Signal power upper bound in parameter estimation

In this note, an upper bound on the signal power corresponding to a hypothesized model is derived assuming unknown signal and noise characteristics. A residual matrix is obtained from the observed data correlation matrix by subtracting a weighted outer product of the model vector. The upper bound is the largest signal power such that the residual correlation matrix stays nonegative. It is shown that this bound is the same as the minimum variance (or the maximum likelihood with Gaussian assumption) estimate of the signal power for the given model.