  In this work, we propose to utilize Gaussian mixture models (GMMs) to design
pilots for downlink (DL) channel estimation in frequency division duplex (FDD)
systems. The GMM captures prior information during training that is leveraged
to design a codebook of pilot matrices in an initial offline phase. Once shared
with the mobile terminal (MT), the GMM is utilized to determine a feedback
index at the MT in the online phase. This index selects a pilot matrix from a
codebook, eliminating the need for online pilot optimization. The GMM is
further used for DL channel estimation at the MT via observation-dependent
linear minimum mean square error (LMMSE) filters, parametrized by the GMM. The
analytic representation of the GMM allows adaptation to any signal-to-noise
ratio (SNR) level and pilot configuration without re-training. With extensive
simulations, we demonstrate the superior performance of the proposed GMM-based
pilot scheme compared to state-of-the-art approaches.
