Chernoff bound of trellis-coded modulation over correlated fading channels

N radio and satellite channels, system performance is 0 degraded by Rician or Rayleigh fading resulting from multipath propagation. Performance can be improved by channel coding combined with interleaving; the deinterleaver at the receiver allows decorrelation of the fading. A criterion, deduced from a Chemoff error probability bound, for the design of trellis-coded modulation for uncorrelated fading channel was given in [ 2 ] . It consists of maximizing the Hamming distance in symbols between the coded transmitted sequences, and the Euclidean distance between trellis branches. When deriving the error probability bound, it was assumed that the received samples are affected by uncorrelated fades. This implies that perfect interleaving has been accomplished. In some cases, like the mobile radio channel whose fading autocorrelation function is a slowly decreasing Bessel function, such interleaving cannot be achieved since it requires unacceptable large time delay. In this paper, we derive a Chernoff painvise error probability bound for the case of correlated fades. Obviously, uncorrelated fading represents a special case of our result. The bound is valid for any type of convolutional encoding and linear modulation. We use trellis-coded modulation as an application. We apply it to design the optimum codes for systems with correlated fading. The paper is organized as follows. Section I1 describes the system model under study. The calculation of the painvise error probability bound is presented in Section 111. In Section IV, we give indications on the design of codes for correlated fading channel. In order to illustrate our results, we apply them, in Section V, to the case of mobile radio channel. The conclusion is summarized in Section VI.