Sample covariance matrix based parameter estimation for digital synchronization

In this paper we develop a new, versatile framework for the design of optimal non-data-aided (NDA) parameter estimators based on the exploitation of the received signal sample covariance matrix. The estimator coefficients are optimized in. order to yield minimum mean squared error (MSE) estimates of the parameter. Some linear constraints are introduced into the optimization process allowing the designer to have control over the estimator characteristic response. For those scenarios where bias is forbidden, as it happens in ranging applications, we provide the optimal solution minimizing the estimates bias within the range of the received parameter. The adopted approach is Bayesian as we treat the wanted parameter as a random variable with a known a priori probability distribution (prior). This modeling allows us to unify the design of both open- and closed-loop estimators. The proposed formulation encompasses all the linear modulations as well as the binary continuous phase modulation (CPM). The new approach supplies optimal estimation schemes without the need of assuming a given statistics for the unknown symbols, that is, avoiding the common adoption of the Gaussian assumption, which does not apply in digital communications. Special attention is paid to those low-complexity implementations for which the maximum likelihood efficiency is not guaranteed.