Maximum Likelihood Signal Amplitude Estimation Based on Permuted Blocks of Differently Binary Quantized Observations of a Signal in Noise

Parameter estimation based on binary quantized observations is considered given the estimation system does not know which of a set of quantizers was used, without replacement, for each block of observations. Thus the estimation system receives permutated blocks of quantized samples of a signal in noise with unknown signal amplitude. Maximum likelihood (ML) estimators are utilized to estimate both the permutation matrix and unknown signal amplitude under arbitrary, but known, signal shape and quantizer thresholds. Sufficient conditions are provided under which an ML estimator can be found in polynomial time. In addition, model identifiability is also studied, and an alternating maximization algorithm is proposed to solve the general problem via good initial estimates. Finally numerical simulations are performed to evaluate the performances of the ML estimators.