Steady-State MSE Performance of the Set-Membership Affine Projection Algorithm |
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Authors: | Markus V S Lima Paulo S R Diniz |
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Affiliation: | 1. LPS, PEE/COPPE/Poli, Federal University of Rio de Janeiro, P.O. Box 68504, Rio de Janeiro, RJ, 21941-972, Brazil
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Abstract: | The set-membership affine projection (SM-AP) algorithm has many desirable characteristics such as fast convergence speed, low power consumption due to data-selective updates, and low misadjustment. The main reason hindering the widespread use of the SM-AP algorithm is the lack of analytical results related to its steady-state performance. In order to bridge this gap, this paper presents an analysis of the steady-state mean square error (MSE) of a general form of the SM-AP algorithm. The proposed analysis results in closed-form expressions for the excess MSE and misadjustment of the SM-AP algorithm, which are also applicable to many other algorithms. This work also provides guidelines for the analysis of the whole family of SM-AP algorithms. The analysis relies on the energy conservation method and has the attractive feature of not assuming a specific model for the input signal. In addition, the choice of the upper bound for the error of the SM-AP algorithm is addressed for the first time. Simulation results corroborate the accuracy of the proposed analysis. |
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