  Channel-state-information (CSI) feedback methods are considered, especially
for massive or very large-scale multiple-input multiple-output (MIMO) systems.
To extract essential information from the CSI without redundancy that arises
from the highly correlated antennas, a receiver transforms (sparsifies) a
correlated CSI vector to an uncorrelated sparse CSI vector by using a
Karhunen-Loeve transform (KLT) matrix that consists of the eigen vectors of
covariance matrix of CSI vector and feeds back the essential components of the
sparse CSI, i.e., a principal component analysis method. A transmitter then
recovers the original CSI through the inverse transformation of the feedback
vector. Herein, to obtain the covariance matrix at transceiver, we derive
analytically the covariance matrix of spatially correlated Rayleigh fading
channels based on its statistics including transmit antennas' and receive
antennas' correlation matrices, channel variance, and channel delay profile.
With the knowledge of the channel statistics, the transceiver can readily
obtain the covariance matrix and KLT matrix. Compression feedback error and
bit-error-rate performance of the proposed method are analyzed. Numerical
results verify that the proposed method is promising, which reduces
significantly the feedback overhead of the massive-MIMO systems with marginal
performance degradation from full-CSI feedback (e.g., feedback amount reduction
by 80%, i.e., 1/5 of original CSI, with spectral efficiency reduction by only
2%). Furthermore, we show numerically that, for a given limited feedback
amount, we can find the optimal number of transmit antennas to achieve the
largest spectral efficiency, which is a new design framework.
