Estimation Diversity and Energy Efficiency in Distributed Sensing

Distributed estimation based on measurements from multiple wireless sensors is investigated. It is assumed that a group of sensors observe the same quantity in independent additive observation noises with possibly different variances. The observations are transmitted using amplify-and-forward (analog) transmissions over non-ideal fading wireless channels from the sensors to a fusion center, where they are combined to generate an estimate of the observed quantity. Assuming that the Best Linear Unbiased Estimator (BLUE) is used by the fusion center, the equal-power transmission strategy is first discussed, where the system performance is analyzed by introducing the concept of estimation outage and estimation diversity, and it is shown that there is an achievable diversity gain on the order of the number of sensors. The optimal power allocation strategies are then considered for two cases: minimum distortion under power constraints; and minimum power under distortion constraints. In the first case, it is shown that by turning off bad sensors, i.e., sensors with bad channels and bad observation quality, adaptive power gain can be achieved without sacrificing diversity gain. Here, the adaptive power gain is similar to the array gain achieved in Multiple-Input Single-Output (MISO) multi-antenna systems when channel conditions are known to the transmitter. In the second case, the sum power is minimized under zero-outage estimation distortion constraint, and some related energy efficiency issues in sensor networks are discussed.Comment: To appear at IEEE Transactions on Signal Processin

Optimal Quantization in Energy-Constrained Sensor Networks under Imperfect Transmission

This paper addresses the optimization of quantization at local sensors under strict energy constraint and imperfect transmission to improve the reconstruction performance at the fusion center in the wireless sensor networks (WSNs). We present optimized quantization scheme including the optimal quantization bit rate and the optimal transmission power allocation among quantization bits for BPSK signal and binary orthogonal signal with envelope detection, respectively. The optimization of the quantization is formulated as a convex problem and the optimal solution is derived analytically in both cases. Simulation results demonstrate the effectiveness of our proposed quantization schemes

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

On the Effect of Correlated Measurements on the Performance of Distributed Estimation

We address the distributed estimation of an unknown scalar parameter in Wireless Sensor Networks (WSNs). Sensor nodes transmit their noisy observations over multiple access channel to a Fusion Center (FC) that reconstructs the source parameter. The received signal is corrupted by noise and channel fading, so that the FC objective is to minimize the Mean-Square Error (MSE) of the estimate. In this paper, we assume sensor node observations to be correlated with the source signal and correlated with each other as well. The correlation coefficient between two observations is exponentially decaying with the distance separation. The effect of the distance-based correlation on the estimation quality is demonstrated and compared with the case of unity correlated observations. Moreover, a closed-form expression for the outage probability is derived and its dependency on the correlation coefficients is investigated. Numerical simulations are provided to verify our analytic results.Comment: 5 page

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