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：大多数现有针对大规模免授权接入的研究（旨在支持物联网大规模机器类通信）为简化起见通常假设瑞利衰落和完美同步。然而实际场景中视距分量普遍存在，且时间和频率同步通常难以完美实现。本文系统研究了莱斯衰落信道下基于最大似然估计的设备活动检测方法，同时考虑了完美与非完美同步两种情况。我们假设大尺度衰落功率、莱斯因子及归一化视距分量可通过离线方式估计。将同步场景下的设备活动检测问题，以及三种异步场景（时间异步、频率异步、时频联合异步）中的设备活动与偏移联合检测问题，均建模为MLE问题。针对同步场景，我们提出一种迭代算法以获取MLE问题的驻点。针对每种异步场景，提出两种检测性能相同但计算复杂度不同的迭代算法：前者适用于小偏移范围的高效计算，后者基于快速傅里叶变换及其逆变换，适用于大偏移范围的高效计算。所提算法实现了对现有瑞利衰落与完美同步条件下MLE方法的泛化。数值结果表明，与现有最优MLE方法相比，同步场景下所提算法在计算时间增加78.6%的情况下，可将检测错误概率降低高达50.4%；三种异步场景下所提算法则可将检测错误概率和计算时间分别降低高达65.8%和92.0%。