Assessment of the Sparsity-Diversity Trade-offs in Active Users Detection for mMTC

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.