Analysis of the adaptive correlation enhancer

Abstract

Adaptive filtering has become a major component in the field of digital signal processing, presumably because of the self-adjusting property of the filters. Because noise statistics are often unknown or are time-varying, designing a fixed filter that performs well in all cases may not be possible. The adaptive filter is able to adjust the impulse response according to the input data and normally provide a filter suitable for processing the current input data. The majority of adaptive algorithms require the use of feedback and the minimization of an error criterion, such as mean-squared error (MSE). To minimize the error, the coefficients of the filter are recursively updated in a manner that forces error reduction. The most well-known technique for adjusting the filter weights is the method of steepest descent, which searches for the minimum point on a performance surface by finding the gradient and adjusting the filter weights in a direction opposite the gradient [l, 21. Computation of the gradient requires knowledge of the correlation matrix of the input data and a cross-correlation vector between the input data and data which represent the desired filter output. These statistical quantities are normally not known in advance, making the method of steepest descent extremely difficult to implement. Because the necessary statistical parameters were not available, instantaneous estimates were used, which led to the popular least-mean-square (LMS) adaptive filter update algorithm [ 1,2 1. The LMS algorithm, while easy to implement, is capable of providing excellent performance, even though it has relatively slow convergence characteristics and its performance is governed by the ratio of the maximum and