Spectrum Recovery for Noise-Corrupted Sparse Signal : A Sparse Fourier Transform Approach

The spectrum-sparse signal, which includes a fraction of large Fourier coefficients in frequency domain, is an important signal form that widely adopted in numerous fields. To handle the spectrum-sparse signal with large data sets demanded by big data applications or wideband spectrum sensing, sparse Fourier transform (SFT) has been developed and actively studied in recent years, which exploits the sparsity to circumvent the prohibitive complexity involved in the conventional Fourier transform tools. In this paper, we propose a new SFT algorithm for the robust spectrum recovery from the noise-corrupted time-domain observations. It deploys a set of sensing cells configured with different down-sampling factors, which robustly estimate the non-aliased frequency tones via two steps: coarse estimation and fine localization. Then by jointly utilizing the information from different sensing cells, a reliable-ware recovery scheme is designed to address the aliased frequency tones while avoiding error propagation. Compared with the exiting noise-robust SFT schemes, it is demonstrated from numerical analysis and simulation results that the proposed SFT algorithm can lower the memory occupation and computational burden while retaining high estimation accuracy