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Improved Scaling Law for Activity Detection in Massive MIMO Systems

by   Saeid Haghighatshoar, et al.
Berlin Institute of Technology (Technische Universität Berlin)

In this paper, we study the problem of activity detection (AD) in a massive MIMO setup, where the Base Station (BS) has M ≫ 1 antennas. We consider a flat fading channel model where the M-dim channel vector of each user remains almost constant over a coherence block (CB) containing D_c signal dimensions. We study a setting in which the number of potential users K_c assigned to a specific CB is much larger than the dimension of the CB D_c (K_c ≫ D_c) but at each time slot only A_c ≪ K_c of them are active. Most of the previous results, based on compressed sensing, require that A_c< D_c, which is a bottleneck in massive deployment scenarios such as Internet-of-Things (IoT) and Device-to-Device (D2D) communication. In this paper, we propose a novel scheme for AD and show that it overcomes this limitation when the number of antennas M is sufficiently large. We also derive a scaling law on the parameters (M, D_c, K_c, A_c) and also Signal-to-Noise Ratio (SNR) under which our proposed AD scheme succeeds. Our analysis indicates that with a CB of dimension D_c, and a sufficient number of BS antennas M=O(A_c), one can identify the activity of A_c=O(D_c^2/ (K_c/A_c)) active users, which is much larger than the previous bound A_c=O(D_c) obtained via traditional compressed sensing techniques. In particular, in our proposed scheme one needs to pay only a negligible logarithmic penalty O( (K_c/A_c)) for increasing the number of potential users K_c, which makes it perfect for AD in IoT setups. We propose very low-complexity algorithms for AD and provide numerical simulations to illustrate the validity of our results.


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