K -User Interference Channels with Backhaul Cooperation: DoF vs. Backhaul Load Trade-Off

Borna Kananian, Mohammad Ali Maddah-Ali, Babak Hossein Khalaj

Research output: Contribution to journalArticlepeer-review

2 Scopus citations


In this paper, we consider $K$ -user interference channels with $M$ antennas per node and with backhaul collaboration in one side (among the transmitters or among the receivers), for $M,K\in \mathbb {N}$ , and investigate the tradeoff between the rate in the channel versus the communication load in the backhaul. In this investigation, each node is equipped with $M$ antennas and we focus on a first order approximation result, where the rate of the wireless channel is measured by the degrees of freedom (DoF) per user, and the load of the backhaul is measured by the entropy of backhaul messages per user normalized by $\log $ of transmit power, at high power regimes. This tradeoff is fully characterized for the case of even values of $K$ and approximately characterized for the case of odd values of $K$ , with vanishing approximation gap as $K$ grows. To achieve DoF of $M$ per user, this result establishes the asymptotic optimality of the most straightforward scheme, called central processing, in which the messages are collected at one of the nodes, centrally processed, and forwarded back to each node. In addition, this result shows that the gain of the schemes, relying on distributed processing, through pairwise communication among the nodes (e.g., cooperative alignment) does not scale with the size of the network. For the converse, we develop a new outer-bound on the tradeoff based on splitting the set of collaborative nodes (transmitters or receivers) into two subsets and assuming full cooperation within each group. We further present a sufficient condition on the wireless channel connectivity, which although more relaxed, guarantees the validity of the above tradeoff. Finally, we show that verifying this condition takes a polynomial time in the network size.

Original languageEnglish (US)
Article number8753416
Pages (from-to)7253-7267
Number of pages15
JournalIEEE Transactions on Information Theory
Issue number11
StatePublished - Nov 2019
Externally publishedYes

Bibliographical note

Funding Information:
Manuscript received July 23, 2018; revised March 19, 2019; accepted June 14, 2019. Date of publication July 2, 2019; date of current version October 18, 2019. B. Hossein Khalaj was supported in part by a grant from the Institute for Research in Fundamental Sciences (IPM) and in part by the Iran National Science Foundation under Grant 97022420. This paper was presented in part at the 2017 International Symposium on Information Theory (ISIT).

Publisher Copyright:
© 1963-2012 IEEE.


  • centralized processing
  • cooperation alignment
  • degrees of freedom
  • Interference alignment


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