8. Variable Parameter APAs

The standard APA has three parameters: the step-size parameter, the projection order, and the regularization factor, which are all assumed to be invariable in the preceding chapters. However, by adjusting those parameters adaptively, it is possible to improve the performance of the APA. This chapter gives an overview of such variable parameter APAs. First, two variable step-size APAs are reviewed. The second topic is the proportionate APA, in which each component of the coefficient vector of the adaptive filter is given a step-size that is approximately proportional to its own magnitude. The proportionate technique is effective for echo cancellation, where the impulse response of the unknown system is sparse and long. The third topic is the evolving order APA. The projection order gives a definite influence on the behavior of the APA, i.e., a larger projection order results in faster convergence with a larger misadjustment. In the evolving order APA, the projection order is so adjusted that it takes a large value in the initial convergence phase, and a small value in the steady-state phase. The last topic is the variable regularized APA. Two methods are described, one based on minimization of the a posteriori error, and the other using a variable regularization matrix. In the latter method, the eigenvalues of the matrix to be regularized are given different regularization parameters individually.