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In high-speed analog-to-digital converters (ADCs), two main factors contribute to high power consumption. The first is the super linear relationship with the sampling rate; i.e., by doubling the sampling rate, the power consumption more than doubles. The second factor arises from the consumption of analog circuitry responsible to mitigate the jitter noise. By employing a multichannel sampling system, one can achieve high sampling rates by incorporating multiple low sampling-rate channels, which results in a linear scaling of power consumption with the number of channels. The main drawback of this system is the timing mismatch between the sampling channels. In this paper, we intend to jointly compensate the jitter noise and the timing mismatch between the channels using statistical methods. We first approximate the acquisition system and derive a stochastic model. Then, we propose an iterative maximum likelihood algorithm to estimate the parameters of the input signal. We further evaluate the Cramér-Rao lower bound (CRLB) for the estimation error to examine the proposed algorithm. Simulation results indicate that our algorithm is capable of closely following the CRLB curve for reasonable values of jitter noise and a wide range of timing mismatch errors. Moreover, it is shown that the mismatch-compensated multichannel sampling system performs almost equivalently to a single-channel high rate sampler without having its shortcomings. [ABSTRACT FROM AUTHOR]

Sensor-based online process monitoring has extensive applications, such as in manufacturing and service industries. In real environments, though, sensor data are often contaminated with noise, leading to severe challenges in accurate data analysis. In the existing literature, noise is generally modeled as Gaussian to analyze sensor data for various applications, for example in fault detection and diagnostics. However, in some applications, such as due to challenging field conditions, sensor data may be disturbed by high levels of outliers such that the Gaussian assumption of sensor noise is inadequate, thus leading to large estimation errors. This paper focuses on online classification applications. A robust sparse representation classification method is proposed, which considers non-Gaussian noise, and thus can effectively analyze sensor data with higher levels of outliers. Case studies were completed, based on both numerically simulated sensor data and actual wearable sensor data from occupational manual material handling process monitoring. The proposed classification method could effectively analyze sensor data with non-Gaussian noise, and outperformed commonly used methods in the literature. Thus, this new method may be advantageous for solving classification problems in challenging field conditions, to address the difficulties of high levels of sensor outliers. [ABSTRACT FROM AUTHOR]

Principal component analysis (PCA) aims at estimating the direction of maximal variability of a high-dimensional data set. A natural question is: does this task become easier, and estimation more accurate, when we exploit additional knowledge on the principal vector? We study the case in which the principal vector is known to lie in the positive orthant. Similar constraints arise in a number of applications, ranging from the analysis of gene expression data to spike sorting in neural signal processing. In the unconstrained case, the estimation performances of PCA have been precisely characterized using the random matrix theory, under a statistical model known as the spiked model. It is known that the estimation error undergoes a phase transition as the signal-to-noise ratio crosses a certain threshold. Unfortunately, tools from the random matrix theory have no bearing on the constrained problem. Despite this challenge, we develop an analogous characterization in the constrained case, within a one-spike model. In particular: 1) we prove that the estimation error undergoes a similar phase transition, albeit at a different thresholds in signal-to-noise ratio that we determine exactly; 2) we prove that—unlike in the unconstrained case—the estimation error depends on the spike vector, and characterize the least favorable vectors; and 3) we show that a non-negative principal component can be approximately computed—under the spiked model—in nearly linear time. This despite the fact that the problem is non-convex and, in general, NP-hard to solve exactly. [ABSTRACT FROM AUTHOR]

This paper deals with area-based subpixel image registration under the rotation-isometric scaling-translation transformation hypothesis. Our approach is based on parametrical modeling of geometrically transformed textural image fragments and maximum-likelihood estimation of the transformation vector between them. Due to the parametrical approach based on the fractional Brownian motion modeling of the local fragments' texture, the proposed estimator \mboxML_\mathrmfBm (ML stands for “maximum likelihood” and fBm stands for “fractal Brownian motion”) has the ability to better adapt to real image texture content compared with other methods relying on universal similarity measures such as mutual information or normalized correlation. The main benefits are observed when assumptions underlying the fBm model are fully satisfied, e.g., for isotropic normally distributed textures with stationary increments. Experiments on both simulated and real images and for high and weak correlations between registered images show that the \mboxML_\mathrmfBm estimator offers significant improvement compared with other state-of-the-art methods. It reduces translation vector, rotation angle, and scaling factor estimation errors by a factor of about 1.75–2, and it decreases the probability of false match by up to five times. In addition, an accurate confidence interval for \mboxML_\mathrmfBm estimates can be obtained from the Cramér–Rao lower bound on rotation-scaling-translation parameter estimation error. This bound depends on texture roughness, noise level in reference and template images, correlation between these images, and geometrical transformation parameters. [ABSTRACT FROM AUTHOR]

We show that the rate regions achieved by linear-feedback coding schemes over dual multi-antenna Gaussian multi-access channels (MACs) and broadcast channels (BCs) with independent noises coincide. By dual here we mean: •

the channel matrices of the MAC and the BC are transposes of each other and [ABSTRACT FROM PUBLISHER]

This paper considers the problem of resource-constrained and noise-limited localization and estimation of dynamic targets that are sparsely distributed over a large area. We generalize an existing framework [Bashan , 2008] for adaptive allocation of sensing resources to the dynamic case, accounting for time-varying target behavior such as transitions to neighboring cells and varying amplitudes over a potentially long time horizon. The proposed adaptive sensing policy is driven by minimization of a surrogate function for mean squared error within locations containing targets. We provide theoretical upper bounds on the performance of adaptive sensing policies by analyzing solutions with oracle knowledge of target locations, gaining insight into the effect of target motion and amplitude variation as well as sparsity. Exact minimization of the multistage objective function is infeasible, but myopic optimization yields a closed-form solution. We propose a simple non-myopic extension, the Dynamic Adaptive Resource Allocation Policy (D-ARAP), that allocates a fraction of resources for exploring all locations rather than solely exploiting the current belief state. Our numerical studies indicate that D-ARAP has the following advantages: (a) it is more robust than the myopic policy to noise, missing data, and model mismatch; (b) it performs comparably to well-known approximate dynamic programming solutions but at significantly lower computational complexity; and (c) it improves greatly upon nonadaptive uniform resource allocation in terms of estimation error and probability of detection. [ABSTRACT FROM PUBLISHER]

This paper establishes a nearly optimal algorithm for denoising a mixture of sinusoids from noisy equispaced samples. We derive our algorithm by viewing line spectral estimation as a sparse recovery problem with a continuous, infinite dictionary. We show how to compute the estimator via semidefinite programming and provide guarantees on its mean-squared error rate. We derive a complementary minimax lower bound on this estimation rate, demonstrating that our approach nearly achieves the best possible estimation error. Furthermore, we establish bounds on how well our estimator localizes the frequencies in the signal, showing that the localization error tends to zero as the number of samples grows. We verify our theoretical results in an array of numerical experiments, demonstrating that the semidefinite programming approach outperforms three classical spectral estimation techniques. [ABSTRACT FROM PUBLISHER]

We study the theoretical performance of two full-duplex multiple-input multiple-output (MIMO) radio systems: a full-duplex bi-directional communication system and a full-duplex relay system. We focus on the effect of a (digitally manageable) residual self-interference due to imperfect channel estimation (with independent and identically distributed (i.i.d.) Gaussian channel estimation error) and transmitter noise. We assume that the instantaneous channel state information (CSI) is not available the transmitters. To maximize the system ergodic mutual information, which is a nonconvex function of power allocation vectors at the nodes, a gradient projection algorithm is developed to optimize the power allocation vectors. This algorithm exploits both spatial and temporal freedoms of the source covariance matrices of the MIMO links between transmitters and receivers to achieve higher sum ergodic mutual information. It is observed through simulations that the full-duplex mode is optimal when the nominal self-interference is low, and the half-duplex mode is optimal when the nominal self-interference is high. In addition to an exact closed-form ergodic mutual information expression, we introduce a much simpler asymptotic closed-form ergodic mutual information expression, which in turn simplifies the computation of the power allocation vectors. [ABSTRACT FROM PUBLISHER]

In this paper we present a generic framework for the asymptotic performance analysis of subspace-based parameter estimation schemes. It is based on earlier results on an explicit first-order expansion of the estimation error in the signal subspace obtained via an SVD of the noisy observation matrix. We extend these results in a number of aspects. Firstly, we demonstrate that an explicit first-order expansion of the Higher-Order SVD (HOSVD)-based subspace estimate can be derived. Secondly, we show how to obtain explicit first-order expansions of the estimation error of arbitrary ESPRIT-type algorithms and provide the expressions for R-D Standard ESPRIT, R-D Unitary ESPRIT, R-D Standard Tensor-ESPRIT, as well as R-D Unitary Tensor-ESPRIT. Thirdly, we derive closed-form expressions for the mean square error (MSE) and show that they only depend on the second-order moments of the noise. Hence, to apply this framework we only need the noise to be zero mean and possess finite second order moments. Additional assumptions such as Gaussianity or circular symmetry are not needed. [ABSTRACT FROM PUBLISHER]

In this correspondence, we propose an efficient estimator of optimal memory (averaging interval) for discrete-time finite impulse response (FIR) filters in state-space. Its crucial property is that only real measurements and the filter output are involved with no reference and noise statistics. Testing by the two-state polynomial model has shown a very good correspondence with predicted values. Even in the worst case of the harmonic model, the estimator demonstrates practical applicability. [ABSTRACT FROM AUTHOR]

The accurate determination of the steering vector of a sensor array that corresponds to a desired signal is often hindered by uncertainties due to array imperfections, such as the presence of a direction-of-arrival (DOA) estimation error, mutual coupling, array sensor gain/phase uncertainties, and senor position perturbations. Consequently, the performance of conventional beamforming algorithms that use the nominal steering vector may be significantly degraded. A new method for recursively correcting possible deterministic errors in the estimated steering vector is proposed here. It employs the subspace principle and estimates the desired steering vector by using a convex optimization approach. We show that the solution can be obtained in closed form by using the Lagrange multiplier method. As the proposed method is based on an extended version of the conventional orthonormal PAST (OPAST) algorithm, it has low implementation complexity, and moving sources can be handled. In addition, a robust beamformer with a new error bound that uses the proposed steering vector estimate is derived by optimizing the worst case performance of the array after taking the uncertainties of the array covariance matrix into account. This gives a diagonally loaded Capon beamformer, where the loading level is related to the bound of the uncertainty in the array covariance matrix. Numerical results show that the proposed algorithm performs well, especially at high signal-to-noise ratio (SNR) and in the presence of deterministic sensor uncertainties. [ABSTRACT FROM PUBLISHER]

This paper proposes a Kalman filter-based attitude (i.e., roll and pitch) estimation algorithm using an inertial sensor composed of a triaxial accelerometer and a triaxial gyroscope. In particular, the proposed algorithm has been developed for accurate attitude estimation during dynamic conditions, in which external acceleration is present. Although external acceleration is the main source of the attitude estimation error and despite the need for its accurate estimation in many applications, this problem that can be critical for the attitude estimation has not been addressed explicitly in the literature. Accordingly, this paper addresses the combined estimation problem of the attitude and external acceleration. Experimental tests were conducted to verify the performance of the proposed algorithm in various dynamic condition settings and to provide further insight into the variations in the estimation accuracy. Furthermore, two different approaches for dealing with the estimation problem during dynamic conditions were compared, i.e., threshold-based switching approach versus acceleration model-based approach. Based on an external acceleration model, the proposed algorithm was capable of estimating accurate attitudes and external accelerations for short accelerated periods, showing its high effectiveness during short-term fast dynamic conditions. Contrariwise, when the testing condition involved prolonged high external accelerations, the proposed algorithm exhibited gradually increasing errors. However, as soon as the condition returned to static or quasi-static conditions, the algorithm was able to stabilize the estimation error, regaining its high estimation accuracy. [ABSTRACT FROM AUTHOR]

Numerous variable step-size normalized least mean-square (VSS-NLMS) algorithms have been derived to solve the dilemma of fast convergence rate or low excess mean-square error in the past two decades. This paper proposes a new, easy to implement, nonparametric VSS-NLMS algorithm that employs the mean-square error and the estimated system noise power to control the step-size update. Theoretical analysis of its steady-state behavior shows that, when the input is zero-mean Gaussian distributed, the misadjustment depends only on a parameter \beta controlling the update of step size. Simulation experiments show that the proposed algorithm performs very well. Furthermore, the theoretical steady-state behavior is in very good agreement with the experimental results. [ABSTRACT FROM PUBLISHER]

This paper considers linear minimum mean-square-error (MMSE) transceiver design problems for downlink multiuser multiple-input multiple-output (MIMO) systems where imperfect channel state information is available at the base station (BS) and mobile stations (MSs). We examine robust sum mean-square-error (MSE) minimization problems. The problems are examined for the generalized scenario where the power constraint is per BS, per BS antenna, per user or per symbol, and the noise vector of each MS is a zero-mean circularly symmetric complex Gaussian random variable with arbitrary covariance matrix. For each of these problems, we propose a novel duality based iterative solution. Each of these problems is solved as follows. First, we establish a novel sum average mean-square-error (AMSE) duality. Second, we formulate the power allocation part of the problem in the downlink channel as a Geometric Program (GP). Third, using the duality result and the solution of GP, we utilize alternating optimization technique to solve the original downlink problem. To solve robust sum MSE minimization constrained with per BS antenna and per BS power problems, we have established novel downlink-uplink duality. On the other hand, to solve robust sum MSE minimization constrained with per user and per symbol power problems, we have established novel downlink-interference duality. For the total BS power constrained robust sum MSE minimization problem, the current duality is established by modifying the constraint function of the dual uplink channel problem. And, for the robust sum MSE minimization with per BS antenna and per user (symbol) power constraint problems, our duality are established by formulating the noise covariance matrices of the uplink and interference channels as fixed point functions, respectively. We also show that our sum AMSE duality are able to solve other sum MSE-based robust design problems. Computer simulations verify the robustness of the proposed robust designs compared to the nonrobust/naive designs. [ABSTRACT FROM PUBLISHER]

This paper considers the problem of adaptive array processing for interference canceling to drive very deep nulls in difficult signal environments. In many practical scenarios, the achievable null depth is limited by covariance matrix estimation error leading to poor identification of the interference subspace. We address the particularly troublesome cases of low interference-to-noise ratio (INR), relatively rapid interference motion, and correlated noise across the receiving array. A polynomial-based model is incorporated in the proposed algorithm to track changes in the array covariance matrix over time, mitigate interference subspace estimation errors, and improve canceler performance. The application of phased array feeds for radio astronomical telescopes is used to illustrate the problem and proposed solution. Here even weak residual interference after cancelation may obscure a signal of interest, so very deep beampattern nulls are required. Performance for conventional subspace projection (SP) is compared with polynomial-augmented SP using simulated and real experimental data, showing null-depth improvement of 6 to 30 dB. [ABSTRACT FROM PUBLISHER]