Analysis of convolutional code performance in generalized fading channels

An elegant method for analytical evaluation of the bit error probability in multipath fading channels is presented. Even though that method can be applied for more general problems, we restrict ourselves on the investigation of convolutionally coded user data transmission in UMTS FDD and cdma2OOO systems, i.e. the data is channel encoded by a rate 1/2 or rate 1/3 256-state maximum free distance convolutional code and a rate 1/4 or rate 1/6 256-state optimum distance spectrum code, respectively. We generalize the well-known analytical expression for the pairwise error probability of a single path Rayleigh channel to the case of a generalized multipath fading channel, where the individual paths are not necessarily identically distributed. The error probability can be tightly bounded (union bound) in a closed form expression by use of a sum over the code's information error weight distribution and an integral over a finite interval which is easily evaluated numerically. We present some examples that show the behavior of the error probability in AWGN as well as in single and multipath Nakagami-m fading channels.