Theoretical limits on time delay estimation for ultra-wideband cognitive radios

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 nonlinearly 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.