A Framework for Computing Detection and False Alarm Probabilities for IR-UWB Transmitted Reference Receivers over Generalized Fading Channels with Tone Interference

Abstract

In this paper, we propose an analytical framework for computing detection (Pd) and false alarm (Pfa) probabilities for impulse radio ultra wide band (IR-UWB) transmitted- reference (TR) receivers in a quite general scenario, which includes generalized multipath fading channels and narrowband interference as well. The proposed framework is intended to overcome the limitations of current frameworks developed to analyze timing acquisition performance of IR-UWB TR receivers, which either resort to central limit theorem (CLT) arguments and to semi-analytical approaches for performance analysis over multipath fading channels or do not consider narrow-band interference in the reference scenario. In this contribution, we exploit some properties of "quadratic-form" receivers, and the Gil-Pelaez inversion theorem to develop simple formulas for computing the average Pd and Pfa probabilities, thus providing final expressions that take on the form of a single finite-limit integral, which can be easily integrated using standard techniques. We show that the proposed framework is exact for performance analysis of TR schemes over generalized fading channels, while it provides a very tight approximation for performance analysis in faded scenarios further impaired by narrow-band interference. Numerical and simulation results are also provided to substantiate the accuracy of the developed framework.