Long-Term Rate-Fairness-Aware Beamforming Based Massive MIMO Systems

W. Zhu, H. D. Tuan, E. Dutkiewicz, Y. Fang, H. V. Poor, L. Hanzo

Research output: Contribution to journalArticlepeer-review


This is the first treatise on multi-user (MU) beamforming designed for achieving long-term rate-fairness in full-dimensional MU massive multi-input multi-output (m-MIMO) systems. Explicitly, based on the channel covariances, which can be assumed to be known beforehand, we address this problem by optimizing the following objective functions: the users' signal-to-leakage-noise ratios (SLNRs) using SLNR max-min optimization, geometric mean of SLNRs (GM-SLNR) based optimization, and SLNR soft max-min optimization. We develop a convex-solver based algorithm, which invokes a convex subproblem of cubic time-complexity at each iteration for solving the SLNR max-min problem. We then develop closed-form expression based algorithms of scalable complexity for the solution of the GM-SLNR and of the SLNR soft max-min problem. The simulations provided confirm the users' improved-fairness ergodic rate distributions.

Original languageEnglish (US)
Pages (from-to)2386-2398
Number of pages13
JournalIEEE Transactions on Communications
Issue number4
StatePublished - Apr 1 2024
Externally publishedYes

All Science Journal Classification (ASJC) codes

  • Electrical and Electronic Engineering


  • Full-dimensional massive MIMO
  • ergodic rate
  • signal to leakage plus noise ration (SLNR) optimization
  • statistical beamforming


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