Wireless communication systems must increasingly support a multitude of machine-type communications (MTC) devices, thus calling for advanced strategies for active user detection (AUD). Recent literature has delved into AUD techniques based on compressed sensing, highlighting the critical role of signal sparsity. This study investigates the relationship between frequency diversity and signal sparsity in the AUD problem. Single-antenna users transmit multiple copies of non-orthogonal pilots across multiple frequency channels and the base station independently performs AUD in each channel using the orthogonal matching pursuit algorithm. We note that, although frequency diversity may improve the likelihood of successful reception of the signals, it may also damage the channel sparsity level, leading to important trade-offs. We show that a sparser signal significantly benefits AUD, surpassing the advantages brought by frequency diversity in scenarios with limited temporal resources and/or high numbers of receive antennas. Conversely, with longer pilots and fewer receive antennas, investing in frequency diversity becomes more impactful, resulting in a tenfold AUD performance improvement.

翻译：无线通信系统必须日益支持大量机器类通信（MTC）设备，因此需要先进的活跃用户检测（AUD）策略。近期文献深入研究了基于压缩感知的AUD技术，强调了信号稀疏性的关键作用。本研究探讨了AUD问题中频率分集与信号稀疏性之间的关系。单天线用户通过多个频率信道传输多个副本的非正交导频，基站使用正交匹配追踪算法在每个信道上独立执行AUD。我们注意到，尽管频率分集可能提高信号成功接收的概率，但也可能损害信道稀疏性水平，导致重要的权衡。研究表明，信号越稀疏对AUD的益处越显著，在时域资源有限和/或接收天线数量较多的场景中，其优势超过频率分集带来的增益。相反，当导频长度较长且接收天线数量较少时，频率分集投入更具效果，可使AUD性能提升十倍。