Distributed Estimation of a Parametric Field Using Sparse Noisy Data

The problem of distributed estimation of a parametric physical field is stated as a maximum likelihood estimation problem. Sensor observations are distorted by additive white Gaussian noise. Prior to data transmission, each sensor quantizes its observation to $M$ levels. The quantized data are then communicated over parallel additive white Gaussian channels to a fusion center for a joint estimation. An iterative expectation-maximization (EM) algorithm to estimate the unknown parameter is formulated, and its linearized version is adopted for numerical analysis. The numerical examples are provided for the case of the field modeled as a Gaussian bell. The dependence of the integrated mean-square error on the number of quantization levels, the number of sensors in the network and the SNR in observation and transmission channels is analyzed.Comment: to appear at Milcom-201

Distributed Quantization for Compressed Sensing

We study distributed coding of compressed sensing (CS) measurements using vector quantizer (VQ). We develop a distributed framework for realizing optimized quantizer that enables encoding CS measurements of correlated sparse sources followed by joint decoding at a fusion center. The optimality of VQ encoder-decoder pairs is addressed by minimizing the sum of mean-square errors between the sparse sources and their reconstruction vectors at the fusion center. We derive a lower-bound on the end-to-end performance of the studied distributed system, and propose a practical encoder-decoder design through an iterative algorithm.Comment: 5 Pages, Accepted for presentation in ICASSP 201

Limited-Feedback-Based Channel-Aware Power Allocation for Linear Distributed Estimation

This paper investigates the problem of distributed best linear unbiased estimation (BLUE) of a random parameter at the fusion center (FC) of a wireless sensor network (WSN). In particular, the application of limited-feedback strategies for the optimal power allocation in distributed estimation is studied. In order to find the BLUE estimator of the unknown parameter, the FC combines spatially distributed, linearly processed, noisy observations of local sensors received through orthogonal channels corrupted by fading and additive Gaussian noise. Most optimal power-allocation schemes proposed in the literature require the feedback of the exact instantaneous channel state information from the FC to local sensors. This paper proposes a limited-feedback strategy in which the FC designs an optimal codebook containing the optimal power-allocation vectors, in an iterative offline process, based on the generalized Lloyd algorithm with modified distortion functions. Upon observing a realization of the channel vector, the FC finds the closest codeword to its corresponding optimal power-allocation vector and broadcasts the index of the codeword. Each sensor will then transmit its analog observations using its optimal quantized amplification gain. This approach eliminates the requirement for infinite-rate digital feedback links and is scalable, especially in large WSNs.Comment: 5 Pages, 3 Figures, 1 Algorithm, Forty Seventh Annual Asilomar Conference on Signals, Systems, and Computers (ASILOMAR 2013

Power Allocation for Distributed BLUE Estimation with Full and Limited Feedback of CSI

This paper investigates the problem of adaptive power allocation for distributed best linear unbiased estimation (BLUE) of a random parameter at the fusion center (FC) of a wireless sensor network (WSN). An optimal power-allocation scheme is proposed that minimizes the $L^2$-norm of the vector of local transmit powers, given a maximum variance for the BLUE estimator. This scheme results in the increased lifetime of the WSN compared to similar approaches that are based on the minimization of the sum of the local transmit powers. The limitation of the proposed optimal power-allocation scheme is that it requires the feedback of the instantaneous channel state information (CSI) from the FC to local sensors, which is not practical in most applications of large-scale WSNs. In this paper, a limited-feedback strategy is proposed that eliminates this requirement by designing an optimal codebook for the FC using the generalized Lloyd algorithm with modified distortion metrics. Each sensor amplifies its analog noisy observation using a quantized version of its optimal amplification gain, which is received by the FC and used to estimate the unknown parameter.Comment: 6 pages, 3 figures, to appear at the IEEE Military Communications Conference (MILCOM) 201

Network Code Design for Orthogonal Two-hop Network with Broadcasting Relay: A Joint Source-Channel-Network Coding Approach

This paper addresses network code design for robust transmission of sources over an orthogonal two-hop wireless network with a broadcasting relay. The network consists of multiple sources and destinations in which each destination, benefiting the relay signal, intends to decode a subset of the sources. Two special instances of this network are orthogonal broadcast relay channel and the orthogonal multiple access relay channel. The focus is on complexity constrained scenarios, e.g., for wireless sensor networks, where channel coding is practically imperfect. Taking a source-channel and network coding approach, we design the network code (mapping) at the relay such that the average reconstruction distortion at the destinations is minimized. To this end, by decomposing the distortion into its components, an efficient design algorithm is proposed. The resulting network code is nonlinear and substantially outperforms the best performing linear network code. A motivating formulation of a family of structured nonlinear network codes is also presented. Numerical results and comparison with linear network coding at the relay and the corresponding distortion-power bound demonstrate the effectiveness of the proposed schemes and a promising research direction.Comment: 27 pages, 9 figures, Submited to IEEE Transaction on Communicatio