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

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.

A Joint Data Compression and Time-Delay Estimation Method For Distributed Systems via Extremum Encoding

Motivated by the proliferation of mobile devices, we consider a basic form of the ubiquitous problem of time-delay estimation (TDE), but with communication constraints between two non co-located sensors. In this setting, when joint processing of the received signals is not possible, a compression technique that is tailored to TDE is desirable. For our basic TDE formulation, we develop such a joint compression-estimation strategy based on the notion of what we term "extremum encoding", whereby we send the index of the maximum of a finite-length time-series from one sensor to another. Subsequent joint processing of the encoded message with locally observed data gives rise to our proposed time-delay "maximum-index"-based estimator. We derive an exponentially tight upper bound on its error probability, establishing its consistency with respect to the number of transmitted bits. We further validate our analysis via simulations, and comment on potential extensions and generalizations of the basic methodology.