Power-efficient nonuniform 2-D fourier analysis using compressive sensing in WSNs

Nonuniform Discrete Fourier Transform (NDFT) has been well-investigated for performing fast computation of the frequency content of nonequispaced data samples. This nonuniform formulation is also well-suited for Fourier analysis of data samples collected in randomly deployed wireless sensors. However, most of the existing NDFT formulations employ global communication patterns and thus are inefficient in terms of energy consumption and execution time for in-network realization of NDFT. In this paper, we investigate NDFT implementation that leverages compressive sensing (CS) to reduce the amount of data and global communication, thus allowing the use of a few random measurements to adequately represent sparse signal. Our main idea is to organize 2D random deployment of sensors into a hierarchy of clusters. A local interpolation step is performed in the clusters at the lowest level to convert a nonuniform grid into a uniform grid. The global 2D Fast Fourier Transform (FFT) is then implemented using a multiresolution data aggregation architecture and exploiting CS to reduce data transmission. Using theoretical analysis as well as SIDnet-SWANS based simulations, we demonstrate significant advantages of the proposed method over existing state of the art, in terms of execution time, transmission energy efficiency, signal-to-noise ratio and communication overhead.