Wireless compressive sensing for energy harvesting sensor nodes over fading channels
2013 IEEE International Conference on Communications (ICC)
We consider the scenario in which multiple sensors send spatially correlated data to the fusion center (FC) via independent Rayleigh-fading channels with additive noise. Assuming that the sensor data is sparse in some basis, we show that the recovery of the signal can be formulated as a compressive sensing (CS) problem. To model the scenario where sensors operate with intermittently available energy that is harvested from the environment, we propose that each sensor transmits independently with
... independently with some probability, and adapts the transmit power to its harvested energy. Due to probabilistic transmissions, the elements of the equivalent sensing matrix are not Gaussian. Since sensors have different energy-harvesting rates and different sensor-to-FC distances, the FC has different receive signal-to-noise ratios (SNRs) for all sensors, referred to as the inhomogeneity of SNRs. Thus, the elements of the sensing matrix are also not identically distributed. We provide guarantees on the number of measurements for reliable reconstruction, by showing that the corresponding sensing matrix satisfies the restricted isometry property (RIP), under some mild conditions. We then compute an achievable spectral efficiency (SE) under an allowable mean-square-error (MSE). Furthermore, we analyze the impact of inhomogeneity on the RIP. Our analysis is corroborated by numerical results.