Network Coherence Time Matters—Aligned Image Sets and the Degrees of Freedom of Interference Networks With Finite Precision CSIT and Perfect CSIR

Arash Gholami Davoodi,Syed Ali Jafar

doi:10.1109/tit.2018.2837880

Abstract

This paper obtains the first degrees of freedom (DoFs) 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 (CSIRs) is perfect, the channel state information at the transmitters (CSITs) 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, the network coherence time matters, i.e., it has a DoF impact.

Highlights

The impact of coherence time in a wireless network is a topic that has been studied extensively [1, 2, 3, 4, 5, 6, 7, 8, 9]
It is well known that longer coherence time is beneficial to amortize the cost of learning the channel state information at the receivers (CSIR) and/or the delays in feeding back channel state information to the transmitters (CSIT)
If CSIR is assumed to be perfectly available and the channel state information at the transmitters (CSIT), limited to finite precision as it may be, is assumed to be available instantaneously, it is not known whether the network coherence time still impacts the DoF of interference networks

Summary

Introduction

The impact of coherence time in a wireless network is a topic that has been studied extensively [1, 2, 3, 4, 5, 6, 7, 8, 9]. If CSIR is assumed to be perfectly available and the CSIT, limited to finite precision as it may be, is assumed to be available instantaneously, it is not known whether the network coherence time still impacts the DoF of interference networks. Partial insights into this question have emerged recently through novel achievable schemes [6, 8, 9]. A conclusive answer to this question has remained elusive due to the difficulty of obtaining DoF outer bounds that are sensitive to network coherence time No such bounds exist, to the best of our knowledge. The lack of such bounds is underscored by various open problems noted in [9, 10]

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Conclusion