Ziv-Zakai-Optimal OFDM Resource Allocation for Time-of-Arrival Estimation

This paper presents methods of optimizing the placement and power allocations of pilots in an orthogonal frequency-division multiplexing (OFDM) signal to minimize time-of-arrival (TOA) estimation errors under power and resource allocation constraints. TOA errors in this optimization are quantified through the Ziv-Zakai bound (ZZB), which captures error thresholding effects caused by sidelobes in the signal's autocorrelation function (ACF) which are not captured by the Cramer-Rao lower bound. This paper is the first to solve for these ZZB-optimal allocations in the context of OFDM signals, under integer resource allocation constraints, and under both coherent and noncoherent reception. Under convex constraints, the optimization of the ZZB is proven to be convex; under integer constraints, the optimization is lower bounded by a convex relaxation and a branch-and-bound algorithm is proposed for efficiently allocating pilot resources. These allocations are evaluated by their ZZBs and ACFs, compared against a typical uniform allocation, and deployed on a software-defined radio TOA measurement platform to demonstrate their applicability in real-world systems.