Log-moment estimators of the Nakagami-lognormal distribution

Juan Reig,Conor Brennan,Lorenzo Rubio,Vicent M Rodrigo Peñarrocha

doi:10.1186/s13638-018-1328-6

Abstract

In this paper, estimators of the Nakagami-lognormal (NL) distribution based on the method of log-moments have been derived and thoroughly analyzed. Unlike maximum likelihood (ML) estimators, the log-moment estimators of the NL distribution are obtained using straightforward equations with a unique solution. Also, their performance has been evaluated using the sample mean, confidence regions and normalized mean square error (NMSE). The NL distribution has been extensively used to model composite small-scale fading and shadowing in wireless communication channels. This distribution is of interest in scenarios where the small-scale fading and the shadowing processes cannot be easily separated such as the vehicular environment.

Highlights

1 Introduction In wireless communications, the composite Nakagamilognormal (NL) distribution has been extensively employed to model the mixture of small-scale fading and shadowing [1,2,3,4,5,6,7,8,9,10,11,12,13,14]
The results show that the normalized mean square error (NMSE) of the fading parameter estimator is very dependent on both the shadowing standard deviation and the fading parameter even when the number of samples is significant, N = 100, 000
The NMSE of the shadowing standard deviation estimator remains significantly small for a number of samples not excessively high, i.e., N = 10, 000, with values ranging from 5.3 × 10−4 to 1.2 × 10−1 for m = 2.7, σd = 8 dB and m = 1.3, σd = 1 dB, respectively

Summary

Introduction

The composite Nakagamilognormal (NL) distribution has been extensively employed to model the mixture of small-scale fading and shadowing [1,2,3,4,5,6,7,8,9,10,11,12,13,14] This distribution was initially proposed in [1] to obtain the outage probability in scenarios involving multiple co-channel interferers. In order to analyze the performance of cellular networks over different conditions (modulations schemes, diversity techniques, etc) in a given scenario where the propagation channel is modeled as a NL distribution, one first needs to estimate the parameters of the NL distribution in real environments from measurement campaigns.

Methods

Log-cumulants of the Nakagami-lognormal Distribution

Findings

Conclusions