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Fast Affine Projection Algorithm: Full Version
Authors
	Djigan V.I.
Date of publication
	2016
Abstract
	The paper considers a fast affine projection algorithm for multichannel adaptive filters with complex-valued weights. The filter may have different number of weights in its channel. The architecture of such filter is presented. It is shown a general form of the multichannel affine projection algorithm. The normalization matrix of the algorithm consists of the sum of such matrices over all channels. All the matrices have the same dimension, that is a square of the projection size. Each of the matrices is evaluated on its own sliding window of the samples which corresponds the number of the weights of the proper channels of the adaptive filter. It is presented a full computational procedure of the fast version of the algorithm, which takes into the consideration the above peculiarity of the multichannel adaptive filter. The procedure also includes the linear prediction of input signals, used for the fast computation of the vector of the normalized errors of the adaptive filter. The procedure is adopted from the sliding window stabilized fast recursive least squares algorithm. Original version of the single-channel fast affine projection algorithm does not compute the adaptive filter output signal explicitly. At the same time, the signal is required in a number of applications of adaptive filters. It is shown how to compute the signal in the multichannel fast affine projection algorithm without increasing the algorithm complexity. Besides, a procedure of a variable step-size computation, based on the gradient search strategy, is also presented. The computation complexity of the different parts of the fast affine projection algorithm is evaluated. According the evaluation, the complexity is a linear function of the total number of weights in the adaptive filter channels, number of the channels and projection order. Simulation results of the two-channel adaptive filter in the active noise control task demonstrates the developed algorithm efficiency.
Keywords
	multichannel adaptive filter, fast affine projection algorithm, variable step-size, output signal calculation.
Library reference
	Djigan V.I. Fast Affine Projection Algorithm: Full Version // Problems of Perspective Micro- and Nanoelectronic Systems Development - 2016. Proceedings / edited by A. Stempkovsky, Moscow, IPPM RAS, 2016. Part 1. P. 202-209.
URL of paper
	http://www.mes-conference.ru/data/year2016/pdf/D096.pdf