Theoretical Limits on Time Delay Estimation for Ultra-Wideband Cognitive Radios

TL;DR

This paper derives the theoretical limits of time delay estimation in ultra-wideband cognitive radios, analyzing the impact of unknown channel parameters and CFOs, with numerical results supporting the analysis.

Contribution

It provides the first derivation of the CRLB for UWB cognitive radios considering unknown channel coefficients and CFOs, including specific expressions for different modulation schemes.

Findings

Unknown channel coefficients and CFOs significantly affect estimation accuracy.

Linear modulations with constant envelope mitigate the effects of unknown parameters.

Numerical results validate the theoretical CRLB expressions.

Abstract

In this paper, theoretical limits on time delay estimation are studied for ultra-wideband (UWB) cognitive radio systems. For a generic UWB spectrum with dispersed bands, the Cramer-Rao lower bound (CRLB) is derived for unknown channel coefficients and carrier-frequency offsets (CFOs). Then, the effects of unknown channel coefficients and CFOs are investigated for linearly and non-linearly modulated training signals by obtaining specific CRLB expressions. It is shown that for linear modulations with a constant envelope, the effects of the unknown parameters can be mitigated. Finally, numerical results, which support the theoretical analysis, are presented.