Using FFT to reduce the computational complexity of sub-Nyquist sampling based wideband spectrum sensing

Abstract

Sub-Nyquist sampling based wideband spectrum sensing can usually be summarized as two steps. The first step estimates the signal power spectrum. The second step uses the energy detection method to make a decision. The traditional method usually adopts the least square algorithm to estimate the power spectrum. In order to reduce the computational complexity of the power spectrum estimation, a novel algorithm is proposed to replace the least square algorithm. We find the system matrix of Multi-Coset Sampling (MCS) based power spectrum estimation has a special structure. Its row vectors are all selected from the row vectors of the Discrete Fourier Transform (DFT) matrix. We exploit this special structure and use Fast Fourier Transform (FFT) to reduce the computational complexity of power spectrum estimation. Simulation shows the proposed algorithm can achieve the spectrum sensing performance similar to the traditional method at much lower computational complexity.