Most existing studies on massive grant-free access, proposed to support massive machine-type communications (mMTC) for the Internet of things (IoT), assume Rayleigh fading and perfect synchronization for simplicity. However, in practice, line-of-sight (LoS) components generally exist, and time and frequency synchronization are usually imperfect. This paper systematically investigates maximum likelihood estimation (MLE)-based device activity detection under Rician fading for massive grant-free access with perfect and imperfect synchronization. We assume that the large-scale fading powers, Rician factors, and normalized LoS components can be estimated offline. We formulate device activity detection in the synchronous case and joint device activity and offset detection in three asynchronous cases (i.e., time, frequency, and time and frequency asynchronous cases) as MLE problems. In the synchronous case, we propose an iterative algorithm to obtain a stationary point of the MLE problem. In each asynchronous case, we propose two iterative algorithms with identical detection performance but different computational complexities. In particular, one is computationally efficient for small ranges of offsets, whereas the other one, relying on fast Fourier transform (FFT) and inverse FFT, is computationally efficient for large ranges of offsets. The proposed algorithms generalize the existing MLE-based methods for Rayleigh fading and perfect synchronization. Numerical results show that the proposed algorithm for the synchronous case can reduce the detection error probability by up to 50.4% at a 78.6% computation time increase, compared to the MLEbased state-of-the-art, and the proposed algorithms for the three asynchronous cases can reduce the detection error probabilities and computation times by up to 65.8% and 92.0%, respectively, compared to the MLE-based state-of-the-arts.

翻译：现有大规模免授权接入研究多为支持物联网大规模机器类通信而提出，其简化假设为瑞利衰落与完美同步。然而实际信道普遍存在视距分量，且时间与频率同步往往非完美。本文系统研究瑞利衰落与同步与异步场景下基于最大似然估计的设备活动检测问题。我们假设大尺度衰落功率、莱斯因子及归一化视距分量可离线估计。将同步情况下的设备活动检测，以及三种异步情况（时间异步、频率异步、时间与频率异步）下的联合设备活动与偏移检测建模为MLE问题。同步情况下，我们提出迭代算法获得MLE问题的稳定点。每种异步情况下，提出两种检测性能相同但计算复杂度不同的迭代算法：一种在偏移范围较小时计算高效，另一种基于快速傅里叶变换及逆快速傅里叶变换，在偏移范围较大时计算高效。所提算法推广了现有基于MLE的瑞利衰落与完美同步方法。数值结果表明，相较于现有最优MLE方法，同步情况算法在计算时间增加78.6%时可将检测错误概率降低高达50.4%；三种异步情况算法相比现有最优MLE方法，可将检测错误概率与计算时间分别降低高达65.8%与92.0%。