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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.
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Training for Chanel Estimation in Nonlinear Multi-Antenna Transceivers
Recent efforts to obtain high data rates in wireless systems have focused on what can be achieved in systems that have nonlinear or coarsely quantized transceiver architectures. Estimating the channel in such a system is challenging because the nonlinearities distort the channel estimation process. It is therefore of interest to determine how much training is needed to estimate the channel sufficiently well so that the channel estimate can be used during data communication. We provide a way to determine how much training is needed by deriving a lower bound on the achievable rate in a training-based scheme that can be computed and analyzed even when the number of antennas is very large. This lower bound can be tight, especially at high SNR. One conclusion is that the optimal number of training symbols may paradoxically be smaller than the number of transmitters for systems with coarselyquantized transceivers. We show how the training time can be strongly dependent on the number of receivers, and give an example where doubling the number of receivers reduces the training time by about 37 percent.
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- Award ID(s):
- 1731056
- PAR ID:
- 10104226
- Date Published:
- Journal Name:
- Information Theory and Applications
- Page Range / eLocation ID:
- 1-11
- Format(s):
- Medium: X
- Sponsoring Org:
- National Science Foundation
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Accepted Manuscript1.0
- Conference Paper:
- The DOI is not currently available.
