Performance bounds for remote estimation with an energy harvesting sensor

Self Cite

We consider the remote estimation of a time-correlated signal using an energy harvesting (EH) sensor.The sensor observes the unknown signal and communicates its observations to a remote fusion center using an amplify-and-forward strategy. We consider the design of optimal power allocation strategies in order to minimize the mean-square error at the fusion center. Contrary to the traditional approaches, the degree of correlation between the signal values constitutes an important aspect of our formulation. We provide the optimal power allocation strategies for a number of illustrative scenarios. We show that the most majorized power allocation strategy, i.e. the power allocation as balanced as possible, is optimal for the cases of circularly wide-sense stationary (c.w.s.s.) signals with a static correlation coefficient, and sampled low-pass c.w.s.s. signals for a static channel. We show that the optimal strategy can be characterized as a water-filling type solution for sampled low-pass c.w.s.s. signals for a fading channel.Motivated by the high-complexity of the numerical solution of the optimization problem, we propose low-complexity policies for the general scenario. Numerical evaluations illustrate the close performance of these low-complexity policies to that of the optimal policies, and demonstrate the effect of the EH constraints and the degree of freedom of the signal.

Section: E Problem Statementmentioning

confidence: 99%

“…Here, (29) follows from the fact that F s and D are unitary matrices. In (31), we have used the fact that σ 2 x = P x /n.…”

Section: Remark 31: Regardless Of the Value Of ρ Ie The Level Of mentioning

confidence: 99%

Transmission Strategies for Remote Estimation With an Energy Harvesting Sensor

Özçelikkale

McKelvey

Viberg

2017

Self Cite

“…the online scheme. A preliminary version of this setup is considered in [34], where energy arrival process is restricted to be a Bernoulli process and signal model is restricted to circularly wide-sense stationary signals.…”

Section: B Contributionsmentioning

confidence: 99%

“…If (38) holds, the matrix U † s GU s is invertible with probability at least 1 − δ. Hence, the meansquare error will be zero in (34). Note that (38) is derived under the assumption that support is fixed and known, as in our set-up.…”

Section: Connections To Compressive Sensingmentioning

confidence: 99%

Remote Estimation of Correlated Sources Under Energy Harvesting Constraints

Özçelikkale

McKelvey

Viberg

2018

Self Cite

Remote estimation with an energy harvesting sensor with a limited data and energy buffer is considered. The sensor node observes an unknown temporally correlated field and communicates its observations to a remote fusion center using the energy it harvested. The fusion center employs linear minimum mean-square error (LMMSE) estimation to reconstruct the unknown field. We provide performance guarantees for the estimation error under a block transmission scheme, where at each transmission block, data and energy buffers are completely emptied. Our bounds provide insights into how statistical properties of the energy harvesting process and buffer sizes may affect the estimation error. In particular, these bounds suggest insensitivity of the performance to buffer sizes for signals with low degree of freedom and suggest performance improvements with increasing buffer sizes for signals with relatively higher degree of freedom. Depending only on the mean, variance and finite support of the energy arrival process, these results provide insights for the energy and data buffer sizes for deployment in future energy harvesting wireless sensing systems.

“…In fact, both the reliability and the efficiency of extracting information from the recovered samples are dominated by the distortion of the network. In these works, the fusion center tries to recover the uncoded signals using mean-squared error (MSE) estimators [14], [15] or best linear unbiased estimators (BLUE) [17], [18]. Moreover, since the environmental information collected by adjacent nodes is highly correlated with each other, the energy efficiency of the network can be increased by removing the redundancy among these samples using distributed lossy source coding, i.e., the rate-distortion theory for multi-source networks [19].…”

Section: Introductionmentioning

confidence: 99%

Optimal Power Control for Transmitting Correlated Sources With Energy Harvesting Constraints

Dong

Chen

Wang

et al. 2018

Abstract-We investigate the weighted-sum distortion minimization problem in transmitting two correlated Gaussian sources over Gaussian channels using two energy harvesting nodes. To this end, we develop offline and online power control policies to optimize the transmit power of the two nodes. In the offline case, we cast the problem as a convex optimization and investigate the structure of the optimal solution. We also develop a generalized water-filling based power allocation algorithm to obtain the optimal solution efficiently. For the online case, we quantify the distortion of the system using a cost function and show that the expected cost equals the expected weightedsum distortion. Based on Banach's fixed point theorem, we further propose a geometrically converging algorithm to find the minimum cost via simple iterations. Simulation results show that our online power control outperforms the greedy power control where each node uses all the available energy in each slot and performs close to that of the proposed offline power control. Moreover, the performance of our offline power control almost coincides with the performance limit of the system.