Decentralized Estimation over Orthogonal Multiple-access Fading Channels in Wireless Sensor Networks - Optimal and Suboptimal Estimators

Optimal and suboptimal decentralized estimators in wireless sensor networks (WSNs) over orthogonal multiple-access fading channels are studied in this paper. Considering multiple-bit quantization before digital transmission, we develop maximum likelihood estimators (MLEs) with both known and unknown channel state information (CSI). When training symbols are available, we derive a MLE that is a special case of the MLE with unknown CSI. It implicitly uses the training symbols to estimate the channel coefficients and exploits the estimated CSI in an optimal way. To reduce the computational complexity, we propose suboptimal estimators. These estimators exploit both signal and data level redundant information to improve the estimation performance. The proposed MLEs reduce to traditional fusion based or diversity based estimators when communications or observations are perfect. By introducing a general message function, the proposed estimators can be applied when various analog or digital transmission schemes are used. The simulations show that the estimators using digital communications with multiple-bit quantization outperform the estimator using analog-and-forwarding transmission in fading channels. When considering the total bandwidth and energy constraints, the MLE using multiple-bit quantization is superior to that using binary quantization at medium and high observation signal-to-noise ratio levels

Estimation in Phase-Shift and Forward Wireless Sensor Networks

We consider a network of single-antenna sensors that observe an unknown deterministic parameter. Each sensor applies a phase shift to the observation and the sensors simultaneously transmit the result to a multi-antenna fusion center (FC). Based on its knowledge of the wireless channel to the sensors, the FC calculates values for the phase factors that minimize the variance of the parameter estimate, and feeds this information back to the sensors. The use of a phase-shift-only transmission scheme provides a simplified analog implementation at the sensor, and also leads to a simpler algorithm design and performance analysis. We propose two algorithms for this problem, a numerical solution based on a relaxed semidefinite programming problem, and a closed-form solution based on the analytic constant modulus algorithm. Both approaches are shown to provide performance close to the theoretical bound. We derive asymptotic performance analyses for cases involving large numbers of sensors or large numbers of FC antennas, and we also study the impact of phase errors at the sensor transmitters. Finally, we consider the sensor selection problem, in which only a subset of the sensors is chosen to send their observations to the FC.Comment: 28 pages, 5 figures, accepted by IEEE Transactions on Signal Processing, Apr. 201

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

Massive MIMO for Wireless Sensing with a Coherent Multiple Access Channel

We consider the detection and estimation of a zero-mean Gaussian signal in a wireless sensor network with a coherent multiple access channel, when the fusion center (FC) is configured with a large number of antennas and the wireless channels between the sensor nodes and FC experience Rayleigh fading. For the detection problem, we study the Neyman-Pearson (NP) Detector and Energy Detector (ED), and find optimal values for the sensor transmission gains. For the NP detector which requires channel state information (CSI), we show that detection performance remains asymptotically constant with the number of FC antennas if the sensor transmit power decreases proportionally with the increase in the number of antennas. Performance bounds show that the benefit of multiple antennas at the FC disappears as the transmit power grows. The results of the NP detector are also generalized to the linear minimum mean squared error estimator. For the ED which does not require CSI, we derive optimal gains that maximize the deflection coefficient of the detector, and we show that a constant deflection can be asymptotically achieved if the sensor transmit power scales as the inverse square root of the number of FC antennas. Unlike the NP detector, for high sensor power the multi-antenna ED is observed to empirically have significantly better performance than the single-antenna implementation. A number of simulation results are included to validate the analysis.Comment: 32 pages, 6 figures, accepted by IEEE Transactions on Signal Processing, Feb. 201