In this work, we propose a versatile feedback scheme which can be deployed for both single- and multi-user multiple-input multiple-output (MIMO) frequency division duplex (FDD) systems. Particularly, we propose to use a Gaussian mixture model (GMM) with a reduced number of parameters for codebook construction, feedback encoding, and precoder design. The GMM is fitted offline at the base station (BS) to uplink (UL) training samples to approximate the channel distribution of all possible mobile terminals (MTs) located inside the BS cell. Afterwards, a codebook is constructed, where each codebook entry is based on one GMM component. By extracting directional information of the constructed codebook, the proposed GMM-based feedback approach allows to jointly design the precoders of a multi-user MIMO (MU-MIMO) system using common precoding algorithms. Alternatively, the GMM's sample generation ability can be utilized to design the precoders using a state-of-the-art stochastic iterative algorithm. After offloading the GMM to the MTs, they determine their feedback simply as the index of the GMM component with the highest responsibility for their received pilot signal. This strategy exhibits low complexity and allows for parallelization. Simulation results show that the proposed approach outperforms conventional methods, especially for a reduced number of pilots.

翻译：本文提出一种适用于单用户和多用户多输入多输出（MIMO）频分双工（FDD）系统的通用反馈方案。具体而言，我们采用参数数量精简的高斯混合模型（GMM）实现码本构建、反馈编码与预编码器设计。该GMM在基站端利用上行训练样本进行离线拟合，以近似基站小区内所有可能移动终端（MT）的信道分布。随后构建码本，其中每个码本条目对应一个GMM分量。通过提取所构建码本的方向信息，本方案可基于通用预编码算法联合设计多用户MIMO（MU-MIMO）系统的预编码器。此外，利用GMM的样本生成能力，可借助先进随机迭代算法设计预编码器。将GMM下传至移动终端后，终端仅需选择对其接收导频信号责任度最高的GMM分量索引作为反馈。该策略具有低复杂度且支持并行化的优势。仿真结果表明，所提方法优于传统方案，尤其在导频数量受限时性能提升更为显著。