Mixed noise suppression in hyperspectral imagery (HSI) constitutes an important preprocessing step in numerous remote sensing applications. Tensor decomposition-based approaches have proved successful also in this HSI data processing task, given the multi-way nature of the HSI cube and its underlying spatial-spectral correlation. Block-term decomposition (BTD), in its special yet widely applicable format of decomposition into rank-(Lr,Lr,1) terms, has been more recently adopted in HSI processing as a natural generative model, in which the R block terms represent the constituent endmembers, and their ranks, Lr, r = 1,2,…,R, quantify the spatial correlation in the corresponding abundance maps. In this paper, a BTD-based denoising method is developed, robust to sparse outliers, and with the model ranks a-priori unknown and recovered in the course of the algorithm with the aid of appropriate ℓ1,2-norm regularization. Its computational efficiency and effectiveness in rank determination and mixed noise removal are demonstrated via simulations involving both synthetic and HSI noisy tensors. For the latter, it is also seen to be robust to model order under-estimation.

This paper delves into the dynamic field of hyperspectral imaging, focusing on the challenging task of denoising hyperspectral images given the presence of diverse noise types in the data. Within this context, we propose an innovative blind model-data-driven learning algorithm that combines a Bayesian low-rank matrix factorization-based scheme with a deep image prior convolutional neural network. Significantly, the algorithm estimates the spectrum-related image component via the Bayesian algorithm and the spatial information-related component by the network, resulting in improved denoising performance. Simulation results demonstrate the algorithm’s efficacy, surpassing contemporary unsupervised model-driven and model-data-driven HSI denoising algorithms. This work contributes to advancing the field by integrating model-driven principles with deep learning networks for enhanced hyperspectral image denoising.

The so-called block-term decomposition (BTD) tensor model has been recently receiving increasing attention due to its enhanced ability of representing systems and signals that are composed of blocks of rank higher than one, a scenario encountered in numerous and diverse applications. In this paper, BTD is employed for the completion of a tensor from its partially observed entries. A novel method is proposed, which is based on the idea of imposing column sparsity jointly on the BTD factors and in a hierarchical manner. This way the number of block terms and their ranks can also be estimated, as the numbers of factor columns of non-negligible magnitude. Following a block successive upper bound minimization (BSUM) approach with appropriate choice of the surrogate majorizing functions is shown to result in an alternating hierarchical iteratively reweighted least squares (HIRLS) algorithm, which is fast converging and enjoys high computational efficiency, as it relies in its iterations on small-sized sub-problems with closed-form solutions. Simulation results with both synthetic and real data are reported, which demonstrate the effectiveness of the proposed scheme.

The Schatten-$p$ quasi-norm with $p\in(0,1)$ has recently gained considerable attention in various low-rank matrix estimation problems offering significant benefits over relevant convex heuristics such as the nuclear norm. However, due to the nonconvexity of the Schatten-$p$ quasi-norm, minimization suffers from two major drawbacks: 1) the lack of theoretical guarantees and 2) the high computational cost which is demanded for the minimization task even for trivial tasks such as finding stationary points. In an attempt to reduce the high computational cost induced by Schatten-$p$ quasi-norm minimization, variational forms, which are defined over smaller-size matrix factors whose product equals the original matrix, have been proposed. Here, we propose and analyze a novel {\it variational form of Schatten-$p$ quasi-norm} which, for the first time in the literature, is defined for any continuous value of $p\in(0,1]$ and decouples along the columns of the factorized matrices. The proposed form can be considered as the natural generalization of the well-known variational form of the nuclear norm to the nonconvex case i.e., for $p\in(0,1)$. Notably, low-rankness is now imposed via a group-sparsity promoting regularizer. The resulting formulation gives way to SVD-free algorithms thus offering lower computational complexity than the one that is induced by the original definition of the Schatten-$p$ quasi-norm. A local optimality analysis is provided which shows~that we can arrive at a local minimum of the original Schatten-$p$ quasi-norm problem by reaching a local minimum of the matrix factorization based surrogate problem. In addition, for the case of the squared Frobenious loss with linear operators obeying the restricted isometry property (RIP), a rank-one update scheme is proposed, which offers a way to escape poor local minima. Finally, the efficiency of our approach is empirically shown on a matrix completion problem.

The letter deals with the problem known as robust principal component analysis (RPCA), that is, the decomposition of a data matrix as the sum of a low-rank matrix component and a sparse matrix component. After expressing the low-rank matrix component in factorized form, we develop a novel online RPCA algorithm that is based entirely on reweighted least squares recursions and is appropriate for sequential data processing. The proposed algorithm is fast, memory optimal and, as corroborated by indicative empirical results on simulated data and a video processing application, competitive to the state-of-the-art in terms of estimation performance.

Nonnegative matrix factorization (NMF) has attracted considerable attention over the past few years as is met in many modern machine learning applications. NMF presents some inherent challenges when it comes both to its theoretical understanding and the task of devising efficient algorithmic tools. In this paper, we deal with an issue that is inherent in NMF, i.e., the a priori unawareness of the true nonnegative rank. To this end, a novel constrained NMF formulation is proposed. The main premise of the new formulation is to first assume an overestimate of the rank and then reduce it by imposing column sparsity jointly on the nonnegative matrix factors using proper penalization. Borrowing ideas from the block successive upper bound minimization framework, an alternating minimization strategy is followed, while inexact projected Newton-type updates are used in order to guarantee the descent direction of the cost function at each iteration. The effectiveness of the proposed approach is verified on simulated data and a real music signal decomposition experiment.

Nowadays, many modern imaging applications generate large-scale and high-dimensional data. In order to efficiently handle these data, statistical tools amenable to exploiting their intrisic low-dimensional nature are needed. PCA is a ubiquitous method which has been widely applied in a variety of applications. However a major shortcoming of PCA is its sensitivity to gross errors - outliers. In light of this, robust PCA has been recently proposed. Robust PCA accounts for gross errors by assuming that the data matrix is the superposition of a low-rank matrix and a sparse matrix. In this work, a matrix factorization-based formulation of robust PCA which can efficiently handle large scale data is proposed. Low-rankness is imposed via a novel low-rank promoting term applied on the matrix factors, which can be viewed as a weighted version of the variational form of the nuclear norm. The newly formulated robust PCA problem is addressed via an alternating iteratively reweighted least squares-type algorithm. Simulated and real data experiments verify the effectiveness of the proposed algorithm as compared to other state-of-the-art robust PCA algorithms.

We introduce a tensor completion algorithm that uses a group-sparse regularizer with respect to the PARAFAC factors and is based on an optimization scheme that alternatingly minimizes a quadratic upper bound of the associated cost function. The proposed scheme allows matrixwise updates of the PARAFAC factors and, thus, leads to an efficient and scalable iterative algorithm, suitable for big-data applications. Experiments conducted on both synthetic and real data, corroborate the superior performance, in terms of runtime, of the proposed algorithm as compared with the other state-of-the-art approaches.

In this paper, a convergence proof for the recently proposed cost function optimization sparse possibilistic c-means (SPCM) algorithm is provided. Specifically, it is shown that the algorithm will converge to one of the local minima of its associated cost function. It is also shown that similar convergence results can be derived for the well-known possibilistic c-means (PCM) algorithm proposed by Krishnapuram and Keller, 1996, if we view it as a special case of SPCM. Note that the convergence results for PCM are stronger than those established in previous works.

In this paper, a novel possibilistic c-means clustering algorithm, called adaptive possibilistic c-means, is presented. Its main feature is that its parameters, after their initialization, are properly adapted during its execution. Provided that the algorithm starts with a reasonable overestimate of the number of physical clusters formed by the data, it is capable, in principle, to unravel them (a long-standing issue in the clustering literature). This is due to the fully adaptive nature of the proposed algorithm that enables the removal of the clusters that gradually become obsolete. In addition, the adaptation of all its parameters increases the flexibility of the algorithm in following the variations in the formation of the clusters that occur from iteration to iteration. Theoretical results that are indicative of the convergence behavior of the algorithm are also provided. Finally, extensive simulation results on both synthetic and real data highlight the effectiveness of the proposed algorithm.

In this paper, two novel possibilistic clustering algorithms are presented, which utilize the concept of sparsity. The first one, called sparse possibilistic c-means, exploits sparsity and can deal well with closely located clusters that may also be of significantly different densities. The second one, called sparse adaptive possibilistic c-means, is an extension of the first, where now the involved parameters are dynamically adapted. The latter can deal well with even more challenging cases, where, in addition to the above, clusters may be of significantly different variances. More specifically, it provides improved estimates of the cluster representatives, while, in addition, it has the ability to estimate the actual number of clusters, given an overestimate of it. Extensive experimental results on both synthetic and real datasets support the previous statements.

In a plethora of applications dealing with inverse problems, e.g., image processing, social networks, compressive sensing, and biological data processing, the signal of interest is known to be structured in several ways at the same time. This premise has recently guided research into the innovative and meaningful idea of imposing multiple constraints on the unknown parameters involved in the problem under study. For instance, when dealing with problems whose unknown parameters form sparse and low-rank matrices, the adoption of suitably combined constraints imposing sparsity and low rankness is expected to yield substantially enhanced estimation results. In this paper, we address the spectral unmixing problem in hyperspectral images. Specifically, two novel unmixing algorithms are introduced in an attempt to exploit both spatial correlation and sparse representation of pixels lying in the homogeneous regions of hyperspectral images. To this end, a novel mixed penalty term is first defined consisting of the sum of the weighted ℓ1and the weighted nuclear norm of the abundance matrix corresponding to a small area of the image determined by a sliding square window. This penalty term is then used to regularize a conventional quadratic cost function and impose simultaneous sparsity and low rankness on the abundance matrix. The resulting regularized cost function is minimized by: 1) an incremental proximal sparse and low-rank unmixing algorithm; and 2) an algorithm based on the alternating direction method of multipliers. The effectiveness of the proposed algorithms is illustrated in experiments conducted both on simulated and real data.

In several wireless communication systems, low complexity channel selection schemes are required, as power efficient mechanisms to improve performance. In this context, the best selection scheme, in terms of performance, comes at the cost of increased complexity, since it necessitates a continuous monitoring of all available channels. In this paper, a new threshold-based channel selection strategy is proposed, which decreases the system complexity, without considerably affecting the system performance. Assuming independent but nonidentically distributed channel conditions, a generic analytical framework is first presented, based on the Markov chain theory. Then, the proposed selection scheme is applied to three specific communication scenarios, namely multichannel reception, transmit antenna selection with diversity reception, and cooperative relay selection. In all three cases, closed-form results are obtained and used to analyze the performance of the systems under consideration. It is shown that based on the proposed scheme, computational complexity is reduced and thus important energy savings can be achieved, without a significant loss in performance.

Abstract A new user selection strategy is investigated and analyzed in a multiuser relaying environment in the presence of co‐channel interference. The proposed selection scheme aims at avoiding unnecessary feedback load processing, in cases where a target threshold, in the received instantaneous signal‐to‐noise ratio, is exceeded. Assuming that perfect channel state information is available, closed‐form lower bound expressions are derived for the cumulative distribution function of the output signal to interference plus noise ratio. Moreover, the impact of outdated channel state information on the system's performance is also investigated. In addition, under the assumption of high signal‐to‐noise ratio conditions, simplified approximated expressions are also provided for the cumulative distribution functions of the output signal to interference plus noise ratio, which are employed to study the outage probability and bit error probability performance of the system. It is shown that with the proposed approach, a significant reduction in feedback load processing is achieved, with only a slight loss in performance. Copyright © 2016 John Wiley & Sons, Ltd.

In this paper a joint spectral unmixing and clustering approach for the identification of homogeneous regions in hyperspectral images is proposed. The endmembers required in the unmixing stage are manually selected based on the most significant principal components of the image at hand. Each pixel is decomposed as a linear combination of the endmembers and is represented by the vector of the coefficients of its corresponding linear combination. The clustering stage utilizes the complete-link hierarchical agglomerative clustering algorithm in a layer-wise fashion in order to retrieve the optimal clusters, based on the latter pixels representation. Experiments conducted on real images support the high-quality performance of the proposed approach.

In this paper a new feature selection method suitable for hyperspectral image clustering is presented. The proposed spectral band selection method selects bands that exhibit significant discrimination ability, based on the optimization of a sparsity promoting cost function. This allows clustering algorithms to export results of the same quality compared to cases where all spectral bands are used, while, in some cases, it allows the unravelling of some less-obvious patterns. Experimental results on real hyperspectral data sets highlight the enhanced performance of the proposed technique.

In this paper, the effects of interference on composite fading environments, where multipath fading coexists with shadowing, are investigated. Based on some mathematical convenient expressions for the sum of squared K-distributed random variables, which are derived for the first time, important statistical metrics for the signal to interference and noise ratio (SINR) are studied for various cases including non identical, identical and fully correlated statistics. Furthermore, our analysis is extended to multi-channel receivers and in particular to selection diversity (SD) receivers, investigating two distinct cases, namely, signal-to-noise ratio based and SINR-based SD. For all scenarios, simplified expressions are also provided for the interference limited case, where the influence of thermal noise is ignored. The derived expressions are used to analyze the performance, in terms of the average bit error probability (ABEP) and the outage probability (OP), of such systems operating over composite fading environments. A high SNR analysis is also presented for the OP and the ABEP, giving a clear physical insight of the system's performance in terms of the diversity and coding gains. The analysis is accompanied by numerical evaluated results, clearly demonstrating the usefulness of the proposed theoretical framework.

This paper presents an online version of the widely used sparse Bayesian learning (SBL) algorithm. Exploiting the variational Bayes framework, an efficient online SBL algorithm is constructed, that acts as a fully automatic learning method for the adaptive estimation of sparse time-varying signals. The new method is based on second order statistics and comprises a simple, automated sparsity-imposing mechanism, different from that of other known schemes. The effectiveness of the proposed online Bayesian algorithm is illustrated using experimental results conducted on synthetic data. These results show that the proposed scheme achieves faster initial convergence and superior estimation performance compared to other related state-of-the-art schemes.

In this paper a new sparse adaptive possibilistic clustering algorithm is presented. The algorithm exhibits high immunity to outliers and provides improved estimates of the cluster representatives by adjusting dynamically certain critical parameters. In addition, the proposed scheme manages - in principle - to estimate the actual number of clusters and by properly imposing sparsity, it becomes capable to deal well with closely located clusters of different densities. Extensive experimental results verify the previous statements.

In this paper a new algorithm suitable for hyperspectral image clustering, called L-SAPCM, is proposed. The algorithm works in layers where at each layer, after suitable pre-processing, the SAPCM clustering algorithm ([1]) is applied. Preliminary results on real hyperspectral images show enhanced performance compared to other related methods.

In this paper the performance of a cooperative communication system operating over a composite fading environment and is also subject to interference is investigated. More specifically, assuming a decode-and-forward (multi-relay) cooperative network with relay selection, exact and approximated expressions are derived for the cumulative distribution function of the output signal to interference plus noise ratio. Based on these expressions, the outage and the average bit error probabilities of the system under consideration are studied and used to obtain various numerical performance evaluation results, depicting in all cases the usefulness of the proposed approach.

Selection diversity (SD) represents an attractive solution in various wireless communication scenarios, since it offers relatively low complexity and improved performance. However, in many practical situations the continuously monitoring of all the available diversity paths, which is mandatory in SD schemes, adds unnecessary overhead to the systems. In this paper, in order to alleviate this complexity, a new threshold-based SD (t-SD) receiver is proposed. In particular, in t-SD, the current path is used as long as its signal to noise ratio is above a predefined threshold, otherwise the receiver becomes a pure SD. For this new concept we present an analytical framework for important statistical metrics accompanied by a complexity analysis. Various numerical evaluated results illustrate that the proposed scheme outperforms other well known schemes in terms of the performance and complexity trade off.

In this paper the outage probability of a cognitive decode-and-forward relay network operating over Nakagami-m fading channels is evaluated. Based on the underlay approach, secondary transmissions are allowed only in cases where interference constraints on the primary destination receivers are satisfied. Additionally, by taking into consideration the interfering effects coming from the multiple primary transmitters, the signal-to-interference-plus-noise-ratio statistic of the secondary nodes is investigated. The derived results include exact expressions as well as approximated ones for high values of the maximum allowed transmitted power at the cognitive network and/or the interference limited case. We present numerical performance evaluation results for various channel conditions and communication scenarios. These results are complemented by equivalent computer simulated ones, which validate the accuracy of the proposed analysis.

In this paper, training design is studied for a single relay amplify-and-forward cooperative network. The taps of the frequency selective channels are assumed to be correlated and OFDM modulation is used for transmission. Based on the least squares (LS) criterion, conditions for pilot tone positioning and a number of power allocation schemes are described. Analytical closed-form power allocation expressions are provided for both the source and the relay. The theoretical results are fully corroborated by simulations.

An analytical bit error rate (BER) performance study of three detect-and-forward (DaF) policies under a common framework is presented in this paper. More specifically, the direct, thresholded and link-adaptive schemes are studied, which differ in the way the decision on the transmitted symbol is forwarded from the relay to the destination. The analysis is carried out for a single relay DaF transmission protocol and takes into account the symbol decision errors that may occur at the relay. Simple closed-form analytical BER expressions are derived for all three schemes, which are completely verified by simulations. Moreover, by minimizing a properly selected conditional BER expression, a novel optimal DaF strategy is proposed, which outperforms all previously known related methods.

Filter bank-based multicarrier modulation (FBMC) using offset quadrature amplitude modulation (OQAM), known as FBMC/OQAM, provides an attractive alternative to the conventional cyclic prefix-based orthogonal frequency division multiplexing (CP-OFDM), especially in terms of increased robustness to frequency offset and Doppler spread, and high bandwidth efficiency. However, channel equalization in FBMC/OQAM is a nontrivial task, mainly because of the fact that the subchannels are no longer flat, in general. In multiple-antenna (MIMO) time-varying systems, equalizing the channel becomes even more challenging. This paper presents an adaptive T/2-spaced decision-feedback equalization (DFE) algorithm for MIMO-FBMC/OQAM systems, that is both computationally efficient and numerically stable. Its structure follows the V-BLAST idea and the algorithm is applied in a per subcarrier fashion. Simulation results are reported that demonstrate its effectiveness in time-varying MIMO channels with high frequency selectivity.

A unified analytical framework for evaluating the performance of maximal ratio combining (MRC) and orthogonal space-time block coding (OSTBC) over generalized fading channels is presented. The basic motivation for developing such a framework pertains to analyzing the distribution of a sum of squared random variables (RVs) belonging to different families of fading distributions. Following a novel analytical approach stemming from the definition of a common moment generating function (MGF) model for these families of distributions, the probability density function (PDF) and the cumulative distribution function (CDF) of a general sum of squared RVs are expressed by simple infinite Gamma series expansions. Based on these expressions, the capacity and error probability of MRC/OSTBC over generalized fading channels is thoroughly studied. The developed theory is used to evaluate the performance of OSTBC for a mixed Nakagami-m/Rice fading model and novel analytical results are presented. The accuracy of the derived expressions is validated by extensive Monte Carlo simulations.

A new constellation shaping technique has been proposed, which efficiently and effectively reduces the peak-to-average power ratio (PAPR) of orthogonal-frequency-division-multiplexing (OFDM) systems. Its novelty is based upon a simple transformation in the time domain instead of the commonly used frequency domain. This transformation is shown to ensure PAPR reduction regardless of the OFDM system input. As compared with previously known PAPR reduction methods, the proposed technique requires minimal implementation complexity, while it offers considerable performance gains. Closed form analytical expressions for the distribution of the PAPR and the bit error rate are derived. The accuracy of these analytical expressions is verified via equivalent performance evaluation results obtained by means of Monte Carlo computer simulations. Furthermore, performance comparisons made with other competitive techniques show that the proposed technique is an attractive alternative for PAPR reduction.

In this paper, the statistics of quadratic forms in normal random variables (RVs) are studied and their impact on performance analysis of wireless communication systems is explored. First, a chi-squared series expansion is adopted to represent the probability density function of a quadratic form in normal RVs and novel series truncation error bounds are derived, which are much tighter compared to already known ones. Secondly, it is theoretically shown that when an orthogonal space time block coding (OSTBC) transmission scheme is used, the signal to noise ratio (SNR) at the receiver under various fading conditions can be expressed as a quadratic form in normal RVs. Capitalizing on these results, a thorough error probability and capacity analysis is presented for the performance of OSTBC systems over Nakagami-q (Hoyt) fading channels. For all error probability and capacity performance criteria considered, simple, closed-form truncation error bounds expressions are derived, which avoid the use of infinite sums and complicated functions. The proposed theoretical analysis is validated through extensive Monte Carlo simulations.

In this paper, a novel error probability analysis of orthogonal space-time block coding (OSTBC) over independent but not necessarily identical Hoyt (Nakagami-q) fading channels is presented. First, it is shown that for a precise performance analysis the derivation of the distribution of a quadratic form in normal random variables is necessary. After representing this distribution using a chi-squared series expansion a new, tight upper bound on the series truncation error is obtained. The proposed bound has a simple form, which allows the derivation of closed-form truncation error bound expressions for several performance analysis criteria. Based on the chi-squared series formulation, closed-form error probability expressions are also provided. Simulation results show that the proposed bounds are much tighter compared to previously derived ones and verify our analytical results.

The equalization of MIMO frequency selective channels is a challenging task due to the increased filter lengths required and the presence of interstream interference. In wideband systems where high delay spread channels arise and long transmission bursts are employed, adaptive equalization is necessary. In this work, we develop an adaptive MIMO DFE for wideband time varying systems. To reduce computational complexity and accelerate convergence rate, the equalizer is fully implemented in the frequency domain, while an inherent causality problem is efficiently solved through an iterative scheme. As verified by simulations, the proposed method offers a good trade off in terms of complexity and convergence, compared to other related adaptive algorithms.

Among the methods that have been proposed for a Multiple-Input Multiple-Output (MIMO) receiver, the V-BLAST algorithm provides a good compromise between transmission rate, achievable diversity, and decoding complexity. In this paper, we derive a new adaptive V-BLAST type equalization scheme for fast time varying, flat fading MIMO channels. The proposed equalizer stems from the Cholesky factorization of MIMO system's output data autocorrelation matrix and the equalizer's filters are updated in time using numerically robust unitary Givens rotations. The new square-root algorithm exhibits identical performance to a recently proposed V-BLAST adaptive algorithm, offering at the same time substantially reduced computational complexity. Moreover, as expected due to its square-root form and verified by simulations, the algorithm exhibits particularly favourable numerical behaviour.

Among the methods that have been proposed for a multiple-input multiple-output (MIMO) receiver, the V-BLAST algorithm provides a good compromise between transmission rate, achievable diversity, and decoding complexity. In this letter, we derive a new adaptive V-BLAST-type equalization scheme for fast time-varying, flat-fading MIMO channels. The proposed equalizer stems from the Cholesky factorization of the MIMO system's output data autocorrelation matrix, and the equalizer filters are updated in time using numerically robust unitary Givens rotations. The new square-root algorithm exhibits identical performance to a recently proposed V-BLAST adaptive algorithm, offering at the same time noticeable reduction in computational complexity. Moreover, as expected due to its square-root form and verified by simulations, the algorithm exhibits particularly favorable numerical behavior.

A parametric method for estimating the unknown channel impulse response (CIR) in a semi-blind manner is proposed. The main trait of this method is that, instead of seeking the whole CIR sequence, only the unknown time delays and attenuation factors of the physical channel multipath components are estimated. The technique is based on a suitable application of the subchannel response matching (SRM) criterion. The resulting cost function is separable with respect to the two sets of unknown parameters, i.e. time delays and attenuations. Thus, an efficient two step optimization procedure can be applied. The new method offers significant computational savings and a lower mean square estimation error as compared to existing semi-blind channel estimation methods.

A new efficient decision feedback equalizer (DFE) appropriate for channels with long and sparse impulse response (IR) is proposed. Such channels are encountered in many high-speed wireless communications applications. It is shown that, in cases of sparse channels, the feedforward and feedback (FB) filters of the DFE have a particular structure, which can be exploited to derive efficient implementations of the DFE, provided that the time delays of the channel IR multipath components are known. This latter task is accomplished by a novel technique, which estimates the time delays based on the form of the channel input-output cross-correlation sequence in the frequency domain. A distinct feature of the resulting DFE is that the involved FB filter consists of a reduced number of active taps. As a result, it exhibits considerable computational savings, faster convergence, and improved tracking capabilities as compared with the conventional DFE. Note that faster convergence implies that a shorter training sequence is required. Moreover, the new algorithm has a simple form and its steady-state performance is almost identical to that of the conventional DFE.

In this paper a computationally e cient Decision Feedback Equalizer (DFE) is proposed. The new equalizer is appropriate for channels with long and sparse impulse response (IR) as those encountered in many wireless communications applications. The main feature of the algorithm is that the actual size of the computationally demanding feedback lter is signi cantly reduced. This is achieved by exploiting the particular form of the multipath channel to derive a tractable expression for the causal part of the overall discrete channel IR (including the feedforward lter). Based on the above expression the feedback lter can be built so as to act only to a properly selected set of tap positions. The new DFE exhibits considerable computational savings and faster convergence as compared to the conventional DFE, o ering the same steady-state performance. 1.

A new block adaptive decision feedback equalizer is developed. Both the feedforward (FF) and the feedback (FB) filters are updated once every K sample time intervals, with K being the block length. It should be noted that this block adaptation is done in such a way that the resulting filters, and the decisions as well, are identical to those computed by the conventional sample by sample LMS-based decision feedback equalizer (LMS-DFE). The new algorithm offers substantial computational savings as compared to the sample-by-sample LMS-DFE with no loss in performance. The new block DFE turns out to be particularly suitable for applications requiring long equalizers.

The paper presents two new, closely related adaptive algorithms for LS system identification. The starting point for the derivation of the algorithms is the inverse Cholesky factor of the data correlation matrix, obtained via a QR decomposition (QRD). Both are of O(p) computational complexity with p being the order of the system. The first algorithm is a fixed order QRD scheme with enhanced parallelism. The second is a lattice type algorithm based on Givens rotations, with lower complexity compared to previously derived ones.