Alternating Minimization Algorithms for Hybrid Precoding in Millimeter Wave MIMO Systems

X. Yu, J.-C. Shen, Jun Zhang, K.B. Letaief

Research output: Journal article publicationJournal articleAcademic researchpeer-review

800 Citations (Scopus)


© 2016 IEEE.Millimeter wave (mmWave) communications has been regarded as a key enabling technology for 5G networks, as it offers orders of magnitude greater spectrum than current cellular bands. In contrast to conventional multiple-input-multiple-output (MIMO) systems, precoding in mmWave MIMO cannot be performed entirely at baseband using digital precoders, as only a limited number of signal mixers and analog-to-digital converters can be supported considering their cost and power consumption. As a cost-effective alternative, a hybrid precoding transceiver architecture, combining a digital precoder and an analog precoder, has recently received considerable attention. However, the optimal design of such hybrid precoders has not been fully understood. In this paper, treating the hybrid precoder design as a matrix factorization problem, effective alternating minimization (AltMin) algorithms will be proposed for two different hybrid precoding structures, i.e., the fully-connected and partially-connected structures. In particular, for the fully-connected structure, an AltMin algorithm based on manifold optimization is proposed to approach the performance of the fully digital precoder, which, however, has a high complexity. Thus, a low-complexity AltMin algorithm is then proposed, by enforcing an orthogonal constraint on the digital precoder. Furthermore, for the partially-connected structure, an AltMin algorithm is also developed with the help of semidefinite relaxation. For practical implementation, the proposed AltMin algorithms are further extended to the broadband setting with orthogonal frequency division multiplexing modulation. Simulation results will demonstrate significant performance gains of the proposed AltMin algorithms over existing hybrid precoding algorithms. Moreover, based on the proposed algorithms, simulation comparisons between the two hybrid precoding structures will provide valuable design insights.
Original languageEnglish
Article number7397861
Pages (from-to)485-500
Number of pages16
JournalIEEE Journal on Selected Topics in Signal Processing
Issue number3
Publication statusPublished - 1 Apr 2016
Externally publishedYes


  • Alternating minimization
  • hybrid precoding
  • low-complexity
  • manifold optimization
  • millimeter wave communications
  • Semidefinite relaxation

ASJC Scopus subject areas

  • Signal Processing
  • Electrical and Electronic Engineering


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