Performance Analysis of l_0 Norm Constraint Least Mean Square Algorithm

As one of the recently proposed algorithms for sparse system identification, $l_0$ norm constraint Least Mean Square ($l_0$-LMS) algorithm modifies the cost function of the traditional method with a penalty of tap-weight sparsity. The performance of $l_0$-LMS is quite attractive compared with its various precursors. However, there has been no detailed study of its performance. This paper presents all-around and throughout theoretical performance analysis of $l_0$-LMS for white Gaussian input data based on some reasonable assumptions. Expressions for steady-state mean square deviation (MSD) are derived and discussed with respect to algorithm parameters and system sparsity. The parameter selection rule is established for achieving the best performance. Approximated with Taylor series, the instantaneous behavior is also derived. In addition, the relationship between $l_0$-LMS and some previous arts and the sufficient conditions for $l_0$-LMS to accelerate convergence are set up. Finally, all of the theoretical results are compared with simulations and are shown to agree well in a large range of parameter setting.Comment: 31 pages, 8 figure

Algorithms and structures for long adaptive echo cancellers

The main theme of this thesis is adaptive echo cancellation. Two novel independent approaches are proposed for the design of long echo cancellers with improved performance. In the first approach, we present a novel structure for bulk delay estimation in long echo cancellers which considerably reduces the amount of excess error. The miscalculation of the delay between the near-end and the far-end sections is one of the main causes of this excess error. Two analyses, based on the Least Mean Squares (LMS) algorithm, are presented where certain shapes for the transitions between the end of the near-end section and the beginning of the far-end one are considered. Transient and steady-state behaviours and convergence conditions for the proposed algorithm are studied. Comparisons between the algorithms developed for each transition are presented, and the simulation results agree well with the theoretical derivations. In the second approach, a generalised performance index is proposed for the design of the echo canceller. The proposed algorithm consists of simultaneously applying the LMS algorithm to the near-end section and the Least Mean Fourth (LMF) algorithm to the far-end section of the echo canceller. This combination results in a substantial improvement of the performance of the proposed scheme over both the LMS and other algorithms proposed for comparison. In this approach, the proposed algorithm will be henceforth called the Least Mean Mixed-Norm (LMMN) algorithm. The advantages of the LMMN algorithm over previously reported ones are two folds: it leads to a faster convergence and results in a smaller misadjustment error. Finally, the convergence properties of the LMMN algorithm are derived and the simulation results confirm the superior performance of this proposed algorithm over other well known algorithms

Mid-Price Movement Prediction in Limit Order Books Using Feature Engineering and Machine Learning

The increasing complexity of financial trading in recent years revealed the need for methods that can capture its underlying dynamics. An efficient way to organize this chaotic system is by contracting limit order book ordering mechanisms that operate under price and time filters. Limit order book can be analyzed using linear and nonlinear models. The thesis develops novelmethods for the identification of limit order book characteristics which provide traders and market makers an information edge in their trading. A good proxy for traders and market makers is the prediction of mid-price movement, which is the main target of this thesis. The contributions of this thesis are categorized chronologically into three parts. The first part refers to the introduction in the literature of the first publicly available limit order book dataset for high-frequency trading for the task of mid-price movement prediction. This dataset comes together with the development of an experimental protocol that utilizes methods inspired by ridge regression and a single layer feed-forward neural network as classifiers. These classifiers use state-of-the-art limit order book features as inputs for the target task. The next contribution of this thesis is the use and development of a wide range of technical and quantitative indicators for the task of mid-price movement prediction via an extensive feature selection process. This feature selection process identifies which features improve predictability performance. The results suggest that the newly introduced quantitative feature based on an adaptive logistic regression model for online learning was selected first according to several criteria. These criteria operate according to entropy, linear discriminant analysis, and least mean square error. The third contribution is the introduction of econometric features as inputs to deep learning models for the task of mid-price movement prediction. An extensive comparison against other state-of-the-art hand-crafted features and fully automated feature extraction processes is provided. Furthermore, a new experimental protocol is developed for the task of mid-price prediction, to overcome the problem of time irregularities, which characterizes high-frequency data. Results suggest that advanced hand-crafted features such as econometric indicators can predict movements of proxies, such as mid-price

Proceedings of the Second International Mobile Satellite Conference (IMSC 1990)

Presented here are the proceedings of the Second International Mobile Satellite Conference (IMSC), held June 17-20, 1990 in Ottawa, Canada. Topics covered include future mobile satellite communications concepts, aeronautical applications, modulation and coding, propagation and experimental systems, mobile terminal equipment, network architecture and control, regulatory and policy considerations, vehicle antennas, and speech compression