Completely Stale Transmitter Channel State Information is Still Very Useful

TL;DR

This paper demonstrates that even completely outdated transmitter channel state information (CSI) can significantly improve multiplexing gains in MIMO broadcast channels by leveraging side information from past transmissions, challenging traditional assumptions.

Contribution

It introduces a novel scheme where stale CSI is used to enhance degrees of freedom, showing this approach is optimal and provides gains in memoryless channels.

Findings

Achieves more than 1 degree of freedom with completely stale CSI.

Stale CSI can be used to learn side information, not predict current channels.

First example of feedback providing DoF gain in memoryless channels.

Abstract

Transmitter channel state information (CSIT) is crucial for the multiplexing gains offered by advanced interference management techniques such as multiuser MIMO and interference alignment. Such CSIT is usually obtained by feedback from the receivers, but the feedback is subject to delays. The usual approach is to use the fed back information to predict the current channel state and then apply a scheme designed assuming perfect CSIT. When the feedback delay is large compared to the channel coherence time, such a prediction approach completely fails to achieve any multiplexing gain. In this paper, we show that even in this case, the completely stale CSI is still very useful. More concretely, we show that in a MIMO broadcast channel with $K$ transmit antennas and $K$ receivers each with 1 receive antenna, $\frac{K}{1+1/2+ ...+ \frac{1}{K}} (> 1) $ degrees of freedom is achievable even when the fed back channel state is completely independent of the current channel state. Moreover, we establish that if all receivers have independent and identically distributed channels, then this is the optimal number of degrees of freedom achievable. In the optimal scheme, the transmitter uses the fed back CSI to learn the side information that the receivers receive from previous transmissions rather than to predict the current channel state. Our result can be viewed as the first example of feedback providing a degree-of-freedom gain in memoryless channels.