Mean Estimation from One-Bit Measurements

We consider the problem of estimating the mean of a symmetric log-concave distribution under the constraint that only a single bit per sample from this distribution is available to the estimator. We study the mean squared error as a function of the sample size (and hence the number of bits). We consider three settings: first, a centralized setting, where an encoder may release $n$ bits given a sample of size $n$, and for which there is no asymptotic penalty for quantization; second, an adaptive setting in which each bit is a function of the current observation and previously recorded bits, where we show that the optimal relative efficiency compared to the sample mean is precisely the efficiency of the median; lastly, we show that in a distributed setting where each bit is only a function of a local sample, no estimator can achieve optimal efficiency uniformly over the parameter space. We additionally complement our results in the adaptive setting by showing that \emph{one} round of adaptivity is sufficient to achieve optimal mean-square error

Optimum energy allocation for detection in wireless sensor networks

The problem of binary hypothesis testing in a wireless sensor network is studied in the presence of noisy channels and for non-identical sensors. We have designed a mathematically tractable fusion rule for which optimal energy allocation for individual sensors can be achieved. In this thesis we considered two methods for transmitting the sensor observations; binary modulation and M-ary modulation. In binary modulation we are able to allocate the energy among the sensors and protect the individual quantized bits where as the M-ary modulation provides optimum energy allocation only among the sensors. The goal is to design a fusion rule and an energy allocation for the nodes subject to a limit on the total energy of all the nodes so as to optimize a cost function. Two cost functions were considered; the probability of error and the J-divergence distance measure. Probability of error is the most natural criteria used for binary hypothesis testing problem. Distance measure is applied when it is difficult to obtain a closed form for the error probability. Results of optimal energy allocation and the resulting probability of error are presented for the two cost functions. Comparisons are drawn between the two cost functions regarding the fusion rule, energy allocations and the error probability

Distributed Detection and Estimation in Wireless Sensor Networks

Wireless sensor networks (WSNs) are typically formed by a large number of densely deployed, spatially distributed sensors with limited sensing, computing, and communication capabilities that cooperate with each other to achieve a common goal. In this dissertation, we investigate the problem of distributed detection, classification, estimation, and localization in WSNs. In this context, the sensors observe the conditions of their surrounding environment, locally process their noisy observations, and send the processed data to a central entity, known as the fusion center (FC), through parallel communication channels corrupted by fading and additive noise. The FC will then combine the received information from the sensors to make a global inference about the underlying phenomenon, which can be either the detection or classification of a discrete variable or the estimation of a continuous one.;In the domain of distributed detection and classification, we propose a novel scheme that enables the FC to make a multi-hypothesis classification of an underlying hypothesis using only binary detections of spatially distributed sensors. This goal is achieved by exploiting the relationship between the influence fields characterizing different hypotheses and the accumulated noisy versions of local binary decisions as received by the FC, where the influence field of a hypothesis is defined as the spatial region in its surrounding in which it can be sensed using some sensing modality. In the realm of distributed estimation and localization, we make four main contributions: (a) We first formulate a general framework that estimates a vector of parameters associated with a deterministic function using spatially distributed noisy samples of the function for both analog and digital local processing schemes. ( b) We consider the estimation of a scalar, random signal at the FC and derive an optimal power-allocation scheme that assigns the optimal local amplification gains to the sensors performing analog local processing. The objective of this optimized power allocation is to minimize the L 2-norm of the vector of local transmission powers, given a maximum estimation distortion at the FC. We also propose a variant of this scheme that uses a limited-feedback strategy to eliminate the requirement of perfect feedback of the instantaneous channel fading coefficients from the FC to local sensors through infinite-rate, error-free links. ( c) We propose a linear spatial collaboration scheme in which sensors collaborate with each other by sharing their local noisy observations. We derive the optimal set of coefficients used to form linear combinations of the shared noisy observations at local sensors to minimize the total estimation distortion at the FC, given a constraint on the maximum average cumulative transmission power in the entire network. (d) Using a novel performance measure called the estimation outage, we analyze the effects of the spatial randomness of the location of the sensors on the quality and performance of localization algorithms by considering an energy-based source-localization scheme under the assumption that the sensors are positioned according to a uniform clustering process

Sigma-Delta modulation based distributed detection in wireless sensor networks

We present a new scheme of distributed detection in sensor networks using Sigma-Delta modulation. In the existing works local sensor nodes either quantize the observation or directly scale the analog observation and then transmit the processed information independently over wireless channels to a fusion center. In this thesis we exploit the advantages of integrating modulation as a local processor into sensor design and propose a novel mixing topology of parallel and serial configurations for distributed detection system, enabling each sensor to transmit binary information to the fusion center, while preserving the analog information through collaborative processing. We develop suboptimal fusion algorithms for the proposed system and provide both theoretical analysis and various simulation results to demonstrate the superiority of our proposed scheme in both AWGN and fading channels in terms of the resulting detection error probability by comparison with the existing approaches

Dynamic quantization for multisensor estimation over bandlimited fading channels with fusion center feedback.

This paper considers the state estimation of hidden Markov models(HMMs) in a network of sensors which communicate with the fusion center viafinite symbols by fading channels. The objective is to minimize the long term meansquare estimation error for the underlying Markov chain. By using feedback fromthe fusion center, a dynamic quantization scheme for the sensor nodes is proposedand analyzed by a Markov decision approach. The performance improvement byfeedback, as well as the effect of fading, is illustrated

Robust Anomaly Detection in Dynamic Networks

We propose two robust methods for anomaly detection in dynamic networks in which the properties of normal traffic are time-varying. We formulate the robust anomaly detection problem as a binary composite hypothesis testing problem and propose two methods: a model-free and a model-based one, leveraging techniques from the theory of large deviations. Both methods require a family of Probability Laws (PLs) that represent normal properties of traffic. We devise a two-step procedure to estimate this family of PLs. We compare the performance of our robust methods and their vanilla counterparts, which assume that normal traffic is stationary, on a network with a diurnal normal pattern and a common anomaly related to data exfiltration. Simulation results show that our robust methods perform better than their vanilla counterparts in dynamic networks.Comment: 6 pages. MED conferenc