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In this paper, we investigate a class of distortion outage minimization problems for a wireless sensor network in the presence of an eavesdropper. The observation signals transmitted from the sensors to the fusion center (FC) are overheard by the eavesdropper. Both the FC and the eavesdropper reconstruct minimum mean squared error estimates of the physical quantity observed. We address the problem of transmit power allocation to minimize the distortion outage at the FC, subject to an expected total transmit power constraint across the sensor(s) and a secrecy outage constraint at the eavesdropper. Applying a rigorous probabilistic power allocation technique, we derive power policies for the full channel state information (CSI) case. Suboptimal power control policies are studied for the partial CSI case in order to reduce the high computational cost associated with large numbers of sensors or receive antennas. Numerical results show that significantly improved performance can be achieved by adding multiple receive antennas at the FC. In the case of multiple transmit antennas, the distortion outage at the FC can be dramatically reduced and in some cases completely eliminated, by transmitting the observations on the null space of the eavesdropper's channel or deploying an artificial noise technique, in the full CSI and partial CSI cases, respectively. Refereed/Peer-reviewed

In this paper, we investigate the performance of distributed estimation schemes in a wireless sensor network in the presence of an eavesdropper. The sensors transmit observations to the fusion center (FC), which at the same time are overheard by the eavesdropper. Both the FC and the eavesdropper reconstruct a minimum mean-squared error estimate of the physical quantity observed. We address the problem of transmit power allocation for system performance optimization subject to a total average power constraint on the sensor(s), and a security/secrecy constraint on the eavesdropper. We mainly focus on two scenarios: 1) a single sensor with multiple transmit antennas and 2) multiple sensors with each sensor having a single transmit antenna. For each scenario, given perfect channel state information (CSI) of the FC and full or partial CSI of the eavesdropper, we derive the transmission policies for short-term and long-term cases. For the long-term power allocation case, when the sensor is equipped with multiple antennas, we can achieve zero information leakage in the full CSI case, and dramatically enhance the system performance by deploying the artificial noise technique for the partial CSI case. Asymptotic expressions are derived for the long-term distortion at the FC as the number of sensors or the number of antennas becomes large. In addition, we also consider multiple-sensor multiple-antenna scenario, and simulations show that given the same total number of transmitting antennas the multiple-antenna sensor network is superior to the performance of the multiple-sensor single-antenna network. Refereed/Peer-reviewed

In this paper, we investigate the distortion outage minimization problem for a wireless sensor network (WSN) in the presence of an eavesdropper. The observation signals transmitted from the sensors to the fusion center (FC) are over-heard by the eavesdropper. Both the FC and the eavesdropper reconstruct minimum mean squared error (MMSE) estimates of the physical quantity observed. We address the problem of transmit power allocation to minimize the distortion outage at the FC, subject to a long-term transmit power constraint among the sensors and a secrecy outage constraint at the eavesdropper. Applying a rigorous probabilistic power allocation technique we derive power policies for the full channel state information (CSI) case. Additional suboptimal power control policies are studied for the partial CSI case in order to reduce the high computational cost as the number of sensors or receive antennas grows. Numerical results show better performance can be achieved by adding multiple receive antennas at the FC. Refereed/Peer-reviewed

We study stochastic stability of centralized Kalman filtering for linear time-varying systems equipped with wireless sensors. Transmission is over fading channels where variable channel gains are counteracted by power control to alleviate the effects of packet drops. We establish sufficient conditions for the expected value of the Kalman filter covariance matrix to be exponentially bounded in norm. The conditions obtained are then used to formulate stabilizing power control policies which minimize the total sensor power budget. In deriving the optimal power control laws, both statistical channel information and full channel information are considered. The effect of system instability on the power budget is also investigated for both these cases. (C) 2012 Elsevier Ltd. All rights reserved. Refereed/Peer-reviewed

This paper studies the optimal control of linear systems over continuous valued fading channels. The sensor measurements are sent over a fading wireless channel to a remote controller using the analog amplify and forward technique. The controller then computes a control signal, which is transmitted over another fading channel to the actuator. Under the assumption of full channel state information (CSI) for both wireless links, we derive the optimal LQG control law. In the case where full channel state information is not available but channel statistics are available, we present the optimal linear static estimator and controller. Numerical comparisons are made between the full CSI and statistical CSI solutions. Refereed/Peer-reviewed

This paper studies the outage probability minimization problem for state estimation of linear dynamical systems using multiple sensors, where an estimation outage is defined as an event when the state estimation error exceeds a pre-determined threshold. The sensors amplify-and-forward their measurements (using uncoded analog transmission) to a remote fusion center over wireless fading channels. For stable systems, the resulting infinite horizon problem can be formulated as a constrained average cost Markov decision process (MDP) control problem. A suboptimal power allocation that is less computationally intensive is proposed and numerical results demonstrate very close performance to the power allocation obtained from the solution of the MDP based average cost optimality equation. Motivated by practical considerations, assuming that sensors can transmit with only a finite number of power levels, optimization of the values of these levels is also considered using a stochastic approximation technique. In the case of unstable systems, a finite horizon formulation of the estimation outage minization problem is presented and solved. An extension to the problem of minimization of the expected error covariance is also studied. Refereed/Peer-reviewed

We study stochastic stability for Kalman filtering over fading wireless channels where variable channel gains are counteracted by the use of power control to alleviate the effects of packet drops. The Kalman filter and the controller are located at a single gateway which acquires data from the wireless sensors. We establish sufficient conditions which ensure that the Kalman filter covariance matrix is exponentially bounded in norm. The conditions obtained are then used to formulate stabilizing optimal power allocation laws which minimize the total sensor power budget. In deriving the optimal power allocation laws, both statistical channel information and full channel information are considered. The effect of system instability on the power budget is also investigated for both these cases. Refereed/Peer-reviewed

This paper is concerned with decentralized estimation of a Gaussian source using multiple sensors. We consider a diversity scheme where only the sensor with the best channel sends their measurements over a fading channel to a fusion center, using the analog amplify and forwarding technique. The fusion centre reconstructs an MMSE estimate of the source based on the received measurements. A distributed version of the diversity scheme where sensors decide whether to transmit based only on their local channel information is also considered. We derive asymptotic expressions for the expected distortion (of the MMSE estimate at the fusion centre) of these schemes as the number of sensors becomes large. For comparison, asymptotic expressions for the expected distortion for a coherent multi-access scheme and an orthogonal access scheme are derived. We also study for the diversity schemes, the optimal power allocation for minimizing the expected distortion subject to average total power constraints. The effect of optimizing the probability of transmission on the expected distortion in the distributed scenario is also studied. It is seen that as opposed to the coherent multi-access scheme and the orthogonal scheme (where the expected distortion decays as 1/M, M being the number of sensors), the expected distortion decays only as 1/ln(M) for the diversity schemes. This reduction of the decay rate can be seen as a tradeoff between the simplicity of the diversity schemes and the strict synchronization and large bandwidth requirements for the coherent multi-access and the orthogonal schemes, respectively., Comment: 23 pages

This paper considers a sensor network where single or multiple sensors amplify and forward their measurements of a common linear dynamical system (analog uncoded transmission) to a remote fusion center via noisy fading wireless channels. We show that the expected error covariance (with respect to the fading process) of the time-varying Kalman filter is bounded and converges to a steady state value, based on some earlier results on asymptotic stability of Kalman filters with random parameters. More importantly, we provide explicit expressions for sequences which can be used as upper bounds on the expected error covariance, for specific instances of fading distributions and scalar measurements (per sensor). Numerical results illustrate the effectiveness of these bounds. Refereed/Peer-reviewed