Compressive Sensing-Based Power Allocation Optimization for Energy Harvesting IoT Nodes

In this paper, we address the problem of optimizing the power allocation at each time slot for energy-harvesting sensors in an IoT system, where each sensor transmits its observation via a coherent multiple access channel, and thus the observation vector received at the fusion center (FC) becomes a compressed version of the original observations. Our goal is to minimize the number of transmissions required by the high-fidelity reconstruction of the original observations in the FC. In this scenario, the power allocation, coupling with the channel effect, constitute an effective measurement matrix in compressive sensing. Because its performance decides the requirement on the number of transmissions, the goal can be achieved through constructing the measurement matrix as good as possible, or equivalently, solving the power optimization allocation problem, subject to the available energy constraints at each sensor. However, the sensors can only obtain unreliable and intermittent available energy, so that the traditional performance metric, i.e., mutual coherence (MC), of the measurement matrix cannot be directly used to guide the optimization, because an “equal-norm columns” assumption is implicitly required, but not satisfied in our scenario due to the available energy constraints. Moreover, this optimization problem is also non-convex. To overcome these obstacles, we first carry out a distortion analysis based on the generalized MC, which abandons the “equal-norm columns” assumption. The theoretical results indicate that the measurement matrix construction can be formulated as an optimization problem that not only minimizes the MC, but also minimizes the maximum and maximizes the minimum of the column norms of the effective matrix. We further transform this problem into a sequence of surrogate convex problems and iteratively find the solution. Numerical results show that the proposed framework improves the tradeoffs between reconstruction accuracy and the number of transmissions over various power allocation strategies. In some cases, where other strategies achieve a probability of exact recovery of below 0.7, the proposed framework can achieve a more than 0.9 probability.