On the statistical properties of selection combining cooperative diversity over double Rice fading channels

This paper investigates the statistical properties of selection combining (SC) cooperative diversity over double Rice narrow-band fading channels under the transparent or amplify-and-forward (AF) strategy. It is assumed that the source, the destination, and relay stations are all equipped with single antenna. The Doppler power spectral density, associated with each of the double Rice fading processes, is considered to be symmetrical about the carrier frequency. Under the above conditions, analytical integral expressions are derived for the probability density function (PDF) and the cumulative distribution function (CDF) of the SC fading envelopes. Also, expressions for the level crossing rate (LCR) as well as the average duration of fades (ADF) are determined. For some cases, the integral expressions are shown to be approximated using the Laplace's method of integration. The approximations are verified to be accurate when the number of relay stations is large. The obtained results include those corresponding to the double Rayleigh and combined Rayleigh×Rice models as special cases of the double Rice fading channel. The validity of all the presented theoretical results are checked by computer simulations.