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

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. Copyright © 2011 John Wiley & Sons, Ltd.