Parallel Nonuniform Discrete Fourier Transform (P-NDFT) Over a Random Wireless Sensor Network

Reduced execution time and increased power efficiency are important objectives in the distributed execution of collaborative signal processing tasks over wireless sensor networks (WSNs). Meanwhile, Fourier transforms are among the most widely used frequency analysis tools in WSNs for studying the behavior of sensed phenomena. Several energy-efficient in-network Fourier transform computation algorithms have been proposed for WSNs. Most of these works assume that the sensors are equally spaced over a one-dimensional (1D) region. However, in practice, the sensors are usually randomly distributed over a two-dimensional (2D) plane. Consequently, the conventional 2D Fast Fourier Transform (FFT) designed for data sampled on a uniform grid is not applicable in such environments. We address this problem by designing a distributed hybrid structure consisting of local Non-equispaced Discrete Fourier Transform (NDFT) and global FFT computations. First, the NDFT method is applied within suitably selected clusters to obtain the initial uniform Fourier coefficients within allowable estimation error bounds. We investigate both classical linear and generalized interpolation methods for computing the NDFT coefficients within each cluster. Second, a separable 2D FFT is applied over all clusters using our proposed energy-efficient 1D FFT computation method, which reduces communication costs by employing a novel binary representation mapping strategy for data exchanges between sensors. The proposed techniques are implemented on the SIDnet-SWANS platform, and the tradeoffs between communication cost, execution time, and energy consumption are studied.