Partial-Update L∞ -Norm Based Algorithms

Dept. of Electr. & Comput. Eng., Concordia Univ., Montreal, Que.
Circuits and Systems I: Regular Papers, IEEE Transactions on (Impact Factor: 2.4). 03/2007; 54(2):411 - 419. DOI: 10.1109/TCSI.2006.883863
Source: IEEE Xplore


The computational complexity of an adaptive filtering algorithm increases with increasing the filter tap length and therefore, the use of such a filter can become prohibitive for certain applications, especially for real-time implementation. In this paper, we develop low-complexity adaptive filtering algorithms by incorporating the concept of partial updating of the filter coefficients into the technique of finding the gradient vector in the hyperplane based on the Linfin-norm criterion. Two specific partial update algorithms based on the sequential and M-Max coefficient updating are proposed. The statistical analyses of the two algorithms are carried out, and evolution equations for the mean and mean-square of the filter coefficient misalignment as well as the stability bounds on the step size are obtained. It is shown that the proposed partial update algorithm employing the M-Max coefficient updating can achieve a convergence rate that is closest to that of the full update algorithm. Finally, simulations are carried out to validate the theoretical results and study the convergence rate of the proposed algorithms

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    • "Since it is not feasible to obtain the exact value in (11), we replace it with an instantaneous value. For a large M, the fluctuations in the input signal energy ||u i || 2 from one iteration to the next are small enough to justify the approximation below [1], [15]. "
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    ABSTRACT: We present a new structure for parallel affine projection (AP) filters with different step-sizes. By observing their error signals, the proposed alternating AP (A-AP) filter selects one of the two AP filters and updates the weights of the selected filter for each iteration. As a result, the total computations required for the proposed structure is almost the same as that for a single AP filter. Experimental results show that the proposed alternating selection scheme extracts the best properties of each component filter, namely fast convergence and small steady-state error.
    IEICE Transactions on Fundamentals of Electronics Communications and Computer Sciences 07/2011; 94-A(7):1576-1580. DOI:10.1587/transfun.E94.A.1576 · 0.23 Impact Factor
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    • "Since , can be rewritten as (6) where we assume that the noise signal is identically and independently distributed (i.i.d.) and statistically independent of the input data , and we ignore the dependency of on past noise [11]. For a high-order adaptive filter, the fluctuations of from one iteration to the next can be assumed to be small, so the following approximation can be acceptable [12]: "
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    ABSTRACT: We present a novel normalized subband adaptive filter (NSAF) which dynamically selects subband filters in order to reduce computational complexity while maintaining convergence performance of conventional NSAF. The selection operation is performed to achieve the largest decrease between the successive mean square deviations at every iteration. As a result, an efficient and competent NSAF algorithm is derived. The experimental results show that the proposed NSAF algorithm gains an advantage over the conventional NSAF in that it leads to a similar convergence performance with a substantial saving of overall computational burden.
    IEEE Signal Processing Letters 04/2010; 17(3-17):245 - 248. DOI:10.1109/LSP.2009.2038109 · 1.75 Impact Factor
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    • "The mean square error (MSE), E{|e(i)| 2 }, is taken and averaged over 2000 independent trials. Fig. ?? compares the MSE curves of the NSLMS, the SM-NSLMS [7], the PU- NSLMS [5], the NLMS, the SM-PU-NLMS [4], and the proposed algorithm with L = 16. To get similar the steady-state error level, we set the step-size of the NLMS, the NSLMS, and the PU-NSLMS algorithm as 0.7, 0.51, and 0.38, respectively . "
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    ABSTRACT: This paper provides a partial-update normalized sign least-mean square (NSLMS) algorithm with sparse up-dates. The proposed algorithm reduces the computational complexity compared with the conventional L ∞ -norm adap-tive filtering algorithms by decreasing the frequency of up-dating the filter coefficients and updating only a part of the filter coefficients. And we develop a mean square analysis to present the convergence of the proposed algorithm. Experi-mental results show that the proposed algorithm has the good convergence performance with greatly reduced computational complexity.
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