Search

Motivated by the simplicity of energy detector and capability of higher order and fractional lower order statistics in non-Gaussian signal processing, this paper proposes a new spectrum sensing method based on kernel theory, referred to as Kerenlized Energy Detector (KED), which exhibits a moderate complexity, it is easy to implement, and it compares favourably against competing solutions in the case of various Gaussian and non-Gaussian impulsive noises. The incorporation of the nonlinear kernel function in the KED test statistic allows for the development of a nonlinear algorithm capable of considering both higher order and fractional lower order moments (FLOMs) in the sensing task. We show that the proposed KED detector can serve as an optimal spectrum sensing method under both Gaussian and non-Gaussian noise scenarios. In addition, the detection performance of the proposed KED scheme is analyzed by employing U-statistics theory. The Kernel parameter selection for the KED method has been discussed in both theoretical and practical points of view. Potential of considering the KED scheme in either single user multi-antennas or cooperative spectrum sensing is investigated. [ABSTRACT FROM PUBLISHER]

This paper investigates an optimal energy allocation problem for multisensor estimation of a random source where sensors communicate their measurements to a remote fusion center (FC) over orthogonal fading wireless channels using uncoded analog transmissions. The FC reconstructs the source using the best linear unbiased estimator (BLUE). The sensors have limited batteries but can harvest energy and also transfer energy to other sensors in the network. A distortion minimization problem over a finite-time horizon with causal and noncausal centralized information is studied and the optimal energy allocation policy for transmission and sharing is derived. Several structural necessary conditions for optimality are presented for the two sensor problem with noncausal information and a horizon of two time steps. A decentralized energy allocation algorithm is also presented where each sensor has causal information of its own channel gain and harvested energy levels and has statistical information about the channel gains and harvested energies of the remaining sensors. Various other suboptimal energy allocation policies are also proposed for reducing the computational complexity of dynamic programming based solutions to the energy allocation problems with causal information patterns. Numerical simulations are included to illustrate the theoretical results. These illustrate that energy sharing can reduce the distortion at the FC when sensors have asymmetric fading channels and asymmetric energy harvesting processes. [ABSTRACT FROM PUBLISHER]

Bayesian filtering is a statistical approach that naturally appears in many signal processing problems. Ranging from Kalman filter to particle filters, there is a plethora of alternatives depending on model assumptions. With the exception of very few tractable cases, one has to resort to suboptimal methods due to the inability to analytically compute the Bayesian recursion in general dynamical systems. This is why it has attracted the attention of many researchers in order to develop efficient algorithms to implement it. We focus our interest into a recently developed algorithm known as the Quadrature Kalman filter (QKF). Under the Gaussian assumption, the QKF can tackle arbitrary nonlinearities by resorting to the Gauss-Hermite quadrature rules. However, its complexity increases exponentially with the state-space dimension. In this paper we study a complexity reduction technique for the QKF based on the partitioning of the state-space, referred to as the Multiple QKF. We prove that partitioning schemes can effectively be used to reduce the curse of dimensionality in the QKF. Simulation results are also provided to show that a nearly-optimal performance can be attained, while drastically reducing the computational complexity with respect to state-of-the-art algorithms that are able to deal with such nonlinear filtering problems. [ABSTRACT FROM PUBLISHER]

This work proposes a new tensor-based approach to solve the problem of blind identification of underdetermined mixtures of complex-valued sources exploiting the cumulant generating function (CGF) of the observations. We show that a collection of second-order derivatives of the CGF of the observations can be stored in a third-order tensor following a constrained factor (CONFAC) decomposition with known constrained structure. In order to increase the diversity, we combine three derivative types into an extended third-order CONFAC decomposition. A detailed uniqueness study of this decomposition is provided, from which easy-to-check sufficient conditions ensuring the essential uniqueness of the mixing matrix are obtained. From an algorithmic viewpoint, we develop a CONFAC-based enhanced line search (CONFAC-ELS) method to be used with an alternating least squares estimation procedure for accelerated convergence, and also analyze the numerical complexities of two CONFAC-based algorithms (namely, CONFAC-ALS and CONFAC-ELS) in comparison with the Levenberg-Marquardt (LM)-based algorithm recently derived to solve the same problem. Simulation results compare the proposed approach with some higher-order methods. Our results also corroborate the advantages of the CONFAC-based approach over the competing LM-based approach in terms of performance and computational complexity. [ABSTRACT FROM PUBLISHER]

Total least squares (TLS) estimation is a popular solution technique for overdetermined systems of linear equations with a noisy data matrix. In this paper, we revisit the distributed total least squares (D-TLS) algorithm, which operates in an ad hoc network, where each node has access to a subset of the linear equations. The D-TLS algorithm computes the TLS solution of the full system of equations in a fully distributed fashion (without fusion center). To reduce the large computational complexity due to an eigenvalue decomposition (EVD) at every node and in each iteration, we modify the D-TLS algorithm based on inverse power iterations (IPIs). In each step of the modified algorithm, a single IPI is performed, which significantly reduces the computational complexity. We show that this IPI-based D-TLS algorithm still converges to the network-wide TLS solution under certain assumptions, which are often satisfied in practice. We provide simulation results to demonstrate the convergence of the algorithm, even when some of these assumptions are not satisfied. [ABSTRACT FROM PUBLISHER]

Estimation of the covariance matrix and its inverse, the precision matrix, in high-dimensional situations is of great interest in many applications. In this paper, we focus on the estimation of a class of sparse precision matrices which are assumed to be approximately inversely closed for the case that the dimensionality p can be much larger than the sample size n, which is fundamentally different from the classical case that p < n. Different in nature from state-of-the-art methods that are based on penalized likelihood maximization or constrained error minimization, based on the truncated Neumann series representation, we propose a computationally efficient precision matrix estimator that has a computational complexity of O(p^3). We prove that the proposed estimator is consistent in probability and in L^2 under the spectral norm. Moreover, its convergence is shown to be rate-optimal in the sense of minimax risk. We further prove that the proposed estimator is model selection consistent by establishing a convergence result under the entry-wise \infty-norm. Simulations demonstrate the encouraging finite sample size performance and computational advantage of the proposed estimator. The proposed estimator is also applied to a real breast cancer data and shown to outperform existing precision matrix estimators. [ABSTRACT FROM AUTHOR]

In this paper, we consider the problem of direction of arrival (DOA) estimation in the presence of sensor gain-phase errors. Under some mild assumptions, we propose a new DOA estimation method based on the eigendecomposition of a covariance matrix which is constructed by the dot product of the array output vector and its conjugate. By combining the new DOA estimation with the conventional gain-phase error estimation, a method is proposed to simultaneously estimate the DOA and gain-phase errors without joint iteration. Theoretical analysis shows that the proposed method performs independently of phase errors and thus behaves well regardless of phase errors. However, the resolution capability of the proposed method is lower than that of the method in [A. J. Weiss and B. Friedlander, “Eigenstructure methods for direction finding with sensor gain and phase uncertainties,” Circuits Systems Signal Process., vol. 9, no. 3, pp. 271–300, 1990], named as the WF method. In order to improve the resolution capability and maintain phase error independence, a combined strategy is developed using the proposed and WF methods. The advantage of the proposed methods is that they are independent of phase errors, leading to the cancellation of phase error calibration during the operation life of an array. Moreover, the proposed methods avoid the problem of suboptimal convergence which occurs in the WF method. The drawbacks of the proposed methods are their high computational complexity and their requirement for the condition that at least two signals are spatially far from each other, and they are not applicable to a linear array. Simulation results verify the effectiveness of the proposed methods. [ABSTRACT FROM AUTHOR]

In this paper, the clock synchronization for wireless sensor networks in the presence of unknown exponential delay is investigated under the two-way message exchange mechanism. The maximum-likelihood estimator for joint estimation of clock offset, clock skew and fixed delay is first cast into a linear programming problem. Based on novel geometric analyses of the feasible domain, a low-complexity maximum likelihood estimator is then proposed. Complexities of the proposed estimators and existing algorithms are compared analytically and numerically. Simulation results further demonstrate that our proposed algorithms have advantages in terms of both performance and computational complexities. [ABSTRACT FROM PUBLISHER]

We consider the problem of sensor selection for event detection in wireless sensor networks (WSNs). We want to choose a subset of p out of n sensors that yields the best detection performance. As the sensor selection optimality criteria, we propose the Kullback–Leibler and Chernoff distances between the distributions of the selected measurements under the two hypothesis. We formulate the maxmin robust sensor selection problem to cope with the uncertainties in distribution means. We prove that the sensor selection problem is NP hard, for both Kullback–Leibler and Chernoff criteria. To (sub)optimally solve the sensor selection problem, we propose an algorithm of affordable complexity. Extensive numerical simulations on moderate size problem instances (when the optimum by exhaustive search is feasible to compute) demonstrate the algorithm's near optimality in a very large portion of problem instances. For larger problems, extensive simulations demonstrate that our algorithm outperforms random searches, once an upper bound on computational time is set. We corroborate numerically the validity of the Kullback–Leibler and Chernoff sensor selection criteria, by showing that they lead to sensor selections nearly optimal both in the Neyman–Pearson and Bayes sense. [ABSTRACT FROM PUBLISHER]

This paper proposes a new paradigm for adaptive Volterra filtering using a time-variant size of the quadratic kernel memory in order to optimally identify any unknown transversal second-order nonlinear system. To this end, competing Volterra structures of different sizes are employed in a hierarchical combination scheme so as to find the best configuration of the second-order kernel memory, using the already known diagonal-coordinate representation. The length and number of required quadratic kernel diagonals can be concurrently estimated by monitoring the combination performance. Subsequently, the memory size of the involved models is dynamically increased or decreased, following a set of intuitive rules. Since this automatic memory adaptation is performed along with the coefficient updates, an efficient Volterra filter is realized, offering great flexibility and minimizing the risk of under- or overmodeling any given quadratic nonlinearity. Besides the straightforward scheme, a simplified version is presented, greatly reducing the algorithmic demands. This efficient version is based on a virtualization of the competing Volterra filters by jointly using common coefficients and hence exhibits a computational complexity suitable for practical implementations. The robust estimation performance of the approach is demonstrated by various examples for a nonlinear acoustic echo cancellation scenario, involving stationary noise, real speech signals and realistic Volterra kernels. [ABSTRACT FROM AUTHOR]

This paper examines the estimation of the order of an autoregressive model using the minimum description length principle. A closed form for an approximation of the parametric complexity of the autoregressive model class is derived by exploiting a relationship between coefficients and partial autocorrelations. The parametric complexity over the complete parameter space is found to diverge. A model selection criterion is subsequently derived by bounding the parameter space, and simulations suggest that it compares well against standard autoregressive order selection techniques in terms of correct order identification and prediction error. [ABSTRACT FROM AUTHOR]

A new signal subspace approach for estimating the frequency of a single complex tone in additive white noise is proposed in this correspondence. Our main ideas are to use a matrix without repeated elements to represent the observed signal and exploit the principal singular vectors of this matrix for frequency estimation. It is proved that for small error conditions, the frequency estimate is approximately unbiased and its variance is equal to Cramér–Rao lower bound. Computer simulations are included to compare the proposed approach with the generalized weighted linear predictor, periodogram, and phase-based maximum likelihood estimators in terms of estimation accuracy, computational complexity, and threshold performance. [ABSTRACT FROM AUTHOR]

In this correspondence, we focus on blind estimation of the chip duration of time-hopping signals by introducing a cost function based on time-of-arrival (ToA) folding over multiple observation sets. An optimization algorithm that takes advantage of the highly oscillatory behavior in the nearby of the global minimum is proposed and a performance bound for the chip time estimate is derived. The pertinence of our approach is shown through numerical results, considering alternative methods like periodogram and separable least squares line search. The proposed technique enables a good tradeoff between statistical accuracy and computational complexity. [ABSTRACT FROM AUTHOR]

The adaptive estimation of a time-varying parameter vector in a linear Gaussian model is considered where we a priori know that the parameter vector belongs to a known arbitrary subset. We consider a family of efficient recursive estimators for this problem: the recursive constrained maximum likelihood (ML) estimator, the recursive affine minimax, and the recursive minimum mean square error (MMSE) estimator. We show that all three estimators can be substantially simplified by using the recursive weighted least squares (RWLS) algorithm in a first step as the RWLS computes the sufficient statistic for this estimation problem. The recursive constrained ML needs to solve an optimization problem in the second step for the case that the RWLS solution does not fulfill the constraint. In case of affine minimax, we have to solve an optimization problem and to perform an affine transform. The MMSE estimator needs to calculate the mean of a truncated Gaussian density in the second step which is done by Monte Carlo integration. A simple rejection scheme is used to take general constraints for the parameter vector into account. An example shows the superior performance of our proposed estimators in comparison to many other estimators. [ABSTRACT FROM PUBLISHER]

In this paper, a new algorithm for approximate joint diagonalization (AJD) of positive-definite Hermitian matrices is presented. The AJD matrix, which is assumed to be square non-unitary, is derived via minimization of a quasi-maximum likelihood (QML) objective function. This objective function coincides asymptotically with the maximum likelihood (ML) objective function, hence enabling the proposed algorithm to asymptotically approach the ML estimation performance. In the proposed method, the rows of the AJD matrix are obtained independently, in an iterative manner. This feature enables direct estimation of full row-rank rectangular AJD sub-matrices. Under some mild assumptions, convergence of the proposed algorithm is asymptotically guarantied, such that the error norm corresponding to each row of the AJD matrix reduces significantly after the first iteration, and the convergence is almost Q-super linear. This property results rapid convergence, which leads to low computational load in the proposed method. The performance of the proposed algorithm is evaluated and compared to other state-of-the-art algorithms for AJD and its practical use is demonstrated in the blind source separation and blind source extraction problems. The results imply that under the assumptions of high signal-to-noise ratio and large amount of matrices, the proposed algorithm is computationally efficient with performance similar to state-of-the-art algorithms for AJD. [ABSTRACT FROM PUBLISHER]

Consider the problem of estimating the parameters of multiple polynomial phase signals observed by a sensor array. In practice, it is difficult to maintain a precisely calibrated array. The array manifold is then assumed to be unknown, and the estimation is referred to as blind estimation. To date, only an approximated maximum likelihood estimator (AMLE) was suggested for blindly estimating the polynomial coefficients of each signal. However, this estimator requires a multidimensional search over the entire coefficient space. Instead, we propose an estimation approach which is based on two steps. First, the signals are separated using a blind source separation technique, which exploits the constant modulus property of the signals. Then, the coefficients of each polynomial are estimated using a least squares method applied to the unwrapped phase of the estimated signal. This estimator does not involve any search in the coefficient spaces. The computational complexity of the proposed estimator increases linearly with respect to the polynomial order, whereas that of the AMLE increases exponentially. Simulation results show that the proposed estimator achieves the Cramér-Rao lower bound at moderate or high signal to noise ratio. [ABSTRACT FROM PUBLISHER]

This paper presents estimation and detection techniques in homogeneous spaces that are optimal under the squared error loss function. The data is collected on a manifold which forms a homogeneous space under the transitive action of a compact Lie group. Signal estimation problems are addressed by formulatingWiener-Hopf equations for homogeneous spaces. The coefficient functions of these equations are the signal correlations which are assumed to be known. The resulting coupled integral equations on the manifold are converted to Wiener-Hopf convolutional integral equations on the group. These are solved using the Peter-Weyl theory of Fourier transform on compact Lie groups. The computational complexity of this algorithm is reduced using the bi-invariance of the correlations with respect to a stabilizer subgroup. The theory of matched filtering for isotropic signal fields is developed for signal classification where given a set of template signals on the manifold and a noisy test signal, the objective is to optimally detect the template buried in the test signal. This is accomplished by designing a filter on the manifold that maximizes the signal-to-noise-ratio (SNR) of the filtered output. An expression for the SNR is obtained as a ratio of quadratic forms expressed as Haar integrals over the transformation group. These integrals are expressed in the Fourier domain as infinite sums over the irreducible representations. Simplification of these sums is achieved by invariance properties of the signal function and the noise correlation function. TheWiener filter and matched filter are developed for an abstract homogeneous space and then specialized to the case of spherical signals under the action of the rotation group. Applications of these algorithms to denoising of 3D surface data, visual navigation with omnidirectional camera and detection of compact embedded objects in the stochastic background are discussed with experimental results. [ABSTRACT FROM AUTHOR]

In this paper, we create a framework for trainingbased channel estimation under different channel and interference statistics. The minimum mean square error (MMSE) estimator for channel matrix estimation in Rician fading multi-antenna systems is analyzed, and especially the design of mean square error (MSE) minimizing training sequences. By considering Kronecker-structured systems with a combination of noise and interference and arbitrary training sequence length, we collect and generalize several previous results in the framework. We clarify the conditions for achieving the optimal training sequence structure and show when the spatial training power allocation can be solved explicitly. We also prove that spatial correlation improves the estimation performance and establish how it determines the optimal training sequence length. The analytic results for Kronecker-structured systems are used to derive a heuristic training sequence under general unstructured statistics. The MMSE estimator of the squared Frobenius norm of the channel matrix is also derived and shown to provide far better gain estimates than other approaches. It is shown under which conditions training sequences that minimize the non-convex MSE can be derived explicitly or with low complexity. Numerical examples are used to evaluate the performance of the two estimators for different training sequences and system statistics. We also illustrate how the optimal length of the training sequence often can be shorter than the number of transmit antennas. [ABSTRACT FROM AUTHOR]

Recently, cooperative recurrent neural networks for solving three linearly constrained L1 estimation problems were developed and applied to linear signal and image models under non-Gaussian noise environments. For wide applications, this paper proposes a compact cooperative recurrent neural network (CRNN) for calculating general constrained L1 norm estimators. It is shown that the proposed CRNN converges globally to the constrained L1 norm estimator without any condition. The proposed CRNN includes three existing CRNNs as its special cases. Unlike the three existing CRNNs, the proposed CRNN is easily applied and can deal with the nonlinear elliptical sphere constraint. Moreover, when computing the general constrained L1 norm estimator, the proposed CRNN has a fast convergence speed due to low computational complexity. Simulation results confirm further the good performance of the proposed CRNN. [ABSTRACT FROM AUTHOR]

This paper presents the theory and the design of intra-predictive transforms, which unify the inter-block prediction and block-based transforms in block-based image coding. Motivated by interpreting inter-block prediction as a transform with a larger size, we derive the concept of intra-predictive transforms. Conventional predictions and transforms can be viewed as special cases of intra-predictive transforms. Intra-predictive transforms are able to exploit both inter and intra-block correlations. We derive the tight upper bound of the coding gain of intra-predictive transforms for stationary Gaussian sources. It turns out that the coding gain can be greater than that of conventional transforms. The optimal intra-predictive transform that achieves the upper bound is also derived. We also design a practical intra-predictive transform using frequency-domain prediction that can achieve better performance in image coding while exhibiting low computational complexity. Experimental results confirm the effectiveness of the proposed intra-predictive transforms in block-based image coding systems and show the improvements over the current design. [ABSTRACT FROM AUTHOR]

This paper is concerned with dynamic quantizer design for state estimation of hidden Markov models (HMM) using multiple sensors under a sum power constraint at the sensor transmitters. The sensor nodes communicate with a fusion center over temporally correlated flat fading channels modelled by finite state Markov chains. Motivated by energy limitations in sensor nodes, we develop optimal quantizers by minimizing the long term average of the mean square estimation error with a constraint on the long term average of total transmission power across the sensors. Instead of introducing a cost function as a weighted sum of our two objectives, we propose a constrained Markov decision formulation as an average cost problem and employ a linear programming technique to obtain the optimal policy for the constrained problem. Our experimental results assert that the constrained approach is quite efficient in terms of computational complexity and memory requirements for our average cost problem and leads to the same optimal deterministic policies and optimal cost as the unconstrained approach under an irreducibility assumption on the underlying Markov chain and some mild regularity assumptions on the sensor measurement noise processes. We illustrate via numerical studies the performance results for the dynamic quantization scheme. We also study the effect of varying degrees of channel and measurement noise on the performance of the proposed scheme. [ABSTRACT FROM AUTHOR]

We consider range-Doppler imaging via transmitting a train of probing pulses. We present two methods for range-Doppler imaging. The first one is based on the instrumental variables (IV) filter and the second one is based on the iterative adaptive approach (IAA). Numerical results show that both methods can suppress interference from neighboring range and Doppler bins. An attractive feature of the IV filter is that it can be computed offline. IAA has better performance than IV and has super resolution, but at the cost of a higher computational complexity. [ABSTRACT FROM AUTHOR]

The most popular algorithms for blind equalization are the constant-modulus algorithm (CMA) and the Shalvi-Wein- stein algorithm (SWA). It is well-known that SWA presents a higher convergence rate than CMA, at the expense of higher computational complexity. If the forgetting factor is not sufficiently close to one, if the initialization is distant from the optimal solution, or if the signal-to-noise ratio is low, SWA can converge to undesirable local minima or even diverge. In this paper, we show that divergence can be caused by an inconsistency in the nonlinear estimate of the transmitted signal, or (when the algorithm is implemented in finite precision) by the loss of positiveness of the estimate of the autocorrelation matrix, or by a combination of both. In order to avoid the first cause of divergence, we propose a dual-mode SWA. In the first mode of operation, the new algorithm works as SWA; in the second mode, it rejects inconsistent estimates of the transmitted signal. Assuming the persistence of excitation condition, we present a deterministic stability analysis of the new algorithm. To avoid the second cause of divergence, we propose a dual-mode lattice SWA, which is stable even in finite-precision arithmetic, and has a computational complexity that increases linearly with the number of adjustable equalizer coefficients. The good performance of the proposed algorithms is confirmed through numerical simulations. [ABSTRACT FROM AUTHOR]

In this paper we propose and analyze a distributed algorithm for achieving globally optimal decisions, either estimation or detection, through a self-synchronization mechanism among linearly coupled integrators initialized with local measurements. We model the interaction among the nodes as a directed graph with weights (possibly) dependent on the radio channels, and we pose special attention to the effect of the propagation delay occurring in the exchange of data among sensors, as a function of the network geometry. We derive necessary and sufficient conditions for the proposed system to reach a consensus on globally optimal decision statistics. One of the major results proved in this work is that a consensus is reached with exponential convergence speed for any bounded delay condition if and only if the directed graph is quasi-strongly connected. We provide a closed form expression for the global consensus, showing that the effect of delays is, in general, the introduction of a bias in the final decision. Finally, we exploit our closed form expression to devise a double-step consensus mechanism able to provide an unbiased estimate with minimum extra complexity, without the need to know or estimate the channel parameters. [ABSTRACT FROM AUTHOR]

We consider the problem of adaptive subspace tracking, when the rank of the subspace we seek to. estimate is assumed to be known. Starting from the Data Projection Method (DPM), which constitutes a simple and reliable means for adaptively estimating and tracking subspaces, we develop a fast and numerically robust implementation of DPM, which comes at a considerably lower computational cost. Most existing schemes track subspaces corresponding either to the largest or to the smallest singular values, while our DPM version can switch from one subspace type to the other with a simple change of sign of its single parameter. The proposed algorithm provides orthonormal vector estimates of the subspace basis that are numerically stable since they do not accumulate roundoff errors. In fact, our scheme constitutes the first numerically stable, low complexity, algorithm for tracking subspaces corresponding to the smallest singular values. Regarding convergence towards orthonormality our scheme exhibits the fastest speed among all other subspace tracking algorithms of similar complexity. [ABSTRACT FROM AUTHOR]

In this paper, energy-based localization methods for source localization in sensor networks are examined. The focus is on least-squares-based approaches due to a good tradeoff between performance and complexity. A suite of methods are developed and compared. First, two previously proposed methods (quadratic elimination and one step) are shown to yield the same location estimate for a source. Next, it is shown that, as the errors which perturb the least-squares equations are nonidentically distributed, it is more appropriate to consider weighted least-squares methods, which are observed to yield significant performance gains over the unweighted methods. Finally, a new weighted direct least-squares formulation is presented and shown to outperform the previous methods with much less computational complexity. Unlike the quadratic elimination method, the weighted direct least-squares method is amenable to a correction technique which incorporates the dependence of unknown parameters leading to further performance gains. For a sufficiently large number of samples, simulations show that the weighted direct solution with correction (WDC) can be more accurate with significantly less computational complexity than the maximum-likelihood estimator and approaches Cramér-Rao bound (CRB). Furthermore, it is shown that WDC attains CRB for the case of a white source. [ABSTRACT FROM AUTHOR]

The constrained least absolute deviation (L1) estimator is an attractive alternative to both the unconstrained L1 estimator and the least-square estimator. This paper introduces a constrained L1 method and proposes two cooperative recurrent neural networks (CRNNs) for the constrained L1 estimator. Unlike existing cooperative neural networks, the proposed two CRNNs have a novel weighting cooperation scheme to integrate individual neural network information automatically. As a special case, the proposed continuous-time CRNN includes the existing continuous-time neural network for unconstrained L1 estimator. Compared with existing continuous-time neural networks for the constrained L1 estimator, the proposed continuous-time CRNN has a lower model complexity and the finite-time convergence to the exact optimal solution without any additional condition. Furthermore, compared with existing numerical algorithms for the constrained L1 estimator, in addition to a low computational complexity, the proposed two CRNNs are suitable for parallel implementation and can deal with the L1 estimation problem with degeneracy. The proposed two CRNNs are applied to parameter estimation problems under non-Gaussian noise environments. Simulation results demonstrate that the proposed CRNNs are indeed effective in dealing with the L1 estimation problem with nonunique solutions and in obtaining a better solution than relevant algorithms. [ABSTRACT FROM AUTHOR]

This correspondence investigates the Abel bound in order to predict the estimators mean square error (mse) threshold effect. A tractable and computationally efficient form of this bound is derived. This form combines the Chapman-Robbins and the Crameacuter-Rao bounds. This bound is applied to a data-aided carrier frequency estimation problem for which a closed-form expression is provided. An indicator of the signal-to-noise ratio threshold is proposed. A comparison with recent results on the Barankin bound (Chapman-Robbins version) shows the superiority of the Abel-bound version to predict the mse threshold without increasing the computational complexity [ABSTRACT FROM PUBLISHER]

In this correspondence, we extend the recently introduced one-dimensional Capon-based Magnitude Square Coherence (MSC) spectral estimator, to form two-dimensional Capon- and Amplitude and Phase EStimation (APES)-based MSC spectral estimators. The resulting estimators are found to yield significantly improved estimates as compared to the typical Welch-based estimator. Furthermore, we introduce a computationally efficient time-updating of the presented MSC estimators, exploiting their inherent time-varying displacement structure. The presented updating is found to dramatically lower the computational requirement of reevaluating the MSC spectral estimates [ABSTRACT FROM PUBLISHER]

The problem of estimating the frequency and carrier phase of a single sinusoid observed in additive, white, Gaussian noise is addressed. Much of the work in the literature considers maximum likelihood (ML) estimation. However, the ML estimator given by the location of the peak of a periodogram in the frequency domain shown in D.C. Rife and R. R. Boorstyn, ‘Single-tone parameter estimation from discrete-time observations,’ IEEE TRANSACTIONS ON INFORMATION THEORY, vol. IT-20, pp. 591–598, Sep. 1974, has a very high computational complexity. This paper derives the explicit structure of the ML estimator for data processing in the time domain, assuming only reasonably high signal-to-noise ratio (SNR). The result of this approximate ML estimator shows that both the phase and the magnitude of the noisy signal samples are utilized in the estimator, and the phase data alone as assumed in S. A. Tretter, ‘Estimating the frequency of a noisy sinusoid by linear regression,’ IEEE TRANSACTIONS ON INFORMATION THEORY, vol. IT-31, pp. 832–835, Nov. 1985 and S. Kay, ‘A fast and accurate single frequency estimator,’ IEEE TRANSACTIONS ON ACOUSTICS, SPEECH, AND SIGNAL PROCESSING, vol. 39, pp. 1203-1205, May 1991, is not a sufficient statistic. The sample-by-sample iterative processing nature of the estimator enables us to propose a novel, recursive phase-unwrapping algorithm that allows the estimator to be implemented efficiently. To facilitate the performance analysis, a new, linearized observation model for the instantaneous signal phase that is more accurate than that of S. A. Tretter, ‘Estimating the frequency of a noisy sinusoid by linear regression,’ IEEE TRANSACTIONS ON INFORMATION THEORY, vol. IT-31, pp. 832–835, Nov. 1985 and of S. Kay, "A fast and accurate single frequency estimator," vol. 39, pp. 1203–1205, May 1991, is proposed. This new model explains physically why the phase data are weighted by the magnitude information in the ML estimator. Moreover, by incorporating a priori knowledge via the a priori probability density function of the unknown frequency and the carrier phase, the explicit structure of the approximate maximum a posteriori probability (MAP) estimator is derived, and the Bayesian Cramer-Rao lower bound (BCRLB) on the mean-square error (mse) is obtained. Our analysis shows that the mse performance of the MAP estimator can approach the BCRLB very closely. [ABSTRACT FROM AUTHOR]

The polynomial time frequency transform is one of important tools for estimating the coefficients of the polynomial-phase signals (PPSs) with the maximum likelihood method. The transform converts a one-dimensional (1-D) data sequence into a multidimensional output array from which the phase coefficients of the data sequence are estimated. A prohibitive computational load is generally needed for high-order polynomial-phase signals although the 1-D fast Fourier transform (FFT) algorithm can be used. Based on the split-radix concept, this paper derives a fast algorithm for arbitrary order of polynomial time frequency transforms to significantly reduce the computational complexity. Comparisons on the computational complexity needed by various algorithms are also made to show the merits of the proposed algorithm. [ABSTRACT FROM AUTHOR]

In this paper, some new estimators of the frequency of a single complex sinusoid are presented. The rotate-add-decimate (RAD) method of Crozier is first refined to more closely approach the Cramer-Rao Bound (CRB). An additional modification yields an unbiased estimator (ERAD) that essentially achieves the CRB above a signal-to-noise ratio (SNR) threshold comparable to that of RAD. In addition, this estimator is proven to achieve the CRB for high SNR. The ERAD method requires approximately 2N complex multiply-adds and log2 N arctangents. A modified ERAD (MERAD) is proposed that matches the SNR threshold and computational complexity of the RAD method (approximately 3N complex multiply-adds and log2 N arctangents) but achieves the CRB for high SNR. [ABSTRACT FROM AUTHOR]

In this paper, we present a novel joint algorithm to estimate the symbol timing and carrier frequency offsets of wireless orthogonal frequency division multiplexing (OFDM) signals. To jointly estimate synchronization parameters using the maximum likelihood (ML) criterion, researchers have derived conventional models only from additive white Gaussian noise (AWGN) or single-path fading channels. We develop a general ML estimation algorithm that can accurately calculate symbol timing and carrier frequency offsets over a fast time-varying multipath channel. To reduce overall estimation complexity, the proposed scheme consists of two estimation stages: coarse and fine synchro nizations. A low complexity coarse synchronization based on the least-squares (LS) method can rapidly estimate the rough symbol timing and carrier frequency offsets over a fast time-varying multipath channel. The subsequent ML fine synchronization can then obtain accurate final results based on the previous coarse synchronization. Simulations demonstrate that the coarse-to-fine method provides a good tradeoff between estimation accuracy and computational complexity. [ABSTRACT FROM AUTHOR]

In this paper, the computational complexity of the marginalized particle filter is analyzed and a general method to perform this analysis is given. The key is the introduction of the equivalent flop measure. In an extensive Monte Carlo simulation, different computational aspects are studied and compared with the derived theoretical results. [ABSTRACT FROM AUTHOR]

In this correspondence, we propose a soft-input soft-output (SISO) decorrelating detector for iterative receivers of coded multiuser systems. Based on the soft inputs from a bank of single-user decoders, the cross-correlation matrix of multiple users is updated and employed in each iteration. Due to negligible residual interference and reduced noise enhancement in successive iterations, the resulting system performance quickly approaches to that of the single-user system. Furthermore, the detector is shown to have good near-far resistance. The computational complexity of the SISO decorrelator is proportional to the number of users cubed. Monte Carlo simulation results are provided and compared. [ABSTRACT FROM AUTHOR]

This paper is concerned with recursive estimation using augmented data. We study two recursive procedures closely linked with the well-known expectation and maximization (EM) and space alternating generalized EM (SAGE) algorithms. Unlike iterative methods, the recursive EM and SAGE-inspired algorithms give a quick update on estimates given new data. Under mild conditions, estimates generated by these procedures are strongly consistent and asymptotically normally distributed. These mathematical properties are valid for a broad class of problems. When applied to direction of arrival (DOA) estimation, the recursive EM and SAGE-inspired algorithms lead to a very simple and fast implementation of the maximum-likelihood (ML) method. The most complicated computation in each recursion is inversion of the augmented information matrix. Through data augmentation, this matrix is diagonal and easy to invert. More importantly, there is no search in such recursive procedures. Consequently, the computational time is much less than that associated with existing numerical methods for finding ML estimates. This feature greatly increases the potential of the ML approach in real-lime processing. Numerical experiments show that both algorithms provide good results with low computational cost. [ABSTRACT FROM AUTHOR]

The particle filter offers a general numerical tool to approximate the posterior density function for the state in nonlinear and non-Gaussian filtering problems. While the particle filter is fairly easy to implement and tune, its main drawback is that it is quite computer intensive, with the computational complexity increasing quickly with the state dimension. One remedy to this problem is to marginalize out the states appearing linearly in the dynamics. The result is that one Kalman filter is associated with each particle. The main contribution in this paper is the derivation of the details for the marginalized particle filter for a general nonlinear state-space model. Several important special cases occurring in typical signal processing applications will also be discussed. The marginalized particle filter is applied to an integrated navigation system for aircraft. It is demonstrated that the complete high-dimensional system can be based on a particle filter using marginalization for all but three states. Excellent performance on real flight data is reported. [ABSTRACT FROM AUTHOR]

The problem of blind adaptive channel estimation in code-division multiple access (CDMA) systems is considered. Motivated by the iterative power method, which is used in numerical analysis for estimating singular values and singular vectors, we develop recursive least squares (RLS) and least mean squares (LMS) subspace-based adaptive algorithms in order to identify the impulse response of the miltipath channel. The schemes proposed in this paper use only the spreading code of the user of interest and the received data and are therefore blind. Both versions (RLS and LMS) exhibit rapid convergence combined with low computational complexity. With the help of simulations, we demonstrate the improved performance of our methods as compared with the already-existing techniques in the literature. [ABSTRACT FROM AUTHOR]

This paper presents a novel scheme for identifying the impulse response of a sparse channel. The scheme consists of two adaptive filters operating sequentially. The first adaptive filter adapts using a partial Haar transform of the input and yields an estimate of the location of the peak of the sparse impulse response. The second adaptive filter is then centered about this estimate. Both filters are short in comparison to the delay uncertainty of the unknown channel. The principle advantage of this scheme is that two short adaptive filters can be used instead of one long adaptive filter, resulting in faster overall convergence and reduced computational complexity and storage. The scheme is analyzed in detail for a least mean squares (LMS) LMS-LMS type of structure, although it can be implemented using any combination of adaptive algorithms. Monte Carlo simulations are shown to be in good agreement with the theoretical model for the behavior of the peak estimating filter as well as for the mean square error (MSE) behavior of the second filter. [ABSTRACT FROM AUTHOR]

This paper develops a new fast recursive total least squares (N-RTLS) algorithm to recursively compute the total least squares (TLS) solution for adaptive infinite-impulse-response (IIR) filtering. The new algorithm is based on the minimization of the constraint Rayleigh quotient in which the first entry of the parameter vector is fixed to the negative one. The highly computational efficiency of the proposed algorithm depends on the efficient computation of the gain vector and the adaptation of the Reyleigh quotient. Using the shift structure of the input data vectors, a fast algorithm for computing the gain vector is established, which is referred to as the fast gain vector (FGV) algorithm. The computational load of the FGV algorithm is smaller than that of the fast Kalman algorithm. Moreover, the new algoritlun is numerically stable since it does not use the well-known matrix inversion lenuna. The computational complexity of the new algorithm per iteration is also 0(L). The global convergence of the new algorithm is studied. The performances of the relevant algorithms are compared via simulations. [ABSTRACT FROM AUTHOR]

The efficient representation of a signal as a linear combination of elementary "atoms" or building blocks is central to much signal processing theory and many applications. Wavelets provide a powerful, flexible, and efficiently implementable class of such atoms. In this paper, we develop an efficient method for selecting an orthonormal wavelet that is matched to a given signal in the sense that the squared error between the signal and some finite resolution wavelet representation of it is minimized. Since the squared error is not an explicit function of the design parameters, some form of approximation of this objective is required if conventional optimization techniques are to be used. Previous approximations have resulted in nonconvex optimization problems, which require delicate management of local minima. In this paper, we employ an approximation that results in a design problem that can be transformed into a convex optimization problem and efficiently solved. Constraints on the smoothness of the wavelet can be efficiently incorporated into the design. We show that the error incurred in our approximation is bounded by a function that decays to zero as the number of vanishing moments of the wavelet grows. In our examples, we demonstrate that our method provides wavelet bases that yield substantially better performance than members of standard wavelet families and are competitive with those designed by more intricate nonconvex optimization methods. [ABSTRACT FROM AUTHOR]

In this paper, we present a new design method of infinite impulse response (IIR) digital filters with quasi-equiripple absolute error in the complex domain. This method is based on solving a least squares solution iteratively. At each iteration, the desired response for the least squares approximation is transformed to have equiripple error. This algorithm is efficient because there is no need for any initial value or complex optimization algorithm. By this method, a quasi-equiripple solution is obtained very quickly with less computational complexity. Moreover, by multiplying an arbitrary weighting function on the desired responses of passband and stopband, respectively, the error at the passband and stopband can be controlled. Finally, we show some examples to validate the proposed method. [ABSTRACT FROM AUTHOR]

Presents information on a study which described the MUSIC, Root-MUSIC and MODE algorithms for direction of arrival estimation that exploit antenna arrays with multiple identical translated subarrays. Advantage of the techniques; Computational complexity of the algorithms; Conclusions.