A generalisation of the Rayleigh distribution with applications in wireless fading channels

Abstract

The signal received in a mobile radio environment exhibits rapid signal level fluctuations which are generally Rayleigh-distributed. These result from interference by multiple scattered radio paths between the base station and the mobile receptor. Fading-shadowing effects in wireless channels are usually modelled by means of the Rayleigh-Lognormal distribution (RL), which has a complicated integral form. The K-distribution (K) is similar to RL but it has a simpler form and its probability density function admits a closed form; however, due to the Bessel function, parameter estimates are not direct. Another possible approach is that of the Rayleigh-inverse Gaussian distribution (RIG). In this paper, an alternative is presented, a generalisation of the Rayleigh distribution which is simpler than the RL, K and RIG distributions, and thus more suitable for the analysis and design of contemporary wireless communication systems. Closed-form expressions for the bit error rate (BER) for differential phase-shift keying (DPSK) and minimum shift keying (MSK) modulations with the proposed distribution are obtained. Theoretical results based on statistically well-founded distance measurements validate the new distribution for the cases analysed.