Efficient and Robust Adaptive Filtering Framework Based on Individualized Log-Term Time-Varying Stepsize Adjustment Mechanism

Date of Award


Degree Name

Doctor of Philosophy


Electrical and Computer Engineering

First Advisor

Dr. Ikhlas Abdel-Qader

Second Advisor

Dr. Janos Grantner, Ph.D.

Third Advisor

Dr. Azim Houshyar


Variable step size adaptive filters, time- varying step size LMS algorithms, sparse- aware time-adjusting step size algorithms, adaptive system identification, sparsity and sparse systems, LI-norm and LO-norm


Adaptive filtering is one of the most significant advancements in communications and signal processing with an endless list of successful applications such as echo cancellation, inverse modeling, interference canceling, and prediction. Moreover, adaptive filtering has become an intrinsic part of various systems including telecommunications, radar, sonar, video and audio signal processing. In fact, the number of very diverse applications in which adaptive techniques are being utilized has rapidly increased during the last decade to include most real-time systems such as medical equipment and devices among many others.

A successful adaptive algorithm must 1) be computationally efficient, 2) be robust against unknown conditions, 3) have fast convergence speed, and 4) have a small steady-state error. Current adaptive algorithms do not completely meet all these qualifications, and specifically convergence rate and stability. It has been an essential goal of this dissertation to investigate performance, realization, and propose improvements.

A new individualized time-varying stepsize scheme for the least-mean-square (LMS) algorithm, Absolute Weighted Input using Log function (AWILOG), is proposed along with two different realizations depending on the nature of the intended system. The novelty of the proposed algorithm is to assign, individually, to each coefficient of the adaptive filter a variable stepsize that adapts according to the absolute value of a Log-function using the information in the input signal. This approach was designed to reduce the steady-state mean-square-deviation (MSD) of the coefficients during high levels of the input signal without sacrificing the speed of convergence, as is the case in existing approaches.

In this dissertation, sparsity- something that appears in many signals and systems while tackling adaptive signal processing problems- is also exploited. This resulted in the achievement of a low-complexity sparse-aware scheme through the integration of the novel features of AWILOG with some of the recently reported sparse-aware approaches. Two realizations of the proposed algorithm, AWILOG, were implemented by adopting the proposed time-adjusting stepsize in the gradient correction and in the zero-attractor terms. In the first one, the advantages of the novel time-varying stepsize combined with 𝑙1-norm penalty for sparse system identification in time domain was proposed, while in the second, an improvement of the filtering performance was aimed for. A scheme that combined the unique features of the novel time-varying stepsize and a form of 𝑙0-norm constraint was developed. Results show that the proposed schemes deliver faster convergence rate while attaining lower levels of MSD than the comparable algorithms under various sparseness conditions.

Finally, to enforce further performance improvements, an integrated version of the novel AWILOG with the conventional normalized LMS (NLMS) algorithm was pursued. A modified stepsize adjusting function has been developed to efficiently alleviate the impact of the conflict in demands between the convergence speed and the quality of system identification results, and also to enhance the robustness of the algorithm against unknown sparsity levels for long filter applications. Results show that the proposed approach outperforms comparable algorithms regardless of the sparsity level. Also, based on the results of the echo cancellation simulations, the proposed algorithm efficiently replaced the high computational complexity of the compared algorithms with similar performance in the initial convergence speed and superior performance in the steady-state MSD, under various system patterns and tested signals.

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