In this work, we propose variations of a Gaussian mixture model (GMM) based channel estimator that was recently proven to be asymptotically optimal in the minimum mean square error (MMSE) sense. We account for the need of low computational complexity in the online estimation and low cost for training and storage in practical applications. To this end, we discuss modifications of the underlying expectation-maximization (EM) algorithm, which is needed to fit the parameters of the GMM, to allow for structurally constrained covariances. Further, we investigate splitting the 2D time and frequency estimation problem in wideband systems into cascaded 1D estimations with the help of the GMM. The proposed cascaded GMM approach drastically reduces the complexity and memory requirements. We observe that due to the training on realistic channel data, the proposed GMM estimators seem to inherently perform a trade-off between saving complexity/parameters and estimation performance. We compare these low-complexity approaches to a practical and low cost method that relies on the power delay profile (PDP) and the Doppler spectrum (DS). We argue that, with the training on scenario-specific data from the environment, these practical baselines are outperformed by far with equal estimation complexity.

翻译：本文提出基于高斯混合模型（GMM）的信道估计器的变体，该估计器近期被证明在最小均方误差（MMSE）意义上具有渐近最优性。针对实际应用中在线估计的低计算复杂度以及训练与存储的低成本需求，我们讨论了为拟合GMM参数所需的基础期望最大化（EM）算法的改进方案，使其能够支持具有结构约束的协方差矩阵。此外，我们研究了利用GMM将宽带系统中的二维时频联合估计问题分解为级联一维估计的方法。所提出的级联GMM方法大幅降低了计算复杂度和内存需求。通过在实际信道数据上的训练，我们发现所提出的GMM估计器能自发地在降低复杂度/参数数量与估计性能之间实现权衡。我们将这些低复杂度方法与基于功率时延谱（PDP）和多普勒频谱（DS）的实用低成本方法进行对比。研究表明，在利用环境特定场景数据进行训练后，这些实用基准方法在相同估计复杂度下表现远逊于所提方案。