Compressed Sensing of IR-UWB Wireless Sensor Network Data Based on Two-Dimensional Measurements

A novel Compressed sensing (CS) method based on two-dimensional measurements is proposed that can be effectively utilized in Impulse radio ultra-wideband wireless sensor networks (IR-UWB WSNs) to significantly reduce the energy consumption and sampling rate in sensor data transferring. We start by establishing the CS measurement model by taking both spatial and temporal correlations of Wireless sensor network (WSN) data into account. Since our model incorporates a new type of measurement matrix: the block quasi-Toeplitz structured matrix, we derive the Restricted isometry property (RIP) of the block quasi-Toeplitz structured matrix to ensure the performance of the two-dimensional recovery of WSNs data. We substantiate our mathematical analysis by numerical examples in the context of ideal spares vector and real WSN data, and results demonstrate that the approach achieves significantly saving of energy and sampling rate with small reconstruction error.