多速率互质采样下的超分辨谱估计方法

摘要

针对稀疏频谱信号的获取和感知问题,提出了一种多速率互质采样下的超分辨谱估计技术.首先对信号进行多通道采样,建立起多速率互质采样下的接收信号模型,并推导了采样频率的最优选取准则.然后基于超分辨理论将不同采样速率下的基带混叠谱估计出来,并给出精确恢复的唯一性定理.在谱重构过程中,为了降低恢复算法的复杂度,又提出了一种支撑集缩减准则.以上方法既避免了栅格划分对重构模型的影响,也克服了有限长时域数据造成的频谱展宽效应,因此可以有效地提高谱估计的精度和分辨率.数据模拟实验验证了上述方法的正确性和有效性.%To effectively acquire and sense signal which is sparse in the frequency domain,a super-resolution spectrum estimation method based on multirate co-prime sampling is proposed.Firstly,the signal is sampled via several sampling channels to construct the receiving model and the optimal sampling frequency selection criterion is given.Then the aliasing baseband of each sampling channel is estimated based on the super-resolution theory and the uniqueness theorem is derived.In the process of frequency spectrum recovery,an innovative support set reduction rule is proposed to further decrease the complexity of the candidate frequency support set.The proposed method can improve the estimation accuracy and resolution ability effectively as the reconstruction model is not influenced by the discretized grids,and the spectrum broadening effect arising from the truncated data is overcome.Simulation results demonstrate the correctness and effectiveness of the proposed method.