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exer - Solutions to Problem Set#2 EECE-595 Section II...

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Solutions to Problem Set #2 EECE-595, Section II Spring 2003, Adaptive Filtering Date Assigned: 03/04/03 Date Due: 03/11/03 Observations Experiment I For the experiments with α = 0 . 6, we can observe that the smallest MSE is achieved when the normalized step-size β = 0 . 5 due to the fact that the excess mean-squared error and consequently the misadjustment is small, but the convergence of the tap-weights is slow due to the fact that we are taking smaller steps towards the optimal solution. When we increase the step-size the convergence time decreases but this comes at the price of larger misadjustment. Particularly when the normalized step-size is β = 1 . 5 and β = 1 . 9 the misadjutment is very large and renders the solution completely unacceptable. We can further observe that increasing the order of the filter improves the MSE performance of the NLMS adaptive equalizer by a small amount but this also comes at the price of larger convergence time due to the fact that there are more tap-weight error modes that need to converge. In a real equalizer design problem this would amount to requiring more training or pilot symbols. This can be attributed to the fact that to ideally invert the effect of the channel an IIR
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