Active User Detection and Channel Estimation via Fast ADMM

Lijun Zhu, Kaihui Liu, Liangtian Wan, Lu Sun

Abstract: This paper considers a joint active user detection and channel estimation (JADCE) problem in the grant-free massive machine-type communications (mMTC) circumstances. Specifically, we exploit the millimeter-wave (mmWave) channel in the uplink with the continuous angular domains based on massive multi-input multi-output systems. The sporadic communication nature of the mMTC scenario and the inherent angular domain sparsity of the mmWave channel make the space-angle domain sparsity of the mmWave channel even more serious. Hence, the JADCE problem is formulated as a convex optimization problem under the gridless reweighted atomic norm minimization (RAM) framework in a multiple measurement vector settings (MMV), which can enhance the sparsity in the continuous anular domains. Moreover, RAM has nature of Semidefinite programming (SDP) which can be computed by CVX solver. Meanwhile, to reduce the computational complexity of CVX, we design a fast alternating direction method of multipliers approach to settle the SDP formulation. The simulation results demonstrate that our proposed method has achieved excellent estimation performance and a substantial reduction in computational complexity compared with conventional JADCE methods.