| Summary: | This paper proposes an approach toward solving an issue pertaining to measuring compressible data in large-scale energy-harvesting wireless sensor networks with channel fading. We consider a scenario in which N sensors observe hidden phenomenon values, transmit their observations using amplify-and-forward protocol over fading channels to a fusion center (FC), and the FC needs to choose a number of sensors to collect data and recover them according to the desired approximation error using the compressive sensing. In order to reduce the communication cost, sparse random matrices are exploited in the pre-processing procedure. We first investigate the sparse representation for sensors with regard to recovery accuracy. Then, we present the construction of sparse random projection matrices based on the fact that the energy consumption can vary across the energy harvesting sensor nodes. The key ingredient is the sparsity level of the random projection, which can greatly reduce the communication costs. The corresponding number of measurements is chosen according to the desired approximation error. Analysis and simulation results validate the potential of the proposed approach.
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