A unified approach to tracking performance analysis of the selective partial update adaptive filter algorithms in nonstationary environment

In this paper, a unified approach to mean-square performance analysis of the family of selective partial update (SPU) adaptive filter algorithms in nonstationary environment is presented. Using this analysis, the tracking performance of Max normalized least mean squares (Max-NLMS), N-Max NLMS, the various types of SPU-NLMS algorithms, SPU transform domain LMS (SPU-TD-LMS), the family of SPU affine projection algorithms (SPU-APA), the family of selective regressor APA (SR-APA), the dynamic selection of APA (DS-APA), the family of SPU-SR-APA, the family of SPU-DS-APA, SPU subband adaptive filters (SPU-SAF), and the periodic, sequential, and stochastic partial update LMS, NLMS, and APA as well as classical adaptive filter algorithms can be analyzed with a unified approach. Two theoretical expressions are introduced to study the performance. The analysis is based on energy conservation arguments and does not need to assume a Gaussian or white distribution for the regressors. We demonstrate through simulations that the derived expressions are useful in predicting the performance of this family of adaptive filters in nonstationary environment.

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