5. Computer Exercise Consider the following observation model where B and are statistically independent else E B (a) Compute the AMMSE estimator of B from Y. Simplify as much as possible (b) Determine the expression for the associated mean-square error, again, simplify as much as possible (c) Compute the causal AMMSE estimator of B from Y. Simplify as much as possible (d) Determine the expression for the associated mean-square error, again, simplify as much as possible (e) Design a simulation study to investigate the performance of the AMMSE and causal AMMSE estimators. Generate B as a Gaussian vector (zero-mean, unit variance, iid) and also as a binary vector where B-1 with probability 1 and the components of B are independent Plot the computed MSEs (derived above) and simulated MSEs as a function of i, different values of a (consider values such as -0.1 and -_0.8, so less than one in magnitude, but positive and negative) ii. different values of 2 (eg. . 0.01, 0.1, 0.5 etc.) ii. different values of the length of the vectors, 10, 20,50, 100etc.. For your simulations, you will want to generate at least a few hundred realizations of the vectors in order to average your empirical MSE. The Matlab command toeplit:z will be helpful. You should have at least three plots with four to six curves each depending on how many curves you want to include in a single plot (i.e. Gaussian binary B, two different estimators and the MSEs of the two different estimators, etc.) The MSE will be along the y-axis and either varying or n along the r-axis (f) Discuss your results. Provide the plots and a discussion and include your code (g) Something to consider -how is the computed MSE for the Gaussian B different from that for the binary B? 5. Computer Exercise Consider the following observation model where B and are statistically independent else E B (a) Compute the AMMSE estimator of B from Y. Simplify as much as possible (b) Determine the expression for the associated mean-square error, again, simplify as much as possible (c) Compute the causal AMMSE estimator of B from Y. Simplify as much as possible (d) Determine the expression for the associated mean-square error, again, simplify as much as possible (e) Design a simulation study to investigate the performance of the AMMSE and causal AMMSE estimators. Generate B as a Gaussian vector (zero-mean, unit variance, iid) and also as a binary vector where B-1 with probability 1 and the components of B are independent Plot the computed MSEs (derived above) and simulated MSEs as a function of i, different values of a (consider values such as -0.1 and -_0.8, so less than one in magnitude, but positive and negative) ii. different values of 2 (eg. . 0.01, 0.1, 0.5 etc.) ii. different values of the length of the vectors, 10, 20,50, 100etc.. For your simulations, you will want to generate at least a few hundred realizations of the vectors in order to average your empirical MSE. The Matlab command toeplit:z will be helpful. You should have at least three plots with four to six curves each depending on how many curves you want to include in a single plot (i.e. Gaussian binary B, two different estimators and the MSEs of the two different estimators, etc.) The MSE will be along the y-axis and either varying or n along the r-axis (f) Discuss your results. Provide the plots and a discussion and include your code (g) Something to consider -how is the computed MSE for the Gaussian B different from that for the binary B
