Due to employing different frequencies in the uplink and downlink path of frequency-division duplex (FDD) systems, the required training signals for estimating downlink channel would be prohibitively large. Therefore, an effective solution is essential to cope with the pilot and channel state information feedback overhead. In this paper, we focus on the superposition method, which combines the data and pilot signal at the same time and/or frequency domain that has not yet been seriously studied for FDD systems. By defining a new orthogonal pilot matrix and deriving the least squares and linear minimum mean square error formulations of our superposition signaling, we prove that the conventional superposition definition can alleviate the pilot overhead problem. Furthermore, we compute a closed form equation for the mean square error of both estimators, which obviously show the impact of the number of antennas and training signals on the estimation error. The theoretical and Monte-Carlo simulation results indicate that the proposed scheme is capable of estimating the channel efficiently, while herein, we do not encounter the pilot overhead problem in the downlink path of FDD large-scale MIMO systems.
