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

Effects of Multirate Systems on the Statistical Properties of Random Signals

In multirate digital signal processing, we often encounter time-varying linear systems such as decimators, interpolators, and modulators. In many applications, these building blocks are interconnected with linear filters to form more complicated systems. It is often necessary to understand the way in which the statistical behavior of a signal changes as it passes through such systems. While some issues in this context have an obvious answer, the analysis becomes more involved with complicated interconnections. For example, consider this question: if we pass a cyclostationary signal with period K through a fractional sampling rate-changing device (implemented with an interpolator, a nonideal low-pass filter and a decimator), what can we say about the statistical properties of the output? How does the behavior change if the filter is replaced by an ideal low-pass filter? In this paper, we answer questions of this nature. As an application, we consider a new adaptive filtering structure, which is well suited for the identification of band-limited channels. This structure exploits the band-limited nature of the channel, and embeds the adaptive filter into a multirate system. The advantages are that the adaptive filter has a smaller length, and the adaptation as well as the filtering are performed at a lower rate. Using the theory developed in this paper, we show that a matrix adaptive filter (dimension determined by the decimator and interpolator) gives better performance in terms of lower error energy at convergence than a traditional adaptive filter. Even though matrix adaptive filters are, in general, computationally more expensive, they offer a performance bound that can be used as a yardstick to judge more practical "scalar multirate adaptation" schemes

An affine combination of two LMS adaptive filters - Transient mean-square analysis

This paper studies the statistical behavior of an affine combination of the outputs of two LMS adaptive filters that simultaneously adapt using the same white Gaussian inputs. The purpose of the combination is to obtain an LMS adaptive filter with fast convergence and small steady-state mean-square deviation (MSD). The linear combination studied is a generalization of the convex combination, in which the combination factor $\lambda(n)$ is restricted to the interval $(0,1)$. The viewpoint is taken that each of the two filters produces dependent estimates of the unknown channel. Thus, there exists a sequence of optimal affine combining coefficients which minimizes the MSE. First, the optimal unrealizable affine combiner is studied and provides the best possible performance for this class. Then two new schemes are proposed for practical applications. The mean-square performances are analyzed and validated by Monte Carlo simulations. With proper design, the two practical schemes yield an overall MSD that is usually less than the MSD's of either filter

Frequency Controlled Noise Cancellation for Audio and Hearing Purposes

Methods for hearing aids sought to compensate for loss in hearing by amplifying signals of interest in the audio band. In real-world, audio signals are prone to outdoor noise which can be destructive for hearing aid.  Eliminating interfering noise at high speed and low power consumption became a target for recent researches. Modern hearing compensation technologies use digital signal processing which requires minimum implementation costs to reduce power consumption, as well as avoiding delay in real time processing. In this paper, frequency controlled noise cancellation (FCNC) strategy for hearing aid and audio communication is developed with low complexity and least time delay. The contribution of the current work is made by offering a method that is capable of removing inherent distortion due filter-bank insertion and assigning adaptive filtering to a particular sub-band to remove external noise. The performance of the proposed FCNC was examined under frequency-limited noise, which corrupts particular parts of the audio spectrum. Results showed that the FCNC renders noise-immune audio signals with minimal number of computations and least delay. Mean square error (MSE) plots of the proposed FCNC method reached below -30 dB compared to -25 dB using conventional sub-band method and to -10 dB using standard full-band noise canceller. The proposed FCNC approach gave the lowest number of computations compared to other methods with a total of 346 computations per sample compared to 860 and 512 by conventional sub-band and full-band methods respectively. The time delay using FCNC is the least compared to the other methods

Adaptive poleplacement: the division by zero problem

We re-examine the division by zero problem which occurs in certainty equivalence based indirect adaptive control algorithms applied to linear systems. By exploiting a parametrization for linear systems induced by the continued fraction description of its transfer function, the division by zero problem obtains a very simple geometric representation that can be used to virtually eliminate the problem in the adaptive algorith

Advancements of MultiRate Signal processing for Wireless Communication Networks: Current State Of the Art

With the hasty growth of internet contact and voice and information centric communications, many contact technologies have been urbanized to meet the stringent insist of high speed information transmission and viaduct the wide bandwidth gap among ever-increasing high-data-rate core system and bandwidth-hungry end-user complex. To make efficient consumption of the limited bandwidth of obtainable access routes and cope with the difficult channel environment, several standards have been projected for a variety of broadband access scheme over different access situation (twisted pairs, coaxial cables, optical fibers, and unchanging or mobile wireless admittance). These access situations may create dissimilar channel impairments and utter unique sets of signal dispensation algorithms and techniques to combat precise impairments. In the intended and implementation sphere of those systems, many research issues arise. In this paper we present advancements of multi-rate indication processing methodologies that are aggravated by this design trend. The thesis covers the contemporary confirmation of the current literature on intrusion suppression using multi-rate indication in wireless communiquE9; networks