Signal Amplitude Estimation and Detection from Unlabeled Binary
Quantized Samples
release_jq4xg7n44vc5hhdz3xfxhgqlm4
by
Guanyu Wang, Jiang Zhu, Rick S. Blum, Peter Willett, Stefano Marano,
Vincenzo Matta, Paolo Braca
2018
Abstract
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
initial estimates. In addition, the statistical identifiability of the model is
studied.
Furthermore, the generalized likelihood ratio test (GLRT) detector is adopted
to detect the presence of signal. In addition, an accurate approximation to the
probability of successful permutation matrix recovery is derived, and explicit
expressions are provided to reveal the relationship between the number of
signal samples and the number of quantizers. Finally, numerical simulations are
performed to verify the theoretical results.
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