基于压缩感知的加权宽带谱重构算法

压缩感知利用宽带无线信号的频域稀疏特性，能够在低于奈奎斯特速率的采样下利用少量观测数据实现宽带频谱估计和空穴检测。但相关频谱压缩感知算法的性能并不理想，为了实现宽带信道的快速准确感知，本文基于宽带信道的时频统计特性，在去噪基追踪算法(BPDN)的基础上提出了一种优化的加权去噪算法(WBPDN)。该算法利用子频段历史平均功率密度水平来构建各子频段权重以优化目标函数，改善算法性能。实验结果表明:该算法能通过少量观测数据准确重构宽带信道的谱估计，且比传统的BPDN和OMP算法具有更好的压缩性能及更小的重构误差；另外加权后的算法收敛速度更快，显著减少了算法所需的运行时间。 

Weighted compressive sensing for wireless wideband spectrum sensing

Compressive sensing (CS) can achieve spectral detection and estimation from far fewer samples at sub-Nyquist sampling rates. However, efforts to design CS reconstruction algorithms for wideband spectrum sensing are very limited. Considering the characteristics of spectrum distribution are partially known in advance, we proposed a new algorithm, called weighted basis pursuit denoising(WBPDN), based on the famous -minimization algorithm in order to add prior information on the support of the sparse domain. The WBPDN incorporates the statistical properties of spectrum usages to reweight the coefficients of the previous -minimization algorithm. This underlying optimization corresponds to encouraging nonzero coefficients to gain performance improvement. There are empirical evidences of the fact that the proposed algorithm not only guarantees accurate spectral estimation from fewer measurements, but also outperforms basis pursuit denoising (BPDN) and OMP in terms of measurements requirements and reconstruction error. Moreover, WBPDN has faster convergence speed and significantly reduces the computation time required by BPDN.