A New Method for The Evaluation of Pair Error Probabilities in the Correlated Rayleigh Fading Channel

Abstract—We present an new method for the analytical calculation of the error probability in a Rayleigh fading channel with correlated fading amplitudes. Even though the method can be applied for more general problems, we restrict ourselves on the investigation of a multicarrier CDMA transmission. The frequency correlation between the fading amplitudes of the carriers is given by the delay power spectrum of the channel. We generalize the wellknown analytical expressions for the pairwise error probability of the uncorrelated Rayleigh channel to this case of correlated fading. This probability can be expressed in a closed form by an integral over a finite interval which can be easily evaluated numerically. We present some examples to show how much of the diversity of a code remains useful if the transmission channel does not provide an arbitrary degree of diversity. Keywords— Multicarrier CDMA, Diversity, Coding, Correlated Rayleigh Fading.