Research on Fast Time–Frequency Reconstruction Algorithm for Wideband Compressive Spectrum Sensing

Cognitive Radio (CR) is widely acknowledged as a pivotal technology for mitigating the scarcity of spectrum resources, with Transform Domain Communication Systems (TDCSs) regarded as one of the primary candidate technologies for CR. However, conventional Wideband Spectrum Sensing (WBSS) techniques utilized in TDCS exhibit limitations and are insufficient for adapting to the current complex electromagnetic environment. This paper tackles the time-frequency reconstruction challenge in WBSS by proposing a fast time-frequency reconstruction (FTFR) algorithm. The proposed algorithm acquires sub-Nyquist samples through the introduction of a Multi-Coset Sampling structure and reconstructs the autocorrelation of signals across various windows through a series of low-complexity operations. It captures the dynamic variations of signals by integrating spectra from adjacent time windows. In comparison to existing time-frequency reconstruction algorithms in WBSS, the proposed algorithm demonstrates reduced computational complexity. Simulation experiments indicate that the FTFR algorithm can effectively reconstruct the time-frequency characteristics of signals and significantly restore the primary temporal and frequency distributions, even in low Signal-to-Noise Ratio (SNR) environments.