Mean-Squared Error Analysis of Adaptive Subband-Based System Identification

Subband-based system identification is considered. The analysis in this paper gives geometric insights into the source of error in subband-based system identification. In particular, the mean-squared error arises as the residual after an orthogonal projection onto a subspace defined by the analysis filter impulse response. The minimum mean-squared identification error, which depends on the impulse response of the unknown system, is shown to be upper bounded by the error in a deterministic least-squares problem that involves the analysis filter response but is independent of the unknown system. The upper bounds may be used as criteria for analysis filter design that minimize the mean-squared error for the worst case unknown system, i.e., this is a minimax approach. An alternative subband processing structure is inspired by minimizing the projection residual. Examples show that significant reduction in minimum mean-squared error is possible.