Distributed Algorithms for Asynchronous Activity Detection in Cell-Free Massive MIMO

Device activity detection in the emerging cell-free massive multiple-input multiple-output systems has been recognized as a crucial task in machine-type communications, in which multiple access points jointly identify the active devices from a large number of potential devices based on the received signals. Most of the existing works addressing this problem rely on the impractical assumption that different active devices transmit signals synchronously. However, in practice, synchronization cannot be guaranteed due to the low-cost oscillators, which brings additional discontinuous and nonconvex constraints to the detection problem. To address this challenge, this paper reveals an equivalent reformulation to the asynchronous activity detection problem, which facilitates the development of a distributed algorithm that satisfies the highly nonconvex constraints in a gentle fashion as the iteration number increases. To reduce the capacity requirements of the fronthauls, we further design a communication-efficient accelerated distributed algorithm. Simulation results demonstrate that the proposed two distributed algorithms outperform state-of-the-art approaches. Moreover, the accelerated distributed algorithm requires a very small number of quantization bits to approach the ideal detection performance.