Transmission Strategies for Remote Estimation With an Energy Harvesting Sensor

Abstract

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.

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].…”

“…[30], where the focus is on the off-line scheme and no high probability results are presented. Together with the off-line results of [30], the performance bounds presented here support the possible flexibility in energy management for sensing of low-pass c.w.s.s. signals under energy harvesting constraints.…”

“…;w NT ] ∈ C N ×1 is modeled as complex proper zero mean with K w = E[ww † ] = σ 2 w I N . The above type of block transmission scheme allows us to spread the energy over multiple signal samples and facilitates connections with uniform power allocation strategies which are optimal for white sources in the offline scheme [17], [30], and the power allocation strategies which match the average arrival rate of the EH process and optimal for white sources in the online scheme [19]. It is also supported by the fact that for devices with low power budgets, it is more energy efficient to send relatively larger amount of data at each transmission [38].…”

“…Remark 3.2: Energy allocations which are as uniform as possible, or alternatively as balanced as possible are optimal for white sources [17], [19], [30]. In our formulation, the data buffer and energy buffer allows us to mimic these uniform-like allocations, where larger buffer sizes allow energy allocations that are more uniform over the whole time duration of interest, i.e.…”

“…As a benchmark for our bounds in Thm. 3.1, we now consider an associated off-line scheme [30]. In particular, we consider the case where amplification factors are not modeled as random variables that depend on the energy arrivals but deterministic variables to be optimized.…”