In machine-type communications (MTC), a large number of devices are connected to an access point (AP), but only a few devices are active at a time. This sparse activity of devices makes compressed sensing (CS) technique a possible solution for joint activity detection and channel estimation problem in MTC. In this paper, we improve the performance of greedy CS based detection in MTC, by exploiting the prior probability of each device being active. We propose new improved greedy algorithms that minimize the probability of incorrect selection of nonzero indices using a correction function. Simulation results demonstrate the performance improvement of CS recovery with the improved greedy algorithms. In addition, we investigate the empirical performance of the improved algorithms when the prior information is inaccurate, which is natural in practice. With inaccurate prior information, we demonstrate that the performance of CS based joint activity detection and channel estimation employing the improved orthogonal matching pursuit (OMP) is superior to that of OMP with partially known support (OMP-PKS) in which the AP knows 30% or less active devices in advance.

在机器类型通信（MTC）中，大量设备连接到访问点（AP），但一次仅激活几个设备。设备的这种稀疏活动使压缩感知（CS）技术成为MTC中联合活动检测和信道估计问题的可能解决方案。在本文中，我们通过利用每个设备处于活动状态的先验概率来提高MTC中基于贪婪CS的检测的性能。我们提出了新的改进的贪婪算法，该算法使用校正函数将非零索引的错误选择的可能性降到最低。仿真结果表明，采用改进的贪婪算法可以提高CS恢复的性能。另外，我们研究了当先验信息不准确时改进算法的经验性能，这在实践中是很自然的。