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Master of Science / Department of Electrical and Computer Engineering / Balasubramaniam Natarajan / In this thesis, we first consider the problem of distributed estimation in an energy and rate-constrained wireless sensor network. To this end, we study three estimators namely - (1) Best Linear Unbiased Estimator (BLUE-1) that accounts for the variance of noise in measurement, uniform quantization and channel, and derive its variance and its lower bound; (2) Best Linear Unbiased Estimator (BLUE-2) that accounts for the variance of noise in measurement and uniform quantization, and derive lower and upper bounds for its variance; (3) Best Linear Unbiased Estima- tor (BLUE-3) that incorporates the effects of probabilistic quantization noise and measurement noise, and derive an upper bound for its variance. Then using BLUE-1, we analyze the tradeoff between estimation error (BLUE variance) at the fusion center and the total amount of resources utilized (power and rate) using three different system design approaches or optimization formulations. For all the formulations, we determine optimum quantization bits and transmission power per bit (or optimum actions) for all sensors jointly. Unlike prior efforts, we in- corporate the operating state (characterized by the amount of residual battery power) of the sensors in the optimization framework. We study the e®ect of channel quality, local measurement noise, and operating states of the sensors on their optimum choice for quantization bits and transmit power per bit. In the sequel, we consider a problem in distributed detection and signal processing in the context of biomedical wireless sensors and more specifically pulse- oximeter devices that record photoplethysmographic data. We propose an automated, two-stage PPG data processing method to minimize the effect of motion artifact. Regarding stage one, we present novel and consistent techniques to detect the presence of motion artifact in photoplethysmograms given higher order statistical information present in the data.For stage two, we propose an effective motion artifact reduction method that involves enhanced PPG data preprocessing followed by frequency domain Independent Component Analysis (FD-ICA). Experimental results are presented to demonstrate the efficacy of the overall motion artifact reduction method. Finally, we analyze a wireless ad hoc/sensor network where nodes are connected via random channels and information is transported in the network in a cooperative multihop fashion using amplify and forward relay strategy.

This dissertation develops optimal algorithms for distributed detection and estimation in static and mobile sensor networks. In distributed detection or estimation scenarios in clustered wireless sensor networks, sensor motes observe their local environment, make decisions or quantize these observations into local estimates of finite length, and send/relay them to a Cluster-Head (CH). For event detection tasks that are subject to both measurement errors and communication errors, we develop an algorithm that combines a Maximum a Posteriori (MAP) approach for local and global decisions with low-complexity channel codes and processing algorithms. For event estimation tasks that are subject to measurement errors, quantization errors and communication errors, we develop an algorithm that uses dithered quantization and channel compensation to ensure that each mote's local estimate received by the CH is unbiased and then lets the CH fuse these estimates into a global one using a Best Linear Unbiased Estimator (BLUE). We then determine both the minimum energy required for the network to produce an estimate with a prescribed error variance and show how this energy must be allocated amongst the motes in the network. In mobile wireless sensor networks, the mobility model governing each node will affect the detection accuracy at the CH and the energy consumption to achieve this level of accuracy. Correlated Random Walks (CRWs) have been proposed as mobility models that accounts for time dependency, geographical restrictions and nonzero drift. Hence, the solution to the continuous-time, 1-D, finite state space CRW is provided and its statistical behavior is studied both analytically and numerically. The impact of the motion of sensor on the network's performance is also studied.

abstract: Distributed inference has applications in a wide range of fields such as source localization, target detection, environment monitoring, and healthcare. In this dissertation, distributed inference schemes which use bounded transmit power are considered. The performance of the proposed schemes are studied for a variety of inference problems. In the first part of the dissertation, a distributed detection scheme where the sensors transmit with constant modulus signals over a Gaussian multiple access channel is considered. The deflection coefficient of the proposed scheme is shown to depend on the characteristic function of the sensing noise, and the error exponent for the system is derived using large deviation theory. Optimization of the deflection coefficient and error exponent are considered with respect to a transmission phase parameter for a variety of sensing noise distributions including impulsive ones. The proposed scheme is also favorably compared with existing amplify-and-forward (AF) and detect-and-forward (DF) schemes. The effect of fading is shown to be detrimental to the detection performance and simulations are provided to corroborate the analytical results. The second part of the dissertation studies a distributed inference scheme which uses bounded transmission functions over a Gaussian multiple access channel. The conditions on the transmission functions under which consistent estimation and reliable detection are possible is characterized. For the distributed estimation problem, an estimation scheme that uses bounded transmission functions is proved to be strongly consistent provided that the variance of the noise samples are bounded and that the transmission function is one-to-one. The proposed estimation scheme is compared with the amplify and forward technique and its robustness to impulsive sensing noise distributions is highlighted. It is also shown that bounded transmissions suffer from inconsistent estimates if the sensing noise variance goes to infinity. For the distributed detection problem, similar results are obtained by studying the deflection coefficient. Simulations corroborate our analytical results. In the third part of this dissertation, the problem of estimating the average of samples distributed at the nodes of a sensor network is considered. A distributed average consensus algorithm in which every sensor transmits with bounded peak power is proposed. In the presence of communication noise, it is shown that the nodes reach consensus asymptotically to a finite random variable whose expectation is the desired sample average of the initial observations with a variance that depends on the step size of the algorithm and the variance of the communication noise. The asymptotic performance is characterized by deriving the asymptotic covariance matrix using results from stochastic approximation theory. It is shown that using bounded transmissions results in slower convergence compared to the linear consensus algorithm based on the Laplacian heuristic. Simulations corroborate our analytical findings. Finally, a robust distributed average consensus algorithm in which every sensor performs a nonlinear processing at the receiver is proposed. It is shown that non-linearity at the receiver nodes makes the algorithm robust to a wide range of channel noise distributions including the impulsive ones. It is shown that the nodes reach consensus asymptotically and similar results are obtained as in the case of transmit non-linearity. Simulations corroborate our analytical findings and highlight the robustness of the proposed algorithm. / Dissertation/Thesis / Ph.D. Electrical Engineering 2013

One of the problems with the modern radio communication is the lack of availableradio frequencies. Recent studies have shown that, while the available licensed radiospectrum becomes more occupied, the assigned spectrum is significantly underutilized.To alleviate the situation, cognitive radio (CR) technology has been proposedto provide an opportunistic access to the licensed spectrum areas. Secondary CRsystems need to cyclically detect the presence of a primary user by continuouslysensing the spectrum area of interest. Radiowave propagation effects like fading andshadowing often complicate sensing of spectrum holes. When spectrum sensing isperformed in a cooperative manner, then the resulting sensing performance can beimproved and stabilized. In this thesis, two fully distributed and adaptive cooperative Primary User (PU)detection solutions for CR networks are studied. In the first part of this thesis we study a distributed energy detection schemewithout using any fusion center. Due to reduced communication such a topologyis more energy efficient. We propose the usage of distributed, diffusion least meansquare (LMS) type of power estimation algorithms with different network topologies.We analyze the resulting energy detection performance by using a commonframework and verify the theoretical findings through simulations. In the second part of this thesis we propose a fully distributed detection scheme,based on the largest eigenvalue of adaptively estimated correlation matrices, assumingthat the primary user signal is temporally correlated. Different forms of diffusionLMS algorithms are used for estimating and averaging the correlation matrices overthe CR network. The resulting detection performance is analyzed using a commonframework. In order to obtain analytic results on the detection performance, theadaptive correlation matrix estimates are approximated by a Wishart distribution.The theoretical findings are verified through simulations. / <p>QC 20170908</p>