Performance Analysis of Channel Extrapolation in FDD Massive MIMO Systems

Channel estimation for the downlink of frequency division duplex (FDD) massive multiple-input-multiple output (MIMO) systems is well known to generate a large overhead as the amount of training generally scales with the number of transmit antennas in a MIMO system. In this paper, we consider the solution of extrapolating the channel frequency response from uplink pilot estimates to the downlink frequency band. This drastically reduces the downlink pilot overhead and completely removes the need for a feedback from the users. The price to pay is a degradation in the quality of the channel estimates, which reduces the downlink spectral efficiency. We first show that conventional estimators fail to achieve reasonable accuracy. We propose instead to use high-resolution channel estimation. We derive the Cramer-Rao lower bound (CRLB) of the mean squared error (MSE) of the extrapolated channel. Furthermore, a relationship between the imperfect channel state information (CSI) and the downlink user performance is derived. The extrapolation-based FDD massive MIMO performance is validated through numerical simulations and compared to a corresponding time division duplex (TDD) system. Considered figures of merit for extrapolation performance include channel MSE, beamforming efficiency, extrapolation range, spectral efficiency and uncoded symbol error rate. Our main conclusion is that channel extrapolation is a viable solution for FDD massive MIMO systems.