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Superdirective arrays have been extensively studied because of their considerable potential accompanied, unfortunately, by a high sensitivity to random errors that affect the responses and positions of array elements. However, the statistics of their actual beam pattern (BP) has never been systematically investigated. This paper shows that the Rician probability density function (PDF), sometimes adopted to study the impact of errors in conventional arrays, is a valid approximation for superdirective BP statistics only where some mathematical terms are negligible. The paper also shows that this is the case for all linear end-fire arrays considered. A similar study is proposed concerning the correlation between BP lobes, showing that for the superdirective arrays considered the lobes, especially non-adjacent ones, are almost independent. Furthermore, knowledge of the PDF of the actual BP allows one to define quantile BP functions, whose probability of being exceeded, at any point, is fixed. Combining the lobes’ independence with quantile BP functions, an empirical equation for the probability that the entire actual BP will not exceed a quantile function over an interval larger than a given size is obtained. This new knowledge and these tools make it possible to devise new methods to design robust superdirective arrays via optimization goals with clearer and more relevant statistical meaning. [ABSTRACT FROM AUTHOR]

The rising interest in pattern recognition and data analytics has spurred the development of innovative machine learning algorithms and tools. However, as each algorithm has its strengths and limitations, one is motivated to judiciously fuse multiple algorithms in order to find the “best” performing one, for a given dataset. Ensemble learning aims at such high-performance meta-algorithm, by combining the outputs from multiple algorithms. The present work introduces a blind scheme for learning from ensembles of classifiers, using a moment matching method that leverages joint tensor and matrix factorization. Blind refers to the combiner who has no knowledge of the ground-truth labels that each classifier has been trained on. A rigorous performance analysis is derived and the proposed scheme is evaluated on synthetic and real datasets. [ABSTRACT FROM AUTHOR]

This paper investigates secrecy performance of finite-sized cooperative full-duplex relay (FDR) systems with unreliable wireless backhaul connections across multiple transmitters under Nakagami- $m$ fading. Closed-form expressions for the secrecy outage probability and probability of nonzero achievable secrecy rate are derived in terms of self-interference (SI), transmitter cooperation, and backhaul reliability. It is shown that transmitter cooperation can effectively enhance the secrecy performance, while the asymptotic limits on the secrecy outage probability and probability of nonzero achievable secrecy rate are exclusively determined by backhaul reliability. With the aid of transmitter cooperation, the burden of SI cancelation can be alleviated for the FDR system in achieving the smallest allowed secrecy outage probability. Compared to that of a half-duplex relay (HDR) system, the FDR system achieves a lower secrecy outage probability with well suppressed SI. The analysis shows that the secrecy outage probability achieved by the FDR system converges to that of the HDR system under perfect backhaul as the target secrecy rate becomes small. The secrecy performance metrics of the considered system are verified by simulations for various backhaul scenarios. [ABSTRACT FROM PUBLISHER]

Polar codes are of great interests because they provably achieve the symmetric capacity of discrete memoryless channels with arbitrary input alphabet sizes while having an explicit construction. Most existing decoding algorithms of polar codes are based on bit-wise hard or soft decisions. In this paper, we propose symbol-decision successive cancellation (SC) and successive cancellation list (SCL) decoders for polar codes, which use symbol-wise hard or soft decisions for higher throughput or better error performance. First, we propose to use a recursive channel combination to calculate symbol-wise channel transition probabilities, which lead to symbol decisions. Our proposed recursive channel combination has lower complexity than simply combining bit-wise channel transition probabilities. The similarity between our proposed method and Arıkan's channel transformations also helps to share hardware resources between calculating bit- and symbol-wise channel transition probabilities. Second, a two-stage list pruning network is proposed to provide a trade-off between the error performance and the complexity of the symbol-decision SCL decoder. Third, since memory is a significant part of SCL decoders, we propose a pre-computation memory-saving technique to reduce memory requirement of an SCL decoder. Finally, to evaluate the throughput advantage of our symbol-decision decoders, we design an architecture based on a semi-parallel successive cancellation list decoder. In this architecture, different symbol sizes, sorting implementations, and message scheduling schemes are considered. Our synthesis results show that in terms of area efficiency, our symbol-decision SCL decoders outperform existing bit-decision and multi-bit SCL decoders. [ABSTRACT FROM PUBLISHER]

In sparse target inference problems, it has been shown that significant gains can be achieved by adaptive sensing using convex criteria. We generalize this previous work on adaptive sensing to: a) include multiple classes of targets with different levels of importance and b) accommodate multiple sensor models. Optimization policies are developed to allocate a limited resource budget to simultaneously locate, classify and estimate a sparse number of targets embedded in a large space. Bounds on the performance of the proposed policies are derived by analyzing a baseline policy, which allocates resources uniformly across the scene, and an oracle policy which has a priori knowledge of the target locations/classes. These bounds quantify the potential benefit of adaptive sensing as a function of target frequency and importance. Numerical results indicate that the proposed policies perform close to the oracle bound when signal quality is sufficiently high. Moreover, the proposed policies improve on previous policies in terms of reducing estimation error, reducing misclassification probability, and increasing expected return. To account for sensors with different levels of agility, three sensor models are considered: global adaptive (GA), which can allocate different amounts of resource to each location in the space? global uniform (GU), which can allocate resources uniformly across the scene? and local adaptive (LA), which can allocate fixed units to a subset of locations. Policies that use a mixture of GU and LA sensors are shown to perform similarly to those that use GA sensors while being more easily implementable. [ABSTRACT FROM AUTHOR]

The application of nonlinear transformations to a cyclostationary signal for the purpose of revealing hidden periodicities has proven to be useful for applications requiring signal selectivity and noise tolerance. The fact that the hidden periodicities, referred to as cyclic moments, are often compressible in the Fourier domain motivates the use of compressive sensing (CS) as an efficient acquisition protocol for capturing such signals. In this paper, we consider the class of Temporal Higher Order Cyclostationary Statistics (THOCS) estimators when CS is used to acquire the cyclostationary signal assuming compressible cyclic moments in the Fourier domain. We develop a theoretical framework for estimating THOCS using the low-rate nonuniform sampling protocol from CS and illustrate the performance of this framework using simulated data. [ABSTRACT FROM PUBLISHER]

Distributed estimation of a deterministic mean-shift parameter in additive zero-mean noise is studied when using quantized data in the presence of Byzantine attacks. Several subsets of sensors are assumed to be tampered with by adversaries using different attacks such that the compromised sensors transmit fictitious data. First, we consider the task of identifying and categorizing the attacked sensors into different groups according to distinct types of attacks. It is shown that increasing the number K of time samples at each sensor and enlarging the size N of the sensor network can both ameliorate the identification and categorization, but to different extents. As K\rightarrow\infty, the attacked sensors can be perfectly identified and categorized, while with finite but sufficiently large K, as N\rightarrow\infty, it can be shown that the fusion center can also ascertain the number of attacks and obtain an approximate categorization with a sufficiently small percentage of sensors that are misclassified. Next, in order to improve the estimation performance by utilizing the attacked observations, we consider joint estimation of the statistical description of the attacks and the parameter to be estimated after the sensors have been well categorized. When using the same quantization approach successfully employed without attacks, it can be shown that the corresponding Fisher Information Matrix (FIM) is singular. To overcome this, a time-variant quantization approach is proposed, which will provide a nonsingular FIM, provided that K\geq 2. Furthermore, the FIM is employed to provide necessary and sufficient conditions under which utilizing the compromised sensors in the proposed fashion will lead to better estimation performance when compared to approaches where the compromised sensors are ignored. [ABSTRACT FROM PUBLISHER]

We propose a new system identification method, called Sign–Perturbed Sums (SPS), for constructing non-asymptotic confidence regions under mild statistical assumptions. SPS is introduced for linear regression models, including but not limited to FIR systems, and we show that the SPS confidence regions have exact confidence probabilities, i.e., they contain the true parameter with a user-chosen exact probability for any finite data set. Moreover, we also prove that the SPS regions are star convex with the Least-Squares (LS) estimate as a star center. The main assumptions of SPS are that the noise terms are independent and symmetrically distributed about zero, but they can be nonstationary, and their distributions need not be known. The paper also proposes a computationally efficient ellipsoidal outer approximation algorithm for SPS. Finally, SPS is demonstrated through a number of simulation experiments. [ABSTRACT FROM PUBLISHER]

Detecting the presence of signals in noise from multiple sources is a fundamental problem in statistical signal processing. In this paper, we consider multi-antenna signal detection when the noise covariance matrix is assumed to be arbitrary and unknown. We address this problem in the context of cognitive radio, where a multiple-primary-user detector is analyzed. This detector is known as Wilks' detector in statistics literature, which was derived under the generalized likelihood ratio criterion. We calculate the moments of Wilks' detector, which lead to simple and accurate approximate analytical formulae for the false alarm probability, the detection probability and the receiver operating characteristic. From the considered simulation settings, performance gain over existing detection algorithms is observed in scenarios with arbitrary and unknown noise correlation and multiple primary users. [ABSTRACT FROM PUBLISHER]

This paper presents a fixed interval smoothing multi-scan algorithm for target tracking in clutter. Both the probability of target existence and the target trajectory probability density function are calculated using all available measurements. This improves both the false track discrimination and the target trajectory estimate. The fixed interval smoothing fuses the forward and the backward multi-scan predictions, to obtain the smoothing predictions and smoothing innovations. Both trajectory estimates and the data association probabilities are calculated using the smoothing innovations. An overlapping batch procedure is described which limits the smoothing delay. [ABSTRACT FROM PUBLISHER]

In cognitive radio (CR), the soft decision fusion (SDF) rule plays a critical role in cooperative spectrum sensing (CSS). However, the computational cost on obtaining efficient SDF rule becomes infeasible even with a small number of cooperative users. In this paper, the efficiency of SDF rule in inhomogeneous background is studied from the perspective of quantization theory. We formulate the calculation of sensing performance including the probabilities of detection and false alarm when regarding both i) the quantization impact and ii) the inhomogeneous background, and then conclude a condition under which the sensing performance can be calculated by the fast Fourier transform (FFT). Based on this condition, two novel quantization schemes with two optimization methods are proposed to guarantee both the quantizer and decision threshold of SDF rule can be obtained efficiently, at the same time, the SDF can achieve high sensing performance. [ABSTRACT FROM PUBLISHER]

Topic models have been proposed to model a collection of data such as text documents and images in which each object (e.g., a document) contains a set of instances (e.g., words). In many topic models, the dimension of the latent topic space (the number of topics) is assumed to be a deterministic unknown. The number of topics significantly affects the prediction performance and interpretability of the estimated topics. In this paper, we propose a confidence-constrained rank minimization (CRM) to recover the exact number of topics in topic models with theoretical guarantees on recovery probability and mean squared error of the estimation. We provide a computationally-efficient optimization algorithm for the problem to further the applicability of the proposed framework to large real world datasets. Numerical evaluations are used to verify our theoretical results. Additionally, to illustrate the applicability of the proposed framework to practical problems, we provide results in image classification for two real world datasets and text classification for three real world datasets. [ABSTRACT FROM PUBLISHER]

A network of distributed agents wants to minimize a global cost given by a sum of local terms involving nonlinear convex functions of self and neighboring variables. Agents update their variables at random times by observing the values of neighboring agents and applying a random heuristic rule intent on minimizing the local cost with respect to their own variables. The heuristic rules are rational in that their average result is the actual optimal action with respect to the given values of neighboring variables. By identifying heuristic rational optimization with stochastic coordinate descent, it is shown that all agents visit a neighborhood of the optimal cost infinitely often with probability 1. An exponential probability bound on the worst deviation from optimality between visits to near optimal operating points is also derived. Commonly used models of consensus and opinion propagation in social networks, Markov random field estimation in wireless sensor networks, and cohesive foraging of animal herds are cast in the language of heuristic rational optimization. Numerical simulations for these three examples are presented to corroborate analytical results. [ABSTRACT FROM PUBLISHER]

In this correspondence, considering dual-hop channel state information (CSI)-assisted amplify-and-forward (AF) relaying over Nakagami- m fading channels, the cumulative distribution function (CDF) of the end-to-end signal-to-noise ratio (SNR) is derived. In particular, when the fading shape factors m1 and m2 at consecutive hops take non-integer values, the bivariate H-function and G -function are exploited to obtain an exact analytical expression for the CDF. The obtained CDF is then applied to evaluate the outage performance of the system under study. The analytical results of outage probability coincide exactly with Monte-Carlo simulation results and outperform the previously reported upper bounds in the low and medium SNR regions. [ABSTRACT FROM PUBLISHER]

This correspondence investigates the statistical properties of the ratio T = λ1/Σi=1mλi , where are λ1 ≥ λ2 ≥ ··· ≥ λm the m eigenvalues of an m × m complex central Wishart matrix W with n degrees of freedom. We derive new exact analytical expressions for the probability density function (PDF) and cumulative distribution function (CDF) of T for complex central Wishart matrices with arbitrary dimensions. We also formulate simplified statistics of T for the special case of dual uncorrelated and dual correlated complex central Wishart matrices (m = 2) . The investigated ratio T is the most important ratio in blind spectrum sensing, since it represents a sufficient statistics for the generalized likelihood ratio test (GLRT). Thus, the derived analytical results are used to find the exact decision threshold for the desired probability of false alarm for Blind-GLRT (B-GLRT) detector. It is shown that the exact decision threshold based B-GLRT detector gives superior performance over the asymptotic decision threshold schemes proposed in the literature, which leads to efficient spectrum usage in cognitive radio. [ABSTRACT FROM PUBLISHER]

We consider joint optimization of cooperative spectrum sensing, channel access and power allocation in an overlay multiband cognitive radio network. A soft-decision cooperative spectrum sensing concept using continuous-valued sensing test statistics is considered, instead of making hard binary decisions as in traditional hypothesis testing spectrum sensing schemes. The channel access decision about whether to access the channel or not is relaxed into allowing the secondary user to access channels with some probability. The sensing decision is made at the secondary base station based on the sensing statistics received from all or a subset of secondary users. This joint optimization problem is aimed at maximizing the secondary users' sum instantaneous throughput while keeping the interference to primary users under a specified threshold. The problem is shown to be a convex optimization problem and the Lagrangian dual method is employed to obtain the optimal solution. Two heuristic algorithms are also proposed to reduce computational complexity. We also discuss an alternative formulation where additionally interference to individual PUs is also constrained. Simulation results show that our soft sensing based algorithm significantly outperforms a traditional hard decision sensing algorithm. [ABSTRACT FROM PUBLISHER]

This paper proposes for single carrier signaling a simple structure that combines turbo equalization and decoding of correlated sources in multipath-rich multiuser Rayleigh fading multiple access channels (MAC), where the correlation between the sources is exploited by vertical iterations (VI) between the decoders. The bit-flipping model with a flipping probability pe is used to express the correlation ρ between the sources as ρ = 1-2pe. The proposed simple structure, spatially concatenated codes (SpCC), can achieve turbo-like performance over MAC channels suffering from severe inter-symbol interference (ISI), even though it uses short memory convolutional codes. First of all, to achieve turbo-like performance we introduce VIs to exploit the knowledge about the source correlation by exchanging extrinsic log-likelihood ratio (LLR) between the two decoders. We then add a rate-1 doped accumulator (D-ACC) to flexibly adapt for the variation of correlations between the sources. The results of computer simulations and extrinsic information transfer (EXIT) analysis confirm that in multipath-rich environments the proposed structure can achieve excellent performances, 1.02-1.28 dB away from the Slepian-Wolf-Shannon limit, at 1% outage probability for 0 <; ρ ≤ 1. [ABSTRACT FROM PUBLISHER]

A kernel regression technique for the ill-posed range-based localization problem is proposed. We introduce a generic kernel design method which relies on a probabilistic modeling of the respective physical environment in terms of a class of stochastic differential equations. The combination of dynamic modeling with physical and stochastic interpretability leads to a unique solution in a Reproducing Kernel Hilbert Space and thus eliminates the need for a time-discrete representation of the localization solution. By design of the problem formulation, an extended Kalman filter naturally evolves as an iterative optimization method. As a practical example, we tackle an ill-posed localization problem that stems from a preinstalled sensor network of unknown geometry, providing nonsynchronous range information to a moving beacon. To obtain a unique solution for the beacon positions and the network geometry, we apply the proposed kernel regression technique and kernel design method. The proposed approach eventually leads to a least squares optimization problem that can be interpreted as a maximum a posteriori estimation problem. While the methodology is not restricted to localization problems only, its validity is shown by a demonstrator which is comprised of a mobile robot and a network of multiple nonmoving beacons that provide time-of-arrival measurements of ultra wide band signals. [ABSTRACT FROM PUBLISHER]

We study and compare the performance of two bidirectional network beamforming schemes, namely the multiple access broadcast channel (MABC) strategy and the time division broadcast channel (TDBC) protocol, using joint optimal power control and beamforming design. To do so, we first design two TDBC-based bidirectional network beamformers, through minimization of the total power consumed in the whole network subject to quality of service (QoS) constraints, for the two cases with and without a direct link between the two transceivers. The corresponding power minimization problems are carried out over the transceiver transmit powers as well as relay beamforming weights, thus resulting in a jointly optimal power allocation and beamforming criterion. We devise optimal second-order cone programming based solutions as well as fast gradient-based solutions to these problems. We then use these solutions to compare the performance of the underlying TDBC-based approach to that of the MABC-based technique. This comparison is important because the TDBC approach appears to have certain advantages which can be exploited towards improving the performance of two-way network beamforming. These advantages include the additional degrees of freedom as well as the possibility of benefitting from the availability of a direct link between the two transceivers. Interestingly, in the absence of a direct link between the two transceivers, we show that when the QoS constraints are imposed to meet certain given probabilities of uncoded error [or, equivalently, to meet certain signal-to-noise ratio (SNR) constraints], these two schemes perform closely in terms of the minimum total transmit power. However, when the QoS constraints are used to guarantee certain given rates, the MABC-based scheme outperforms the TDBC counterpart. In the case when a direct link exists between the two transceivers, the TDBC-based approach can outperform the MABC-based method, even for rate satisfying QoS constraints, provided that the direct link is strong enough. [ABSTRACT FROM PUBLISHER]

We consider distributed state estimation in a wireless sensor network without a fusion center. Each sensor performs a global estimation task-based on the past and current measurements of all sensors-using only local processing and local communications with its neighbors. In this estimation task, the joint (all-sensors) likelihood function (JLF) plays a central role as it epitomizes the measurements of all sensors. We propose a distributed method for computing, at each sensor, an approximation of the JLF by means of consensus algorithms. This “likelihood consensus” method is applicable if the local likelihood functions of the various sensors (viewed as conditional probability density functions of the local measurements) belong to the exponential family of distributions. We then use the likelihood consensus method to implement a distributed particle filter and a distributed Gaussian particle filter. Each sensor runs a local particle filter, or a local Gaussian particle filter, that computes a global state estimate. The weight update in each local (Gaussian) particle filter employs the JLF, which is obtained through the likelihood consensus scheme. For the distributed Gaussian particle filter, the number of particles can be significantly reduced by means of an additional consensus scheme. Simulation results are presented to assess the performance of the proposed distributed particle filters for a multiple target tracking problem. [ABSTRACT FROM PUBLISHER]

Notwithstanding the popularity of conventional clustering algorithms such as K-means and probabilistic clustering, their clustering results are sensitive to the presence of outliers in the data. Even a few outliers can compromise the ability of these algorithms to identify meaningful hidden structures rendering their outcome unreliable. This paper develops robust clustering algorithms that not only aim to cluster the data, but also to identify the outliers. The novel approaches rely on the infrequent presence of outliers in the data, which translates to sparsity in a judiciously chosen domain. Leveraging sparsity in the outlier domain, outlier-aware robust K-means and probabilistic clustering approaches are proposed. Their novelty lies on identifying outliers while effecting sparsity in the outlier domain through carefully chosen regularization. A block coordinate descent approach is developed to obtain iterative algorithms with convergence guarantees and small excess computational complexity with respect to their non-robust counterparts. Kernelized versions of the robust clustering algorithms are also developed to efficiently handle high-dimensional data, identify nonlinearly separable clusters, or even cluster objects that are not represented by vectors. Numerical tests on both synthetic and real datasets validate the performance and applicability of the novel algorithms. [ABSTRACT FROM PUBLISHER]

We investigate selection beamforming for a cooperative network that consists of a source, a destination, and two amplify-and-forward (AF) relays, which are all equipped with multiple antennas. The transmit and receive beamforming techniques are respectively applied at the source and destination, and the linear processing operator of the selected AF multiple-input multiple-output (MIMO) relay is optimized. We consider that the source has the instantaneous channel state information (CSI) of the channels from the source to relays but no information regarding the CSI of the channels from the relays to the destination. Partial relay selection (PRS) is employed, i.e., the source routes its information signal to the relay which offers better first-hop signal-to-noise ratio (SNR). Considering a Rayleigh fading environment, we derive an exact closed-form expression for the outage probability at the destination. The validity of the outage probability expression has been confirmed with numerical simulations. We also present the asymptotic analysis of the PRS scheme for the considered multiantenna system and derive the expressions of diversity gain. It is shown that, the overall diversity gain is \min(\min(nr,1nd,nr,2nd),nr,1ns+nr,2ns) where ns, nd, and nr,q are, respectively, the numbers of antennas at the source, destination and the qth relay. For the condition C:\min(nr,1nd,nr,2nd)\geq nr,1ns+nr,2ns that can be easily met with practically realizable antenna configurations, it is shown that PRS provides the same diversity order as opportunistic relaying (OR). [ABSTRACT FROM AUTHOR]

This paper deals with the detection of hidden bits in the Least Significant Bit (LSB) plane of a natural image. The mean level and the covariance matrix of the image, considered as a quantized Gaussian random matrix, are unknown. An adaptive statistical test is designed such that its probability distribution is always independent of the unknown image parameters, while ensuring a high probability of hidden bits detection. This test is based on the likelihood ratio test except that the unknown parameters are replaced by estimates based on a local linear regression model. It is shown that this test maximizes the probability of detection as the image size becomes arbitrarily large and the quantization step vanishes. This provides an asymptotic upper-bound for the detection of hidden bits based on the LSB replacement mechanism. Numerical results on real natural images show the relevance of the method and the sharpness of the asymptotic expression for the probability of detection. [ABSTRACT FROM PUBLISHER]

This paper focuses on the performance analysis and comparison of hard decision (HD) and soft decision (SD) based approaches for cooperative spectrum sensing in the presence of reporting channel errors. For cooperative sensing (CS) in cognitive radio networks, a distributed detection approach with displaced sensors and a fusion center (FC) is employed. For HD based CS, each secondary user (SU) sends a one-bit hard local decision to the FC. For SD based CS, each SU sends a quantized version of a local decision statistic such as the log-likelihood ratio or any suitable sufficient statistic. The decision statistics are sent through channels that may cause errors. The effects of channel errors are incorporated in the analysis through the bit error probability (BEP). For HD based CS, the counting rule or the K-out-of-N rule is used at the FC. For SD based CS, the optimal fusion rule in the presence of reporting channel errors is derived and its distribution is established. A comparison of the two schemes is conducted to show that there is a performance gain in using SD based CS even in the presence of reporting channel errors. In addition, a BEP wall is shown to exist for CS such that if the BEP is above a certain value, then irrespective of the received signal strength corresponding to the primary user, the constraints on false alarm probability and detection probability cannot be met. It is shown that the performance of HD based CS is very sensitive to the BEP wall phenomenon while the SD based CS is more robust in that sense. [ABSTRACT FROM PUBLISHER]

In this paper, we consider the problem of detecting a signal in Gaussian noise with unknown covariance matrix, in partially homogeneous environments where the test and training data samples share the same noise covariance matrix up to an unknown scaling factor. One solution to this problem is the adaptive subspace detector (ASD) with a single or multiple observations. However, the probabilities of false alarm and detection of this ASD have not been obtained yet. In this paper, these expressions are derived on the basis of a single observation, which are confirmed with Monte Carlo simulations. It is shown that the ASD has a constant false alarm rate property with respect to both the shared noise covariance matrix structure and the independent scaling of the noise in the test data. In addition, we prove that for the First-Order model where the signal of interest is assumed to be a deterministic but unknown vector, the ASD derived with the generalized likelihood ratio test is consistent with that derived with an ad hoc two-step design procedure. [ABSTRACT FROM AUTHOR]

In this correspondence, we provide a multiple hypothesis test to detect the number of latent noncircular signals in a complex Gaussian random vector. Our method sequentially tests the results of individual generalized likelihood ratio test (GLRT) statistics with known asymptotic distributions to form the multiple hypothesis detector. Specifically, we are able to set a threshold yielding a precise probability of error. This test can be used to statistically determine if a given complex observation is circular Gaussian, and if not, how many latent signals in the observation are noncircular. Simulations are used to quantify the performance of the detector as compared to a detector based on the minimum description length (MDL) criterion. The utility of the detector is shown by applying it to a beamforming application using independent component analysis (ICA). [ABSTRACT FROM AUTHOR]

In this paper, we provide a performance analysis of cognitive radio systems employing energy detection based on power spectral density estimation. Specifically, we derive mathematical expressions for the probabilities of false alarm and missed detection when the periodogram estimate is used as a decision statistic. First, using the characteristic function of the quadratic form representation of the periodogram, we study the characteristics of the product of the sample covariance matrix of the observed vector and the symmetric matrix of the quadratic form. We have found that this product is Rank-1 with one non-zero eigenvalue and therefore a simplified expression for the cumulative density function (CDF) is obtained. Second, the CDF is exploited to derive accurate mathematical expressions for the probabilities of false alarm and missed detection in both Rayleigh and Rician fading channels. Also, for each case, we have derived the probability distribution function (PDF) of the corresponding eigenvalues. The results demonstrate that the probabilities of false alarm and missed detection are independent of the length of the observations when all the other parameters remain fixed. The results also reveal that the considered frequency-domain based energy detector is superior to its conventional time-domain counterpart as it provides fewer false alarms. [ABSTRACT FROM PUBLISHER]

With increasing spatial reuse of radio spectrum, co-channel interference is becoming a dominant noise source and may severely degrade the communication performance of wireless transceivers. In this paper, we consider the problem of statistical-physical modeling of co-channel interference from an annular field of Poisson or Poisson-Poisson cluster distributed interferers. Poisson and Poisson-Poisson cluster processes are commonly used to model interferer distributions in large wireless networks without and with interferer clustering, respectively. Further, by considering the interferers distributed over a parametric annular region, we derive interference statistics for finite- and infinite- area interference region with and without a guard zone around the receiver. Statistical modeling of interference is a useful tool to analyze outage probabilities in wireless networks and design interference-aware transceivers. Our contributions include: 1) developing a unified framework for deriving interference models for various wireless network environments; 2) demonstrating the applicability of the symmetric alpha stable and Gaussian mixture (with Middleton Class A as a particular form) distributions in modeling co-channel interference; and 3) deriving analytical conditions on the system model parameters for which these distributions accurately model the statistical properties of the interference. Applications include co-channel interference modeling for various wireless networks, including wireless ad hoc, cellular, local area, and femtocell networks. [ABSTRACT FROM AUTHOR]

This paper deals with the problem of adaptive reconstruction and identification of nonstationary AR processes with randomly missing observations. Existent methods use a direct realization of the filter. Therefore, the estimated parameters may not correspond to a stable all-pole filter. In addition, when the probability of missing a sample is high, existent methods may converge slowly or even fail to converge. We propose, at our knowledge, the first algorithm based on the lattice structure for online processing of signals with missing samples. It is an extension of the RLSL algorithm to the case of missing observations, using a Kalman filter for the prediction of missing samples. The estimated parameters guarantee the stability of the corresponding all-pole filter. In addition it is robust to high probabilities of missing a sample. It offers a fast parameter tracking even for high probabilities of missing a sample. It is compared to the Kalman pseudolinear RLS algorithm, an already proposed algorithm using a direct realization of the filter. The proposed algorithm shows better performance in reconstruction of audio signals. [ABSTRACT FROM PUBLISHER]

The majority of analog-to-digital converters (ADCs) are designed without taking into consideration the distribution of input signal. In this correspondence, we present a novel ADC architecture that is optimized for a given input signal's statistics. The new robust data-optimized stochastic flash (RDSF) ADC achieves robustness and high accuracy by employing a) a large number of 1-bit quantizers operating in parallel with an additive noise and b) a novel probability density transform (PDT). We demonstrate the performance gain of the RDSF over the conventional flash ADC using simulations and theoretical analysis [ABSTRACT FROM PUBLISHER]

Recognizing the uncertainty present in all real-world problems, this correspondence extends the mathematical framework of a previously presented information-based sensor manager to permit operation with uncertain sensor probabilities of detection and false alarm. Simulation results demonstrate the importance of proper uncertainty modeling for the attainment of robust sensor manager performance [ABSTRACT FROM PUBLISHER]

This paper examines differential binary modulation for wireless networks that utilize wireless relays to seek cooperative diversity and improved performance. Two differential cooperative transmission schemes, referred to as differential amplify-and-forward (DAF) and differential decode-and-forward (DDF), respectively, are introduced. These schemes require no channel state information at any node in the system. A set of analytical results pertaining to the probability density function of the instantaneous signal-to-noise ratio, average bit error rate, outage probability, and diversity order of the proposed schemes in Rayleigh fading channels are obtained. The analytical results are confirmed by numerical simulations. It is shown that the differential cooperative DAF and DDF schemes achieve cooperative diversity and outperform the conventional noncooperative differential modulation [ABSTRACT FROM PUBLISHER]

This correspondence deals with the problem of estimating signal parameters using an array of sensors. In source localization, two main maximum-likelihood methods have been introduced: the conditional maximum-likelihood method which assumes the source signals nonrandom and the unconditional maximum-likelihood method which assumes the source signals random. Many theoretical investigations have been already conducted for the large samples statistical properties. This correspondence studies the behavior of unconditional maximum likelihood at high signal-to-noise ratio for finite samples. We first establish the equivalence between the unconditional and the conditional maximum-likelihood criterions at high signal-to-noise ratio. Then, thanks to this equivalence we prove the non-Gaussianity and the non-efficiency of the unconditional maximum-likelihood estimator. We also rediscover the closed-form expressions of the probability density function and of the variance of the estimates in the one source scenario and we derive a closed-form expression of this estimator variance in the two sources scenario [ABSTRACT FROM PUBLISHER]

A probabilistic Boolean network (PBN) is a discrete network composed of a family of Boolean networks such that at each time instant the transition of the PBN is governed by one of its constituent networks. A random variable determines when the governing Boolean network switches and, when a switch occurs, a new constituent network is chosen according to a selection distribution to govern the PBN transitions until another switch is called for. As nonlinear models of genetic regulatory networks, PBNs incorporate the indeterminacy owing to latent variables external to the model that have biological interaction with genes in the model. Besides being used to model biologically phenomena, such as cellular state dynamics and the switch-like behavior of certain genes, PBNs have served as the main model for the application of intervention methods, including optimal control strategies, to favorably effect system dynamics. An obstacle in applying PBNs to large-scale networks is the computational complexity of the model. It is sometimes necessary to construct computationally tractable subnetworks while still carrying sufficient structure for the application at hand. Hence, there is a need for size reducing mappings. This paper proposes a reduction strategy that preserves the dynamical structure of the network, a crucial requirement for the development of intervention strategies based on control theory. In particular, we focus on the following two issues when deleting a gene from the network: 1) maintaining the same number of constituent Boolean networks, and 2) preserving, in an optimal sense, the attractor structure, the relative sizes of the basins of attraction, and the level structures of the state transition diagrams of the constituent Boolean networks. Preservation of the attractor structure is critical because the attractors of a PBN determine its steady-state behavior [ABSTRACT FROM PUBLISHER]

We present two procedures for validating track estimates obtained using the maximum-likelihood probabilistic data association (ML-PDA) algorithm. The ML-PDA, developed for very low observable (VLO) target tracking, always provides a track estimate that must then be tested for target existence by comparing the value of the log likelihood ratio (LLR) at the track estimate to a threshold. Using extreme value theory, we show that in the absence of a target the LLR at the track estimate obeys approximately a Gumbel distribution rather than the Gaussian distribution previously ascribed to it in the literature. The offline track validation procedure relies on extensive offline simulations to obtain a set of track validation thresholds that are then used by the tracking system. The real-time procedure uses the data set that produced the track estimate to also determine the track validation threshold. The performance of these two procedures is investigated through simulation of two active sonar tracking scenarios by comparing the false and true track acceptance probabilities. These techniques have potential for use in a broader class of maximum likelihood estimation problems with similar structure [ABSTRACT FROM PUBLISHER]

This paper discusses underdetermined (i.e., with more sources than sensors) blind source separation (BSS) using a two-stage sparse representation approach. The first challenging task of this approach is to estimate precisely the unknown mixing matrix. In this paper, an algorithm for estimating the mixing matrix that can be viewed as an extension of the DUET and the TIFROM methods is first developed. Standard clustering algorithms (e.g., K-means method) also can be used for estimating the mixing matrix if the sources are sufficiently sparse. Compared with the DUET, the TIFROM methods, and standard clustering algorithms, with the authors' proposed method, a broader class of problems can be solved, because the required key condition on sparsity of the sources can be considerably relaxed. The second task of the two-stage approach is to estimate the source matrix using a standard linear programming algorithm. Another main contribution of the work described in this paper is the development of a recoverability analysis. After extending the results in [7], a necessary and sufficient condition for recoverability of a source vector is obtained. Based on this condition and various types of source sparsity, several probability inequalities and probability estimates for the recoverability issue are established. Finally, simulation results that illustrate the effectiveness of the theoretical results are presented. [ABSTRACT FROM AUTHOR]