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.

翻译：本文研究了多小区大规模多输入多输出（MIMO）系统中基于协方差的活动检测问题，其中活跃设备向多个基站（BS）发送其特征序列，基站基于接收信号协作检测活跃设备。文献中已对单小区场景下基于协方差的活动检测的尺度律进行了深入分析。本文旨在分析多小区大规模MIMO系统中基于协方差的活动检测的尺度律。具体而言，本文证明了在经典路径损耗模型中的指数大于2的假设下，多小区系统中存在二次尺度律，这表明在多小区MIMO系统中，每个小区内可正确检测的活跃设备的最大数量随特征序列长度二次增长，并随小区数量对数减少（当天线数趋于无穷时）。此外，本文还刻画了多小区场景下估计误差的分布。