Abstract: This paper proposes a Simultaneous Advanced Sparsity Adaptive Matching Pursuit algorithm, to improve the speed and accuracy of reconstruction for joint sparse signals reconstruction with unknown sparsity. The algorithm takes full advantage of both intra-and inter-signal correlation. A method based on atom matching test is used to get an initial estimation of sparsity, and then high value of the step size is used to realize the coarse approach of signal sparse. In the later step iterations smaller value of step size decided by recovery progress is used to achieve the precise approach of signal sparse. Experiment results show that the proposed algorithm can get better reconstruction performances in probability of detection and recovery time compared with SOMP and SSAMP under the same test conditions.

Key words: cognitive radio, compressed sensing, collaborative spectrum detection, Matching Pursuit（MP）

摘要： 为了提高联合稀疏频谱环境下未知稀疏度信号的检测精度和速度，提出了一种联合稀疏可变步长的匹配追踪感知算法。算法根据信号内部及信号之间的相关性，利用一种原子匹配测试得到稀疏度的粗估计，采用变步长思想逼近全局最优支撑集，初始阶段利用大步长快速匹配以提高收敛速度，根据恢复情况减小步长以实现精确逼近。实验结果表明：改进的算法在检测概率和收敛速度上均优于SOMP和SSAMP算法。

关键词: 认知无线电, 压缩感知, 协同频谱检测, 匹配追踪