Characterizing Wideband Signal Envelope Fading in Urban Microcells Using the Rice and Nakagami Distributions

In this paper, we show that the cumulative and probability distribution functions (cdf and pdf, respectively) of small-scale wideband signal envelope fading in microcells can be very closely approximated by both the Rice and Nakagami distributions, which are already known to describe the cdfs and pdfs of small-scale narrowband signal envelope fading. Our results are obtained by means of an extensive Monte Carlo-based study of a wideband propagation model by Yan and Kozono, which is itself supported by extensive measurements. Over a comprehensive range of microcell propagation parameters, the average maximum error in the approximation is 1.65% and 1.78% for the Rice and Nakagami cdfs, respectively. The error in the approximation is 3.58% and 3.87% for the 95th percentile and does not exceed 7.61% and 7.80%, respectively, in the worst case. We propose an expression that maps the significant wideband small-scale signal envelope fading parameters to their narrowband counterparts for different standards like Dedicated Short Range Communication, WiMAX, Universal Mobile Telecommunications Service, and the family of the IEEE 802.11 standards. This mapping enables narrowband small-scale signal envelope fading statistical distributions, which are currently used, e.g., in fading simulators, link quality determination algorithms, and outage probability calculators, to be readily adapted to deal with small-scale wideband signal envelope fading. As an application example of this proposed mapping, we derive the appropriate sample spacing and averaging interval (window size) that ought to be used to estimate the large-scale fading signal in an IEEE 802.11 receiver.