Optimal Energy Allocation for Kalman Filtering over Packet Dropping Links with Imperfect Acknowledgments and Energy Harvesting Constraints

This paper presents a design methodology for optimal transmission energy allocation at a sensor equipped with energy harvesting technology for remote state estimation of linear stochastic dynamical systems. In this framework, the sensor measurements as noisy versions of the system states are sent to the receiver over a packet dropping communication channel. The packet dropout probabilities of the channel depend on both the sensor's transmission energies and time varying wireless fading channel gains. The sensor has access to an energy harvesting source which is an everlasting but unreliable energy source compared to conventional batteries with fixed energy storages. The receiver performs optimal state estimation with random packet dropouts to minimize the estimation error covariances based on received measurements. The receiver also sends packet receipt acknowledgments to the sensor via an erroneous feedback communication channel which is itself packet dropping. The objective is to design optimal transmission energy allocation at the energy harvesting sensor to minimize either a finite-time horizon sum or a long term average (infinite-time horizon) of the trace of the expected estimation error covariance of the receiver's Kalman filter. These problems are formulated as Markov decision processes with imperfect state information. The optimal transmission energy allocation policies are obtained by the use of dynamic programming techniques. Using the concept of submodularity, the structure of the optimal transmission energy policies are studied. Suboptimal solutions are also discussed which are far less computationally intensive than optimal solutions. Numerical simulation results are presented illustrating the performance of the energy allocation algorithms.Comment: Submitted to IEEE Transactions on Automatic Control. arXiv admin note: text overlap with arXiv:1402.663

Stochastic Differential Games and Energy-Efficient Power Control

One of the contributions of this work is to formulate the problem of energy-efficient power control in multiple access channels (namely, channels which comprise several transmitters and one receiver) as a stochastic differential game. The players are the transmitters who adapt their power level to the quality of their time-varying link with the receiver, their battery level, and the strategy updates of the others. The proposed model not only allows one to take into account long-term strategic interactions but also long-term energy constraints. A simple sufficient condition for the existence of a Nash equilibrium in this game is provided and shown to be verified in a typical scenario. As the uniqueness and determination of equilibria are difficult issues in general, especially when the number of players goes large, we move to two special cases: the single player case which gives us some useful insights of practical interest and allows one to make connections with the case of large number of players. The latter case is treated with a mean-field game approach for which reasonable sufficient conditions for convergence and uniqueness are provided. Remarkably, this recent approach for large system analysis shows how scalability can be dealt with in large games and only relies on the individual state information assumption.Comment: The final publication is available at http://www.springerlink.com/openurl.asp?genre=article\&id=doi:10.1007/s13235-012-0068-

Partner selection in indoor-to-outdoor cooperative networks: an experimental study

In this paper, we develop a partner selection protocol for enhancing the network lifetime in cooperative wireless networks. The case-study is the cooperative relayed transmission from fixed indoor nodes to a common outdoor access point. A stochastic bivariate model for the spatial distribution of the fading parameters that govern the link performance, namely the Rician K-factor and the path-loss, is proposed and validated by means of real channel measurements. The partner selection protocol is based on the real-time estimation of a function of these fading parameters, i.e., the coding gain. To reduce the complexity of the link quality assessment, a Bayesian approach is proposed that uses the site-specific bivariate model as a-priori information for the coding gain estimation. This link quality estimator allows network lifetime gains almost as if all K-factor values were known. Furthermore, it suits IEEE 802.15.4 compliant networks as it efficiently exploits the information acquired from the receiver signal strength indicator. Extensive numerical results highlight the trade-off between complexity, robustness to model mismatches and network lifetime performance. We show for instance that infrequent updates of the site-specific model through K-factor estimation over a subset of links are sufficient to at least double the network lifetime with respect to existing algorithms based on path loss information only.Comment: This work has been submitted to IEEE Journal on Selected Areas in Communications in August 201