Convergence behavior of NLMS algorithm for Gaussian inputs: Solutions using generalized Abelian integral functions and step size selection

This paper studies the mean and mean square convergence behaviors of the normalized least mean square (NLMS) algorithm with Gaussian inputs and additive white Gaussian noise. Using the Price's theorem and the framework proposed by Bershad in IEEE Transactions on Acoustics, Speech, and Signal Processing (1986, 1987), new expressions for the excess mean square error, stability bound and decoupled difference equations describing the mean and mean square convergence behaviors of the NLMS algorithm using the generalized Abelian integral functions are derived. These new expressions which closely resemble those of the LMS algorithm allow us to interpret the convergence performance of the NLMS algorithm in Gaussian environment. The theoretical analysis is in good agreement with the computer simulation results and it also gives new insight into step size selection. © 2009 Springer Science+Business Media, LLC.published_or_final_versionSpringer Open Choice, 01 Dec 201

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

An intelligent LMS+F algorithm

Published versio

Stochastic Analysis of LMS Algorithm with Delayed Block Coefficient Adaptation

In high sample-rate applications of the least-mean-square (LMS) adaptive filtering algorithm, pipelining or/and block processing is required. In this paper, a stochastic analysis of the delayed block LMS algorithm is presented. As opposed to earlier work, pipelining and block processing are jointly considered and extensively examined. Different analyses for the steady and transient states to estimate the step-size bound, adaptation accuracy and adaptation speed based on the recursive relation of delayed block excess mean square error (MSE) are presented. The effect of different amounts of pipelining delays and block sizes on the adaptation accuracy and speed of the adaptive filter with different filter taps and speed-ups are studied. It is concluded that for a constant speed-up, a large delay and small block size lead to a slower convergence rate compared to a small delay and large block size with almost the same steady-state MSE. Monte Carlo simulations indicate a fairly good agreement with the proposed estimates for Gaussian inputs.Comment: 13 pages, 8 figure

Rate considerations in deep space telemetry

The relationship between transmission rate and source and channel signal-to-noise ratios (SNR's) is discussed for the transmission of a Gaussian source over a binary input, additive Gaussian channel, with a mean-squared distortion criterion. We point out that for any finite rate, and sufficiently high channel SNR, the fidelity criterion (reproduction SNR) is upper bounded by a function of the transmission rate. Thus, the performance becomes rate limited rather than power limited. This effect is not observed with the binary symmetric source, the binary-input Gaussian channel combination, or the Gaussian source, unconstrained-input Gaussian channel combination

Adaptive function approximation based on the Discrete Cosine Transform (DCT)

This paper studies the cosine as basis function for the approximation of univariate and continuous functions without memory. This work studies a supervised learning to obtain the approximation coefficients, instead of using the Discrete Cosine Transform (DCT). Due to the finite dynamics and orthogonality of the cosine basis functions, simple gradient algorithms, such as the Normalized Least Mean Squares (NLMS), can benefit from it and present a controlled and predictable convergence time and error misadjustment. Due to its simplicity, the proposed technique ranks as the best in terms of learning quality versus complexity, and it is presented as an attractive technique to be used in more complex supervised learning systems. Simulations illustrate the performance of the approach. This paper celebrates the 50th anniversary of the publication of the DCT by Nasir Ahmed in 1973.Comment: Accepted paper in 26th International Conference on Circuits, Systems, Communications and Computers (CSCC

Near far resistant detection for CDMA personal communication systems.

The growth of Personal Communications, the keyword of the 90s, has already the signs of a technological revolution. The foundations of this revolution are currently set through the standardization of the Universal Mobile Telecommunication System (UMTS), a communication system with synergistic terrestrial and satellite segments. The main characteristic of the UMTS radio interface, is the provision of ISDN services. Services with higher than voice data rates require more spectrum, thus techniques that utilize spectrum as efficiently as possible are currently at the forefront of the research community interests. Two of the most spectrally efficient multiple access technologies, namely. Code Division Multiple Access (CDMA) and Time Division Multiple Access (TDMA) concentrate the efforts of the European telecommunity.This thesis addresses problems and. proposes solutions for CDMA systems that must comply with the UMTS requirements. Prompted by Viterbi's call for further extending the potential of CDMA through signal processing at the receiving end, we propose new Minimum Mean Square Error receiver architectures. MMSE detection schemes offer significant advantages compared to the conventional correlation based receivers as they are NEar FAr Resistant (NEFAR) over a wide range of interfering power levels. The NEFAR characteristic of these detectors reduces considerably the requirements of the power control loops currently found in commercial CDMA systems. MMSE detectors are also found, to have significant performance gains over other well established interference cancellation techniques like the decorrelating detector, especially in heavily loaded system conditions. The implementation architecture of MMSE receivers can be either Multiple-Input Multiple Output (MIMO) or Single-Input Single-Output. The later offers not only complexity that is comparable to the conventional detector, but also has the inherent advantage of employing adaptive algorithms which can be used to provide both the dispreading and the interference cancellation function, without the knowledge of the codes of interfering users. Furthermore, in multipath fading channels, adaptive MMSE detectors can exploit the multipath diversity acting as RAKE combiners. The later ability is distinctive to MMSE based receivers, and it is achieved in an autonomous fashion, without the knowledge of the multipath intensity profile. The communicator achieves its performance objectives by the synergy of the signal processor and the channel decoder. According to the propositions of this thesis, the form of the signal processor needs to be changed, in order to exploit the horizons of spread spectrum signaling. However, maximum likelihood channel decoding algorithms need not change. It is the way that these algorithms are utilized that needs to be revis ed. In this respect, we identify three major utilization scenarios and an attempt is made to quantify which of the three best matches the requirements of a UMTS oriented CDMA radio interface. Based on our findings, channel coding can be used as a mapping technique from the information bit to a more ''intelligent" chip, matching the ''intelligence" of the signal processor