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

Abstract

This paper considers the massive random access problem in which a large number of sporadically active devices wish to communicate with a base-station (BS) equipped with a large number of antennas. Each device is preassigned a unique signature sequence, and the BS identifies the active devices in the random access by detecting which sequences are transmitted. This device activity detection problem can be formulated as a maximum likelihood estimation (MLE) problem with the sample covariance matrix of the received signal being a sufficient statistic. The aim of this paper is to characterize the parameter space in which this covariance based approach would be able to successfully recover the device activities in the massive multipleinput multiple-output (MIMO) regime. Through an analysis of the asymptotic behaviors of MLE via its associated Fisher information matrix, this paper derives a necessary and sufficient condition on the Fisher information matrix to ensure a vanishing detection error rate as the number of antennas goes to infinity, based on which a numerical phase transition analysis is obtained. This condition is also examined from a perspective of covariance matching that relates the phase transition analysis in this paper to a recently derived scaling law. Furthermore, this paper provides a characterization of the distribution of the estimation error in MLE, based on which the error probabilities in device activity detection can be accurately predicted. Finally, this paper studies a random access scheme with joint device activity and data detection and analyzes its performance in a similar way. Simulation results validate the analysis.

Exploiting Temporal Side Information in Massive IoT Connectivity

“…2) Other approaches for grant-free massive IoT connectivity: Other than the above compressed sensing-based approach, there are other strategies for grant-free massive IoT connectivity, including the covariance-based approach and the unsourced random access based approach. First, in the case when the channel estimation is not necessary, e.g., each device merely transmits a few bits which can be embedded into its preamble selection pattern, it was shown in [22]- [24] that the minimum preamble sequence length for device activity detection can be significantly shortened by the covariance-based approach. However, if each device needs to transmit more bits such that their channels need to be estimated similar to the conventional data transmission, the above approach cannot be applied.…”

Grant-Free Access via Bilinear Inference for Cell-Free MIMO With Low-Coherence Pilots

“…Motivated by the above, various authors [16], [17], [40]- [43] studied random coding schemes and/or its covariance-based receiver designs for URA in grantfree MIMO systems with massive numbers of potential users. In this line of work, the massive MIMO JACE problem was considered in [44], [45] with a similar receiver design based on the sample covariance approach. Finally, as for the Bayesian approach, the authors in [20], [46]- [48] have investigated JACE for massive random access with Bayesian compressed sensing receivers, which was also extended to JACDE in [11]- [13], [49], where informative bits are embedded into spreading codewords.…”

Accelerating Coordinate Descent via Active Set Selection for Device Activity Detection for Multi-Cell Massive Random Access

“…In the covariance approach, the coordinate descent (CD) algorithm that iteratively updates the activity indicator of each device is commonly used since it can achieve excellent detection performance; see [8], [12], [13] for more details. In the single-cell scenario, the CD algorithm is also computationally efficient because it admits a closed-form solution for each update.…”