GMM-based Codebook Construction and Feedback Encoding in FDD Systems

We propose a precoder codebook construction and feedback encoding scheme which is based on Gaussian mixture models (GMMs). In an offline phase, the base station (BS) first fits a GMM to uplink (UL) training samples. Thereafter, it designs a codebook in an unsupervised manner by exploiting the GMM's clustering capability. We design one codebook entry per GMM component. After offloading the GMM-but not the codebook-to the mobile terminal (MT) in the online phase, the MT utilizes the GMM to determine the best fitting codebook entry. To this end, no channel estimation is necessary at the MT. Instead, the MT's observed signal is used to evaluate how responsible each component of the GMM is for the signal. The feedback consists of the index of the GMM component with the highest responsibility and the BS then employs the corresponding codebook entry. Simulation results show that the proposed codebook design and feedback encoding scheme outperforms conventional Lloyd clustering based codebook design algorithms, especially in configurations with reduced pilot overhead.