New generalised approximation methods for the cumulative distribution function of arbitrary multivariate Rayleigh random variables

Based on our previous works, we revise a simple series expansion for multivariate probability density functions (PDF) of the Rayleigh distribution. From there we derive a similar expression for the cumulative density function (CDF) of multivariate Rayleigh random variables of arbitrary dimension and covariance matrix. The CDF is of particular interest as it can be used to compute outage probabilities of multi-channel wireless systems, for which we provide an example. We compare the performance of the newly proposed approximation to recently proposed methods based on numerical integration methods

Efficiency of two decoders based on hash techniques and syndrome calculation over a Rayleigh channel

The explosive growth of connected devices demands high quality and reliability in data transmission and storage. Error correction codes (ECCs) contribute to this in ways that are not very apparent to the end user, yet indispensable and effective at the most basic level of transmission. This paper presents an investigation of the performance and analysis of two decoders that are based on hash techniques and syndrome calculation over a Rayleigh channel. These decoders under study consist of two main features: a reduced complexity compared to other competitors and good error correction performance over an additive white gaussian noise (AWGN) channel. When applied to decode some linear block codes such as Bose, Ray-Chaudhuri, and Hocquenghem (BCH) and quadratic residue (QR) codes over a Rayleigh channel, the experiment and comparison results of these decoders have shown their efficiency in terms of guaranteed performance measured in bit error rate (BER). For example, the coding gain obtained by syndrome decoding and hash techniques (SDHT) when it is applied to decode BCH (31, 11, 11) equals 34.5 dB, i.e., a reduction rate of 75% compared to the case where the exchange is carried out without coding and decoding process

Series approximations for Rayleigh distributions of arbitrary dimensions and covariance matrices

The multivariate Rayleigh distribution is of crucial importance to many applied problems of engineering, such as in the analysis of multi-antenna wireless systems. Due to the lack of a generalised closed form of the distribution, the dependence on effective approximation methods for evaluation has created numerous numerical approaches with considerable restrictions in both dimensionality, as well as the structure of covariance matrices. In this paper we extend a previously introduced method [1] without either of these limitations. We then compare the performance of the new algorithms to recent integration methods of fixed dimension, presented by Beaulie and Zhang [2] and highlight the advantages of the new method

Distributions of multiuser-MIMO under correlated generalised-Rayleigh fading

Under even degrees of freedom, new single-integral and infinite-summation selection combiner output signal-to-noise ratio and signal-to-interference-and-noise ratio distributions of multivariate equally-correlated generalised-Rayleigh fading for multiuser-multiple-input-multiple-output (MU-MIMO) systems are obtained. The proposed findings can be employed to approximate intractable distributions of multivariate exponentially-correlated Rician fading. An average bit error rate of the differential binary phase-shift keying scheme for MIMO networks is derived using the new distributions, showing their efficiency for network assessment

Distributions of multiuser-MIMO under correlated generalised-Rayleigh fading

Under even degrees of freedom, new single-integral and infinite-summation selection combiner output signal-to-noise ratio and signal-to-interference-and-noise ratio distributions of multivariate equally-correlated generalised-Rayleigh fading for multiuser-multiple-input-multiple-output (MU-MIMO) systems are obtained. The proposed findings can be employed to approximate intractable distributions of multivariate exponentially-correlated Rician fading. An average bit error rate of the differential binary phase-shift keying scheme for MIMO networks is derived using the new distributions, showing their efficiency for network assessment