宽带稀疏信号调制变换欠采样频谱感知

Sub-Nyquist wideband spectrum sensing methods which could solve the bottlenecks of high sampling rate and processing speed for broadband signals are drawing more and more attention in both academia and industry. Rregarding to the ubiquitous problems of sub-Nyquist wideband spectrum sensing, such as lack of blind spectrum sensing ability, poor instantaneity and inferior spectrum sensing performance, the following problems will be studied with the sub-Nyquist approach in wideband modulated converter scheme: (1)Sparsity. With the sparsity pre-decision algorithm based on the branch power cancellation and the comparison result between zero norm of support and the maximal signal number of reconstruction, the sparsity of broadband signal is jointly determined. (2)Exact support recovery. Based on eigenvalue detection algorithm and orthogonal matching pursuit, a support recovery method which treats the ratio of maximal eigenvalue to the trace of correlation matrix as test statistics is discussed, and the accurate stop condition of optimization algorithmis is deduced via correlation matrix whitening, which could provide theoretical basis for analyzing the performance of sub-Nyquist wideband spectrum sensing in complex electromagnetic environment. (3)Convergence rate acceleration. The change of support can be quickly detected by utilizing the probability distribution of the ratio of the instantaneous power to the average power of residual, and then the support occupied in sequential sensing period will be picked out by correlation analysis of subband energy. As support recovery method is executed to the remaining support, the number of iteration of optimization algorithm will be reduced noteworthily. These researches provide the　foundation to implement blind, robust and real-time sub-Nyquist wideband spectrum sensing.

欠采样频谱感知方法可以解决宽带频谱感知模拟采样和数字处理的速率瓶颈问题，是其发展的新方向。课题针对该方法存在的盲感知能力缺失、感知时效低以及感知性能差的问题，结合宽带调制变换欠采样机理，从以下方面展开研究：(1)稀疏性判定。研究基于支路功率对消的稀疏预判决技术，并通过支集零范数与最大重构信号约束个数的对比，联合确定宽带信号的稀疏性。(2)准确支集输出。提出基于特征值检测正交匹配追踪的支集确定算法，将相关随机矩阵白化变换成独立随机矩阵，以矩阵最大特征值与迹的比值为检验统计量，推导出优化算法迭代停止的准确条件，为分析复杂电磁环境下欠采样感知的性能极限提供理论依据。(3)收敛速度提升。利用残差瞬时与平均功率比值的分布快速判决支集改变，然后以子带短时能量的相关性估计连续周期同被占用的支集，再对剩余支集执行迭代判决，可显著减少迭代次数，改善感知实时性。课题的研究对实现实时稳健欠采样盲感知有支撑意义。

欠采样频谱感知方法可以解决宽带频谱感知模拟采样和数字处理的速率瓶颈问题，是宽带频谱感知发展的新方向。针对欠采样宽带频谱感知不具备全盲频谱感知能力、感知时效性较低以及复杂电磁环境下感知性能差的问题，本项目结合宽带调制变换器(Modulated Wideband Converter，MWC)的特殊压缩采样机理，重点在压缩测量矩阵校准、宽带频谱稀疏性判决和欠采样宽带频谱感知等方面开展研究。.（1）针对带宽限制和非线性因素引起的测量矩阵失配严重影响欠采样频谱感知性能的问题，本文提出压缩测量矩阵列满秩适定校准(Full-column-rank Well-posed Calibration, FWC)方法，该方法通过控制MWC输入信号个数将欠定压缩采集重构转换成适定形式，计算出对应的两列测量矩阵元素，然后依据MWC系统配置顺序更换输入信号频点，并重复进行适定方程求解，可完成整个测量矩阵的校准，从而保证支集恢复的正确性和完整性；.（2）针对稀疏性前提严重影响欠采样宽带频谱感知判决结果可信度的问题，利用信号存在与否条件下支路功率概率分布的差异性，设计出通道能量逐对相消的信号稀疏性预判决技术（Pairwise Channel Energy Ratio detector，PCER），通过将该预判决技术融入到经典欠采样频谱感知算法中，可以提前判决宽带接收信号的稀疏性，从而避免稀疏性未知带来的欠采样频谱感知错误；.（3）针对先验信息全盲条件下欠采样频谱感知方法难以准确停止支集恢复迭代的难题，提出基于残差相关矩阵检测(Residual corrElation mAtrix Detection, READ)的欠采样盲频谱感知方法，该方法对每次迭代形成的残差矩阵引入信号的存在性判断，并依据检测结果来确定是否还需要进一步的迭代，可以不利用任何先验知识实现重构迭代过程的精确控制，有效提升低信噪比条件下的欠采样频谱感知性能。 .所提方法可实现200-3000MHz宽带稀疏信号的欠采样频谱快速感知，子带带宽不大于20MHz，瞬时占用子带个数不少于10个，信噪比不低于-2dB时，正确检测概率大于95%，虚警概率小于0.05，相关研究内容在国际主流会议或期刊上发表论文28篇，申请或授权国家发明专利7项，为欠采样宽带频谱感知技术在认知无线电系统应用提供强有力的理论依据和实验支撑。