Hidden Markov Modeling of Error Patterns and Soft Outputs for Simulation of Wideband CDMA Transmission Systems

In this paper, a Hidden Markov Modeling (HMM) technique for a fast and accurate simulation of bit errors and soft outputs in wireless communication systems is presented. HMMs with continuous probability distributions are considered. Soft outputs and bit errors are combined to error patterns. We focus on binary phase–shift keying (BPSK) modulation for direct–sequence spread spectrum (code–division multiple access, CDMA) transmission as proposed e.g. for the third generation wireless communication system UMTS (uplink for the frequency division duplex mode (FDD)). Comparisons of simulated bit error rates for HMM models and Rake receivers are shown for AWGN, flat fading, and vehicular channel conditions. In order to assess the ability of the HMM to describe the dynamical behaviour of the channel a comparison for transmission with interleaving and convolutional coding is presented. Furthermore calculated autocorrelation functions of the error patterns and error gap distributions corresponding to the Rake receiver and to the HMM, respectively, are presented. Our investigations show a strong dependence of the required HMM order on E_b/N₀ and the channel conditions. The degree of accordance of the HMM outputs and the training data is examined based on calculated statistical scoring indicators.