Optimal Sensor Collaboration for Parameter Tracking Using Energy Harvesting Sensors

In this paper, we design an optimal sensor collaboration strategy among neighboring nodes while tracking a time-varying parameter using wireless sensor networks in the presence of imperfect communication channels. The sensor network is assumed to be self-powered, where sensors are equipped with energy harvesters that replenish energy from the environment. In order to minimize the mean square estimation error of parameter tracking, we propose an online sensor collaboration policy subject to real-time energy harvesting constraints. The proposed energy allocation strategy is computationally light and only relies on the second-order statistics of the system parameters. For this, we first consider an offline non-convex optimization problem, which is solved exactly using semidefinite programming. Based on the offline solution, we design an online power allocation policy that requires minimal online computation and satisfies the dynamics of energy flow at each sensor. We prove that the proposed online policy is asymptotically equivalent to the optimal offline solution and show its convergence rate and robustness. We empirically show that the estimation performance of the proposed online scheme is better than that of the online scheme when channel state information about the dynamical system is available in the low SNR regime. Numerical results are conducted to demonstrate the effectiveness of our approach

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

Training Optimization for Energy Harvesting Communication Systems

Energy harvesting (EH) has recently emerged as an effective way to solve the lifetime challenge of wireless sensor networks, as it can continuously harvest energy from the environment. Unfortunately, it is challenging to guarantee a satisfactory short-term performance in EH communication systems because the harvested energy is sporadic. In this paper, we consider the channel training optimization problem in EH communication systems, i.e., how to obtain accurate channel state information to improve the communication performance. In contrast to conventional communication systems, the optimization of the training power and training period in EH communication systems is a coupled problem, which makes such optimization very challenging. We shall formulate the optimal training design problem for EH communication systems, and propose two solutions that adaptively adjust the training period and power based on either the instantaneous energy profile or the average energy harvesting rate. Numerical and simulation results will show that training optimization is important in EH communication systems. In particular, it will be shown that for short block lengths, training optimization is critical. In contrast, for long block lengths, the optimal training period is not too sensitive to the value of the block length nor to the energy profile. Therefore, a properly selected fixed training period value can be used.Comment: 6 pages, 5 figures, Globecom 201

Max-min Fair Beamforming for SWIPT Systems with Non-linear EH Model

We study the beamforming design for multiuser systems with simultaneous wireless information and power transfer (SWIPT). Employing a practical non-linear energy harvesting (EH) model, the design is formulated as a non-convex optimization problem for the maximization of the minimum harvested power across several energy harvesting receivers. The proposed problem formulation takes into account imperfect channel state information (CSI) and a minimum required signal-to-interference-plus-noise ratio (SINR). The globally optimal solution of the design problem is obtained via the semidefinite programming (SDP) relaxation approach. Interestingly, we can show that at most one dedicated energy beam is needed to achieve optimality. Numerical results demonstrate that with the proposed design a significant performance gain and improved fairness can be provided to the users compared to two baseline schemes.Comment: Invited paper, IEEE VTC 2017, Fall, Toronto, Canad