Extremum Encoding for Joint Baseband Signal Compression and Time-Delay Estimation for Distributed Systems

TL;DR

This paper extends the extremum encoding scheme for joint baseband signal compression and time-delay estimation to complex-valued RF signals, addressing phase uncertainties and demonstrating improved performance over benchmarks.

Contribution

It introduces a novel extension of extremum encoding for complex RF signals, including new statistical analysis and error bounds, enabling practical RF applications.

Findings

The extended scheme performs better than benchmark methods.

Asymptotic behavior similar to original scheme despite complexities.

Simulation results validate theoretical error bounds.

Abstract

The ubiquitous time-delay estimation (TDE) problem becomes nontrivial when sensors are non-co-located and communication between them is limited. Building on the recently proposed "extremum encoding" compression-estimation scheme, we address the critical extension to complex-valued signals, suitable for radio-frequency (RF) baseband processing. This extension introduces new challenges, e.g., due to unknown phase of the signal of interest and random phase of the noise, rendering a na\"ive application of the original scheme inapplicable and irrelevant. In the face of these challenges, we propose a judiciously adapted, though natural, extension of the scheme, paving its way to RF applications. While our extension leads to a different statistical analysis, including extremes of non-Gaussian distributions, we show that, ultimately, its asymptotic behavior is akin to the original scheme. We derive an exponentially tight upper bound on its error probability, corroborate our results via simulation experiments, and demonstrate the superior performance compared to two benchmark approaches.