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

TL;DR

This paper analyzes the covariance-based activity detection in multi-cell massive MIMO systems, revealing a quadratic scaling law for the maximum detectable active devices as system parameters grow, and characterizing error distribution.

Contribution

It extends the understanding of activity detection scaling laws from single-cell to multi-cell massive MIMO systems, highlighting quadratic growth under certain path-loss conditions.

Findings

Maximum active devices detected scale quadratically with sequence length.

Detection capability decreases logarithmically with the number of cells.

Distribution of estimation error is characterized in the multi-cell scenario.

Abstract

This paper studies the covariance based activity detection problem in a multi-cell massive multiple-input multiple-output (MIMO) system, where the active devices transmit their signature sequences to multiple base stations (BSs), and the BSs cooperatively detect the active devices based on the received signals. The scaling law of covariance based activity detection in the single-cell scenario has been thoroughly analyzed in the literature. This paper aims to analyze the scaling law of covariance based activity detection in the multi-cell massive MIMO system. In particular, this paper shows a quadratic scaling law in the multi-cell system under the assumption that the exponent in the classical path-loss model is greater than 2, which demonstrates that in the multi-cell MIMO system the maximum number of active devices that can be correctly detected in each cell increases quadratically with the length of the signature sequence and decreases logarithmically with the number of cells (as the number of antennas tends to infinity). This paper also characterizes the distribution of the estimation error in the multi-cell scenario.