  Covariance matrix reconstruction is a topic of great significance in the
field of one-bit signal processing and has numerous practical applications.
Despite its importance, the conventional arcsine law with zero threshold is
incapable of recovering the diagonal elements of the covariance matrix. To
address this limitation, recent studies have proposed the use of non-zero
clipping thresholds. However, the relationship between the estimation error and
the sampling threshold is not yet known. In this paper, we undertake an
analysis of the mean squared error by computing the Fisher information matrix
for a given threshold. Our results reveal that the optimal threshold can vary
considerably, depending on the variances and correlation coefficients. As a
result, it is inappropriate to use a constant threshold to encompass parameters
that vary widely. To mitigate this issue, we present a recovery scheme that
incorporates time-varying thresholds. Our approach differs from existing
methods in that it utilizes the exact values of the threshold, rather than its
statistical properties, to enhance the estimation performance. Our simulations,
including the direction-of-arrival estimation problem, demonstrate the efficacy
of the developed scheme, especially in complex scenarios where the covariance
elements are widely separated.
