基于P-Ifourier观测矩阵的宽带压缩感知方法

针对压缩感知理论在宽带频谱感知领域应用时重构精度差的问题，根据平稳信号在频域所表现出的稀疏特性，提出了一种基于P-Ifourier(Partial-Inverse fourier)观测矩阵的宽带压缩频谱感知方法。新方法首先将频谱感知问题建模为一个典型的压缩感知问题，利用相关性能优良的标准正交傅里叶基构造观测矩阵，使观测矩阵具有良好的重构性能和重构精度。仿真结果表明，相比于高斯随机观测矩阵和嵌入式混沌序列-循环Toeplitz结构观测矩阵，该方法在较低信噪比环境下能够明显降低信号重构的均方误差，并且在相同条件下的重构概率得到了明显改善。

Broadband compressed sensing method based on P-Ifourier observation matrix

Aiming at the problem of poor precision in the application of compressed sensing theory in the field of broadband spectrum sensing, and according to the sparse characteristics of the stationary signal in the frequency domain, this paper developed a broadband compression spectrum sensing method based on P-Ifourier (Partial-Inverse fourier) observation matrix. The new method translated the spectrum sensing problem into a typical compressed sensing problem, and used the standard orthogonal Fourier basis observation matrix which has the excellent incoherence performance to build the observation matrix in order to have good reconstruction performance and reconstruction precision. The simulation results show that compared with the Gaussian random observation matrix and the embedded chaotic sequence - cyclic Toeplitz structure observation matrix, this method can significantly reduce the mean square error of signal reconstruction in the lower SNR environment, and under the same conditions it can significantly improves the probability of reconstruction.