CRLB and Parameter Estimation for OFDM-ISAC with Non-Uniform Sparse Resource Allocation

Abstract

Integrated sensing and communication (ISAC) holds great promise in expanding the applications of wireless communication networks. However, in current communication-centric systems, the time-frequency resources available for sensing may be limited, and also usually non-uniformly and sparsely distributed across the time-frequency domain. Such a non-uniformity destroys the "thumbtack-shaped" ambiguity function of the orthogonal frequency division multiplexing (OFDM) waveform, leading to degraded sensing performance. To this end, this paper explores the parameter estimation algorithm for OFDM-ISAC systems with non-uniform sparse resource allocation. Specifically, for the single target case, we derive the closed-form Cramer-Rao lower bound (CRLB) for parameter estimation as a function of resource indices. Furthermore, we show that simply filling unused resource locations with zeros and applying the classic periodogram estimation is equivalent to maximum likelihood (ML) estimation, which is asymptotically optimal. For the multi-target case, we generate a virtual resource using the autocorrelation function of the original signal, which exhibits a significantly larger virtual bandwidth compared to the original signal, at the cost of higher peak-to-sidelobe ratio (PSLR). Simulation results demonstrate that the proposed approach outperforms the conventional periodogram method for non-uniform sparse resource allocation.