Reconstruction of Correlated Sources With Energy Harvesting Constraints in Delay-Constrained and Delay-Tolerant Communication Scenarios

Abstract

In this paper, we investigate the reconstruction of time-correlated sources in a point-to-point communications scenario comprising an energy-harvesting sensor and a Fusion Center (FC). Our goal is to minimize the average distortion in the reconstructed observations by using data from previously encoded sources as side information. First, we analyze a delayconstrained scenario, where the sources must be reconstructed before the next time slot. We formulate the problem in a convex optimization framework and derive the optimal transmission (i.e., power and rate allocation) policy. To solve this problem, we propose an iterative algorithm based on the subgradient method. Interestingly, the solution to the problem consists of a coupling between a two-dimensional directional water-filling algorithm (for power allocation) and a reverse water-filling algorithm (for rate allocation). Then we find a more general solution to this problem in a delay-tolerant scenario where the time horizon for source reconstruction is extended to multiple time slots. Finally, we provide some numerical results that illustrate the impact of delay and correlation in the power and rate allocation policies, and in the resulting reconstruction distortion. We also discuss the performance gap exhibited by a heuristic online policy derived from the optimal (offline) one.

Stochastic Routing and Scheduling Policies for Energy Harvesting Communication Networks

“…Then, substituting the battery dynamics given by (9) in the energy causality constraint (8) and then taking the ergodic limits on both sides of the inequality, we obtain the following average constraint in the routing variables k∈K j∈Ni…”

“…Assuming data and energy arrival rates satisfying (12b) and (12c) exist, the goal is to design an algorithm such that the instantaneous routing variables r k ij [t] satisfy E r k ij [t] = r k ij and the constraints (1) and (8) are satisfied for all time slots. However, the use of the average energy constraint (12c) presents a causality problem, as a solution satisfying (12c) does not guarantee that the energy causality constraint in (8) is satisfied for all time slots. In order to circumvent this, we propose the introduction of the following modified optimization problem maximize k,j r k ij ≤1,…”

“…This modification is such that the instantaneous values of the dual variables generated by Algorithm 1 can be shown to be bounded above. In turn, having bounded dual variables allows us to establish conditions onx k i that ensure that the energy causality constraints (8) are satisfied for all time slots as shown in Proposition 1. The dual variables associated with energy constraints that would be generated by Algorithm 1 could become arbitrarily large if we write a stochastic dual descent algorithm for the original problem in (12).…”

Remote Estimation of Correlated Sources Under Energy Harvesting Constraints

“…In addition to providing a reasonable model for physical fields, sparsity can be utilized to compensate for the unreliable nature of the energy sources in an EH system. Yet, for EH systems, structural results that directly exploit sparsity or correlation characteristics are available only for a limited number of scenarios, such as estimation of a single parameter [24][25][26], Markov sources [21], [27], [28], circularly wide-sense stationary signals [29], [30], two correlated Gaussian variables [31], and i.i.d. Gaussian sources, as a result of the findings of, for instance, [17][18][19][20], [32], [33].…”

Random access policies for wireless networked control systems with energy harvesting sensors

“…The study of communication systems powered by energy harvesting has recently received considerable attention. Current results available in the literature range from throughput maximization [3]- [6], source-channel coding [7]- [10], estimation [11]- [13], and others (see [14] for a comprehensive overview). However, in general, limited attention has been given to the use of energy harvesting technologies in control applications.…”