[Paper Review] Topological Interference Management with Transmitter Cooperation

Xinping Yi, David Gesbert|arXiv (Cornell University)|Dec 2, 2014

Cooperative Communication and Network Coding39 references4 citations

TL;DR

This paper studies topological interference management in distributed broadcast channels with transmitter cooperation, proposing interference alignment and selective graph coloring techniques to exploit partial channel state information via network topology. It establishes that symmetric degrees of freedom (DoF) can be strictly improved over conventional schemes as long as the network is not fully connected, with exact DoF characterized for regular and arbitrary topologies using graph-theoretic and index coding tools.

ABSTRACT

Interference networks with no channel state information at the transmitter (CSIT) except for the knowledge of the connectivity graph have been recently studied under the topological interference management (TIM) framework. In this paper, we consider a similar problem with topological knowledge but in a distributed broadcast channel setting, i.e. a network where transmitter cooperation is enabled. We show that the topological information can also be exploited in this case to strictly improve the degrees of freedom (DoF) as long as the network is not fully connected, which is a reasonable assumption in practice. Achievability schemes based on selective graph coloring, interference alignment, and hypergraph covering, are proposed. Together with outer bounds built upon generator sequence, the concept of compound channel settings, and the relation to index coding, we characterize the symmetric DoF for so-called regular networks with constant number of interfering links, and identify the sufficient and/or necessary conditions for the arbitrary network topologies to achieve a certain amount of symmetric DoF.

Motivation & Objective

• To investigate the benefits of topological knowledge—specifically, which interference links are weak or strong—in distributed broadcast channels with transmitter cooperation.
• To determine whether topological interference management (TIM) can improve degrees of freedom (DoF) in a network MIMO setting without instantaneous CSIT.
• To characterize the symmetric DoF for regular and arbitrary network topologies under topological knowledge and transmitter cooperation.
• To establish necessary and sufficient conditions for achieving a given symmetric DoF using graph-theoretic and index coding frameworks.
• To bridge the TIM problem with index coding by showing that optimal index coding solutions serve as outer bounds for TIM, and linear solutions are transferrable.

Proposed method

• Proposes a fractional selective graph coloring approach on the square of the line graph of the network topology to enable interference avoidance.
• Introduces an alignment feasibility graph (AFG) to model which message pairs can be aligned based on their interference sets, defined by non-inclusion of transmitter sets.
• Uses hypergraph covering and generator sequences to derive outer bounds on DoF, particularly for regular networks with constant interfering links.
• Applies the compound channel model and index coding duality to relate TIM to the index coding problem, enabling tighter DoF characterization.
• Employs a constructive proof via proper partitioning of messages to show that DoF of 1/(K−1) is achievable when the alignment feasibility graph is non-empty.
• Establishes equivalence between cyclic demand graphs in index coding and non-empty alignment feasibility graphs, linking structural network properties to DoF performance.

Experimental results

Research questions

• RQ1 Can topological interference management with transmitter cooperation achieve higher symmetric degrees of freedom than conventional schemes without instantaneous CSIT?
• RQ2 What are the necessary and sufficient conditions on network topology for achieving a symmetric DoF of 1/K or higher?
• RQ3 How does the structure of the interference graph (e.g., cycle presence in demand graph) affect the achievable DoF in a distributed broadcast channel?
• RQ4 To what extent can index coding duality be used to bound and characterize the DoF in topological interference management with transmitter cooperation?
• RQ5 Can interference alignment be effectively applied in a distributed MIMO setting using only topological knowledge and no instantaneous CSI?

Key findings

• The symmetric DoF can be strictly improved over the 1/K baseline as long as the network is not fully connected, even without instantaneous CSIT.
• For regular networks with a constant number of interfering links, the symmetric DoF is characterized exactly using hypergraph covering and generator sequence techniques.
• A non-empty alignment feasibility graph (AFG) implies that DoF of 1/(K−1) is achievable, which is strictly better than 1/K.
• The existence of a cycle in the index coding demand graph is both necessary and sufficient for the symmetric DoF to exceed 1/K.
• The optimal solution to the index coding problem provides an outer bound on the DoF in the TIM setting, and linear solutions to TIM are transferrable to index coding.
• The characterization shows that topological knowledge alone—specifically, the knowledge of which interference links are weak or absent—can enable significant DoF gains in practical, partially connected networks.