We want to estimate the vector H from the vector Z.We need to know the covariance matrix for Z and the covariance between H and Z.The covariance matrix for Z has the i-th row, j-th column being E[ZiZj].You should be able to complete this for each i and j.Similarly for the covariance between Hi and Zj.

A communication 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 Z1 = H1+ N1, Zz = H2 + N2, Z3 = H3 + N3, where Hi, i = 1, 2, 3 represents the signal fading level at the three different frequencies and Ni, i = 1, 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 0 CH = 1 0 1 where o = 1/2. The noise N1, N2, Na have mean zero and variance 1 and are indepen dent of each other and also independent of the fading H = [H1, H2, Ha]'. (@) Find the best (linear or otherwise) estimate of H1, H2 and He from the observations Z1, Zz, Z3