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Downlink channel estimation in massive MIMO systems is well known to generate a large overhead in frequency division duplex (FDD) mode as the amount of training generally scales with the number of transmit antennas. Using instead an extrapolation of the channel from the measured uplink estimates to the downlink frequency band completely removes this overhead. In this paper, we investigate the theoretical limits of channel extrapolation in frequency. We highlight the advantage of basing the extrapolation on high-resolution channel estimation. A lower bound (LB) on the mean squared error (MSE) of the extrapolated channel is derived. A simplified LB is also proposed, giving physical intuition on the SNR gain and extrapolation range that can be expected in practice. The validity of the simplified LB relies on the assumption that the paths are well separated. The SNR gain then linearly improves with the number of receive antennas while the extrapolation performance penalty quadratically scales with the ratio of the frequency and the training bandwidth. The theoretical LB is numerically evaluated using a 3GPP channel model and we show that the LB can be reached by practical high-resolution parameter extraction algorithms. Our results show that there are strong limitations on the extrapolation range than can be expected in SISO systems while much more promising results can be obtained in the multiple-antenna setting as the paths can be more easily separated in the delay-angle domain. 

This paper investigates the impact of the number of antennas (8 to 64) and the array configuration on massive MIMO channel parameters estimation for multiple propagation scenarios at 3.5 GHz. Different measurement environments are artificially created by placing several reflectors and absorbers in an anechoic chamber. “Ground truth” channel parameters, e.g, path angles, are obtained by geometry and trigonometric rules. Then, these are compared to the channel parameters “extracted” by the applying Space-Alternating Generalized Expectation- Maximization (SAGE) algorithm on the measurements. Overall, the estimation errors for various array configurations and the multiple environments are compared. This paper will help to determine the appropriate configuration of the antenna array and the parameter extraction algorithm for outdoor massive MIMO channel sounding campaigns. 

Channel estimation for the downlink of frequency division duplex (FDD) massive 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, which completely removes the training overhead. We first show that conventional estimators fail to achieve reasonable accuracy. We propose instead to use high-resolution channel estimation. We derive theoretical lower bounds (LB) for the mean squared error (MSE) of the extrapolated channel. Assuming that the paths are well separated, the LB is simplified in an expression that gives considerable physical insight. It is then shown that the MSE is inversely proportional to the number of receive antennas while the extrapolation performance penalty scales with the square of the ratio of the frequency offset and the training bandwidth. The channel extrapolation performance is validated through numeric simulations and experimental measurements taken in an anechoic chamber. Our main conclusion is that channel extrapolation is a viable solution for FDD massive MIMO systems if accurate system calibration is performed and favorable propagation conditions are present. 

Application of massive multiple-input multipleoutput (MIMO) systems to frequency division duplex (FDD) is challenging mainly due to the considerable overhead required for downlink training and feedback. Channel extrapolation, i.e., estimating the channel response at the downlink frequency band based on measurements in the disjoint uplink band, is a promising solution to overcome this bottleneck. This paper presents measurement campaigns obtained by using a wideband (350 MHz) channel sounder at 3.5 GHz composed of a calibrated 64 element antenna array, in both an anechoic chamber and outdoor environment. The Space Alternating Generalized Expectation-Maximization (SAGE) algorithm was used to extract the parameters (amplitude, delay, and angular information) of the multipath components from the attained channel data within the “training” (uplink) band. The channel in the downlink band is then reconstructed based on these path parameters. The performance of the extrapolated channel is evaluated in terms of mean squared error (MSE) and reduction of beamforming gain (RBG) in comparison to the “ground truth”, i.e., the measured channel at the downlink frequency. We find strong sensitivity to calibration errors and model mismatch, and also find that performance depends on propagation conditions: LOS performs significantly better than NLOS.