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A conm1unication system transmits a sinusoidal signal at three different frequencies. The propagation of the signal causes fading. The receiver measures the signal strength at the three frequencies. The measurement results are Z! = HidN1, H2+N2, 3 = H3+N31I .5}? II where Hi, i = 1., 2, 3 represents the signal fading level at the three different frequencies and M, i = II 2, 3 represents the measurement noise. The fading levels at the three different frequencies are known to be zero mean Gaussian with covariance matrix 1 o: [l SH: (1' l. {1' U o: 1 where cr = lf. The noise N1, N2, N3 have mean zero and variance 1 and are indepen- dent of each other and also independent of the fading H = [H1I H2, H3]'. {a} Find the best [linear or otherwise} estimate of H1, H3 and H3 from the observations Zia 321: 33' {11) Find the mean squared error of the estimates of each of the fading levels