagation Algorithm for Delay-Doppler Sensing

In this paper, we investigate delay-Doppler (DD) sensing in a communication-centric integrated sensing and communication (ISAC) framework based on Zak transform-based orthogonal time frequency space (Zak-OTFS) modulation. Specifically, we consider target sensing with communication waveforms and propose a novel backpropagation (BP) algorithm for multi-target DD parameter estimation. We formulate the radar sensing task as a maximum likelihood parameter estimation problem, which is highly non-convex. By exploiting the structural analogy between parameter estimation and neural network training, the BP algorithm treats the DD parameters as tunable network weights and efficiently computes their gradients via the chain rule, enabling accurate and parallelized estimation. To facilitate the algorithm implementation, a successive interference cancellation method based on DD domain twisted convolution is developed to obtain coarse DD estimates. Furthermore, a constant false alarm rate based dynamic merging strategy is introduced to adaptively estimate the number of targets during the BP process. Comprehensive theoretical analyses are conducted, including the derivation of the Cramér–Rao bound (CRB) for Zak-OTFS systems and performance evaluation under various challenging sensing scenarios. Simulation results demonstrate that the proposed algorithm achieves high estimation accuracy and validates the theoretical analysis.