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A Deep Learning Framework for Optimization of MISO Downlink Beamforming
Open accessAbstract
Beamforming is an effective means to improve the quality of the received signals in multiuser multiple-input-single-output (MISO) systems. Traditionally, finding the optimal beamforming solution relies on iterative algorithms, which introduces high computational delay and is thus not suitable for real-time implementation. In this paper, we propose a deep learning framework for the optimization of downlink beamforming. In particular, the solution is obtained based on convolutional neural networks and exploitation of expert knowledge, such as the uplink-downlink duality and the known structure of optimal solutions. Using this framework, we construct three beamforming neural networks (BNNs) for three typical optimization problems, i.e., the signal-to-interference-plus-noise ratio (SINR) balancing problem, the power minimization problem, and the sum rate maximization problem. For the former two problems the BNNs adopt the supervised learning approach, while for the sum rate maximization problem a hybrid method of supervised and unsupervised learning is employed. Simulation results show that the BNNs can achieve near-optimal solutions to the SINR balancing and power minimization problems, and a performance close to that of the weighted minimum mean squared error algorithm for the sum rate maximization problem, while in all cases enjoy significantly reduced computational complexity. In summary, this work paves the way for fast realization of optimal beamforming in multiuser MISO systems.
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“This is due to the reason that quantum channels can have different possibilities in terms of delivering information including quantum information, entanglement-assisted classical information [123] and private classical information [124].”
From Quantum Machine Learning for 6G Communication Networks: State-of-the-Art and Vision for the Future (2019) · cites this paper as [124]
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“roblems P1 and P2 has K neurons but that in the BNN for problem P3 has 2K neurons. The Glorot normal initializer [62] is used for weight initialization and biases are initialized to 0. Adam optimizer [63] is used with the MSE metric-based loss function. However, in the second stage of the BNN for problem P3, the metri…”
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“Practical algorithms to find optimal solutions are available for P1 [8], [12], [47] and P2 [5], [7], [8], [12], [13], thus supervised learning can be adopted for those problems.”
BackgroundMethodZero-Forcing Methods for Downlink Spatial Multiplexing in Multiuser MIMO Channels
Spencer, Q. H., Swindlehurst, A. L., & Haardt, M. (2004) · IEEE Transactions on Signal Processing · doi:10.1109/tsp.2003.821107 · Cited by 3,148 · cited 1×
“To evaluate the performance of the proposed BNNs, we carry out numerical simulations to compare the BNNs with several benchmark solutions (when available), including the optimal beamforming, the ZF beamforming [58], the RZF beamforming [59], and the WMMSE algorithm.”
MethodNon-negative Matrices and Markov Chains
Seneta, E. B. (1981) · Springer series in statistics · doi:10.1007/0-387-32792-4 · Cited by 2,858 · cited 1×
“According to the Perron-Frobenius theory, for any nonnegative real matrix Ω with spectral radius χ ( Ω ) , there exist a vector δ ≥ 0 such that Ω δ = χ ( Ω ) δ [54].”
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“P3 is a difficult nonconvex problem and is usually solved using the iterative WMMSE approach [9, 10], therefore, supervised learning alone is insufficient for this case.”
BackgroundMethodInfluentialOn the optimality of multiantenna broadcast scheduling using zero-forcing beamforming
Taesa, & Goldsmith, A. J. (2006) · IEEE Journal on Selected Areas in Communications · doi:10.1109/jsac.2005.862421 · Cited by 2,054 · cited 2×
“…ratio (SINR) balancing problem (also known as interference balancing problem) under a total power constraint [2–4], as a power minimization problem under quality of service (QoS) constraints [5–8], or as a sum rate maximization problem under a total power constraint [2, 9–11].”
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AI-RAN: The pathway to future wireless networks
Feng, C., Yang, H. H., Guo, K., et al. (2026) · Journal of Information and Intelligence · doi:10.1016/j.jiixd.2025.12.013 · Cited by 5
Self-citationRadio Resource Allocation for 5G Network Using Deep Reinforcement Learning
Umesh, R. G., N, S. K. G., Santhosh, K., et al. (2023) · International Journal for Research in Applied Science and Engineering Technology · doi:10.22214/ijraset.2023.49468 · Cited by 4
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Metadata
- Authors
- Xia, W., Zheng, G., Zhu, Y., Zhang, J., Wang, J., & Petropulu, A. P.
- Affiliations
- Nanjing University of Posts and Telecommunications (CN)
- Loughborough University (GB)
- London South Bank University (GB)
- University of Kent (GB)
- Rutgers, The State University of New Jersey (US)
- Venue
- IEEE Transactions on Communications
- Published
- 2020-03
- Volume
- 68
- Issue
- 3
- Pages
- 1866-1880
- ISSN
- 0090-6778 (ISSN-L)
- 1558-0857
- OpenAlex
- W2908498346
- Semantic Scholar
- f4996081ea7ea0995d70f5ad2e9bb121dfe5d384
- Cited by
- 345
- References
- 70
- Citations by year
- 2026: 27 · 2025: 48 · 2024: 62 · 2023: 61 · 2022: 63 · 2021: 46 · 2020: 33
- FWCI
- 13.21
- Type
- journal article
- Language
- en
- Open access
- green
- doi.org
- Licence
- Locations
- IEEE Transactions on Communications (publishedVersion)
- Research Open (London South Bank University) (acceptedVersion, cc-by)
- arXiv (Cornell University) (submittedVersion)
- Kent Academic Repository (University of Kent) (submittedVersion)
- arXiv (Cornell University)
- Funders
- National Natural Science Foundation of China (61871446, 61671251, U1805262, 61404130218)
- Engineering and Physical Sciences Research Council (EP/N007840/1)
- Leverhulme Trust (RPG-2017-129)
- National Science Foundation (CCF-1526908)
- Topics
- Physical Sciences › Engineering › Electrical and Electronic Engineering › Advanced MIMO Systems Optimization
- Physical Sciences › Engineering › Electrical and Electronic Engineering › Advanced Wireless Network Optimization
- Physical Sciences › Engineering › Electrical and Electronic Engineering › Millimeter-Wave Propagation and Modeling
- Keywords
- convolutional neural networks, SINR balancing, power minimization, sum rate maximization, uplink-downlink duality, supervised learning, unsupervised learning, computational complexity reduction, real-time beamforming
About these checks
Registry, retraction, Cites and statistics results are computed, not judged, with one exception: a printed reference that no index lists is read once by a model before it counts as a citation error. Claims are extracted by a model and kept only when their quote appears verbatim in the text; each cited source is then checked, with a model’s help, for whether it says what the claim relies on. Those verdicts can be wrong — read the claim’s quote and the cited source before relying on one.
Statistics and arithmetic are recomputed, not judged.
Confidence bands are shown only for fields calibrated on our annotated test set. None is calibrated yet, so no band is shown.
What counts as a claim ›How we measure confidence ›How we check this ›
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