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

## TL;DR

This paper introduces a new algorithm for efficiently reconstructing time-frequency signals in cognitive radio systems, improving performance even in noisy environments.

## Contribution

The novel FTFR algorithm reduces computational complexity for wideband spectrum sensing in cognitive radio.

## Key findings

- The FTFR algorithm uses multi-coset sampling to acquire sub-Nyquist samples for signal reconstruction.
- The algorithm effectively restores time-frequency characteristics even in low SNR conditions.
- It outperforms existing methods in reconstructing temporal and frequency distributions.

## Abstract

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.