Adaptive Reduced-rank Filter Research Articles

An enhanced receiver for an impulsive UWB-based PLC system for low-bit rate applications

This paper focuses on the convergence speed improvement and the computational complexity reduction during the training phase of a receiver based on reduced rank adaptive filter, which is applied to a power line communication system based on impulsive ultra wideband modulation. In this regard, the use of variable step-size, set-membership, and soft threshold into the training phase of a reduced rank adaptive filter is introduced. In order to evaluate the effectiveness of our proposal, performance analyses with measured in-home and outdoor power line channels distorted by additive noise, which are modeled as white Gaussian and impulsive Gaussian, are carried out. Based on the numerical results, we show that the convergence speed can be considerably improved with the proposed enhancement for training this adaptive filter. Regardless the types of adopted additive noises and power line channels, we show that the improved convergence speed results in low bit error rate if the number of training symbol is reduced, which is a severe constraint associated with the coherence time of power line channels. Moreover, we show that the use of epochs during the training phase is convenient to deal with short coherence time. Performance comparisons with other receivers show that the proposal is more effective to deal with the hardness of power line channels. Moreover, computational complexity comparison shows that the proposed improvement demands less computational complexity than its predecessors. Finally, we show that proposal yields a receiver that outperforms the receivers based on matched filter or a combination of matched filter with the median filter, when similar computational complexity applies.

A New Approach to Adaptive Signal Processing

A unified linear algebraic approach to adaptive signal processing (ASP) is presented. Starting from just Ax=b, key ASP algorithms are derived in a simple, systematic, and integrated manner without requiring any background knowledge to the field. Algorithms covered are Steepest Descent, LMS, Normalized LMS, Kaczmarz, Affine Projection, RLS, Kalman filter, and MMSE/Least Square Wiener filters. By following this approach, readers will discover a synthesis; they will learn that one and only one equation is involved in all these algorithms. They will also learn that this one equation forms the basis of more advanced algorithms like reduced rank adaptive filters, extended Kalman filter, particle filters, multigrid methods, preconditioning methods, Krylov subspace methods and conjugate gradients. This will enable them to enter many sophisticated realms of modern research and development. Eventually, this one equation will not only become their passport to ASP but also to many highly specialized areas of computational science and engineering.

Reduced-rank space-time adaptive detection for airborne radar

For airborne radar, there are usually insufficient independent and identically distributed (IID) training data because of geometric considerations and terrain variations. The rank reduction technique is one of the most effective approaches to circumvent this problem. In this study, we investigate four reduced-rank spacetime adaptive detectors for airborne radar, namely, the reduced-rank sample-matrix-inversion (RR-SMI), the reduced-rank adaptive matched filter (RR-AMF), the reduced-rank adaptive coherence estimator (RR-ACE), and the reduced-rank generalized likelihood ratio test (RR-GLRT). Their asymptotic analytical probabilities of detection (PD’s) and false alarm (PFA’s) are all derived. These detectors all asymptotically attain a constant false alarm rate (CFAR). It is shown that these four reduced-rank detectors exhibit detection performance which is better than or comparable to that of two existing reduced-rank detectors, proposed by Reed and Gau (RG1 and RG2). Moreover, these four reduced-rank detectors are more robust to change in power of clutter and noise than RG1 and RG2.

Reduced-Rank STAP Algorithms using Joint Iterative Optimization of Filters

We develop a reduced-rank space-time adaptive processing (STAP) method based on joint iterative optimization of filters (JOINT) for airborne radar applications. The proposed method consists of a bank of full-rank adaptive filters, which forms the projection matrix, and an adaptive reduced-rank filter that operates at the output of the bank of filters. We describe the proposed method for both the direct-form processor (DFP) and the generalized sidelobe canceller (GSC) structures. Adaptive algorithms including the stochastic gradient (SG), the recursive least square (RLS), and their hybrid algorithms are derived for the efficient implementation of the JOINT STAP method. The computational complexity analysis of the proposed algorithms is shown in terms of the number of multiplications and additions per snapshot. Furthermore, the convexity analysis of the proposed method is carried out. Simulations for a clutter-plus-jamming suppression application show that the proposed STAP algorithm outperforms the state-of-the-art reduced-rank schemes in convergence and tracking at significantly lower complexity.

Adaptive Reduced-Rank Constrained Constant Modulus Algorithms Based on Joint Iterative Optimization of Filters for Beamforming

This paper proposes a robust reduced-rank scheme for adaptive beamforming based on joint iterative optimization (JIO) of adaptive filters. The novel scheme is designed according to the constant modulus (CM) criterion subject to different constraints. The proposed scheme consists of a bank of full-rank adaptive filters that forms the transformation matrix, and an adaptive reduced-rank filter that operates at the output of the bank of filters to estimate the desired signal. We describe the proposed scheme for both the direct-form processor (DFP) and the generalized sidelobe canceller (GSC) structures. For each structure, we derive stochastic gradient (SG) and recursive least squares (RLS) algorithms for its adaptive implementation. The Gram-Schmidt (GS) technique is applied to the adaptive algorithms for reformulating the transformation matrix and improving the performance. An automatic rank selection technique is developed and employed to determine the most adequate rank for the derived algorithms. A detailed complexity study and a convexity analysis are carried out. Simulation results show that the proposed algorithms outperform the existing full-rank and reduced-rank methods in convergence and tracking performance.

Robust Reduced-Rank Adaptive Algorithm Based on Parallel Subgradient Projection and Krylov Subspace

In this paper, we propose a novel reduced-rank adaptive filtering algorithm exploiting the Krylov subspace associated with estimates of certain statistics of input and output signals. We point out that, when the estimated statistics are erroneous (e.g., due to sudden changes of environments), the existing Krylov-subspace-based reduced-rank methods compute the point that minimizes a ldquowrongrdquo mean-square error (MSE) in the subspace. The proposed algorithm exploits the set-theoretic adaptive filtering framework for tracking efficiently the optimal point in the sense of minimizing the ldquotruerdquo MSE in the subspace. Therefore, compared with the existing methods, the proposed algorithm is more suited to adaptive filtering applications. A convergence analysis of the algorithm is performed by extending the adaptive projected subgradient method (APSM). Numerical examples demonstrate that the proposed algorithm enjoys better tracking performance than the existing methods for system identification problems.

Adaptive reduced-rank LCMV beamforming algorithms based on joint iterative optimization of filters: Design and analysis

This paper presents reduced-rank linearly constrained minimum variance (LCMV) beamforming algorithms based on joint iterative optimization of filters. The proposed reduced-rank scheme is based on a constrained joint iterative optimization of filters according to the minimum variance criterion. The proposed optimization procedure adjusts the parameters of a projection matrix and an adaptive reduced-rank filter that operates at the output of the bank of filters. We describe LCMV expressions for the design of the projection matrix and the reduced-rank filter. We then describe stochastic gradient and develop recursive least-squares adaptive algorithms for their efficient implementation along with automatic rank selection techniques. An analysis of the stability and the convergence properties of the proposed algorithms is presented and semi-analytical expressions are derived for predicting their mean squared error (MSE) performance. Simulations for a beamforming application show that the proposed scheme and algorithms outperform in convergence and tracking the existing full-rank and reduced-rank algorithms while requiring comparable complexity.

Reduced-Rank Adaptive Filtering Based on Joint Iterative Optimization of Adaptive Filters

This letter proposes a novel adaptive reduced-rank filtering scheme based on joint iterative optimization of adaptive filters. The novel scheme consists of a joint iterative optimization of a bank of full-rank adaptive filters that forms the projection matrix and an adaptive reduced-rank filter that operates at the output of the bank of filters. We describe minimum mean-squared error (MMSE) expressions for the design of the projection matrix and the reduced-rank filter and low-complexity normalized least-mean squares (NLMS) adaptive algorithms for its efficient implementation. Simulations for an interference suppression application show that the proposed scheme outperforms in convergence and tracking the state-of-the-art reduced-rank schemes at significantly lower complexity.

Reduced-Rank Adaptive Filtering Using Localized Processing for CDMA Systems

<para xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"> An integrated beamforming (spatial processing) and multiuser-detection (temporal processing) scheme is an effective approach to increase system capacity but is also impractical due to the high associated computational costs. To overcome this problem, researchers have developed reduced-rank approaches. Adding to this class of algorithms, this paper introduces a joint-domain adaptive algorithm, which processes spatial and temporal data within a localized region after transformation to a “beamspace.” This new joint-domain-localized (JDL) adaptive algorithm is developed for single-cell uplink code-division multiple-access (CDMA) systems with a receive-antenna array. Given a rank constraint on the JDL transformation, this paper develops the optimal choice of transformation matrix and justifies a simpler suboptimal choice. The JDL algorithm is shown to have relatively low computation load. We also introduce the JDL-Z algorithm that combines JDL processing with zero forcing for multicell uplink CDMA systems. At the cost of higher computational complexity, this new scheme provides better performance and a faster convergence rate than the JDL algorithm. However, the key contribution is a framework wherein adaptive processing can be followed by yet another stage of adaptive processing. Simulations are used to illustrate the efficacy of the two algorithms. </para>

Genetic Algorithm-Assisted Design of Adaptive Predictive Filters for 50/60 Hz Power Systems Instrumentation

We introduce a genetic algorithm-based method for structural optimization of multiplicative general parameter (MGP) finite impulse response (FIR) filters. These computationally efficient reduced-rank adaptive filters are robust, suitable for predictive configurations, and they have numerous applications in 50/60 Hz power systems instrumentation. The design process of such filters has three independent stages: Lagrange multipliers-based optimization of the sinusoid-predictive basis filter, genetic algorithm-based search of optimal FIR tap cross-connections and, finally, the online MGP-adaptation phase guided by variations in signal statistics. Thus, our multistage design procedure is a complementary fusion of hard computing (HC) and soft computing (SC) methodologies. Such advantageous fusion (or symbiosis) thinking is emerging among researchers and practicing engineers, and it can potentially lead to competitive combinations of individual HC and SC methods.

Evolutionary-Programming-Based Optimization of Reduced-Rank Adaptive Filters for Reference Generation in Active Power Filters

We introduce an evolutionary-programming-based method for designing robust and computationally efficient adaptive bandpass filters. These predictive filters are optimized for generating current references in active power filters (APFs). The accuracy (phase/amplitude) of the reference current is crucial in current-injection-type systems, because it directly affects the harmonics reduction ability of the APF. Our digital filtering approach has the following advantages: selective bandpass response, efficient attenuation of specific harmonic components, capability to handle typical frequency alteration, small number of multiplications, and structural simplicity. In addition, practically no prior knowledge of the electricity distribution network and its loading characteristics is needed for designing the current reference generator. In an illustrative example, the total harmonic distortion of an artificial current waveform was reduced from 36.7% to less than 3.7% within the line frequency range 49-51 Hz. The proposed scheme is a combination of the hard-computing (HC)-type multiplicative general parameter method and evolutionary programming that, on the other hand, is a constituent of soft computing (SC). Such open-minded fusion thinking is emerging among researchers and engineers, and it can potentially lead to efficient combinations of HC and SC methodologies*both on the algorithm level and on the system level.

Reduced-Rank Adaptive Filtering Using Krylov Subspace

A unified view of several recently introduced reduced-rank adaptive filters is presented. As all considered methods use Krylov subspace for rank reduction, the approach taken in this work is inspired from Krylov subspace methods for iterative solutions of linear systems. The alternative interpretation so obtained is used to study the properties of each considered technique and to relate one reduced-rank method to another as well as to algorithms used in computational linear algebra. Practical issues are discussed and low-complexity versions are also included in our study. It is believed that the insight developed in this paper can be further used to improve existing reduced-rank methods according to known results in the domain of Krylov subspace methods.

Adaptive techniques for multiuser CDMA receivers

A number of CDMA receivers have been proposed that cover the whole spectrum of performance/complexity from the simple matched filter to the optimal Viterbi (1995) processor. Adaptive solutions, in particular, have the potential of providing the anticipated multiuser detection (MD) performance gains with a complexity that would be manageable for third generation systems. Our goal, in this article, is to provide an overview of previous work in MD with an emphasis on adaptive methods. We start with (suboptimal) linear receivers and discuss the data-aided MMSE receiver. Blind (nondata-aided) implementations are also reviewed together with techniques that can mitigate possible multipath effects and channel dispersion. In anticipation of those developments, appropriate discrete-time (chip rate) CDMA models are reviewed, which incorporate asynchronism and channel dispersion. For systems with large spreading factors, the convergence and tracking properties of conventional adaptive filters may be inadequate due to the large number of coefficients which must be estimated. In this context, reduced rank adaptive filtering is discussed. In this approach, the number of parameters is reduced by restricting the receiver tap vector to belong to a carefully chosen subspace. In this way the number of coefficients to be estimated is significantly reduced with minimal performance loss.