Estimation-based synthesis of H∞-optimal adaptive FIR filtersfor filtered-LMS problems

This paper presents a systematic synthesis procedure for H∞-optimal adaptive FIR filters in the context of an active noise cancellation (ANC) problem. An estimation interpretation of the adaptive control problem is introduced first. Based on this interpretation, an H∞ estimation problem is formulated, and its finite horizon prediction (filtering) solution is discussed. The solution minimizes the maximum energy gain from the disturbances to the predicted (filtered) estimation error and serves as the adaptation criterion for the weight vector in the adaptive FIR filter. We refer to this adaptation scheme as estimation-based adaptive filtering (EBAF). We show that the steady-state gain vector in the EBAF algorithm approaches that of the classical (normalized) filtered-X LMS algorithm. The error terms, however, are shown to be different. Thus, these classical algorithms can be considered to be approximations of our algorithm. We examine the performance of the proposed EBAF algorithm (both experimentally and in simulation) in an active noise cancellation problem of a one-dimensional (1-D) acoustic duct for both narrowband and broadband cases. Comparisons to the results from a conventional filtered-LMS (FxLMS) algorithm show faster convergence without compromising steady-state performance and/or robustness of the algorithm to feedback contamination of the reference signal

H∞ Estimation Approach to Active Noise Control: Theory, Algorithm and Real-Time Implementation

This paper presents an H∞ estimation approach to active control of acoustic noise inside an enclosure. It is shown how H∞ filter theory and algorithm can be effectively applied to active noise control to provide important robustness property. Real-time implementation of the algorithm is performed on Digital Signal Processor. Experimental comparison to conventional FxLMS algorithm for active noise control is presented for both single channel and multichannel cases. While providing some new results, this paper also serves as a brief review on H∞ filter theory and on active noise control

Efficient time delay estimation and compensation applied to the cancellation of acoustic echo

The system identification problem is notably dealt with using adaptive filtering approaches. In many applications the unknown system response consists of an initial sequence of zero-valued coefficients that precedes the active part of the response. The presence of these coefficients introduces a flat delay in the incoming signals which can take significantly large values. When most adaptive approaches attempt to model such a system, the presence of flat delay impairs their operation and performance. The approach introduced in this thesis aims to model the flat delay and active part of the unknown system separately. An efficient system for time delay estimation (TDE) is introduced to estimate the flat delay of an unknown system. The estimated delay is then compensated within the adaptive system thus allowing the latter to cover the active part ofthe unknown system. The proposed system is applied to the Acoustic Echo Cancellation (ABC) problem

A subband Kalman filter for echo cancellation

This thesis involves the implementation of a Kalman filter for the application of echo cancellation. This particular Kalman filter is implemented in the frequency domain, in subbands, so as to make it faster and of lesser calculational complexity for real time applications. To evaluate the functioning of this subband Kalman filter, comparison of the performance of the subband Kalman filter is done with respect to the original time domain Kalman filter, and also with other subband adaptive filters for echo cancellation such as the NLMS filter. Additionally, since background noise affects the working of any adaptive filter, the newly developed subband Kalman filter\u27s performance at different noise conditions is compared, and an attempt to keep track of and predict this noise is also performed --Abstract, page iii

Channel estimation techniques for filter bank multicarrier based transceivers for next generation of wireless networks

A dissertation submitted to Faculty of Engineering and the Built Environment, University of the Witwatersrand, Johannesburg, in fulfillment of the requirements for the degree of Master of Science in Engineering (Electrical and Information Engineering), August 2017The fourth generation (4G) of wireless communication system is designed based on the principles of cyclic prefix orthogonal frequency division multiplexing (CP-OFDM) where the cyclic prefix (CP) is used to combat inter-symbol interference (ISI) and inter-carrier interference (ICI) in order to achieve higher data rates in comparison to the previous generations of wireless networks. Various filter bank multicarrier systems have been considered as potential waveforms for the fast emerging next generation (xG) of wireless networks (especially the fifth generation (5G) networks). Some examples of the considered waveforms are orthogonal frequency division multiplexing with offset quadrature amplitude modulation based filter bank, universal filtered multicarrier (UFMC), bi-orthogonal frequency division multiplexing (BFDM) and generalized frequency division multiplexing (GFDM). In perfect reconstruction (PR) or near perfect reconstruction (NPR) filter bank designs, these aforementioned FBMC waveforms adopt the use of well-designed prototype filters (which are used for designing the synthesis and analysis filter banks) so as to either replace or minimize the CP usage of the 4G networks in order to provide higher spectral efficiencies for the overall increment in data rates. The accurate designing of the FIR low-pass prototype filter in NPR filter banks results in minimal signal distortions thus, making the analysis filter bank a time-reversed version of the corresponding synthesis filter bank. However, in non-perfect reconstruction (Non-PR) the analysis filter bank is not directly a time-reversed version of the corresponding synthesis filter bank as the prototype filter impulse response for this system is formulated (in this dissertation) by the introduction of randomly generated errors. Hence, aliasing and amplitude distortions are more prominent for Non-PR. Channel estimation (CE) is used to predict the behaviour of the frequency selective channel and is usually adopted to ensure excellent reconstruction of the transmitted symbols. These techniques can be broadly classified as pilot based, semi-blind and blind channel estimation schemes. In this dissertation, two linear pilot based CE techniques namely the least square (LS) and linear minimum mean square error (LMMSE), and three adaptive channel estimation schemes namely least mean square (LMS), normalized least mean square (NLMS) and recursive least square (RLS) are presented, analyzed and documented. These are implemented while exploiting the near orthogonality properties of offset quadrature amplitude modulation (OQAM) to mitigate the effects of interference for two filter bank waveforms (i.e. OFDM/OQAM and GFDM/OQAM) for the next generation of wireless networks assuming conditions of both NPR and Non-PR in slow and fast frequency selective Rayleigh fading channel. Results obtained from the computer simulations carried out showed that the channel estimation schemes performed better in an NPR filter bank system as compared with Non-PR filter banks. The low performance of Non-PR system is due to the amplitude distortion and aliasing introduced from the random errors generated in the system that is used to design its prototype filters. It can be concluded that RLS, NLMS, LMS, LMMSE and LS channel estimation schemes offered the best normalized mean square error (NMSE) and bit error rate (BER) performances (in decreasing order) for both waveforms assuming both NPR and Non-PR filter banks. Keywords: Channel estimation, Filter bank, OFDM/OQAM, GFDM/OQAM, NPR, Non-PR, 5G, Frequency selective channel.CK201

Tracking and convergence of multi-channel Kalman filters for active noise control

The feed-forward broadband active noise control problem can be formulated as a state estimation problem to achieve a faster rate of convergence than the filtered reference least mean squares algorithm and possibly also a better tracking performance. A multiple input/multiple output Kalman algorithm is used to perform this state estimation. To make the algorithm more suitable for real-time applications the Kalman filter is written in a fast array form and the secondary path state matrices are implemented in output normal form. The implementation was tested in simulations and in real-time experiments. It was found that for a constant primary path the Kalman filter has a fast rate of convergence and is able to track changes in the spectrum. For a forgetting factor equal to unity the system is robust, but the filter is unable to track rapid changes in the primary path. It is shown that a forgetting factor lower than unity gives a significantly improved tracking performance. Numerical issues of the fast array form of the algorithm for such forgetting factors are discussed and possible solutions are presented

Active control of time-varying broadband noise and vibrations using a sliding-window Kalman filter

Recently, a multiple-input/multiple-output Kalman filter technique was presented to control time-varying broadband noise and vibrations. By describing the feed-forward broadband active noise control problem in terms of a state estimation problem it was possible to achieve a faster rate of convergence than instantaneousgradient least-mean-squares algorithms and possibly also a better tracking performance. A multiple input/ multiple output Kalman algorithm was derived to perform this state estimation. To make the algorithm more suitable for real-time applications, the Kalman filter was written in a fast array form and the secondary path state matrices were implemented in output normal form. The resulting filter implementation was verified in simulations and in real-time experiments. It was found that for a constant primary path the filter had a fast rate of convergence and was able to track time-varying spectra. For a forgetting factor equal to unity the system was robust but the filter was unable to track rapid changes in the primary path. A forgetting factor lower than unity gave a significantly improved tracking performance but led to a numerical instability for the fast array form of the algorithm. To improve the numerical behavior, while enabling fast tracking and convergence, several variants are described in this paper. Results will be shown for a sliding window Recursive Least Squares filter in fast array form, which will later be extended to a full Kalman filter implementation by taking into account the uncertainty of the secondary path between the control sources and the error sensors. Multiple variants will be discussed in this paper. The first variant is the standard sliding window technique, which applies both updates and downdates to the filter coefficients. The second variant is an algorithm which only applies an update step to the filter coefficients and interprets the downdate step as an addition of a covariance matrix to the Riccati equation. The third variant uses an implicit forgetting factor. These implementations use a factorized form of the hyperbolic orthogonal transformation matrix. The different techniques will be applied to measured data of noise in houses near the runway of an airport. Results are given of the performance regarding tracking, convergence and numerical stability of the algorithms

Digital signal processing algorithms and structures for adaptive line enhancing

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