A Family of Hybrid Analog-Digital Beamforming Methods for Massive MIMO Systems

Shahar Stein Ioushua*, Yonina C. Eldar

*Corresponding author for this work

Research output: Contribution to journalArticlepeer-review


In massive MIMO systems, hybrid beamforming is an essential technique for exploiting the potential array gain without using a dedicated RF chain for each antenna. In this paper, we consider the data phase in massive MIMO communication, where the transmitter and receiver use fewer RF chains than antennas. We examine several different fully and partially connected schemes and consider the design of hybrid beamformers that minimize the estimation error in the data. For the hybrid precoder, we introduce a framework for approximating the optimal fully digital precoder with a feasible hybrid one. We exploit the fact that the fully digital precoder is unique only up to a unitary matrix and optimize over this matrix and the hybrid precoder alternately. Our alternating minimization of approximation gap (Alt-MaG) framework improves the performance over state-of-the-art methods with no substantial increase in complexity. In addition, we present a special case of Alt-MaG, minimal gap iterative quantization (MaGiQ), that results in low complexity and lower mean squared error (MSE) than other common methods, in the case of very few RF chains. MaGiQ is also shown to coincide with the optimal fully digital solution in some scenarios. For combiner design, we exploit the structure of the MSE objective and develop a greedy ratio trace maximization technique that achieves low MSE under various settings. All of our algorithms can be used with multiple hardware architectures.

Original languageEnglish
Article number8691587
Pages (from-to)3243-3257
Number of pages15
JournalIEEE Transactions on Signal Processing
Issue number12
StatePublished - 15 Jun 2019


  • Massive multiple-input multiple-output (MIMO)
  • alternating minimization
  • antenna arrays
  • cellular communication
  • combining
  • hybrid beamforming
  • low-complexity
  • precoding
  • ratio-trace minimization


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