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.
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