Sample covariance matrix parameter estimation: carrier frequency, a case study

The paper presents a novel approach to parameter estimation based on sample covariance matrix linear processing. The originality of this framework relies upon two facts: (1) the Gaussian assumption about the nuisance parameters is avoided; (2) quadratic feed-forward schemes are designed saving the complexity and delay of conventional ML-based algorithms that carry out an exhaustive search throughout the whole parameter range. This second aim is achieved by adopting a Bayesian perspective in which the parameter of interest is modeled as a random variable of known a priori distribution. The Bayesian approach allows us to establish certain optimality criteria (mean squared error, bias and variance) yielding to estimation schemes with the best performance on the average, that is, with respect to the assumed prior of the parameter. In order to illustrate the proposed theory, we address the problem of frequency estimation in digital communications. This example has been chosen because its formulation encompasses several problems of special interest such as non-data-aided open-loop carrier synchronization, direction-of-arrival estimation in narrow-band uniform linear arrays and, if the signal is processed in the frequency domain, timing recovery and time-of-arrival estimation in positioning systems, as well.