We propose a versatile feedback scheme for both single- and multi-user multiple-input multiple-output (MIMO) frequency division duplex (FDD) systems. Particularly, we propose utilizing 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 training samples to approximate the channel distribution of all possible mobile terminals (MTs) within the BS cell. Subsequently, a codebook is constructed, with each element based on one GMM component. Extracting directional information from the codebook or exploiting the GMM's sample generation ability facilitates joint precoder design for a multi-user MIMO system using state-of-the-art precoding algorithms. After offloading the GMM to the MTs, they can easily determine their feedback by selecting the index of the GMM component with the highest responsibility for their received pilot signal. This strategy exhibits low complexity and supports parallelization. Simulations demonstrate that the proposed approach outperforms conventional methods, which either estimate the channel and utilize a Lloyd codebook or use a deep neural network to determine the feedback in terms of spectral efficiency or sum-rate. The performance gains can be exploited to deploy systems with fewer pilots or feedback bits.

翻译：摘要：本文提出一种适用于单用户及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，我们提出利用参数量精简的高斯混合模型（GMM）进行码本构建、反馈编码及预编码器设计。该GMM在基站端通过上行训练样本离线拟合，以逼近基站小区内所有潜在移动终端（MT）的信道分布。随后构建码本，其中每个码字对应一个GMM分量。通过提取码本中的方向性信息或利用GMM的样本生成能力，可基于最新预编码算法实现多用户MIMO系统的联合预编码设计。将GMM卸载至终端后，各终端仅需选取对其接收导频信号贡献最大的GMM分量索引即可完成反馈。该策略兼具低复杂度与可并行化优势。仿真结果表明，相较于传统方法（包括信道估计结合Lloyd码本方案或基于深度神经网络的反馈方案），所提方法在频谱效率或总速率方面表现更优。该性能增益可用于部署导频或反馈比特数更少的系统。