Noise-constrained least mean squares algorithm

• Published in: IEEE transactions on signal processing 2001-09, Vol.49 (9), p.1961-1970
• Main Authors: Yongbin Wei, Gelfand, S.B., Krogmeier, J.V.
• Format: Article
• Language: English
• Subjects: Adaptive algorithm; Adaptive algorithms; Additive noise; Additive white noise; Algorithm design and analysis; Algorithms; Applied sciences; AWGN; Channel estimation; Channels; Computer simulation; Detection, estimation, filtering, equalization, prediction; Exact sciences and technology; Gaussian noise; Impulse response; Information, signal and communications theory; Least mean squares algorithm; Least squares approximation; Mean square error methods; Noise; Signal and communications theory; Signal processing algorithms; Signal, noise; Studies; Telecommunications and information theory; Variance
• ISSN: 1053-587X; 1941-0476
• DOI: 10.1109/78.942625

We consider the design of an adaptive algorithm for finite impulse response channel estimation, which incorporates partial knowledge of the channel, specifically, the additive noise variance. Although the noise variance is not required for the offline Wiener solution, there are potential benefits (and limitations) for the learning behavior of an adaptive solution. In our approach, a Robbins-Monro algorithm is used to minimize the conventional mean square error criterion subject to a noise variance constraint and a penalty term necessary to guarantee uniqueness of the combined weight/multiplier solution. The resulting noise-constrained LMS (NCLMS) algorithm is a type of variable step-size LMS algorithm where the step-size rule arises naturally from the constraints. A convergence and performance analysis is carried out, and extensive simulations are conducted that compare NCLMS with several adaptive algorithms. This work also provides an appropriate framework for the derivation and analysis of other adaptive algorithms that incorporate partial knowledge of the channel.