Accuracy of the Wiener-Hopf Solution When Based on Sample Statistics

This paper addresses the problem of an adaptive linear combiner when using sample statistics. In this case, the Wiener-Hopf solution can be based on sample covariance matrices and cross-correlation vectors. Despite these estimates being inaccurate, the calculated, approximate solution can be very precise. We explore why this is so by interpreting the Wiener-Hopf solution as coming from a least squares problem. We compare this solution to the case where we exploit knowledge about some of the statistics. Surprisingly this has very limited benefits and often is detrimental. We also show why it is disadvantageous to separately estimate the two statistics.