A robust quasi-newton adaptive filtering algorithm for impulse noise suppression

This paper studies the problem of robust adaptive filtering in impulse noise environment using the Quasi-Newton (QN) adaptive filtering algorithm. An M-estimate based cost function is minimized instead of the commonly used mean square error (MSE) to suppress the adverse effect of the impulse noise on the filter coefficients. In particular, a new robust quasi-Newton (R-QN) algorithm using the self-scaling variable metric (SSV) method for unconstrained optimization is studied in details. Simulation results show that the R-QN algorithm is more robust to impulse noise in the desired signal than the RLS algorithm and other QN algorithm considered. Its initial convergence speed and tracking ability to sudden system change are also superior to those of the quasi-Newton algorithm proposed in [1].published_or_final_versio

A robust M-estimate adaptive equaliser for impulse noise suppression

In this paper, a FIR adaptive equaliser for impulse noise suppression is proposed. It is based on the minimization of an M-estimate objective function which has the ability to ignore or down-weight a large error signal when it exceeds certain thresholds. An advantage of the proposed method is that its solution is governed by a system of linear equations, called the M-estimate normal equation. Therefore, traditional fast algorithms like the recursive least squares algorithm can be applied. Using a robust estimation of the thresholds and the recursive least square algorithm, an M-estimate RLS (M-RLS) algorithm is developed. Simulation results show that the proposed algorithm has better convergence performance than the N-RLS and MN-LMS algorithms when the input signal of the equaliser is corrupted by individually or consecutive impulse noises. It also shares the low steady state error of the traditional RLS algorithm.published_or_final_versio

New Sequential Partial Update Normalized Least Mean M-estimate Algorithms for Stereophonic Acoustic Echo Cancellation

ABSTRACT This paper proposes a family of new robust adaptive filtering algorithms for stereophonic acoustic echo cancellation in impulsive noise environment. The new algorithms employ sequential partial update scheme to reduce computational complexity, which is desirable in long echo path case. On the other hand, by employing robust M-estimate technique, the new algorithms become more robust to impulsive noises compared to their conventional least squarebased counterparts. These two advantages enable the proposed algorithms to be good alternatives for stereophonic echo cancellation. Experiments are also conducted to verify their efficiency

On the Development of Distributed Estimation Techniques for Wireless Sensor Networks

Wireless sensor networks (WSNs) have lately witnessed tremendous demand, as evidenced by the increasing number of day-to-day applications. The sensor nodes aim at estimating the parameters of their corresponding adaptive filters to achieve the desired response for the event of interest. Some of the burning issues related to linear parameter estimation in WSNs have been addressed in this thesis mainly focusing on reduction of communication overhead and latency, and robustness to noise. The first issue deals with the high communication overhead and latency in distributed parameter estimation techniques such as diffusion least mean squares (DLMS) and incremental least mean squares (ILMS) algorithms. Subsequently the poor performance demonstrated by these distributed techniques in presence of impulsive noise has been dealt separately. The issue of source localization i.e. estimation of source bearing in WSNs, where the existing decentralized algorithms fail to perform satisfactorily, has been resolved in this thesis. Further the same issue has been dealt separately independent of nodal connectivity in WSNs. This thesis proposes two algorithms namely the block diffusion least mean squares (BDLMS) and block incremental least mean squares (BILMS) algorithms for reducing the communication overhead in WSNs. The theoretical and simulation studies demonstrate that BDLMS and BILMS algorithms provide the same performances as that of DLMS and ILMS, but with significant reduction in communication overheads per node. The latency also reduces by a factor as high as the block-size used in the proposed algorithms. With an aim to develop robustness towards impulsive noise, this thesis proposes three robust distributed algorithms i.e. saturation nonlinearity incremental LMS (SNILMS), saturation nonlinearity diffusion LMS (SNDLMS) and Wilcoxon norm diffusion LMS (WNDLMS) algorithms. The steady-state analysis of SNILMS algorithm is carried out based on spatial-temporal energy conservation principle. The theoretical and simulation results show that these algorithms are robust to impulsive noise. The SNDLMS algorithm is found to provide better performance than SNILMS and WNDLMS algorithms. In order to develop a distributed source localization technique, a novel diffusion maximum likelihood (ML) bearing estimation algorithm is proposed in this thesis which needs less communication overhead than the centralized algorithms. After forming a random array with its neighbours, each sensor node estimates the source bearing by optimizing the ML function locally using a diffusion particle swarm optimization algorithm. The simulation results show that the proposed algorithm performs better than the centralized multiple signal classification (MUSIC) algorithm in terms of probability of resolution and root mean square error. Further, in order to make the proposed algorithm independent of nodal connectivity, a distributed in-cluster bearing estimation technique is proposed. Each cluster of sensors estimates the source bearing by optimizing the ML function locally in cooperation with other clusters. The simulation results demonstrate improved performance of the proposed method in comparison to the centralized and decentralized MUSIC algorithms, and the distributed in-network algorith

Adaptive Equalisation for Impulsive Noise Environments

This thesis addresses the problem of adaptive channel equalisation in environments where the interfering noise exhibits non–Gaussian behaviour due to impulsive phenomena. The family of alpha-stable distributions has proved to be a suitable and flexible tool for the modelling of signals with impulsive nature. However,non–Gaussian alpha–stable signals have infinite variance, and signal processing techniques based on second order moments are meaningless in such environments. In order to exploit the flexibility of the stable family and still take advantage of the existing signal processing tools, a novel framework for the integration of the stable model in a communications context is proposed, based on a finite dynamic range receiver. The performance of traditional signal processing algorithms designed under the Gaussian assumption may degrade seriously in impulsive environments. When this degradation cannot be tolerated, the traditional signal processing methods must be revisited and redesigned taking into account the non–Gaussian noise statistics. In this direction, the optimum feed–forward and decision feedback Bayesian symbol–by–symbol equalisers for stable noise environments are derived. Then, new analytical tools for the evaluation of systems in infinite variance environments are presented. For the centers estimation of the proposed Bayesian equaliser, a unified framework for a family of robust recursive linear estimation techniques is presented and the underlying relationships between them are identified. Furthermore, the direct clustering technique is studied and robust variants of the existing algorithms are proposed. A novel clustering algorithm is also derived based on robust location estimation. The problem of estimating the stable parameters has been addressed in the literature and a variety of algorithms can be found. Some of these algorithms are assessed in terms of efficiency, simplicity and performance and the most suitable is chosen for the equalisation problem. All the building components of an adaptive Bayesian equaliser are then put together and the performance of the equaliser is evaluated experimentally. The simulation results suggest that the proposed adaptive equaliser offers a significant performance benefit compared with a traditional equaliser, designed under the Gaussian assumption. The implementation of the proposed Bayesian equaliser is simple but the computational complexity can be unaffordable. However, this thesis proposes certain approximations which enable the computationally efficient implementation of the optimum equaliser with negligible loss in performance

Concurrent Modified Constant Modulus Algorithm and Decision Directed Scheme With Barzilai-Borwein Method

At present, in robot technology, remote control of robot is realized by wireless communication technology, and data anti-interference in wireless channel becomes a very important part. Any wireless communication system has an inherent multi-path propagation problem, which leads to the expansion of generated symbols on a time scale, resulting in symbol overlap and Inter-symbol Interference (ISI). ISI in the signal must be removed and the signal restores to its original state at the time of transmission or becomes as close to it as possible. Blind equalization is a popular equalization method for recovering transmitted symbols of superimposed noise without any pilot signal. In this work, we propose a concurrent modified constant modulus algorithm (MCMA) and the decision-directed scheme (DDS) with the Barzilai-Borwein (BB) method for the purpose of blind equalization of wireless communications systems (WCS). The BB method, which is two-step gradient method, has been widely employed to solve multidimensional unconstrained optimization problems. Considering the similarity of equalization process and optimization process, the proposed algorithm combines existing blind equalization algorithm and Barzilai-Borwein method, and concurrently operates a MCMA equalizer and a DD equalizer. After that, it modifies the DD equalizer's step size (SS) by the BB method. Theoretical investigation was involved and it demonstrated rapid convergence and improved equalization performance of the proposed algorithm compared with the original one. Additionally, the simulation results were consistent with the proposed technique

The Application of Adaptive Linear and N on-Linear Filters to Fringe Order Identification in White-Light Interferometry Systems

Conventional optical interferometry systems driven by highly coherent light sources have a very short unambiguous operating range, a direct consequence of the flatness of the interference fringes visibility profile at the output of the system. The range can be extended by using a white-light interferometer (WU), which is driven by a low-coherence source and produces a Gaussian visibility profile with a unique maximum in correspondence of the central fringe. Due to system and/or measurement noise, however, the position of the maximum (from which an accurate measurement of the measurand - displacement, temperature, pressure, flow, etc. - can be derived) is not easily detectable, and can lead to large measurement errors. This is especially true in a multiplexing scheme, where the source power is distributed evenly among various sensors, with a corresponding drop in the overall signal-to-noise ratio. The inclusion of a signal processing scheme at the receiver end is thus a necessity. As the fringe pattern at the output of a WLI system is basically a noisy sine wave amplitude modulated by a Gaussian envelope, it can be classified as a non-stationary, narrow-band, linear but non-Gaussian signa\. So far, no attempt has been made to apply digital filtering techniques, as understood in the signal processing community, to the output signal of a WLI system. This thesis constitutes a first step in that direction. Since the only measurable information given by the system is contained in the output signal, the system is modelled as a "black box" driven by the system and measurement noise processes and containing an unknown set of parameters. Standard least squares techniques can then be applied to estimate the parameters of the model, as is usually done in the field of system identification when only noisy output measurements are available. It is shown that identification of the model parameters is equivalent to finding a set of coefficients for an inverse filter which takes the WU signal at its input and delivers the unknown noise process at the output. The non-stationarity of the signal is accounted for by allowing for time variations of the model parameters; this justifies the use of adaptive filters with time-varying coefficients. A new central fringe identification scheme is proposed, based on a modification of the standard least mean square (LMS) adaptive filtering algorithm in combination with amplitude thresholding of the fringe pattern. The new scheme is shown to offer considerable improvement in the identification rate when tested against current schemes over comparable operating ranges, while retaining the computational simplicity and operational speed of the standard LMS. Its performance is also shown to be largely independent of the step-size parameter controlling the rate of convergence and tracking in the standard LMS, which is known to be the main obstacle for a successful application of the algorithm in a practical setting. The non-Gaussianity of the signal is explored and an attempt is made to apply higher-order statistics (HOS) algorithms to central fringe identification. The effectiveness of Gaussianity tests on pilot Gaussian data is seen to depend not only on the number and length of records available but, perhaps more importantly, on the bandwidth of the process. Violation of the stationarity assumption is shown to lead to mis-classification of a seemingly non-Gaussian signal into a Gaussian one, as the visibility profile may alter the distribution of the underlying sinusoid making it appear Gaussian, even when beam diffraction and wavefront aberrations combine to produce a nonGaussian profile. HOS-based adaptive algorithms may still be of some benefit, however, if processing is confined to that region of the fringe pattern where sufficient non-Gaussianity is allowed to develop. Non-linear adaptive filters based on the Volterra theories are finally applied to compensate for possible non-linearities introduced by mismatches in optical components, chromatic aberrations, and analogue-to-digital converters. It is shown that although a Volterra filter is able to reproduce the low-amplitude distortions of the fringe pattern better than a linear filter does, the identification rate does not improve. Reasons are given for such behaviour