Signal Amplitude Estimation and Detection From Unlabeled Binary Quantized Samples

Signal amplitude estimation and detection from unlabeled quantized binary samples are studied, assuming that the order of the time indexes is completely unknown. First, 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, and an alternating maximization algorithm is proposed to solve the general problem via good initialization. In addition, the statistical identifiability of the model is studied. Furthermore, an approximation of the generalized likelihood ratio test detector is adopted to detect the presence of the signal. In addition, an accurate approximation of the probability of successful permutation matrix recovery is derived, and explicit expressions are provided to reveal the relationship between the signal length and the number of quantizers. Finally, numerical simulations are performed to verify the theoretical results.