A generalized data windowing scheme for adaptive conjugate gradient algorithms
Introduction
Adaptive conjugate gradient (CG) algorithms based on the CG method have been successfully introduced to solve the adaptive filtering problems. The advantages are that they have convergence properties superior to those of least mean square (LMS) algorithms and computational cost less than that of the classic recursive least squares (RLS) algorithm. Moreover, the instability problems existing in the RLS algorithm are not likely to occur in the CG algorithm [1], [2]. In the reported modified adaptive CG algorithms [1], [2], [3], [4], [5], [6], two data windowing schemes, i.e., the finite sliding data windowing scheme and the exponentially decaying data windowing scheme, of estimating the correlation matrix and the cross-correlation vector have been applied. However, the analysis and simulations presented in [1], [2] show that the modified CG algorithms, which are implemented using the finite sliding data windowing scheme and run several iterations per data update, have a convergence behavior and misadjustment which depend on the length of data window. A small window size produces slow convergence, whereas a large window size introduces high computational cost and high misadjustment. On the other hand, the modified CG algorithms, which are implemented using the exponentially decaying data windowing scheme and run one iteration per coefficient and data update, have the convergence dependent of the input eigenvalue spread. When the input with large eigenvalue spread is applied, the convergence is considerably slow.
To improve the convergence performance as well as misadjustment of the modified CG algorithms, this paper presents and analyzes a new approach of implementing the CG algorithm using a generalized data windowing scheme which combines the features of the finite sliding data windowing scheme and the exponentially decaying data windowing scheme. In Section 2, we first introduce the generalized data windowing scheme, and analyze the computational complexity and its advantages for CG algorithms. The numerical problems and the convergence behavior of the modified CG algorithms are then studied. Section 3 presents computer simulations to compare the convergence speed, misadjustment and tracking capabilities of the new modified CG algorithms with those of the existing approaches as well as the RLS algorithm. Finally, Section 4 concludes this paper.
Section snippets
Generalized data windowing scheme and accelerated CG algorithms
Consider a minimization problem for the following quadratic performance function:where is square matrix and positive definite, and are vectors of dimension . Solving for the vector that minimizes the quadratic performance function (1) is equivalent to solving the linear equation . It has been shown that the CG algorithm can be used to solve this linear equation iteratively and efficiently in [7], [8]. The algorithm uses the following weight update equation:
Application of adaptive system modeling
The performance of the proposed algorithms is evaluated by carrying out the computer simulation in the framework of adaptive system modeling problem. We use a Hamming window to generate the unknown system as a finite impulse response (FIR) lowpass plant with cutoff frequency of 0.5. The adaptive filter and the unknown system are assumed to have the same number of taps. In the simulations, both the low order filter and the high order filter with stationary and nonstationary input
Conclusion
In this paper, we have presented and analyzed a new approach to the implementation of the CG algorithm for adaptive filtering based on a generalized data windowing scheme which combines the features of the finite sliding window scheme and the exponentially decaying data window scheme. The modified adaptive CG algorithms show improved filter performance of accelerated convergence rate and low misadjustment. Besides the application of adaptive system modeling, we also tested the proposed scheme
References (12)
- et al.
Conjugate gradient techniques for adaptive filtering
IEEE Trans. Circuits Syst. I Fund. Theory Appl.
(January 1992) - et al.
Analysis of conjugate gradient algorithms for adaptive filtering
IEEE Trans. Signal Process.
(February 2000) The constrained conjugate gradient algorithm
IEEE Signal Process. Lett.
(April 2000)- et al.
Conjugate gradient method in adaptive bilinear filtering
IEEE Trans. Signal Process.
(January 1995) - et al.
Adaptive filtering algorithms designed using control Liapunov functions
IEEE Signal Process. Lett.
(April 2006) - et al.
Image restoration using a conjugate gradient based algorithm
J. Circuits Syst. Signal Process.
(February 1997)
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