Performance Analysis of UWB Autocorrelation Receivers Over Nakagami-Fading Channels

We study the performance of the autocorrelation receiver (AcR) with the transmitted-reference (TR) signaling scheme in the multipath UWB channel, where the fading of each resolvable multipath component is characterized by: 1) Nakagami distribution; 2) arbitrary fading parameter; and 3) arbitrary average power. The analysis, compared to conventional Rake receivers, is complicated by the fact that the instantaneous signal-to-noise ratio (SNR) at the AcR output is a nonlinear function of the instantaneous SNR at the receiver input, the latter given by the sum of the SNRs of each resolvable multipath component. Based on the derivation of exact and approximated expressions for the probability density function (pdf) of the output SNR, we evaluate several indicators of the receiver performance, such as: 1) average SNR; 2) amount of fading; 3) outage probability; and 4) average bit-error probability (BEP); all are given in a closed-form. Remarkably, we show that the pdf of the output SNR can be modeled as a gamma distributed random variable, which allows us to write the average BEP in terms of the well-known hypergeometrical Gaussian function. An approximate, yet accurate, expression of the integration time minimizing the average BEP is also derived.