Improved Scaling Law for Activity Detection in Massive MIMO Systems

by   Saeid Haghighatshoar, et al.

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.


page 1

page 2

page 3

page 4


Non-Bayesian Activity Detection, Large-Scale Fading Coefficient Estimation, and Unsourced Random Access with a Massive MIMO Receiver

In this paper, we study the problem of user activity detection and large...

Grant-Free Massive Random Access With a Massive MIMO Receiver

We consider the problem of unsourced random access (U-RA), a grant-free ...

Massive Unsourced Random Access for Massive MIMO Correlated Channels

This paper investigates the massive random access for a huge amount of u...

Low-complexity and Statistically Robust Beamformer Design for Massive MIMO Systems

Massive MIMO is a variant of multiuser MIMO in which the number of anten...

Sparse Signal Processing for Grant-Free Massive IoT Connectivity

The next wave of wireless technologies will proliferate in connecting se...

The Limiting Poisson Law of Massive MIMO Detection with Box Relaxation

Estimating a binary vector from noisy linear measurements is a prototypi...

Scaling Law Analysis for Covariance Based Activity Detection in Cooperative Multi-Cell Massive MIMO

This paper studies the covariance based activity detection problem in a ...

Please sign up or login with your details

Forgot password? Click here to reset