# Network Coherence Time Matters - Aligned Image Sets and the Degrees of Freedom of Interference Networks with Finite Precision CSIT and Perfect CSIR

## TL;DR

This paper demonstrates that network coherence time significantly influences the degrees of freedom in interference networks, even with perfect CSIR and finite precision CSIT, by establishing bounds sensitive to coherence patterns.

## Contribution

It introduces a novel aligned image sets bound that is sensitive to network coherence time and resolves open problems regarding DoF optimality conditions.

## Key findings

- Network coherence time affects DoF even with perfect CSIR and finite precision CSIT.
- Necessary and sufficient conditions for 1/2 DoF per user when T_c=1.
- New bounds that settle previously open questions in interference network analysis.

## Abstract

This work obtains the first bound that is provably sensitive to network coherence time, i.e., coherence time in an interference network where all channels experience the same coherence patterns. This is accomplished by a novel adaptation of the aligned image sets bound, and settles various open problems noted previously by Naderi and Avestimehr and by Gou et al. For example, a necessary and sufficient condition is obtained for the optimality of 1/2 DoF per user in a partially connected interference network where the channel state information at the receivers (CSIR) is perfect, the channel state information at the transmitters (CSIT) is instantaneous but limited to finite precision, and the network coherence time is T_c= 1. The surprising insight that emerges is that even with perfect CSIR and instantaneous finite precision CSIT, network coherence time matters, i.e., it has a DoF impact.