Analog Transmit Signal Optimization for Undersampled Delay-Doppler Estimation

TL;DR

This paper develops an optimization framework for analog transmit waveforms to improve delay-Doppler estimation accuracy under sub-Nyquist sampling conditions, enabling reduced sampling rates without sacrificing performance.

Contribution

It introduces a Bayesian estimation-based design rule for analog waveforms in undersampled delay-Doppler estimation, solved via eigenvalue decomposition, and demonstrates practical benefits through simulations.

Findings

Optimized waveforms improve delay-Doppler estimation accuracy.

Framework allows reduced receiver sampling rates while maintaining performance.

Simulation results validate the approach's effectiveness.

Abstract

In this work, the optimization of the analog transmit waveform for joint delay-Doppler estimation under sub-Nyquist conditions is considered. Based on the Bayesian Cram\'er-Rao lower bound (BCRLB), we derive an estimation theoretic design rule for the Fourier coefficients of the analog transmit signal when violating the sampling theorem at the receiver through a wide analog pre-filtering bandwidth. For a wireless delay-Doppler channel, we obtain a system optimization problem which can be solved in compact form by using an Eigenvalue decomposition. The presented approach enables one to explore the Pareto region spanned by the optimized analog waveforms. Furthermore, we demonstrate how the framework can be used to reduce the sampling rate at the receiver while maintaining high estimation accuracy. Finally, we verify the practical impact by Monte-Carlo simulations of a channel estimation algorithm.