  In a transmit preprocessing aided frequency division duplex (FDD) massive
multi-user (MU) multiple-input multiple-output (MIMO) scheme assisted
orthogonal frequency-division multiplexing (OFDM) system, it is required to
feed back the frequency domain channel transfer function (FDCHTF) of each
subcarrier at the user equipment (UE) to the base station (BS). The amount of
channel state information (CSI) to be fed back to the BS increases linearly
with the number of antennas and subcarriers, which may become excessive. Hence
we propose a novel CSI feedback compression algorithm based on compressive
sensing (CS) by designing a common dictionary (CD) to reduce the CSI feedback
of existing algorithms. Most of the prior work on CSI feedback compression
considered single-UE systems. Explicitly, we propose a common dictionary
learning (CDL) framework for practical frequency-selective channels and design
a CD suitable for both single-UE and multi-UE systems. A set of two methods is
proposed. Specifically, the first one is the CDL-K singular value decomposition
(KSVD) method, which uses the K-SVD algorithm. The second one is the
CDL-orthogonal Procrustes (OP) method, which relies on solving the orthogonal
Procrustes problem. The CD conceived for exploiting the spatial correlation of
channels across all the subcarriers and UEs compresses the CSI at each UE, and
{upon reception} reconstructs it at the BS. Our simulation results show that
the proposed dictionary's estimated channel vectors have lower normalized
mean-squared error (NMSE) than the traditional fixed Discrete Fourier Transform
(DFT) based dictionary. The CSI feedback is reduced by 50%, and the memory
reduction at both the UE and BS starts from 50% and increases with the number
of subcarriers.
