Grant‐Free Random Access via Covariance‐Based Approach
Ya‐Feng Liu, Wei Yu, Ziyue Wang, Zhilin Chen, Foad Sohrabi · 2024
This chapter presents the theory and algorithms for a covariance-based approach for device activity detection in a grant-free random access protocol. We consider the device activity detection problem in massive multi-input multi-output (MIMO) systems, where active devices transmit their non-orthogonal signature sequences to the base stations (BSs), and the BSs cooperatively detect the active devices based on the received signals. The device activity detection problem can be formulated as a maximum likelihood estimation (MLE) problem. Because the sample covariance matrix of the received signals is a sufficient statistic for the device activity pattern in the MLE formulation, the approach based on solving the MLE formulation is often called the covariance-based approach. In this chapter, we study the covariance-based approach in both single-cell and multi-cell massive MIMO systems. Specifically, we first present necessary and sufficient conditions on the problem input parameters to ensure a vanishing error probability as the number of antennas at the BS(s) tends to infinity. We then show that the number of active devices that can be detected by the covariance-based approach (in each cell) can scale quadratically as the length of the devices' signature sequence. In addition to the asymptotic performance analysis, we also present efficient coordinate descent (CD) algorithms and their accelerated variants for solving the device activity detection problem. Numerical results verify the accuracy of the asymptotic analysis results and illustrate the efficiency of the CD algorithms.