Joint Collaboration And Compression Design For Parameter Estimation And Signal Detection

Wireless sensor networks(WSNs)are playing an increasingly important role in a wide range applications and are therefore attracting a lot of attention from both academia and industry.The sensors deployed in a WSN are usually resource constrained in terms of power,bandwidth and computation capabilities.It is challenging to design inference algorithms for such resource constrained WSNs.This dissertation addresses this challenge and develops a novel collaboration-compression framework that allows the WSN to perform inference while minimizing the overall communication cost subject to power and bandwidth constraints.Importantly,the designed strategies are easy to implement and are useful for the systems where individual sensors do not have a large computational budget.In this dissertation,we develop algorithms for solving parameter estimation and detection problems using a WSN.1.To address the challenge of designing inference algorithms for distributed systems under severe resource constraints,we propose a novel joint collaboration-compression framework that first allows the local sensors in the network to collaborate among each other and then only a subset of sensors can communicate with the central server.After collaboration phase is terminated,the local sensors further compress their aggregated information before sharing information with the fusion center.We consider the problem of sequential estimation of a random vector parameter under the proposed collaboration-compression.To take into account the computation limitations of the local sensors we focus on designing easy to implement linear collaboration(via a collaboration matrix)and linear compression(via a compression matrix)strategies for the inference problem.We design near-optimal collaboration and linear compression strategies under power constraints via alternating minimization of the sequential minimum mean square error.The objective function for collaboration design is generally non-convex.We establish correspondence between the sparse collaboration matrix and the non-sparse vector consisting of the nonzero elements of the collaboration matrix.Then,we reformulate and solve the collaboration design problem using quadratically constrained quadratic program(QCQP).The compression design problem is solved using the same methodology.Moreover,we show that our techniques designed for scalar compression can be generalized for compression to arbitrary low dimensional data.We propose two versions of compression design,one centralized scheme where the compression strategies are derived at the FC and decentralized scheme,where the local sensors compute their individual compression strategies independently.Importantly,we show that the proposed methods can also be used for estimating time-varying random vector parameters.Finally,numerical results are provided to demonstrate the effectiveness of the proposed framework.2.Next,we extend our collaboration-compression framework for solving a random signal detection problem using a resource constrained WSN.First,we formulate the random signal detection problem under the collaboration-compression framework.Then,we design near-optimal collaboration and compression strategies which not only limit overall communication but also obtain the best achievable detection performance.We note that the design of collaboration and compression strategies by directly maximizing the detection performance is intractable.Therefore,to resolve this issue we propose the notion of generalized deflection coefficient(GDC),is a tractable surrogate of Kullback-Leibler divergence(KLD),as the criterion for maximizing the detection performance.Importantly,GDC is easy to compute and can be utilized as an optimization criterion even for non-Gaussian problems where both the means and the variances of the observations under the two hypotheses are different.Consequently,collaboration and compression strategies are jointly designed by alternatively maximizing the GDC after reformulating the design problem as the maximization of the general Rayleigh quotient.We experimentally validate the performance of the proposed collaboration and compression strategies via extensive numerical simulations.3.The two problems discussed above are solved for the case when the channels from the local sensors to the central server are coherent channels,i.e.,the compressed observations from the M local sensors to the central server are observed as the aggregated sum of all the locally compressed observations.We further consider a more general case for the known signal detection problem where the compression observations from the local sensors are forwarded to the FC over orthogonal channels.Specifically,we consider a deterministic signal detection problem via a WSN under the collaboration-compression framework.We design near-optimal collaboration and compression strategies for resource constrained WSN that not only limit the overall communication but also obtains the best achievable detection performance.We further explore the detection problem for both the independent observations and the correlated observations settings.Firstly,we derive the detection performance for the case where the observations received at the local sensors are independent and the network connectivity graph is row orthogonal.We show that the detection performance monotonically increases with the deflection coefficient.Then,we jointly design the collaboration and compression strategies to optimize the detection performance.Specifically,we divide the design problem into two sub-problems,a power allocation problem and a set of the independent design problems of collaboration and compression strategies design with the pre-specified power allocation.We provide the closed form solution for the two sub-problems.Specifically,we obtain the optimal strategies by alternatively optimizing these two sub-problems.Next,we derive the detection performance for the case where the observations received at the local sensors are correlated and the network topology is arbitrary.Under this setting,we design the collaboration and the compression strategies by maximizing the detection performance subject to power and bandwidth constraints.As the optimization problem for maximizing the detection problem is generally intractable,we propose two lower bounds to quantify the detection performance.Instead of maximizing the detection performance directly,we maximize these lower bounds to optimize the detection performance of the network.Moreover,we present the closed form solution for maximizing the one of the lower bounds of the detection performance.In addition,to maximize the other lower bound which is a non-convex optimization problem with nonlinear constraints we introduce an inexact Augmented Lagrangian method to obtain a first order stationary point of the problem.Finally,we validate the performance of the proposed algorithms via numerical simulations.We conclude this dissertation with a summary of the completed work and some potential future research directions.