Pilot signal design via constrained optimization with application to delay-Doppler shift estimation in OFDM systems

We address the problem of searching for the optimal pilot signal, i.e. pattern and signature, of an orthogonal frequency-division multiplexing (OFDM) system when the purpose is to estimate the delay and Doppler shift under the assumption of a single-path propagation channel. This problem is relevant for synchronization and for time-based localization using said signals. We propose to use the Cramér-Rao bound and the normalized side-lobe level (NSL) of the ambiguity function as figures of merit to devise the pilot signals. We formulate the design problem as a constrained optimization problem for which we propose a genetic algorithm that computes close-to-optimal solutions. Simulation results demonstrate that the proposed algorithm can efficiently find pilot signals that outperform the state-of-the-art pilot signals in both single-path and multipath propagation scenarios. In addition, we demonstrate that data interference causes a performance loss if a standard non-coherent correlator is used. The results also indicate that the pilot pattern impacts the estimator´s performance more than the pilot signature.