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Statistics of cascaded Rayleigh fading channels with arbitrary correlation

Exact expressions for the probability density function (PDF) and cumulative distribution function (CDF) of cascaded Rayleigh fading channels with arbitrary correlation but not necessarily identically distributed are derived. Furthermore, the PDF and CDF of the instantaneous signal-to-noise ratio are obtained. The cascaded channels are assumed to have slow frequency non-selective arbitrarily correlated Rayleigh fading with arbitrarily values of fading parameters. Indeed, the expressions of the outage probability and average normalised channel capacity for this channel model are derived. The average bit error probability for coherently detected binary signals in additive white Gaussian noise channel as well as in arbitrarily correlated cascaded Rayleigh fading channels is obtained. Numerical results are also provided and authenticated by Monte Carlo simulation. To the best of the authors' knowledge, the derived expressions for this channel model are new and have not been reported in the literature.