Improved Scaling Law for Activity Detection in Massive MIMO Systems
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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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