Improved Scaling Law for Activity Detection in Massive MIMO Systems

Abstract

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 block fading channel model where the M -dim channel vector of each user remains almost constant over a coherence block (CB) containing Dc signal dimensions. We study a setting in which the number of potential users Kc assigned to a specific CB is much larger than the dimension of the CB Dc (Kc Dc) but at each time slot only Ac Kc of them are active. Most of the previous results, based on compressed sensing, require that Ac ≤ Dc, which is a bottleneck in massive deployment scenarios such as Internetof-Things (IoT) and Device-to-Device (D2D) communication. In this paper, we show that one can overcome this fundamental limitation when the number of BS antennas M is sufficiently large. More specifically, we derive a scaling law on the parameters (M, Dc, Kc, Ac) and also Signal-to-Noise Ratio (SNR) under which our proposed AD scheme succeeds. Our analysis indicates that with a CB of dimension Dc, and a sufficient number of BS antennas M with Ac/M = o(1), one can identify the activity of Ac = O(D 2 c / log 2 ( Kc Ac )) active users, which is much larger than the previous bound Ac = O(Dc) obtained via traditional compressed sensing techniques. In particular, in our proposed scheme one needs to pay only a poly-logarithmic penalty O(log 2 ( Kc Ac )) for increasing the number of potential users Kc, which makes it ideally suited for AD in IoT setups. We propose low-complexity algorithms for AD and provide numerical simulations to illustrate our results. We also compare the performance of our proposed AD algorithms with that of other competitive algorithms in the literature.

Phase Transition Analysis for Covariance Based Massive Random Access with Massive MIMO

“…This covariance approach is proposed in [11], [12] for massive MIMO systems, where the sequence detection problem is formulated as either a maximum likelihood estimation (MLE) problem, or a nonnegative least square (NNLS) problem. The covariance based method is used in [11] for device activity detection and in [12] for data decoding. As compared to compressed sensing, the covariance based method exploits the channel hardening effect in the massive MIMO systems by averaging the received signal over antennas.…”

“…As compared to compressed sensing, the covariance based method exploits the channel hardening effect in the massive MIMO systems by averaging the received signal over antennas. It is shown in [11], [12] that when the number of BS antennas is large, the covariance based method with the MLE formulation can outperform AMP.…”

“…Following the approach suggested in [11], we use MLE to estimate γ from Y, thereby obtaining the device activity indicator a n . To compute the likelihood, we first observe from (1) that given γ, the columns of Y, denoted by y m ∈ C L , 1 ≤ m ≤ M , are independent due to the i.i.d.…”

“…A description of the coordinate descent algorithm is given in Algorithm 1. As compared to the algorithm in [11], we add random index permutation and rankone update to further improve the efficiency. The complexity of the coordinate descent is dominated by the matrix-vector multiplications in steps 5-7, whose complexity is O(L 2 ).…”

“…Theorem 6: The sets N defined in (18) and N defined in (11) are identical, hence the condition N ∩ C = {0} is equivalent to N ∩ C = {0}.…”