Mean squared error threshold prediction of adaptive maximum likelihood techniques

Below a threshold signal-to-noise ratio (SNR), the mean squared error (MSB) performance of nonlinear maximum-likelihood (ML) estimation degrades swiftly. Threshold SNR prediction for ML signal parameter estimation requiring intermediate estimation of an unknown colored noise covariance matrix is facilitated via an interval error based method of MSE prediction. Exact pairwise error probabilities are derived, that with the union bound provide accurate prediction of the true interval error probabilities. A new modification of the Cramer-Rao bound involving the analog of the Reed, Mallett, and Brennan beta loss factor appearing in the error probabilities provides excellent prediction of the asymptotic (SNR→∞) MSE performance of the estimator. Together, remarkably accurate prediction of the threshold SNR is obtained.