Aspects of threshold region mean squared error prediction: Method of interval errors, bounds, Taylor's theorem and extensions

Abstract

The method of interval errors (MIE) predicts mean-squared error (MSE) performance at low signal-to-noise ratios (SNR) where global errors dominate. It is algorithm specific and enabled by an estimate of asymptotic MSE performance and sidelobe error probabilities. Parameter bounds are adequate representations of the asymptotic MSE in absence of signal model mismatch, but Taylor theorem can account for this mismatch. Herein limitations of bounds versus Taylor's theorem to represent the asymptotic MSE of nonlinear schemes like maximum-likelihood are discussed. Use of first-order Taylor expansions for the purpose of improved approximation of sidelobe error probability is likewise explored.