Non-Convex Generalized Nash Games for Energy Efficient Power Allocation and Beamforming in mmWave Networks

Wenbo Wang, Amir Leshem

Research output: Contribution to journalArticlepeer-review


Network management is a fundamental ingredient for efficient operation of wireless networks. With increasing bandwidth, number of antennas and number of users, the amount of information required for network management increases significantly. Therefore, distributed network management is a key to efficient operation of future networks. This paper focuses on the problem of distributed joint beamforming control and power allocation in ad-hoc mmWave networks. Over the shared spectrum, a number of multi-input-multi-output links attempt to minimize their supply power by simultaneously finding the locally optimal power allocation and beamformers in a self-organized manner. Our design considers a family of non-convex quality-of-service constraint and utility functions characterized by monotonicity in the strategies of the various users. We propose a two-stage, decentralized optimization scheme, where the adaptation of power levels and beamformer coefficients are iteratively performed by each link. We first prove that given a set of receive beamformers, the power allocation stage converges to an optimal generalized Nash equilibrium of the generalized power allocation game. Then we prove that iterative minimum-mean-square-error adaptation of the receive beamformer results in an overall converging scheme. Several transmit beamforming schemes requiring different levels of information exchange are also compared in the proposed allocation framework. Our simulation results show that allowing each link to optimize its transmit filters using the direct channel results in a near optimum performance with very low computational complexity, even though the problem is highly non-convex.

Original languageEnglish
Pages (from-to)3193-3205
Number of pages13
JournalIEEE Transactions on Signal Processing
StatePublished - 2022

Bibliographical note

Funding Information:
This work was supported by the Israel Science Foundation under Grant 1644/18. This work was presented at IEEE International Conference on Acoustics, Speech and Signal Processing, 2022 and 12th Sensor Array and Multichannel Signal Processing Workshop, 2022 [DOI: 10.1109/ICASSP43922.2022.9747360].

Publisher Copyright:
© 1991-2012 IEEE.


  • Beamforming
  • energy-aware networks
  • generalized nash equilibrium
  • multi-link
  • multiple-input multiple-output


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