Stochastic Analysis of the LMS Algorithm for System Identification with Subspace Inputs

This paper studies the behavior of the low rank LMS adaptive algorithm for the general case in which the input transformation may not capture the exact input subspace. It is shown that the Independence Theory and the independent additive noise model are not applicable to this case. A new theoretical model for the weight mean and fluctuation behaviors is developed which incorporates the correlation between successive data vectors (as opposed to the Independence Theory model). The new theory is applied to a network echo cancellation scheme which uses partial-Haar input vector transformations. Comparison of the new model predictions with Monte Carlo simulations shows good-to-excellent agreement, certainly much better than predicted by the Independence Theory based model available in the literature

Unknown System Identification using LMS Algorithm

An adaptive filter is a digital filter that self adjusts its transfer function according to an optimizing algorithm which is most frequently Least Mean Square (LMS) algorithm. Due to the complexity of adaptive filtering most digital filters are FIR filter. There are numerous applications of adaptive filters like noise cancellations, echo cancellation, system modelling and identification, inverse system modelling, adaptive beam-forming etc. In this research article, adaptive LMS algorithm has been used for unknown system identification. The system identification is a category of adaptive filtering which find its numerous applications in diverse field like communication, image processing, speech processing etc