Optimal and Suboptimal Detection of Gaussian Signals in Noise: Asymptotic Relative Efficiency

The performance of Bayesian detection of Gaussian signals using noisy observations is investigated via the error exponent for the average error probability. Under unknown signal correlation structure or limited processing capability it is reasonable to use the simple quadratic detector that is optimal in the case of an independent and identically distributed (i.i.d.) signal. Using the large deviations principle, the performance of this detector (which is suboptimal for non-i.i.d. signals) is compared with that of the optimal detector for correlated signals via the asymptotic relative efficiency defined as the ratio between sample sizes of two detectors required for the same performance in the large-sample-size regime. The effects of SNR on the ARE are investigated. It is shown that the asymptotic efficiency of the simple quadratic detector relative to the optimal detector converges to one as the SNR increases without bound for any bounded spectrum, and that the simple quadratic detector performs as well as the optimal detector for a wide range of the correlation values at high SNR.Comment: To appear in the Proceedings of the SPIE Conference on Advanced Signal Processing Algorithms, Architectures and Implementations XV, San Diego, CA, Jul. 1 - Aug. 4, 200

Neyman-Pearson Detection of Gauss-Markov Signals in Noise: Closed-Form Error Exponent and Properties

The performance of Neyman-Pearson detection of correlated stochastic signals using noisy observations is investigated via the error exponent for the miss probability with a fixed level. Using the state-space structure of the signal and observation model, a closed-form expression for the error exponent is derived, and the connection between the asymptotic behavior of the optimal detector and that of the Kalman filter is established. The properties of the error exponent are investigated for the scalar case. It is shown that the error exponent has distinct characteristics with respect to correlation strength: for signal-to-noise ratio (SNR) >1 the error exponent decreases monotonically as the correlation becomes stronger, whereas for SNR <1 there is an optimal correlation that maximizes the error exponent for a given SNR.Comment: To appear in the IEEE Transactions on Information Theor

Design of Sensor Networks for Detection Applications via Large -Deviation Theory

107 p.Thesis (Ph.D.)--University of Illinois at Urbana-Champaign, 2004.Distributed sensor systems with the capacity to collect, process, and transmit environmental data have the potential to enable the next revolution in information technology. The rising interest in such sensor systems originates primarily from the low cost of emerging miniature sensing technologies, together with the wide availability of the computing resources necessary to handle complex data. Sensor networks are envisioned to contain legions of wireless nodes. As such, asymptotic regimes where the number of nodes becomes large are important tools in identifying design guidelines for future sensor systems. This work presents interesting applications of large-deviation theory and asymptotic analysis to the design of wireless sensor systems in the context of decentralized detection. Efforts are made to take into consideration the physical components of the communication channels and the structure of the observations available to the sensor nodes. It is found that high node density generally performs well even when observations from adjacent sensors are highly correlated. Furthermore, performance metrics by which sensor node candidates can be compared are established.U of I OnlyRestricted to the U of I community idenfinitely during batch ingest of legacy ETD

Stealthy attacks and defense strategies in competing sensor networks

The fundamental objective of sensor networks underpinning a variety of applications is the collection of reliable information from the surrounding environment. The correctness of the collected data is especially important in applications involving societal welfare and safety, in which the acquired information may be utilized by end-users for decision-making. The distributed nature of sensor networks and their deployment in unattended and potentially hostile environments, however, renders this collection task challenging for both scalar and visual data. In this work we propose and address the twin problem of carrying out and defending against a stealthy attack on the information gathered by a sensor network at the physical sensing layer as perpetrated by a competing hostile network. A stealthy attack in this context is an intelligent attempt to disinform a sensor network in a manner that mitigates attack discovery. In comparison with previous sensor network security studies, we explicitly model the attack scenario as an active competition between two networks where difficulties arise from the pervasive nature of the attack, the possibility of tampering during data acquisition prior to encryption, and the lack of prior knowledge regarding the characteristics of the attack. We examine the problem from the perspective of both the hostile and the legitimate network. The interaction between the networks is modeled as a game where a stealth utility is derived and shown to be consistent for both players in the case of stealthy direct attacks and stealthy cross attacks. Based on the stealth utility, the optimal attack and defense strategies are obtained for each network. For the legitimate network, minimization of the attacker’s stealth results in the possibility of attack detection through established paradigms and the ability to mitigate the power of the attack. For the hostile network, maximization of the stealth utility translates into the optimal attack avoidance. This attack avoidance does not require active communication among the hostile nodes but rather relies on a level of coordination which we quantify. We demonstrate the significance and effectiveness of the solution for sensor networks acquiring scalar and multidimensional data such as surveillance sequences and relate the results to existing image sensor networks. Finally we discuss the implications of these results for achieving secure event acquisition in unattended environments