Massive Machine-Type Communications (mMTC) features a massive number of low-cost user equipments (UEs) with sparse activity. Tailor-made for these features, grant-free random access (GF-RA) serves as an efficient access solution for mMTC. However, most existing GF-RA schemes rely on strict synchronization, which incurs excessive coordination burden for the low-cost UEs. In this work, we propose a receiver design for asynchronous GF-RA, and address the joint user activity detection (UAD) and channel estimation (CE) problem in the presence of asynchronization-induced inter-symbol interference. Specifically, the delay profile is exploited at the receiver to distinguish different UEs. However, a sample correlation problem in this receiver design impedes the factorization of the joint likelihood function, which complicates the UAD and CE problem. To address this correlation problem, we design a partially uni-directional (PUD) factor graph representation for the joint likelihood function. Building on this PUD factor graph, we further propose a PUD message passing based sparse Bayesian learning (SBL) algorithm for asynchronous UAD and CE (PUDMP-SBL-aUADCE). Our theoretical analysis shows that the PUDMP-SBL-aUADCE algorithm exhibits higher signal-to-interference-and-noise ratio (SINR) in the asynchronous case than in the synchronous case, i.e., the proposed receiver design can exploit asynchronization to suppress multi-user interference. In addition, considering potential timing error from the low-cost UEs, we investigate the impacts of imperfect delay profile, and reveal the advantages of adopting the SBL method in this case. Finally, extensive simulation results are provided to demonstrate the performance of the PUDMP-SBL-aUADCE algorithm.

翻译：大规模机器类型通信（mMTC）具有大量低成本用户设备（UE）且活动稀疏的特点。针对这些特征，免授权随机接入（GF-RA）成为mMTC的高效接入方案。然而，现有大多数GF-RA方案依赖严格同步，这给低成本UE带来了过重的协调负担。本文针对异步GF-RA提出一种接收机设计，并解决在异步引起的符号间干扰存在情况下的联合用户活动检测（UAD）与信道估计（CE）问题。具体而言，接收机利用延迟分布来区分不同UE。然而，该接收机设计中的样本相关性问题阻碍了联合似然函数的分解，使得UAD与CE问题复杂化。为解决该相关性问题，我们为联合似然函数设计了一种部分单向（PUD）因子图表示。基于该PUD因子图，我们进一步提出一种基于PUD消息传递的稀疏贝叶斯学习（SBL）算法，用于异步UAD与CE（PUDMP-SBL-aUADCE）。理论分析表明，PUDMP-SBL-aUADCE算法在异步情况下的信干噪比（SINR）高于同步情况，即所提接收机设计可利用异步性抑制多用户干扰。此外，考虑低成本UE可能存在的定时误差，我们研究了非完美延迟分布的影响，并揭示了在此情况下采用SBL方法的优势。最后，通过大量仿真结果验证了PUDMP-SBL-aUADCE算法的性能。