Statistical performance of a data-based covariance estimator

Data covariance is typically estimated by a sample average method. The second-order statistics of this sample covariance are encountered in evaluating the performance of many covariance-based processing methods. This correspondence derives closed-form expressions for the second-order statistics of a vectored sample covariance. Given a baseband communication system model, the results explicitly rely on the channel parameters and the second- and fourth-order statistics of the channel noise and inputs. They can be directly applied to study statistical properties of covariance-based methods such as a correlation-matching-based channel-estimation method in a code-division multiple-access system. Numerical examples are provided to further verify the derived results.