Hypothesis Testing Using Spatially Dependent Heavy-Tailed Multisensor Data

The detection of spatially dependent heavy-tailed signals is considered in this dissertation. While the central limit theorem, and its implication of asymptotic normality of interacting random processes, is generally useful for the theoretical characterization of a wide variety of natural and man-made signals, sensor data from many different applications, in fact, are characterized by non-Gaussian distributions. A common characteristic observed in non-Gaussian data is the presence of heavy-tails or fat tails. For such data, the probability density function (p.d.f.) of extreme values decay at a slower-than-exponential rate, implying that extreme events occur with greater probability. When these events are observed simultaneously by several sensors, their observations are also spatially dependent. In this dissertation, we develop the theory of detection for such data, obtained through heterogeneous sensors. In order to validate our theoretical results and proposed algorithms, we collect and analyze the behavior of indoor footstep data using a linear array of seismic sensors. We characterize the inter-sensor dependence using copula theory. Copulas are parametric functions which bind univariate p.d.f. s, to generate a valid joint p.d.f. We model the heavy-tailed data using the class of alpha-stable distributions. We consider a two-sided test in the Neyman-Pearson framework and present an asymptotic analysis of the generalized likelihood test (GLRT). Both, nested and non-nested models are considered in the analysis. We also use a likelihood maximization-based copula selection scheme as an integral part of the detection process. Since many types of copula functions are available in the literature, selecting the appropriate copula becomes an important component of the detection problem. The performance of the proposed scheme is evaluated numerically on simulated data, as well as using indoor seismic data. With appropriately selected models, our results demonstrate that a high probability of detection can be achieved for false alarm probabilities of the order of 10^-4. These results, using dependent alpha-stable signals, are presented for a two-sensor case. We identify the computational challenges associated with dependent alpha-stable modeling and propose alternative schemes to extend the detector design to a multisensor (multivariate) setting. We use a hierarchical tree based approach, called vines, to model the multivariate copulas, i.e., model the spatial dependence between multiple sensors. The performance of the proposed detectors under the vine-based scheme are evaluated on the indoor footstep data, and significant improvement is observed when compared against the case when only two sensors are deployed. Some open research issues are identified and discussed

Energy-efficient Decision Fusion for Distributed Detection in Wireless Sensor Networks

This paper proposes an energy-efficient counting rule for distributed detection by ordering sensor transmissions in wireless sensor networks. In the counting rule-based detection in an $N-$sensor network, the local sensors transmit binary decisions to the fusion center, where the number of all $N$ local-sensor detections are counted and compared to a threshold. In the ordering scheme, sensors transmit their unquantized statistics to the fusion center in a sequential manner; highly informative sensors enjoy higher priority for transmission. When sufficient evidence is collected at the fusion center for decision making, the transmissions from the sensors are stopped. The ordering scheme achieves the same error probability as the optimum unconstrained energy approach (which requires observations from all the $N$ sensors) with far fewer sensor transmissions. The scheme proposed in this paper improves the energy efficiency of the counting rule detector by ordering the sensor transmissions: each sensor transmits at a time inversely proportional to a function of its observation. The resulting scheme combines the advantages offered by the counting rule (efficient utilization of the network's communication bandwidth, since the local decisions are transmitted in binary form to the fusion center) and ordering sensor transmissions (bandwidth efficiency, since the fusion center need not wait for all the $N$ sensors to transmit their local decisions), thereby leading to significant energy savings. As a concrete example, the problem of target detection in large-scale wireless sensor networks is considered. Under certain conditions the ordering-based counting rule scheme achieves the same detection performance as that of the original counting rule detector with fewer than $N/2$ sensor transmissions; in some cases, the savings in transmission approaches $(N-1)$.Comment: 7 pages, 3 figures. Proceedings of FUSION 2018, Cambridge, U

Low Complexity Optimal Hard Decision Fusion under Neyman-Pearson Criterion

Decision fusion is a fundamental operation in many signal processing systems where multiple sensors collaborate to improve the accuracy and robustness of the decision being made. The decision of each individual binary decision maker (or sensor) is often error-prone due to various environment challenges. These challenges are mitigated to certain extent using the spatial diversity obtained by deploying the sensors over a geographically distributed area. Subsequently, the decisions from the individual sensors are collected and fused at a fusion center to obtain a global decision. One such recent application of decision fusion is cooperative spectrum sensing in cognitive radio networks (CRN). The secondary users (SUs) of the CRN are tasked to garner the much needed unutilized spectrum allocated to the primary users (PUs). It is important for the SUs to precisely detect the spectrum usage opportunities inorder to improve the spectral efficiency and also to restrict the interference caused to PUs in this process. However, these are two conflicting objectives. Tuning the system to low levels of interference to the primary network will result in higher missed spectrum utilization oppurtunities. Similarly, increasing the detection of spectral usage opportunities will lead to increased interference to the primary users. The fusion centers require optimal fusion rules that improve the spectral efficiency of the CRN and minimize the interference caused to the primary network. The spectrum sensing in this case is generally modeled as a binary hypothesis problem: ‘PU signal present’ and ‘PU signal absent’. The fusion rules are broadly classified into two categories, namely (i) non-randomized (ii) randomized. In a ‘non-randomized’ rule, the global decision generated is deterministic for all the combinations of the local observations received. And in a ‘randomized’ rule the global decision generated is random (0 or 1) with a certain probability distribution for some local observations. The design of the optimal randomized decision fusion is generally simple, however introduce randomness in the decision equations and are difficult to implement. Whereas vii the design of the optimal non-randomized hard decision fusion rule is difficult, and under the Neyman-Pearson (NP) criterion is known to be exponential in complexity. In this thesis, we develop low-complexity (i) optimal and (ii) near-optimal algorithms for two variants of non-randomized hard decision fusion problems under NP crierion (i) clairvoyant1 decision fusion and (ii) novel (semi-)blind decision fusion. In all the sub-categories considered therein, we present low-complexity algorithms and obtain receiver operating characteristics (ROCs) for different number of participating sensors (N) which was intractable with the existing approaches. We formulate a more generalized version of this problem called “Generalized Decision Fusion Problem (GDFP)” and relate it to the classical 0−1 Knapsack problem. Consequently we show that the GDFP has a worst case pseudo-polynomial time solution using dynamic programming approach. Additionaly, we show that the decision fusion problem exhibits semi-monotonic property in most practical cases. We propose to exploit this property to reduce the dimension of the feasible solution space. Subsequently, we apply dynamic programming to efficiently solve the problem with further reduction in complexity. Further, we show that though the non-randomized single-threshold likelihood ratio based test (non-rand-st LRT) is sub-optimal, its performance approaches the upper bound obtained by randomized LRT (rand LRT) with increase in N. This alleviates the need for employing the exponentially complex non-randomized optimal solution for N larger than a specific value. As a variant of GDFP, we propose novel (semi-)blind hard decision fusion rules that use the mean of the secondary user characteristics instead of their actual values. We show that these rules with slight (or no) additional system knowledge achieve better ROC than existing (semi-)blind alternatives. Finally, we present a branch and bound algorithm with novel termination to obtain 1A rule that has complete knowledge of the system viii a near-optimal solution as the proposed dynamic programming approach exhibits limitations for the GDFP that require high-precision computations. We validate the performance of the proposed branch and bound algorithm for a wide range of {high, low} precision and {monotonic, semi, non-monotonic} GDFPs. All the algorithms have been rigorously verified by simulations in Matla

Spectrum Sensing Algorithms for Cognitive Radio Applications

Future wireless communications systems are expected to be extremely dynamic, smart and capable to interact with the surrounding radio environment. To implement such advanced devices, cognitive radio (CR) is a promising paradigm, focusing on strategies for acquiring information and learning. The first task of a cognitive systems is spectrum sensing, that has been mainly studied in the context of opportunistic spectrum access, in which cognitive nodes must implement signal detection techniques to identify unused bands for transmission. In the present work, we study different spectrum sensing algorithms, focusing on their statistical description and evaluation of the detection performance. Moving from traditional sensing approaches we consider the presence of practical impairments, and analyze algorithm design. Far from the ambition of cover the broad spectrum of spectrum sensing, we aim at providing contributions to the main classes of sensing techniques. In particular, in the context of energy detection we studied the practical design of the test, considering the case in which the noise power is estimated at the receiver. This analysis allows to deepen the phenomenon of the SNR wall, providing the conditions for its existence and showing that presence of the SNR wall is determined by the accuracy of the noise power estimation process. In the context of the eigenvalue based detectors, that can be adopted by multiple sensors systems, we studied the practical situation in presence of unbalances in the noise power at the receivers. Then, we shift the focus from single band detectors to wideband sensing, proposing a new approach based on information theoretic criteria. This technique is blind and, requiring no threshold setting, can be adopted even if the statistical distribution of the observed data in not known exactly. In the last part of the thesis we analyze some simple cooperative localization techniques based on weighted centroid strategies

On the Design and Analysis of Secure Inference Networks

Parallel-topology inference networks consist of spatially-distributed sensing agents that collect and transmit observations to a central node called the fusion center (FC), so that a global inference is made regarding the phenomenon-of-interest (PoI). In this dissertation, we address two types of statistical inference, namely binary-hypothesis testing and scalar parameter estimation in parallel-topology inference networks. We address three different types of security threats in parallel-topology inference networks, namely Eavesdropping (Data-Confidentiality), Byzantine (Data-Integrity) or Jamming (Data-Availability) attacks. In an attempt to alleviate information leakage to the eavesdropper, we present optimal/near-optimal binary quantizers under two different frameworks, namely differential secrecy where the difference in performances between the FC and Eve is maximized, and constrained secrecy where FC’s performance is maximized in the presence of tolerable secrecy constraints. We also propose near-optimal transmit diversity mechanisms at the sensing agents in detection networks in the presence of tolerable secrecy constraints. In the context of distributed inference networks with M-ary quantized sensing data, we propose a novel Byzantine attack model and find optimal attack strategies that minimize KL Divergence at the FC in the presence of both ideal and non-ideal channels. Furthermore, we also propose a novel deviation-based reputation scheme to detect Byzantine nodes in a distributed inference network. Finally, we investigate optimal jamming attacks in detection networks where the jammer distributes its power across the sensing and the communication channels. We also model the interaction between the jammer and a centralized detection network as a complete information zero-sum game. We find closed-form expressions for pure-strategy Nash equilibria and show that both the players converge to these equilibria in a repeated game. Finally, we show that the jammer finds no incentive to employ pure-strategy equilibria, and causes greater impact on the network performance by employing mixed strategies