Source-Channel Communication in Sensor Networks

Sensors acquire data, and communicate this to an interested party. The arising coding problem is often split into two parts: First, the sensors compress their respective acquired signals, potentially applying the concepts of distributed source coding. Then, they communicate the compressed version to the interested party, the goal being not to make any errors. This coding paradigm is inspired by Shannon’s separation theorem for point-to-point communication, but it leads to suboptimal performance in general network topologies. The optimal performance for the general case is not known. In this paper, we propose an alternative coding paradigm based on joint source-channel coding. This coding paradigm permits to determine the optimal performance for a class of sensor networks, and shows how to achieve it. For sensor networks outside this class, we argue that the goal of the coding system could be to approach our condition for op- timal performance as closely as possible. This is supported by examples for which our coding paradigm significantly outperforms the traditional separation-based coding paradigm. In particular, for a Gaussian exam- ple considered in this paper, the distortion of the best coding scheme according to the separation paradigm decreases like 1/logM, while for our coding paradigm, it decreases like 1/M, where M is the total number of sensors

Simultaneous Sparse Approximation Using an Iterative Method with Adaptive Thresholding

This paper studies the problem of Simultaneous Sparse Approximation (SSA). This problem arises in many applications which work with multiple signals maintaining some degree of dependency such as radar and sensor networks. In this paper, we introduce a new method towards joint recovery of several independent sparse signals with the same support. We provide an analytical discussion on the convergence of our method called Simultaneous Iterative Method with Adaptive Thresholding (SIMAT). Additionally, we compare our method with other group-sparse reconstruction techniques, i.e., Simultaneous Orthogonal Matching Pursuit (SOMP), and Block Iterative Method with Adaptive Thresholding (BIMAT) through numerical experiments. The simulation results demonstrate that SIMAT outperforms these algorithms in terms of the metrics Signal to Noise Ratio (SNR) and Success Rate (SR). Moreover, SIMAT is considerably less complicated than BIMAT, which makes it feasible for practical applications such as implementation in MIMO radar systems

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

Optimal Power Allocation for Parameter Tracking in a Distributed Amplify-and-Forward Sensor Network

We consider the problem of optimal power allocation in a sensor network where the sensors observe a dynamic parameter in noise and coherently amplify and forward their observations to a fusion center (FC). The FC uses the observations in a Kalman filter to track the parameter, and we show how to find the optimal gain and phase of the sensor transmissions under both global and individual power constraints in order to minimize the mean squared error (MSE) of the parameter estimate. For the case of a global power constraint, a closed-form solution can be obtained. A numerical optimization is required for individual power constraints, but the problem can be relaxed to a semidefinite programming problem (SDP), and we show that the optimal result can be constructed from the SDP solution. We also study the dual problem of minimizing global and individual power consumption under a constraint on the MSE. As before, a closed-form solution can be found when minimizing total power, while the optimal solution is constructed from the output of an SDP when minimizing the maximum individual sensor power. For purposes of comparison, we derive an exact expression for the outage probability on the MSE for equal-power transmission, which can serve as an upper bound for the case of optimal power control. Finally, we present the results of several simulations to show that the use of optimal power control provides a significant reduction in either MSE or transmit power compared with a non-optimized approach (i.e., equal power transmission).Comment: 28 pages, 6 figures, accepted by IEEE Transactions on Signal Processing, Jan. 201

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

Robust Distributed Estimation over Multiple Access Channels with Constant Modulus Signaling

A distributed estimation scheme where the sensors transmit with constant modulus signals over a multiple access channel is considered. The proposed estimator is shown to be strongly consistent for any sensing noise distribution in the i.i.d. case both for a per-sensor power constraint, and a total power constraint. When the distributions of the sensing noise are not identical, a bound on the variances is shown to establish strong consistency. The estimator is shown to be asymptotically normal with a variance (AsV) that depends on the characteristic function of the sensing noise. Optimization of the AsV is considered with respect to a transmission phase parameter for a variety of noise distributions exhibiting differing levels of impulsive behavior. The robustness of the estimator to impulsive sensing noise distributions such as those with positive excess kurtosis, or those that do not have finite moments is shown. The proposed estimator is favorably compared with the amplify and forward scheme under an impulsive noise scenario. The effect of fading is shown to not affect the consistency of the estimator, but to scale the asymptotic variance by a constant fading penalty depending on the fading statistics. Simulations corroborate our analytical results.Comment: 28 pages, 10 figures, submitted to IEEE Transactions on Signal Processing for consideratio

One-bit Distributed Sensing and Coding for Field Estimation in Sensor Networks

This paper formulates and studies a general distributed field reconstruction problem using a dense network of noisy one-bit randomized scalar quantizers in the presence of additive observation noise of unknown distribution. A constructive quantization, coding, and field reconstruction scheme is developed and an upper-bound to the associated mean squared error (MSE) at any point and any snapshot is derived in terms of the local spatio-temporal smoothness properties of the underlying field. It is shown that when the noise, sensor placement pattern, and the sensor schedule satisfy certain weak technical requirements, it is possible to drive the MSE to zero with increasing sensor density at points of field continuity while ensuring that the per-sensor bitrate and sensing-related network overhead rate simultaneously go to zero. The proposed scheme achieves the order-optimal MSE versus sensor density scaling behavior for the class of spatially constant spatio-temporal fields.Comment: Fixed typos, otherwise same as V2. 27 pages (in one column review format), 4 figures. Submitted to IEEE Transactions on Signal Processing. Current version is updated for journal submission: revised author list, modified formulation and framework. Previous version appeared in Proceedings of Allerton Conference On Communication, Control, and Computing 200