On Distributional Invariances between Downlink and Uplink MIMO Channels

Recent machine learning applications for frequency division duplex (FDD) systems observed that the algorithms can be trained on uplink (UL) data and then applied to downlink (DL) data, or vice versa, without the need of further parameters tuning and with almost no performance difference. In this paper, we compare distributional properties of DL and UL multiple-input multiple-output (MIMO) channels to gain insight into this phenomenon. A first analysis shows a decrease in the distributional similarity between DL and UL channels with increasing frequency gap. At the same time, we demonstrate that there are specific DL and UL properties whose similarity does not decrease with increasing frequency gap. Such invariant properties offer an explanation for the recent findings on DL/UL training in machine learning applications. For example, we show that the right singular vectors of the DL and UL channels (the “directions” of the channels) stay consistently similar also when there is a large gap between the DL and UL center frequencies. Thus, an algorithm which relies on directional channel information could be trained on either DL or UL data without much performance difference. Such an observation was recently made in a joint precoder codebook design and feedback encoding approach. Further, we explore the feature spaces of neural networks which are evaluated on DL or UL data. We observe that the distributions of features extracted from DL/UL data do not vary as much with the frequency gap as those of the channel data themselves.