  In this work, we propose a Gaussian mixture model (GMM)-based pilot design
scheme for downlink (DL) channel estimation in single- and multi-user
multiple-input multiple-output (MIMO) frequency division duplex (FDD) systems.
In an initial offline phase, the GMM captures prior information during
training, which is then utilized for pilot design. In the single-user case, the
GMM is utilized to construct a codebook of pilot matrices and, once shared with
the mobile terminal (MT), can be employed to determine a feedback index at the
MT. This index selects a pilot matrix from the constructed codebook,
eliminating the need for online pilot optimization. We further establish a sum
conditional mutual information (CMI)-based pilot optimization framework for
multi-user MIMO (MU-MIMO) systems. Based on the established framework, we
utilize the GMM for pilot matrix design in MU-MIMO systems. The analytic
representation of the GMM enables the adaptation to any signal-to-noise ratio
(SNR) level and pilot configuration without re-training. Additionally, an
adaption to any number of MTs is facilitated. Extensive simulations demonstrate
the superior performance of the proposed pilot design scheme compared to
state-of-the-art approaches. The performance gains can be exploited, e.g., to
deploy systems with fewer pilots.
