Search

The normal offset decomposition is an adaptive (nonlinear) multiscale data transform, constructed in a way similar to the lifting scheme for wavelet transforms. The main difference lies in the fact that the detail coefficients are not wavelet coefficients corresponding to a wavelet basis function. Wavelet coefficients carry detail information situated at the location of the basis function. Besides detail information, normal offset coefficients also contain directional/geometrical information, i.e., information on where to locate the details. The normal offset decomposition is a jump-adaptive transform leading to a sparse representation of edges in images and sharp reconstructions of these edges. A major issue in this paper is the design of a new class of wavelet transforms that can be extended to normal offset decompositions. The combination of normal offsets and a stable lifting scheme is nontrivial. A necessary condition for an -stable lifted wavelet transform is that the wavelet basis functions have a vanishing integral (i.e., at least one vanishing moment). Although the normal offset decomposition is not a basis transform in the strict sense, a similar criterion for stability can be established and instability is equally a problem in a naive implementation. This paper constructs an ldquoupdatedrdquo normal offset decomposition that is stable and therefore appropriate for use in applications that sensitive to the numerical condition, such as applications involving (heavy) noise. The new scheme combines numerical stability, fast computation, and sharp edge representations. [ABSTRACT FROM PUBLISHER]

In this paper, we propose a weighted alternating direction method of multipliers (ADMM) to solve the consensus optimization problem over a decentralized network. In the proposed algorithm, every node holds its local objective function, exchanges its current iterate with a subset of neighbors, carries on local computation, and eventually reaches an optimal and consensual solution that minimizes the summation of the local objective functions. Compared with the conventional ADMM that is popular in decentralized network optimization, the weighted ADMM is able to reduce the communication cost spent in the optimization process through tuning the weight matrices, which assign beliefs on the neighboring iterates. We first prove convergence and establish linear convergence rate of the weighted ADMM. Second, we maximize the derived convergence speed and obtain the best weight matrices on a given topology. Third, observing that exchanging information with all the neighbors is expensive, we maximize the convergence speed while limit the number of communication arcs. This strategy finds a subset of arcs within the underlying topology to fulfill the optimization task while leads to a favorable tradeoff between the number of iterations and the communication cost per iteration. Numerical experiments demonstrate advantages of the weighted ADMM over its conventional counterpart in expediting the convergence speed and reducing the communication cost. [ABSTRACT FROM PUBLISHER]

This paper considers the statistical performance of the MUSIC method under the condition that two closely spaced sources impinging on an array of sensors are effectively resolved, i.e., the spectrum exhibits two peaks in the neighborhood of the true directions-of-arrival (DOA). The MUSIC algorithm is known to have an infinite resolution power in theory. However, in the presence of modeling errors, sources can not be resolved with certainty, even if the array correlation matrix is perfectly known. The focus of this paper is to predict the bias and variance of the DOA estimates taking into account the possible resolution failure of MUSIC. This performance prediction, based on our recent mathematical investigation, is new to the best of our knowledge. A general mathematical framework to derive closed form expressions of the bias and variance versus the model mismatch, conditioned on a general statistical resolution test is proposed. In order to illustrate our mathematical approach, statistical tests with one and two conditions, respectively, are investigated. The accuracy of the performance prediction is illustrated in a simulation study. It is found that the proposed approach outperforms the "classical" technique, which ignores the possible resolution failure of the MUSIC algorithm. Therefore, our results provide better tools for determining the necessary antenna calibration accuracy to achieve some targeted specifications on the estimator performance. [ABSTRACT FROM AUTHOR]

This paper considers the noncooperative maximization of mutual information in the vector Gaussian interference channel in a fully distributed fashion via game theory. This problem has been widely studied in a number of works during the past decade for frequency-selective channels, and recently for the more general multiple-input multiple-output (MIMO) case, for which the state-of-the art results are valid only for nonsingular square channel matrices. Surprisingly, these results do not hold true when the channel matrices are rectangular and/or rank deficient matrices. The goal of this paper is to provide a complete characterization of the MIMO game for arbitrary channel matrices, in terms of conditions guaranteeing both the uniqueness of the Nash equilibrium and the convergence of asynchronous distributed iterative waterfilling algorithms. Our analysis hinges on new technical intermediate results, such as a new expression for the MIMO waterfilling projection valid (also) for singular matrices, a mean-value theorem for complex matrix-valued functions, and a general contraction theorem for the multiuser MIMO watefilling mapping valid for arbitrary channel matrices. The quite surprising result is that uniqueness/convergence conditions in the case of tall (possibly singular) channel matrices are more restrictive than those required in the case of (full rank) fat channel matrices. We also propose a modified game and algorithm with milder conditions for the uniqueness of the equilibrium and con- vergence, and virtually the same performance (in terms of Nash equilibria) of the original game. [ABSTRACT FROM AUTHOR]

This paper introduces a general and axiomatic approach to linear signal processing (SP) that we refer to as the algebraic signal processing theory (ASP). Basic to ASP is the linear signal model defined as a triple (A, M, Φ) where familiar concepts like the filter space and the signal space are cast as an algebra A and a module M, respectively. The mapping Φ generalizes the concept of a z-transform to bijective linear mappings from a vector space of signal samples into the module M. Common concepts like filtering, spectrum, or Fourier transform have their equivalent counterparts in ASP. Once these concepts and their properties are defined and understood in the context of ASP, they remain true and apply to specific instantiations of the ASP signal model. For example, to develop signal processing theories for infinite and finite discrete time signals, for infinite or finite discrete space signals, or for multidimensional signals, we need only to instantiate the signal model to one that makes sense for that specific class of signals. Filtering, spectrum, Fourier transform, and other notions follow then from the corresponding ASP concepts. Similarly, common assumptions in SP translate into requirements on the ASP signal model. For example, shift-invariance is equivalent to A being commutative. For finite (duration) signals shift invariance then restricts A to polynomial algebras. We explain how to design signal models from the specification of a special filter, the shift. The paper illustrates the general ASP theory with the standard time shift, presenting a unique signal model for infinite time and several signal models for finite time. The latter models illustrate the role played by boundary conditions and recover the discrete Fourier transform (DFT) and its variants as associated Fourier transforms. Finally, ASP provides a systematic methodology to derive fast algorithms for linear transforms. This topic and the application of ASP to space dependent signals and to multidimensional signals are pursued in companion papers. [ABSTRACT FROM AUTHOR]

In this paper, we consider the problem of blind identification of a convolutive multiple-input-multiple-output (MIMO) system with No outputs and Ni inputs. While many methods have been proposed to blindly identify convolutive MIMO systems with No ≥ Ni (overdetermined), very scarce results exist for the case of No < Ni (underdetermined), all of which refer to systems that either have some special structure or special No and Ni values. In this paper, we show that, as long as min(No, Ni) ≥ 2, independent of whether the system is overdetermined or underdetermined, we can always find the appropriate order of statistics that guarantees identifiability of the system response within trivial ambiguities. We also propose an algorithm to reach the solution, that consists of parallel factorization (PARAFAC) of a K-way tensor containing K th-order statistics of the system outputs, followed by an iterative scheme. For a certain order of statistics K, we provide the description of the class of identifiable MIMO systems. We also show that this class can be expanded by applying PARAFAC decomposition to a pair of tensors instead of one tensor. The proposed approach constitutes a novel scheme for estimation of underdetermined systems, and improves over existing approaches for overdetermined systems. [ABSTRACT FROM AUTHOR]

For about two decades, numerous methods have been developed to blindly identify overdetermined (P ≤ N) mixtures of P statistically independent narrowband (NB) sources received by an array of N sensors. These methods exploit the information contained in the second-order (SO), the fourth-order (FO) or both the SO and FO statistics of the data. However, in practical situations, the probability of receiving more sources than sensors increases with the reception bandwidth and the use of blind identification (BI) methods able to process underdetermined mixtures of sources, for which P > N may be required. Although such methods have been developed over the past few years, they all present serious limitations in practical situations related to the radiocommunications context. For this reason, the purpose of this paper is to propose a new attractive BI method, exploiting the information contained in the FO data statistics only, that is able to process underdetermined mixtures of sources without the main limitations of the existing methods, provided that the sources have different trispectrum and nonzero kurtosis with the same sign. A new performance criterion that is able to quantify the identification quality of a given source and allowing the quantitative comparison of two BI methods for each source, is also proposed in the paper. Finally, an application of the proposed method is presented through the introduction of a powerful direction-finding method built from the blindly identified mixture matrix. [ABSTRACT FROM AUTHOR]

Waveform design is a pivotal component of the fully adaptive radar construct. In this paper, we consider waveform design for radar space time adaptive processing (STAP), accounting for the waveform dependence of the clutter correlation matrix. Due to this dependence, in general, the joint problem of receiver filter optimization and radar waveform design becomes an intractable, nonconvex optimization problem, Nevertheless, it is, however, shown to be individually convex either in the filter or in the waveform variables. We derive constrained versions of a) the alternating minimization algorithm, b) proximal alternating minimization, and c) the constant modulus alternating minimization, which, at each step, iteratively optimizes either the STAP filter or the waveform independently. A fast and slow time model permits waveform design in radar STAP, but the primary bottleneck is the computational complexity of the algorithms. [ABSTRACT FROM PUBLISHER]

In this paper, a computationally efficient algorithm for Bayesian joint change point detection (CPD) in multiple time series is presented. The data generation model includes a number of change configurations (CC), each affecting a unique subset of the time series, which introduces correlation between the positions of change points (CPs) in the monitored time series. The inference objective is to identify joint changes and the associated CC. The algorithm consists of two stages: First, a univariate CPD algorithm is applied separately to each of the involved time series. The outcomes of this step are maximum a posteriori (MAP) detected CPs and posterior distributions of CPs conditioned on the MAP CPs. These outcomes are used in combination to approximate the posterior for the CCs. In the second algorithm stage, dynamic programming is used to find the maxima of this approximate CC posterior. The algorithm is applied to synthetic data, and it is shown to be both significantly faster and more accurate compared to a previously proposed algorithm designed to solve similar problems. Also, the initial algorithm is extended with steps from the maximization–maximization algorithm, which allows the hyperparameters of the data generation model to be estimated jointly with the CCs, and we show that these estimates coincide with estimates obtained from a Markov chain Monte Carlo algorithm. [ABSTRACT FROM AUTHOR]

In this paper, new results and insights are derived for the performance of multiple-input, single-output systems with beamforming at the transmitter, when the channel state information is quantized and sent to the transmitter over a noisy feedback channel. It is assumed that there exists a per-antenna power constraint at the transmitter, hence, the equal gain transmission (EGT) beamforming vector is quantized and sent from the receiver to the transmitter. The loss in received signal-to-noise ratio (SNR) relative to perfect beamforming is analytically characterized, and it is shown that at high rates, the overall distortion can be expressed as the sum of the quantization-induced distortion and the channel error-induced distortion, and that the asymptotic performance depends on the error-rate behavior of the noisy feedback channel as the number of codepoints gets large. The optimum density of codepoints (also known as the point density) that minimizes the overall distortion subject to a boundedness constraint is shown to be the same as the point density for a noiseless feedback channel, i.e., the uniform density. The binary symmetric channel with random index assignment is a special case of the analysis, and it is shown that as the number of quantized bits gets large the distortion approaches the same as that obtained with random beamforming. The accuracy of the theoretical expressions obtained are verified through Monte Carlo simulations. [ABSTRACT FROM AUTHOR]

In this paper, we consider the problem of estimating an unknown deterministic parameter vector in a linear regression model with random Gaussian uncertainty in the mixing matrix. We prove that the maximum-likelihood (ML) estimator is a (de)regularized least squares estimator and develop three alternative approaches for finding the regularization parameter that maximizes the likelihood. We analyze the performance using the Cramér-Rao bound (CRB) on the mean squared error, and show that the degradation in performance due the uncertainty is not as severe as may be expected. Next, we address the problem again assuming that the variances of the noise and the elements in the model matrix are unknown and derive the associated CRB and ML estimator. We compare our methods to known results on linear regression in the error in variables (EIV) model. We discuss the similarity between these two competing approaches, and provide a thorough comparison that sheds light on their theoretical and practical differences. [ABSTRACT FROM AUTHOR]

This paper tackles the theoretical performance analysis of widely linear (WL) multiuser receivers for direct-sequence code-division multiple-access (DS-CDMA) systems, as well as their comparison with conventional linear (L) ones. In particular, receivers based on the minimum output-energy (MOE) criterion are considered, since they offer a good tradeoff between performance and complexity and, moreover, lend to some simplifications in the analysis. After comparing the ideal signal-to-interference-plus-noise-ratio (SINR) performances of the WL-MOE and L-MOE receivers, the paper establishes finite-sample performance results for two typical data-estimated implementations. Specifically, by adopting a first-order perturbative approach, the SINR degradation of the data-estimated WL-MOE receivers is accurately evaluated and compared with that of its linear counterpart. Simulation results are provided to validate and complement the theoretical analysis. [ABSTRACT FROM AUTHOR]

In this paper, we consider the extension of the Fourier transform to biquaternion-valued signals. We introduce a transform that we call the biquaternion Fourier transform (BiQFT). After giving some general properties of this transform, we show how it can be used to generalize the notion of analytic signal to complex-valued signals. We introduce the notion of hyperanalytic signal. We also study the Hermitian symmetries of the BIQFT and their relation to the geometric nature of a biquaternion-valued signal. Finally, we present a fast algorithm for the computation of the BiQFT. This algorithm is based on a (complex) change of basis and four standard complex FFTs. [ABSTRACT FROM AUTHOR]

In this paper, we consider sequential regression of individual sequences under the square-error loss. We focus on the class of switching linear predictors that can segment a given individual sequence into an arbitrary number of blocks within each of which a fixed linear regressor is applied. Using a competitive algorithm framework, we construct sequential algorithms that are competitive with the best linear regression algorithms for any segmenting of the data as well as the best partitioning of the data into any fixed number of segments, where both the segmenting of the data and the linear predictors within each segment can be tuned to the underlying individual sequence. The algorithms do not require knowledge of the data length or the number of piecewise linear segments used by the members of the competing class, yet can achieve the performance of the best member that can choose both the partitioning of the sequence as well as the best regressor within each segment. We use a transition diagram (F. M. J. Willems, 1996) to compete with an exponential number of algorithms in the class, using complexity that is linear in the data length. The regret with respect to the best member is O(ln(n)) per transition for not knowing the best transition times and O(ln(n)) for not knowing the best regressor within each segment, where n is the data length. We construct lower bounds on the performance of any sequential algorithm, demonstrating a form of mm-max optimality under certain settings. We also consider the case where the members are restricted to choose the best algorithm in each segment from a finite collection of candidate algorithms. Performance on synthetic and real data are given along with a Matlab implementation of the universal switching linear predictor. [ABSTRACT FROM AUTHOR]

This paper deals with the problem of detecting a signal, known only to lie on a line in a subspace, in the presence of unknown noise, using multiple snapshots in the primary data. To account for uncertainties about a signal's signature, we assume that the steering vector belongs to a known linear subspace. Furthermore, we consider the partially homogeneous case, for which the covariance matrix of the primary and the secondary data have the same structure but possibly different levels. This provides an extension to the framework considered by Bose and Steinhardt. The natural invariances of the detection problem are studied, which leads to the derivation of the maximal invariant. Then, a detector is proposed that proceeds in two steps. First, assuming that the noise covariance matrix is known, the generalized-likelihood ratio test (GLRT) is formulated. Then, the noise covariance matrix is replaced by its sample estimate based on the secondary data to yield the final detector. The latter is compared with a similar detector that assumes the steering vector to be known. [ABSTRACT FROM AUTHOR]

Integer mapping is critical for lossless source coding and has been used for multicomponent image compression in the new international image compression standard JPEG 2000. In this paper, starting from block factorizations for any nonsingular transform matrix, we introduce two types of parallel elementary reversible matrix (PERM) factorizations which are helpful for the parallelization of perfectly reversible integer transforms. With improved degree of parallelism and parallel performance, the cost of multiplications and additions can be, respectively, reduced to O(log N) and O(log² N) for an N by N transform matrix. These make PERM factorizations an effective means of developing parallel integer transforms for large matrices. We also present a scheme to block the matrix and allocate the load of processors for efficient transformation. [ABSTRACT FROM AUTHOR]

The sparse representation of a multiple-measurement vector (MMV) is a relatively new problem in sparse representation. Efficient methods have been proposed. Although many theoretical results that are available in a simple case—single-measurement vector (SMV)—the theoretical analysis regarding MMV is lacking. In this paper, some known results of SMV are generalized to MMV. Some of these new results take advantages of additional information in the formulation of MMV. We consider the uniqueness under both an l0-norm-like criterion and an l1-norm-like criterion. The consequent equivalence between the l0-norm approach and the l1-norm approach indicates a computationally efficient way of finding the sparsest representation in a redundant dictionary. For greedy algorithms, it is proven that under certain conditions, orthogonal matching pursuit (OMP) can find the sparsest representation of an MMV with computational efficiency, just like in SMV. Simulations show that the predictions made by the proved theorems tend to be very conservative; this is consistent with some recent advances in probabilistic analysis based on random matrix theory. The connections will be discussed. [ABSTRACT FROM AUTHOR]

In frequency-selective multiple-input multiple-output (MIMO) channel, differential space-time-frequency (DSTF) modulations are known as practical alternatives that are capable of exploiting the available spatial and frequency diversities without the requirement of multichannel estimation at the receiver. However, the encoding nature of the DSTF schemes that expand several OFDM symbol periods makes the DSTF schemes susceptible to fast-changing channel conditions. In this paper, we propose a differential scheme for MIMO-OFDM systems that is able to differentially encode signal within two OFDM symbol periods, and the proposed scheme transmits the differentially encoded signal within one OFDM block. The scheme not only reduces encoding and decoding delay but also relaxes the restriction on channel assumption. The successful differential decoding of the proposed scheme depends on the assumption that the fading channels keep constant over two OFDM symbol periods rather than multiple of them as required in the existing DSTF schemes. We also provide pairwise error probability analysis and quantify the performance criteria in terms of diversity and coding advantages. The design criteria reveal that the existing diagonal cyclic codes can be applied to achieve full diversity. Performance simulations under various channel conditions show that our proposed scheme yields superior performance to previously proposed differential schemes. [ABSTRACT FROM AUTHOR]

This paper introduces the general-purpose Gaussian transform of distributions, which aims at representing a generic symmetric distribution as an infinite mixture of Gaussian distributions. We start by the mathematical formulation of the problem and continue with the investigation of the conditions of existence of such a transform. Our analysis leads to the derivation of analytical and numerical tools for the computation of the Gaussian transform, mainly based on the Laplace and Fourier transforms, as well as of the afferent properties set (e.g., the transform of sums of independent variables). The Gaussian transform of distributions is then analytically derived for the Gaussian and Laplacian distributions, and obtained numerically for the generalized Gaussian and the generalized Cauchy distribution families. In order to illustrate the usage of the proposed transform we further show how an infinite mixture of Gaussians model can be used to estimate/denoise non-Gaussian data with linear estimators based on the Wiener filter. The decomposition of the data into Gaussian components is straightforwardly computed with the Gaussian transform, previously derived. The estimation is then based on a two-step procedure: the first step consists of variance estimation, and the second step consists of data estimation through Wiener filtering. To this purpose, we propose new generic variance estimators based on the infinite mixture of Gaussians prior. It is shown that the proposed estimators compare favorably in terms of distortion with the shrinkage denoising technique and that the distortion lower bound under this framework is lower than the classical minimum mean-square error bound. [ABSTRACT FROM AUTHOR]

This paper analyzes the problem of error amplification in frame-based coding schemes derived from oversampled filter banks. Oversampled filter banks are currently being proposed for robust transmission applications, since added redundancy can be used for error recovery in case of losses. Error amplification is determined by the lower bound of the subframe resulting after losses. Theoretical expressions are derived to characterize such lower bound for different loss statistics. Criteria are derived that can be useful for the design of oversampled filter banks in various applications. The analysis and some application examples demonstrate that filter bank performance strongly depends on how the coefficients are organized into packets. [ABSTRACT FROM AUTHOR]

This paper provides a new analytic expression of the bias and RMS error (root mean square) error of the estimated direction of arrival (DOA) in the presence of modeling errors. In [1]–[5], first-order approximations of the RMS error are derived, which are accurate for small enough perturbations. However, the previously available expressions are not able to capture the behavior of the estimation algorithm into the threshold region. In order to fill this gap, we provide a second-order performance analysis, which is valid in a larger interval of modeling errors. To this end, it is shown that the DOA estimation error for each signal source can be expressed as a ratio of Hermitian forms, with a stochastic vector containing the modeling error. Then, an analytic expression for the moments of such a Hermitian forms ratio is provided. Finally, a closed-form expression for the performance (bias and RMS error) is derived. Simulation results indicate that the new result is accurate into the region where the algorithm breaks down. [ABSTRACT FROM AUTHOR]

Integer DCTs have a wide range of applications in lossless coding, especially in image compression. An integer-to-integer DCT of radix-2-length n is a nonlinear, left-invertible mapping, which acts on Zn and approximates the classical discrete cosine transform (DCT) of length n. All known integer-to-integer DCT-algorithms of length 8 are based on factorizations of the cosine matrix C8II into a product of sparse matrices and work with lifting steps and rounding off. For fast implementation one replaces floating point numbers by appropriate dyadic rationals. Both rounding and approximation leads to truncation errors. In this paper, we consider an integer-to-integer transform for (2 × 2) rotation matrices and give estimates of the truncation errors for arbitrary approximating dyadic rationals. Further, using two known integer-to-integer DCT-algorithms, we show examplarily how to estimate the worst-case truncation error of lifting based integer-to-integer algorithms in fixed-point arithmetic, whose factorizations are based on (2 × 2) rotation matrices. [ABSTRACT FROM AUTHOR]

In this paper, we first propose an efficient algorithm for computing one-dimensional (1-D) discrete cosine transform (DCT) for a signal block, given its two adjacent sub blocks in the DCT domain and then introduce several algorithms for the fast computation of multidimensional (m-D) DCT with size N1 × N2 ×…× Nm given 2m subblocks of DCT coefficients with size N1/2 × N2/2 ×… × Nm/2, where Ni(i=1,2,ߪ,m) are powers of 2. Obviously, the row-column method, which employs the most efficient algorithms along each dimension, reduces the computational complexity considerably, compared with the traditional method, which employs only the one-dimensional (1-D) fast DCT and inverse DCT (IDCT) algorithms. However, when m & 2, the traditional method, which employs the most efficient multidimensional DCT/IDCT algorithms, has lower computational complexity than the row-column method. Besides, we propose a direct method by dividing the data into 2m parts for independent fast computation, in which only two steps of r-dimensional (r = 1,2,…, m) IDCT and additional multiplications and additions are required. If all the dimensional sizes are the same, the number of multiplications required for the direct method is only (2m - 1)/m2m-1 times of that required for the row-column method, and if N & 22m-1, the computational efficiency of the direct method is surely superior to that of the traditional method, which employs the most efficient multidimensional DCT/DCT algorithms. [ABSTRACT FROM AUTHOR]

Nonlinear system identification has been studied under the assumption that the noise has finite second and higher order statistics. In many practical applications, impulsive measurement noise severely weakens the effectiveness of conventional methods. In this paper, a-stable noise is used as a noise model. In such case, the minimum mean square error (MMSE) criterion is no longer an appropriate metric for estimation error due to the lack of finite seconds-order statistics of the noise. There- fore, we adopt minimum dispersion criterion, which in turn leads to the adaptive least mean pth power (LMP) algorithm. it is shown that the LMP algorithm under the α-stable noise model converges as long as the step size satisfies certain conditions. The effect of p on the performance is also investigated. Compared with conventional methods, the proposed method is more robust to impulsive noise and has better performance. [ABSTRACT FROM AUTHOR]

This paper is concerned with optimal filtering in a distributed multiple sensor system with the so-called out-of-sequence measurements (OOSM). Based on best linear unbiased estimation (BLUE) fusion, we present two algorithms for updating with OOSM that are optimal for the information available at the time of update. Different minimum storages of information concerning the occurrence time of OOSMs are given for both algorithms. It is shown by analysis and simulation results that the two proposed algorithms are flexible and simple. [ABSTRACT FROM AUTHOR]

The Empirical Mode Decomposition (EMD) is a relatively new adaptive method for multicomponent signal representation which allows for analyzing nonlinear and nonstationary signals. In spite of its lack of mathematical foundations, very few papers are dedicated to defining new decompositions that would preserve the interesting properties of the EMD while improving the mathematical setting. The new decomposition based on direct constrained optimization we introduce in this article is an attempt in that direction. [ABSTRACT FROM AUTHOR]

Distributed source coding schemes are typically based on the use of channels codes as source codes. In this paper we propose a new paradigm, named "distributed arithmetic coding," which extends arithmetic codes to the distributed case employing sequential decoding aided by the side information. In particular, we introduce a distributed binary arithmetic coder for the Slepian-Wolf coding problem, along with a joint decoder. The proposed scheme can be applied to two sources in both the asymmetric mode, wherein one source acts as side information, and the symmetric mode, wherein both sources are coded with ambiguity, at any combination of achievable rates. Distributed arithmetic coding provides several advantages over existing Slepian-Wolf coders, especially good performance at small block lengths, and the ability to incorporate arbitrary source models in the encoding process, e.g., context-based statistical models, in much the same way as a classical arithmetic coder. We have compared the performance of distributed arithmetic coding with turbo codes and low-density parity-check codes, and found that the proposed approach is very competitive. [ABSTRACT FROM AUTHOR]

This paper proposes a multistage decomposition for blind adaptive parameter estimation in the Krylov subspace with the code-constrained constant modulus (CCM) design criterion. Based on constrained optimization of the constant modulus cost function and utilizing the Lanczos algorithm and Arnoldi-like iterations, a multistage decomposition is developed for blind parameter estimation. A family of computationally efficient blind adaptive reduced-rank stochastic gradient (SG) and recursive least squares (RLS) type algorithms along with an automatic rank selection procedure are also devised and evaluated against existing methods. An analysis of the convergence properties of the method is carried out and convergence conditions for the reduced-rank adaptive algorithms are established. Simulation results consider the application of the proposed techniques to the suppression of multiaccess and intersymbol interference in DS-CDMA systems. [ABSTRACT FROM AUTHOR]

In this paper, we present a closed-form expression of a Bayesian Cramer-Ran lower bound for the estimation of a dynamical phase offset in a non-data-aided BPSK transmitting context. This kind of bound is derived considering two different scenarios: a first expression is obtained in an offline context, and then a second expression in an online context logically follows. The SNR-asymptotic expressions of this bound drive us to introduce a new asymptotic bound, namely the asymptotic Bayesian Cramér-Rao Bound. This bound is close to the classical Bayesian bound but is easier to evaluate. [ABSTRACT FROM AUTHOR]

In many situations, multiple-input-multiple-output with orthogonal frequency division multiplexing (MIMO-OFDM) channels tend to be spatially correlated due, for example, to limited scattering. Prior knowledge of this channel spatial correlation and the channel frequency correlation can be exploited by using the linear minimum-mean-square-error (LMMSE) technique. However, the complexity of the 2-D LMMSE technique, which fully utilizes both the channel spatial and frequency correlation is quite high. To solve this problem, this paper presents and analyzes several low-complexity, suboptimal, approximated LMMSE channel estimation techniques in the angle domain, where the channel model lends itself to a physical interpretation. The choice of angle-domain techniques is largely dependent on the extent of channel stochastic information (e.g., channel correlation or power) that is available to the receiver. Nevertheless, all the proposed angle-domain techniques have much lower complexity compared to the 2-D LMMSE technique. Further, all the angle-domain techniques improve over the conventional least square (LS) technique for all the typical MIMO-OFDM models under consideration. More importantly, our simulation results show that the angle-domain quasi 1-D (Q1-D) LMMSE technique can achieve similar performance compared to the 2-D LMMSE technique for all typical MIMO-OFDM models with significantly lower complexity. [ABSTRACT FROM AUTHOR]

Prefilters are generally applied to the discrete multi-wavelet transform (DMWT) for processing scalar signals. To fully utilize the benefit offered by DMWT, it is important to have the pre-filter designed appropriately so as to preserve the important properties of multiwavelets. To this end, we have recently shown that it is possible to have the prefilter designed to be maximally decimated, yet preserve the linear phase and orthogonal properties as well as the approximation power of multiwavelets. However, such design requires the point of symmetry of each channel of the prefilter to match with the scaling functions of the target multiwavelet system. It can be very difficult to find a compatible filter bank structure; and in some cases, such filter structure simply does not exist, e.g., for multiwavelets of multiplicity 2. In this paper, we suggest a new DMWT structure in which the prefilter is combined with the first stage of DMWT. The advantage of the new structure is twofold. First, since the prefiltering stage is embedded into DMWT, the computational complexity can be greatly reduced. Experimental results show that an over 20% saving in arithmetic operations can be achieved comparing with the traditional DMWT realizations. Second, the new structure provides additional design freedom that allows the resulting prefilters to be maximally decimated, orthogonal and symmetric even for multiwavelets of low multiplicity. We evaluated the new DMWT structure in terms of computational complexity, energy compaction ratio as well as the compression performance when applying to a VQ based image coding system. Satisfactory results are obtained in all cases comparing with the traditional approaches. [ABSTRACT FROM AUTHOR]

The optimality of second-order statistics depends heavily on the assumption of Gaussianity. In this paper, we elucidate further the probabilistic and geometric meaning of the recently defined correntropy function as a localized similarity mea- sure. A close relationship between correntropy and M-estimation is established. Connections and differences between correntropy and kernel methods are presented. As such correntropy has vastly different properties compared with second-order statistics that can be very useful in non-Gaussian signal processing, especially in the impulsive noise environment. Examples are presented to illustrate the technique. [ABSTRACT FROM AUTHOR]

Recently, there has been an intense activity in the field of sparse approximations with redundant dictionaries, largely motivated by the practical performances of algorithms such as Matching Pursuit (MP) and Basis Pursuit (BP). However, most of the theoretical results obtained so far are valid only for the restricted class of incoherent dictionaries. This paper investigates a new class of overcomplete dictionaries, called block incoherent dictionaries, where coherence can be arbitrarily big. We show that a simple greedy algorithm can correctly identify stable subdictionaries (called blocks) and demonstrate how one can use the extra coherence freedom for approximation purposes. [ABSTRACT FROM AUTHOR]

This paper uses the Hybrid Steepest Descent Method (HSDM) to design robust smart antennas. Several design criteria as well as robustness are mathematically described by a finite collection of closed convex sets in a real Euclidean space. Desirable beamformers are defined as points of the generalized convex feasible set which is well defined even in the case of inconsistent design criteria. A quadratic cost function is formed by the correlations of the incoming data, and the HSDM constructs a point sequence that (strongly) converges to the (unique) minimizer of the cost function over the generalized convex feasible set. Numerical examples validate the proposed design. [ABSTRACT FROM AUTHOR]

This paper studies a novel decomposition technique, suitable for blind separation of linear mixtures of signals comprising finite-length symbols. The observed symbols are first modeled as channel responses in a multiple-input-multiple-output (MIMO) model, while the channel inputs are conceptually considered sparse positive pulse trains carrying the information about the symbol arising times. Our decomposition approach compensates channel responses and aims at reconstructing the input pulse trains directly. The algorithm is derived first for the overdetermined noiseless MIMO case. A generalized scheme is then provided for the underdetermined mixtures in noisy environments. Although blind, the proposed technique approaches Bayesian optimal linear minimum mean square error estimator and is, hence, significantly noise resistant. The results of simulation tests prove it can be applied to considerably underdetermined convolutive mixtures and even to the mixtures of moderately correlated input pulse trains, with their cross-correlation up to 10% of its maximum possible value. [ABSTRACT FROM AUTHOR]

The lifting scheme is well known to be an efficient tool for constructing second generation wavelets and is often used to design a class of biorthogonal wavelet filter banks. For its efficiency, the lifting implementation has been adopted in the inter- national standard JPEG2000. It is known that the orthogonality of wavelets is an important property for many applications. This paper presents how to implement a class of infinite-impulse-response (IIR) orthogonal wavelet filter banks by using the lifting scheme with two lifting steps. It is shown that a class of IIR orthogonal wavelet filter banks can be realized by using allpass filters in the lifting steps. Then, the design of the proposed IIR orthogonal wavelet filter banks is discussed. The designed IIR orthogonal wavelet filter banks have approximately linear phase responses. Finally, the proposed IIR orthogonal wavelet filter banks are applied to the image compression, and then the coding performance of the proposed IIR filter banks is evaluated and compared with the conventional wavelet transforms. [ABSTRACT FROM AUTHOR]

Weighted vector median (WVM) filters are effective tools for multichannel signal processing. To obtain the desired filtering behavior and characteristic, the WVM filter weights must be determined in an appropriate manner. In this paper, we first analyze previously defined approaches for WVM filter optimization and show their drawbacks related to derivative computation and vector direction information utilization. Based on this analysis, we propose two fast adaptive algorithms for WVM filter design. Proposed Algorithm I computes locally optimal weight changes at each iteration and updates the filter weights accordingly. This algorithm does not involve derivative computation, thus eliminating the instability caused by derivative approximations utilized in previous approaches. Proposed Algorithm H extends the results from established marginal weighted median optimization methods to the vector case by error metric generalization. Both algorithms can be applied to WVM filters using the Lp norm, while Algorithm I can operate on more general distance metrics. The presented simulation results show that both algorithms are effective, fast, and stable; they perform well under a wide range of circumstances. [ABSTRACT FROM AUTHOR]

In certain partial-response (PR) systems, such as the magnetic recording channel, both the timing information as well as the noise statistics are data dependent. In this paper, a class of synchronizers is proposed that incorporates the effect of these two data dependencies. The resulting synchronization algorithm is simplified to trade performance with complexity. Simulation results show that certain channel models exhibit significant performance improvement by the use of such synchronizers. [ABSTRACT FROM AUTHOR]

The paper presents results of local performance analysis of a generalized adaptive notch filter (GANF). GANFs are used for identification/tracking of quasi-periodically varying dynamic systems and can be considered an extension, to the system case, of classical adaptive notch filters. The tracking properties of the algorithm are studied analytically using a direct averaging approach and an approximating linear filter technique. Even though restricted to a single-frequency case, the presented analysis provides valuable insights into the tracking mechanisms of GANF, including the associated speed/accuracy tradeoffs, the achievable performance bounds, and tracking limitations. In addition, it allows one to formulate some useful rules of thumb for choosing design parameters. [ABSTRACT FROM AUTHOR]

This paper addresses the problem of blind equalization in the case of correlated input symbols, and it shows how the knowledge of the symbol sequence probability distribution can be directly incorporated in a Bussgang blind equalization scheme. Numerical results pertaining to both linear and nonlinear modulation schemes show that a significant improvement in equalization performance is obtained by exploiting the symbol sequence probability distribution using the approach herein described. [ABSTRACT FROM AUTHOR]

The difference or a linear combination of two space- time covariance functions (or variograms is not necessarily a valid covariance function (or variogram). In general, there seems no simple condition that makes a linear combination permissible, unless its coefficients are non-negative. The permissibility is investigated in this paper for the linear combination of two spatial or spatio-temporal covariance functions (or variograms) isotropic in space so that we obtain flexible classes of spatial or spatio-temporal covariance functions with various properties such as long-range dependence and having different signs. [ABSTRACT FROM AUTHOR]

This paper introduces two minimal lattice structures for symmetric-antisymmetric multiwavelets (SAMWTs) and symmetric-antisymmetric multifilterbanks (SAMFBs). First, by exploring the relation of the synnnetric'antisymmetric property in multifilterbanks and the linear-phase property in traditional scalar filterbanks, we show that the implementation and design of an SAMIFB can be converted into that of a four-channel scalar linear-phase perfect reconstruction ifiterbank (LPPRFB). Then, based on the lattice factorization for LPPRFBs, we propose two fast, modular, minimal structures for SAMFBs. To demonstrate the effectiveness of the proposed lattice structures, several rational or dyadic-coefficient SAMWT design examples are presented along with their application in image coding. [ABSTRACT FROM AUTHOR]

In multicarrier systems with a cyclic prefix, in. terblock interference can be limited by shortening the channel impulse response using time-domain equalizers. In this paper, we present two blind channel-shortening algorithms that exploit the second-order statistics of the channel outputs. The equalizer parameter vector is chosen from a nullspace that forces the length constraint on the effective channel impulse response. The first algorithm is less sensitive to channel-order estimation errors, whereas the :second one is simpler to implement. Furthermore, we show that the two algorithms are equivalent for noiseless channels. Simulation examples are provided to demonstrate their superior performance over some existing algorithms. [ABSTRACT FROM AUTHOR]

In this paper, we consider soft decision directed channel estimation for turbo equalization. To take advantage of soft information provided by the decoder, a minimum mean square error linear channel estimator is derived under an uncorrelated channel tap model, and a soft input recursive least squares algorithm is also developed by modifying the cost function of the conventional recursive least squares algorithm. The performance of the proposed channel estimators are analyzed in terms of mean square identification error (MSLE) for stationary channels. Simulation results for both time-invariant and time-varying frequency-selective Rayleigh fading channels are also presented. [ABSTRACT FROM AUTHOR]

CANDECOMP/PARAFAC (CP) analysis is an extension of low-rank matrix decomposition to higher-way arrays, which are also referred to as tensors. CP extends and unifies several array signal processing tools and has found applications ranging from multidimensional harmonic retrieval and angle-carrier estimation to blind multiuser detection. The uniqueness of CP decomposition is not fully understood yet, despite its theoretical and practical significance. Toward this end, we first revisit Kruskal's Permutation Lemma, which is a cornerstone result in the area, using an accessible basic linear algebra and induction approach. The new proof highlights the nature and limits of the identification process. We then derive two equivalent necessary and sufficient uniqueness conditions for the case where one of the component matrices involved in the decomposition is full column rank. These new conditions explain a curious example provided recently in a previous paper by Sidiropoulos, who showed that Kruskal's condition is in general sufficient but not necessary for uniqueness and that uniqueness depends on the particular joint pattern of zeros in the (possibly pretransformed) component matrices. As another interesting application of the Permutation Lemma, we derive a similar necessary and sufficient condition for unique bilinear factorization under constant modulus (CM) constraints, thus providing an interesting link to (and unification with) CP. [ABSTRACT FROM AUTHOR]