Uplink-Downlink Duality between Multiple-Access and Broadcast Channels with Compressing Relays

Liang Liu, Ya Feng Liu, Pratik Patil, Wei Yu

Research output: Journal article publicationJournal articleAcademic researchpeer-review

7 Citations (Scopus)


Uplink-downlink duality refers to the fact that under a sum-power constraint, the capacity regions of a Gaussian multiple-access channel and a Gaussian broadcast channel with Hermitian transposed channel matrices are identical. This paper generalizes this result to a cooperative cellular network, in which remote access-points are deployed as relays in serving the users under the coordination of a central processor (CP). In this model, the users and the relays are connected over noisy wireless links, while the relays and the CP are connected over noiseless but rate-limited fronthaul links. Based on a Lagrangian technique, this paper establishes a duality relationship between such a multiple-access relay channel and broadcast relay channel, under the assumption that the relays use compression-based strategies. Specifically, we show that under the same total transmit power constraint and individual fronthaul rate constraints, the achievable rate regions of the Gaussian multiple-access and broadcast relay channels are identical, when either independent compression or Wyner-Ziv and multivariate compression strategies are used. The key observations are that if the beamforming vectors at the relays are fixed, the sum-power minimization problems under the achievable rate and fronthaul constraints in both the uplink and the downlink can be transformed into either a linear programming or a semidefinite programming problem depending on the compression technique, and that the uplink and downlink problems are Lagrangian duals of each other. Moreover, the dual variables corresponding to the downlink rate constraints become the uplink powers; the dual variables corresponding to the downlink fronthaul constraints become the uplink quantization noises. This duality relationship enables an efficient algorithm for optimizing the downlink transmission and relaying strategies based on the uplink.

Original languageEnglish
Article number9514556
Pages (from-to)7304-7337
Number of pages34
JournalIEEE Transactions on Information Theory
Issue number11
Publication statusPublished - 1 Nov 2021


  • broadcast channel
  • cell-free massive multiple-input multiple-output (MIMO)
  • cloud radio access network
  • multiple-access channel
  • multivariate compression
  • relay channel
  • Uplink-downlink duality
  • Wyner-Ziv compression

ASJC Scopus subject areas

  • Information Systems
  • Computer Science Applications
  • Library and Information Sciences


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