Showing papers by "Ali H. Sayed published in 2011"

Distributed Detection Over Adaptive Networks Using Diffusion Adaptation

Abstract: We study the problem of distributed detection, where a set of nodes is required to decide between two hypotheses based on available measurements. We seek fully distributed and adaptive implementations, where all nodes make individual real-time decisions by communicating with their immediate neighbors only, and no fusion center is necessary. The proposed distributed detection algorithms are based on diffusion strategies [C. G. Lopes and A. H. Sayed, “Diffusion Least-Mean Squares Over Adaptive Networks: Formulation and Performance Analysis,” IEEE Trans. Signal Process., vol. 56, no. 7, pp. 3122-3136, July 2008; F. S. Cattivelli and A. H. Sayed, “Diffusion LMS Strategies for Distributed Estimation,” IEEE Trans. Signal Process., vol. 58, no. 3, pp. 1035-1048, March 2010; F. S. Cattivelli, C. G. Lopes, and A. H. Sayed, “Diffusion Recursive Least-Squares for Distributed Estimation Over Adaptive Networks,” IEEE Trans. Signal Process., vol. 56, no. 5, pp. 1865-1877, May 2008] for distributed estimation. Diffusion detection schemes are attractive in the context of wireless and sensor networks due to their scalability, improved robustness to node and link failure as compared to centralized schemes, and their potential to save energy and communication resources. The proposed algorithms are inherently adaptive and can track changes in the active hypothesis. We analyze the performance of the proposed algorithms in terms of their probabilities of detection and false alarm, and provide simulation results comparing with other cooperation schemes, including centralized processing and the case where there is no cooperation. Finally, we apply the proposed algorithms to the problem of spectrum sensing in cognitive radios.

Mobile Adaptive Networks

Abstract: In this paper, we investigate the self-organization and cognitive abilities of adaptive networks when the individual agents are allowed to move in pursuit of a target. The nodes act as adaptive entities with localized processing and are able to respond to stimuli in real-time. We apply adaptive diffusion techniques to guide the self-organization process, including harmonious motion and collision avoidance. We also provide stability and mean-square performance analysis of the proposed strategies, together with computer simulation to illustrate results.

Modeling Bird Flight Formations Using Diffusion Adaptation

Abstract: Flocks of birds self-organize into V-formations when they need to travel long distances. It has been shown that this formation allows the birds to save energy, by taking advantage of the upwash generated by the neighboring birds. In this work we use a model for the upwash generated by a flying bird, and show that a flock of birds can self-organize into a V-formation if every bird were to process spatial and network information through an adaptive diffusive process. The diffusion algorithm requires the birds to obtain measurements of the upwash, and also to use information from neighboring birds. The result has interesting implications. First, a simple diffusion algorithm can account for self-organization in birds. The algorithm is fully distributed and runs in real time. Second, according to the model, that birds can self-organize based on the upwash generated by the other birds. Third, that some form of information sharing among birds is necessary to achieve flight formation. We also propose a modification to the algorithm that allows birds to organize into a U-formation, starting from a V-formation. We show that this type of formation leads to an equalization effect, where every bird in the flock observes approximately the same upwash.

Analysis of Spatial and Incremental LMS Processing for Distributed Estimation

Abstract: Consider a set of nodes distributed spatially over some region forming a network, where every node takes measurements of an underlying process. The objective is for every node in the network to estimate some parameter of interest from these measurements by cooperating with other nodes. In this work we compare the performance of four adaptive implementations. Two of the implementations are distributed and network-based; they are spatial LMS and incremental LMS. In both algorithms, the nodes share information in a cyclic manner and both algorithms differ by the amount of information shared (less information is shared in the incremental case). The two other adaptive algorithms that we study deal with centralized implementations of spatial and incremental LMS. In these latter cases, all nodes exchange data with a fusion center where the computations are performed. In the centralized approach, all nodes receive the same estimates back from the fusion center, while these estimates differ among the nodes in the distributed implementation. We analyze and compare the performance of fusion-based and network-based versions of spatial LMS and incremental LMS processing and reveal some interesting conclusions. The results indicate that incremental LMS can outperform spatial LMS, and that network-based implementations can outperform the aforementioned fusion-based solutions in some revealing ways.

Diffusion Bias-Compensated RLS Estimation Over Adaptive Networks

Abstract: We study the problem of distributed least-squares estimation over ad hoc adaptive networks, where the nodes have a common objective to estimate and track a parameter vector. We consider the case where there is stationary additive colored noise on both the regressors and the output response, which results in biased local least-squares estimators. Assuming that the noise covariance can be estimated (or is known a priori), we first propose a bias-compensated recursive least-squares algorithm (BC-RLS). However, this bias compensation increases the variance or the mean-square deviation (MSD) of the local estimators, and errors in the noise covariance estimates may still result in residual bias. We demonstrate that the MSD and residual bias can then be significantly reduced by applying diffusion adaptation, i.e., by letting nodes combine their local estimates with those of their neighbors. We derive a necessary and sufficient condition for mean-square stability of the algorithm, under some mild assumptions. Furthermore, we derive closed-form expressions for its steady-state mean and mean-square performance. Simulation results are provided, which agree well with the theoretical results. We also consider some special cases where the mean-square stability improvement of diffusion BC-RLS over BC-RLS can be mathematically verified.

Optimal Spectral Feature Detection for Spectrum Sensing at Very Low SNR

Abstract: Spectrum sensing is one of the enabling functionalities for cognitive radio systems to operate in the spectrum white space. To protect the primary incumbent users from interference, the cognitive radio is required to detect incumbent signals at very low signal-to-noise ratio (SNR). In this paper, we study a spectrum sensing technique based on spectral correlation for detection of television (TV) broadcasting signals. The basic strategy is to correlate the periodogram of the received signal with the a priori known spectral features of the primary signal. We show that this sensing technique is asymptotically equivalent to the likelihood ratio test (LRT) at very low SNR, but with less computational complexity. That is, the spectral correlation-based detector is asymptotically optimal according to the Neyman-Pearson criterion. From the system design perspective, we analyze the effect of the spectral features on the spectrum sensing performance. Through the optimization analysis, we obtain useful insights on how to choose effective spectral features to achieve reliable sensing. Simulation results show that the proposed sensing technique can reliably detect analog and digital TV signals at SNR levels as low as -20 dB.

Optimal combination rules for adaptation and learning over networks

Abstract: Adaptive networks, consisting of a collection of nodes with learning abilities, are well-suited to solve distributed inference problems and to model various types of self-organized behavior observed in nature. One important issue in designing adaptive networks is how to fuse the information collected from the neighbors, especially since the mean-square performance of the network depends on the choice of combination weights. We consider the problem of optimal selection of the combination weights and motivate one combination rule, along with an adaptive implementation. The rule is related to the inverse of the noise variances and is shown to be effective in simulations.

An Adaptive Diffusion Augmented CLMS Algorithm for Distributed Filtering of Noncircular Complex Signals

Abstract: An adaptive diffusion augmented complex least mean square (D-ACLMS) algorithm for collaborative processing of the generality of complex signals over distributed networks is proposed. The algorithm enables the estimation of both second order circular (proper) and noncircular (improper) signals within a unified framework of augmented complex statistics. The analysis shows that the performance advantage of the widely linear D-ACLMS over the strictly linear D-CLMS increases with the degree of noncircularity while maintaining similar performance for proper data. Simulations on both synthetic benchmark and real world noncircular data support the approach.

Collaborative learning of mixture models using diffusion adaptation

Abstract: In large ad-hoc networks, classification tasks such as spam filtering, multi-camera surveillance, and advertising have been traditionally implemented in a centralized manner by means of fusion centers. These centers receive and process the information that is collected from across the network. In this paper, we develop a decentralized adaptive strategy for information processing and apply it to the task of estimating the parameters of a Gaussian-mixture-model (GMM). The proposed technique employs adaptive diffusion algorithms that enable adaptation, learning, and cooperation at local levels. The simulation results illustrate how the proposed technique outperforms non-collaborative learning and is competitive against centralized solutions.

Adaptive Networks with Noisy Links

Abstract: In biological systems, animals exhibit organized behavior that arises from localized interactions. The interaction is implemented through information exchange, either directly or indirectly. Adaptive networks, consisting of a collection of nodes with learning abilities that interact with each other to solve distributed inference problems in real-time, are well-suited to model these kinds of behavior. Usually the information exchange between two nodes is imperfect and the data from neighbors are noisy. In this paper, we examine the effect of noisy communication links on network performance and derive an optimal strategy for adjusting the combination weights.

Cooperative prey herding based on diffusion adaptation

Abstract: Mobile adaptive networks consist of a collection of nodes with learning and motion abilities that interact with each other locally in order to solve distributed processing and distributed inference problems in real-time. In this paper, we develop adaptation algorithms that exhibit self-organization properties and apply them to the model of cooperative hunting among predators. The results help provide an explanation for the agile adjustment of network patterns in the interaction between fish schools and predators.

Bio-inspired swarming for dynamic radio access based on diffusion adaptation

Abstract: The goal of this paper is to study the learning abilities of adaptive networks in the context of cognitive radio networks and to investigate how well they assist in allocating power and communications resources in the frequency domain. The allocation mechanism is based on a social foraging swarm model that lets every node allocate its resources (power/bits) in the frequency regions where the interference is at a minimum while avoiding collisions with other nodes. We employ adaptive diffusion techniques to estimate the interference profile in a cooperative manner and to guide the motion of the swarm individuals in the resource domain. A mean square performance analysis of the proposed strategy is provided and confirmed by simulation results. Numerical examples show that cooperative spectrum sensing improves the performance of the swarm-based resource allocation technique considerably.

Bio-inspired cooperative optimization with application to bacteria motility

Abstract: Inspired by bacterial motility, we propose an algorithm for adaptation over networks with mobile nodes. The nodes have limited abilities and they are allowed to cooperate with their neighbors to optimize a common objective function. In contrast to traditional adaptation formulations, an important consideration in this work is the fact that the nodes do not know the form of the cost function beforehand. The nodes can only sense variations in the values of the objective function as they diffuse through the space, such as sensing the variation in the concentration of nutrients in the environment. We propose a technique for the nodes to pick the search vector as a linear combination of the neighbors' last steps, by attempting to maximize the nutritional gradient. The procedure enables information to flow from “information-rich” nodes to the other nodes.

Distributed optimization via diffusion adaptation

Abstract: We develop an iterative diffusion mechanism to optimize a global cost function in a distributed manner over a network of nodes. The cost function is assumed to consist of a collection of individual components, and diffusion strategy allows the nodes to cooperate and diffuse information in real-time. Compared to incremental methods, diffusion methods do not require the use of a cyclic path over the nodes and are more robust to node and link failure.

Digital Suppression of Spurious PLL Tones in A/D Converters

Abstract: In a nonideal PLL circuit, leakage of the reference signal into the control line produces spurious tones. When the distorted PLL signal is used in an analog-to-digital converter (ADC), it injects the spurious tones into the sampled data. These distortions are particularly harmful for wideband applications, such as spectrum sensing, since they affect the detection of vacant frequency bands. This paper analyzes this distortion effect in some detail and proposes estimation and filtering techniques in the digital domain to clean the data and remove the PLL leakage effects. Rather than remove the PLL sidebands by perfecting the circuitry, the proposed approach focuses on compensating their effect on the sampled data by using signal processing compensation algorithms. We study the performance of the proposed estimation algorithms and compare it with the corresponding Cramer-Rao bound (CRB). Such digitally based approaches are cost effective since the cost of perfecting the analog circuits can be prohibitive due to regular variations and imperfections in circuit fabrication processes.

Transient Analysis of Adaptive Affine Combinations

Abstract: In this correspondence, we provide a transient analysis of an affinely constrained mixture method that adaptively combines the outputs of adaptive filters running in parallel on the same task. The affinely constrained mixture is adapted using a stochastic gradient update to minimize the square of the prediction error. Although we specifically carry out the transient analysis for a combination of two equal length adaptive filters trying to learn a linear model working on real valued data, we also provide the final equations and the necessary extensions in order to generalize the transient analysis to mixtures combining more than two filters; using Newton based updates to train the mixture weights; working on complex valued data; or unconstrained mixtures. The derivations are generic such that the constituent filters can be trained using unbiased updates including the least-mean squares or recursive least squares updates. This correspondence concludes with numerical examples and final remarks.

Probability distribution of steady-state errors and adaptation over networks

Abstract: In this work, we derive a near-optimal combination rule for adaptation over networks. To do so, we first establish a useful result pertaining to the steady-state distribution of the estimator of an LMS filter. Specifically, under small step-sizes and some conditions on the data, we show that the steady-state estimator is approximately Gaussian and provide an expression for its covariance matrix. The result is subsequently used to show that the maximum ratio combining rule over networks, which is used to combine the estimators across neighbors within a network, is near optimal in the minimum variance unbiased sense. The result suggests a rule for combining the estimators within neighborhoods that can lead to improved mean-square error performance.

Performance limits of LMS-based adaptive networks

Abstract: In this work we analyze the mean-square performance of different strategies for adaptation over two-node least-mean-squares (LMS) networks. The results highlight some interesting properties for adaptive networks in comparison to centralized solutions. The analysis reveals that the adapt-then-combine (ATC) adaptive network algorithm can achieve lower excess-mean-square-error (EMSE) than a centralized solution that is based on either block or incremental LMS strategies with the same convergence rate.

Clock jitter estimation in noise

Abstract: Clock timing jitter refers to random perturbations in the sampling time in analog-to-digital converters (ADCs). The perturbations are caused by circuit imperfections in the sampling clock. This paper analyzes the effect of sampling clock jitter on the acquired samples in the midst of quantization noise and random Gaussian noise. The paper proposes a method for estimating the jitter for cognitive radio architectures at high sampling rates. The paper also examines the fixed-point implementation of the algorithm and its theoretical performance.

Honeybee swarming behavior using diffusion adaptation

Abstract: Honeybees swarm when they move to a new site for their hive. During the process of swarming, their behavior can be analyzed by classifying them as informed scouts or uninformed bees, where the scouts have information about the destination while the uninformed bees follow the scouts. We model the network of bees as a network of mobile nodes with the nodes having asymmetric access to information about the location of the new hive. Diffusion adaptation is then used to model and explain the swarming behavior of bees.

Diffusion-based bias-compensated RLS for distributed estimation over adaptive sensor networks

Abstract: We present a diffusion-based bias-compensated recursive least squares (RLS) algorithm for distributed estimation in ad-hoc adaptive sensor networks where nodes cooperate to estimate a common deterministic parameter vector It is assumed that both the regressors and the output response are corrupted by stationary additive noise In this case, the least-squares estimator is biased Assuming that a good estimate of the noise statistics is available, this bias can be removed at the cost of a larger variance of the estimator However, by letting nodes cooperate in a diffusion-based fashion, it is possible to significantly reduce the variance, and furthermore improve the stability of the algorithm If there are estimation errors in the noise statistics, the diffusion also results in a smaller residual bias We provide closed-form expressions for the residual bias and mean-square deviation of the estimate (without full derivations) We also provide simulation results to demonstrate the beneficial effect of diffusion

On the effects of topology and node distribution on learning over complex adaptive networks

Abstract: Adaptive networks consist of a collection of nodes with adaptation and learning abilities The nodes interact with each other on a local level and diffuse information across the network through their collaborations, as dictated by the network topology and by the spatial distribution of the nodes In this work, we consider two types of nodes: informed and uninformed The former collect data and perform processing, while the latter only participate in the processing tasks We examine the performance of adaptive networks as a function of the fraction of informed nodes The results reveal an interesting trade-off between convergence and performance The analysis indicates that the larger the proportion of informed nodes in a network, the faster the convergence rate is at the expense of a deterioration in the mean-square-error performance The conclusion suggests an important interplay relating the number of informed nodes, the desired convergence rate, and the desired estimation accuracy

Diffusion adaptation over networks of particles subject to Brownian fluctuations

Abstract: This work investigates the influence of diffusion adaptation on the behavior of networks of micro-organisms that are subject to Brownian fluctuations in the motion of their constituent agents. The organisms are assumed to share information, usually through chemical signaling. The information may signal the direction of a target (such as a foreign body) towards which the cells need to migrate. The sharing of information enables the nodes to bias the probabilities of their random walks in favor of the desired direction of motion. It is verified that the adaptive diffusion of direction information enhances the foraging and tracking ability of the cells.

Signal Processing Theory and Methods [In the Spotlight]

Abstract: The scope of the IEEE Signal Processing Theory and Methods (SPTM) Technical Committee has a broad span, ranging from digital filtering and adaptive signal processing to statistical signal analysis, estimation, and detection. There have also been significant advances in the estimation of sparse systems. These areas continue to play a key role in classical and timely applications. This paper discusses about solving estimation and tracking problems over cognitive networks that requires optimizing certain global cost functions in a distributed manner.

Continuous-time distributed estimation

Abstract: Adaptive diffusion models endow networks with distributed learning and cognitive abilities. These models have been applied recently to emulate various forms of complex and self-organized patterns of behavior encountered in biological networks. In diffusion adaptation, nodes share information with their neighbors in real-time, and the network evolves towards a common objective through decentralized coordination and in-network processing. Current models are based on discrete-time adaptive diffusion strategies. However, physical phenomena usually are governed by continuous-time dynamics. In this paper, we derive continuous-time diffusion adaptive algorithms, which can help provide more accurate models for exchanges of information, and also for systems with large variations in their time constants.

Spatio-temporal diffusion mechanisms for adaptation over networks

Abstract: This work develops diffusion algorithms for adaptation over networks that endow nodes with both cooperation abilities and temporal processing abilities. Each node is allowed to share information locally with its neighbors. At the same time, each node filters past data and uses them to enhance the collaborative process. In this manner, the resulting algorithms consist of three stages: adaptation, spatial processing, and temporal processing. The order of these operations can be inter-changed leading to a total of six variations. The results indicate that the version that performs adaptation prior to the steps of spatial cooperation and temporal processing leads to best performance.

Frequency domain compensation of spurious sidebands in A/D circuits

Abstract: In a non-ideal PLL circuit, leakage of the reference signal into the control line produces spurious tones. When the distorted PLL signal is used as a clock signal, it creates spurious tones in the sampled data. Our prior work used a training signal to estimate the distortions and then correct the samples. In this work, we propose an alternative approach that estimates and removes the distortions directly from the sampled data without a training signal. Simulations indicate that the proposed solution is able to reduce the root-mean-square (RMS) sampling errors to about 15% of the original values.

Reducing spurious PLL tones in spectrum sensing architectures

Abstract: In a non-ideal PLL circuit, leakage of the reference signal into the control line produces spurious tones. When the distorted PLL signal is used in an analog-to-digital converter (ADC), it creates spurious tones in the sampled data as well. In spectrum sensing applications, the presence of spurious tones can lead to false detection of signals in otherwise empty channels. In a typical spectrum sensing application, there usually exists a Fourier transform block. We propose an algorithm to use this block to estimate the jitter errors from the spurious sidebands and to compensate the distorted samples in the digital domain.

Performance of Deconvolution Methods in Estimating CBOC-Modulated Signals

Abstract: Multipath propagation is one of the most difficult error sources to compensate in global navigation satellite systems due to its environment-specific nature. In order to gain a better understanding of its impact on the received signal, the establishment of a theoretical performance limit can be of great assistance. In this paper, we derive the Cramer Rao lower bounds (CRLBs), where in one case, the unknown parameter vector corresponds to any of the three multipath signal parameters of carrier phase, code delay, and amplitude, and in the second case, all possible combinations of joint parameter estimation are considered. Furthermore, we study how various channel parameters affect the computed CRLBs, and we use these bounds to compare the performance of three deconvolution methods: least squares, minimum mean square error, and projection onto convex space. In all our simulations, we employ CBOC modulation, which is the one selected for future Galileo E1 signals.

A bio-inspired fast swarming algorithm for dynamic radio access

Abstract: The goal of this paper is to propose a bio-inspired algorithm for decentralized dynamic access in cognitive radio systems. We study an improved social foraging swarm model that lets every node allocate its resources (power/bits) in the frequency regions where the interference is minimum while avoiding collisions with other nodes. The proposed approach adapts its behavior with respect to the interference power perceived by every node, thus increasing the speed of convergence and reducing the reaction time needed by the algorithm to react to dynamic changes in the environment. The presence of random disturbances such as link failures, quantization noise and estimation errors is taken into account in the convergence analysis. Numerical results illustrate the performance of the proposed algorithm.