On the Efficiency of SNR Estimation via Birnbaum's Method

The problem of signal-to-noise ratio (SNR) estimation for a linear Gaussian observation model when independent sequences of noisy signal and pure noise measurements are available is considered from the perspective of Birnbaum's sequential sampling method, which transforms the observed signal and noise sequences into a single sequence of Bernoulli random variables. The minimum-variance unbiased estimator for the SNR based on the transformed binary sequence is derived and shown to achieve the corresponding Cramer-Rao lower bound. Some remarks on parameter selection for the transformation are provided and its efficiency is analyzed in relation to that of the standard approach acting on the raw measurements. The proposed method may draw attention due to its simplicity of application in terms of data storage, computation, and bandwidth requirements.