This paper presents a model for RF broadband ultrasonic A-scans obtained from materials composed of microstructures, in which isolated flaws or impurities may exist. The model incorporates both the RF phase and magnitude differences between the microstructure and coherent flaw echo spectra. An adaptive implementation of the maximum-likelihood estimator (MLE) is presented for estimating A-scan amplitudes associated with coherent scatterers embedded in grain echoes. The adaptive implementation is motivated by the nonstationary behavior of the back-scattered energy received over the duration of the A-scan [1]. This nonstationarity results from the frequency dependent absorption, scattering, and diffraction that occurs as the pulse propagates through the material