Numerical Results

Figures 2 and 3 show typical results from Monte-Carlo simulations using Gauss-Markov channel coefficients. Figure 2 shows the direct MAP PSP GVA algorithm for a Gauss-Markov channel with zero mean and covariance ${\bf C} = v {\bf I}$ with v = 0.001. This illustrates that even for small L near optimum results can be obtained. Figure 3 is a comparison of EM and direct MAP, using parameters n = 10, M = 3, $\alpha = 0.995$, v = 0.01, ${\bf d} = {\bf0}$, and ${\bf C} = v ~ {\bf I}$. The direct MAP BER results were obtained by an exhaustive search of the ML cost function. Two different initializations for the EM algorithm were used, both of which produce unreasonably large BER. Initialization 1 (init #1) used known ${\bf h}_1$ and ${\bf h}_k = \alpha {\bf h}_{k-1}, ~ k =2 \ldots n$. Initialization 2 used known ${\bf h}_1$ and 0's for the initial symbol estimates. Other researchers have found that EM initialization can be improved using pilot bits. We have performed many simulations which confirm that EM with proper initialization can provide MAP results.

  

Figure 2: BER for Gauss-Markov PSP

  

Figure 3: BER for different Gauss-Markov EM initializations