Question: A sinusoid of known frequency ω0 is observed in the presence of an additive WGN V (n) with zero mean and variance σ2. The observations can be expressed as
Y (t) = A cos(ω0t) + V (n), for 0 ≤ t ≤ N - 1.
(a) Find the uniform minimum variance unbiased estimate of amplitude A, assuming σ2 is known.
(b) Assuming now that both A and σ2 are unknown, find the minimum variance unbiased estimates of A and σ2.
(c) Repeat parts (a) and (b) for the ML estimates. Are the ML and UMVU estimates identical?
(d) Evaluate the matrix Cram´er-Rao bound for the joint estimation of A and σ2.
(e) Evaluate the bias and variances of the joint ML and UMVU estimates of A and σ2 and compare them to the Cram´er-Rao bound.