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The LMS algorithm was used to adaptively equalize a communication channel for which the autocorrelation matrix r has an eigenvalue spread of Amax/4 min = 11. The number of taps selected for the equalizer was 2K + 1 = 11. The input signal plus noise power xo + N, was normalized to unity. Hence, the upper bound on a given by (11-1-32) is 0.18. Figure 11-1-4 illustrates the initial convergence characteristics of the LMS algorithm for 4 = 0.045, 0.09, and 0.115, by averaging the (estimated) MSE in 200 simulations. We observe that by selecting A = 0.09 (one-half of the upper bound) we obtain relatively fast initial convergence. If we divide A by a factor of 2 to A = 0.045, the convergence rate is reduced but the excess mean square error is also reduced, so that the LMS algorithm performs better in steady state in a time-invariant signal environment). Finally, we note that a choice of A=0.115, which is still far below the upper bound, causes large undesirable fluctuations in the output MSE of the algorithm.