Fundamental Limits and Optimization of Multiband Delay Estimation in OFDM Systems

Multiband technology has recently received incremental attention for its ability to jointly utilize multiple noncontiguous frequency bands to achieve high-resolution delay estimation. In multiband scenarios, numerous signal processing algorithms for delay estimation have been proposed, while research on the fundamental limits remains under explored. In this article, we focus on the analysis of fundamental limits and the optimization of multiband delay estimation in orthogonal frequency division multiplexing (OFDM) systems. We derive a closed-form expression of the Cramer-Rao bound (CRB) for the delay separation to reveal useful insights. Additionally, a metric called statistical resolution limit (SRL) that provides a resolution performance bound is employed to research the fundamental limits of delay resolution. The fundamental limits of the delay estimation error are also investigated using the performance bounds CRB and Ziv-Zakai bound (ZZB). Based on these derived performance bounds, numerical results have been presented to analyse the effect of frequency band apertures and phase distortions on the fundamental limits of the multiband delay estimation error. Inspired by the analysis of fundamental limits, we formulate an optimization problem to find the optimal system configuration in multiband systems with the objective of minimizing the delay SRL. To solve this nonconvex constrained problem, we propose an efficient alternating optimization (AO)-based algorithm that iteratively optimizes the variables using the successive convex approximation (SCA) and 1-D search. Simulation results demonstrate the effectiveness of the proposed algorithm and give useful insights for the multiband system design.