We consider the distributed detection of a zero-mean Gaussian signal in an analog wireless sensor network with a fusion center (FC) configured with a large number of antennas. The transmission gains of the sensor nodes are optimized by minimizing the ratio of the log probability of detection (PD) and log probability of false alarm (PFA). We show that the problem is convex with respect to the squared norm of the transmission gains, and that a closed-form solution can be found using the Karush-Kuhn-Tucker conditions. Our results indicate that a constant PD can be maintained with decreasing sensor transmit gain provided that the number of antennas increases at the same rate. This is contrasted with the case of a single-antenna FC, where PD is monotonically decreasing with transmit gain. On the other hand, we show that when the transmit power is high, the single- and multi-antenna FC both asymptotically achieve the same PD upper bound.
A coprime array consists of two uniform linear subarrays that construct an effective difference co-array with certain desirable characteristics. In this paper, we propose a generalized coprime array concept through the compression of the interelement spacing of one constituting subarray. As such, the existing variations of coprime array and nested array structures are represented as special cases. The achievable unique lags as well as consecutive lags in the resulting virtual array are analytically expressed, and the direction-of-arrival estimation performance is examined using both the MUSIC algorithm and sparse signal reconstruction techniques.
Self localization of nodes in wireless sensor networks (WSN) attracts wide interest in the past few years. The main challenge is to adopt calibration algorithms to the low-power/ low-bandwidth/ low-cost constrains on each sensor in the network. In this paper we present a novel approach, in which position-known anchors transmit special calibration signals simultaneously. Each node measures only the received signal strength (RSSI), i.e. envelope of the sum of received signals, and estimates time difference of arrivals (TDOA) of the signals. Two or more TDOA measurements allow the node to estimate its own position in the WSN. Based on an analysis of the appropriate Cramer Rao Lower Bound (CRLB) on the TDOA estimates, we suggest the choice of calibrating signals which provide optimal performance. The theoretical results are supported by simulations of the Maximum Likelihood (ML) estimators and numerical evaluation of the CRLB for a specific scenario of interest.
The emergence of software defined radio (SDR) aims to increase flexibility as well as reduce cost, size, weight and power (SWAP) inherent in traditional hardware radios. This paper is concerned with addressing issues associated with the formation of an array system from multiple SDR boards where each has an independent local oscillators (LO) in a multi-antenna system using representative examples such as localization and array shape estimation. In particular, practical experimental results are initially presented for estimating the unknown location of a single source using an SDR array of known array geometry. Furthermore, in the case that the SDR array geometry is unknown, a novel array shape estimation algorithm is proposed. The proposed algorithm estimates the antenna locations without requiring any external sources. This is achieved by allowing the array elements operate as transceivers.
We examine power spectrum estimation from wide-sense stationary signals received at different wireless sensors. We organize multiple sensors into several groups, where each group estimates the temporal correlation only at particular lags, which are different from group to group. A fusion centre collects all the correlation estimates from different groups of sensors, and uses them to estimate the power spectrum. This reduces the required sampling rate per sensor. We further investigate the conditions required for the system matrix to have full column rank, which allows for a least-squares reconstruction method.
We consider the problem of direction-of-arrival (DOA) estimation in unknown partially correlated noise environments where the noise covariance matrix is sparse. A sparse noise covariance matrix is a common model for a sparse array of sensors consisted of several widely separated subarrays. Since interelement spacing among sensors in a subarray is small, the noise in the subarray is in general spatially correlated, while, due to large distances between subarrays, the noise between them is uncorrelated. Consequently, the noise covariance matrix of such an array has a block diagonal structure which is indeed sparse. Moreover, in an ordinary nonsparse array, because of small distance between adjacent sensors, there is noise coupling between neighboring sensors, whereas one can assume that non-adjacent sensors have spatially uncorrelated noise which makes again the array noise covariance matrix sparse. Utilizing some recently available tools in low-rank/sparse matrix decomposition, matrix completion, and sparse representation, we propose a novel method which can resolve possibly correlated or even coherent sources in the aforementioned partly correlated noise. In particular, when the sources are uncorrelated, our approach involves solving a second-order cone programming (SOCP), and if they are correlated or coherent, one needs to solve a computationally harder convex program. We demonstrate the effectiveness of the proposed algorithm by numerical simulations and comparison to the Cramer-Rao bound (CRB).
This paper explores a potential approach to fast classifying power system events using online synchrophasor measurements. The approach is based on dimensionality reduction of the emerging ambient phasor measurement unit (PMU) data. In contrast with model-based analysis, the proposed approach does not require a system model. It projects real-time PMU data onto the core subspace constructed from pre-event data, and then utilizes their scatter plots to detect and classify the system events. Projections lying outside the core subspace indicate the occurrence of an event, and the topological shapes of these projections classify the events. Numerical examples using synthetic PMU data are conducted to demonstrate the efficacy of the proposed approach.
This paper considers the problem of tracking multiple sources using observations acquired at spatially scattered sensors. Kalman filtering and smoothing techniques are combined with a sparse matrix estimation framework. A pertinent normone regularized minimization formulation is proposed that jointly searches for source-informative sensors, associates sources with sensors and tracks the unknown sources. Block coordinate descent techniques are used to recover the unknown sparse observation matrix, and subsequently obtain source state estimates. Numerical tests are provided to demonstrate the potential of the novel approach to identify the source-informative sensors and accurately track the field sources.
In this paper, a tensor n-mode matrix unfolding truncated nuclear norm is proposed, which is extended from the matrix truncated nuclear norm, to tensor completion problem. The alternating direction method of multipliers is utilized to solve this optimization problem. Meanwhile, the original two-step solution of the matrix truncated nuclear norm is reduced to one step. Employing the intermediate results returned by singular value shrinkage operator, rank information of each tensor unfolding matrix is not required and thus the computational complexity of the devised approach is not demanding. Computer simulation results demonstrate the effectiveness of the proposed method.
Recently proposed MAT1 scheme achieves high degrees of freedom (DoF) by exploiting delayed channel state information at transmitter side (CSIT) and the concept of interference alignment (IA), where the interference vectors of different time slots are aligned. As the starting work, MAT scheme considers no flexibility when reconstructing symbols at the third time slot, which may lead to performance degradation once the channel varies. In this paper, a probabilistic optimization problem is proposed with the assumption that the unknown channel entries follow given distribution. Instead of maximizing the sum rate directly, we strive to maximize the signal power while keeping the high probability that the interference power is lower than a pre-specified threshold. The Monte Carlo simulation results show that the proposed scheme outperforms the MAT scheme and dual SINR scheme with various channel uncertainties.
This paper develops a closed-form solution that improves the projection matrix method for time of arrival (TOA) source localization in the presence of sensor position inaccuracy. The projection approach is attractive because it does not require the use of an extra variable as in the traditional closed-form solution. Compared with the previous projection method, the proposed algorithm offers a closed-form solution and at the same time attains the Cramer-Rao lower bound (CRLB) performance for Gaussian noise over the small noise region. The performance of the proposed method is validated by simulations.
A measure of the ability of a sensor array to resolve two closely spaced point sources in angle is proposed here based on the framework of information geometry. The consideration of the geometric structure of a measurement model leads to the concept of information resolution which serves as a new metric to measure intrinsic similarities and differences between signal distributions that generate the manifold geometry. The statistical divergence between two sources is characterized in terms of the geodesic distance induced by the Fisher information metric. An analytical expression of the angular information resolution limit (AIRL) is derived using the constraints on the probability of error for a binary hypothesis test associated with the resolution of two sources. The influence of the detection error as well as the signal-to-noise ratio (SNR) on resolvability are demonstrated. The proposed AIRL can be used as a performance measure for sensor arrays in localizing remote sources and is applicable to various applications (e.g. radar, sonar, or astronomy).
We consider the problem of direction of arrival (DOA) estimation using a newly proposed structure of co-prime arrays. A continuous sparse recovery method is implemented in order to increase resolution. We show that in the noiseless case one can theoretically detect up to MN/2 sources with only 2M+N sensors via continuous sparse recovery. The noise statistics of co-prime arrays are also analyzed to demonstrate the robustness of the proposed optimization scheme. Using numerical examples, we show the superiority of the proposed method.
Many nonlinear parameter estimation problems can be described by the class of curved exponential families. The latter are fundamental concept in the framework of Information Geometry. This paper shows that when a closed-form statistical model is available the problem can be mapped onto the corresponding statistical manifolds via fixed parameterizations and thus solved optimally through a manifold gradient method. The solution process involves a dual projection which iteratively operates under the e-connection and m-connection in the flat manifolds with the coordinate systems in which the Cramér Rao Bound is attained. An example of tracking a moving target by two bearings-only sensors with location uncertainties is presented to demonstrate the efficiency and optimality of this manifold based method as well as the associated geometrical interpretation.
Subspace pursuit (SP) is a well-known greedy algorithm capable of reconstructing a sparse signal vector from a set of incomplete measurements. In this paper, by exploiting an approximate orthogonality condition characterized in terms of the achievable angles between two compressed orthogonal sparse vectors, we show that perfect signal recovery in the noiseless case, as well as stable signal recovery in the noisy case, is guaranteed if the sensing matrix satisfies RIP of order 3K with RIC δ 3K ≤ 0.2412 . Our work improves the best-known existing results, namely, δ 3K <; 0.165 for the noiseless case [3] and δ 3K <; 0.139 when noise is present [4]. In addition, for the noisy case we derive a reconstruction error upper bound, which is shown to be smaller as compared to the bound reported in [4].
A novel method is devised to jointly estimate the channel matrices involved in a relay-assisted MIMO communication system. We first propose a trilinear coding structure to be used at the amplify-and-forward (AF) relays for combining the received signals while spreading the combined signals across transmit antennas and time blocks, before retransmission. This structure provides antenna selection at the relays and different amplification schemes with non-diagonal amplification matrices. Then, by exploiting the tensor structure of the end-to-end MIMO links, the channel matrices are iteratively estimated by means of a combined alternating least squares (Comb-ALS-MIMO) algorithm that couples PARAFAC and Tucker2 decompositions for the received signals. The proposed method provides an effective solution to the channel estimation problem due to the efficient use of cooperative diversity and tensor-based signal processing.
A solution to the problem of intraference is obtained by recognising that the current diagonalisation schemes for the complex symmetric pseudocovariance matrix are not adequate to preserve its intrinsic complex-valued nature. To this end, we propose the correlation preserving transform (CPT), which both maintains the degree of the intrinsic correlation within a recovered bivariate source (minimum intraference) and minimises the correlation between different bivariate sources (minimum interference). Unlike the existing literature, this work therefore considers both the correlation structure between the data channels within bivariate sources and inter-source correlation. The efficacy of the proposed method is validated through analysis and simulations.
Unraveling latent structure by means of multilinear models of tensor data is of paramount importance in timely inference tasks encountered with `Big Data' analytics. However, increasingly noisy, heterogeneous, and incomplete datasets as well as the need for real-time processing of streaming data pose major challenges to this end. The present paper introduces a novel online (adaptive) algorithm to decompose low-rank tensors with missing entries, and perform imputation as a byproduct. The novel estimator minimizes an exponentially-weighted least-squares fitting error along with a separable regularizer of the PARAFAC decomposition factors, to trade-off fidelity for complexity of the approximation captured by the decomposition's rank. Leveraging stochastic gradient descent iterations, a scalable, real-time algorithm is developed and its convergence is established under simplifying technical assumptions. Simulated tests with cardiac magnetic resonance imagery (MRI) data confirm the efficacy of the proposed algorithm in imputing up to 75% missing entries.
Coprime Sampling has been recently proposed to efficiently estimate the spectrum of wideband signals, using sampling rates which can be significantly lower than the Nyquist rate. While the method has been shown to work well when large number of samples are available for estimating the autocorrelation, the effect of fewer samples on the performance of coprime spectrum estimation has not been addressed so far. This paper addresses this issue by employing a denoising scheme on the spectral estimates, as a l1 norm penalized quadratic program. The solution to this problem results in the so-called soft thresholding operator on the spectral estimates, which inherently promotes sparsity. It also helps to combat the effect of spurious peaks resulting from the finite sample averaging. The probabilities of detecting active and inactive bands are also explicitly characterized and they converge to unity by increasing the number (L) of sub Nyquist samples available to compute the estimates. The effectiveness of the proposed method is demonstrated through numerical examples.
This paper considers the problem of separating the power spectra and mapping the locations of co-channel transmitters using compound measurements from multiple sensors. This kind of situational awareness is important in cognitive radio practice, for spatial spectrum interpolation, transmission opportunity mining, and interference avoidance. Using temporal auto- and cross-correlations of the sensor outputs, it is shown that the power spectra separation task can be cast as a tensor decomposition problem in the Fourier domain. In particular, a joint diagonalization or (symmetric) parallel factor analysis (PARAFAC) model emerges, with one loading matrix containing the sought power spectra - hence being nonnegative, and locally sparse. Exploiting the latter two properties, it is shown that a very simple algebraic algorithm can be used to speed up the factorization. Assuming a path loss model, it is then possible to identify the transmitter locations by focusing on exclusively used (e.g., carrier) frequencies. The proposed approaches offer identifiability guarantees, and simplicity of implementation. Simulations show that the proposed approaches are effective in separating the spectra and localizing the transmitters.
