The DOI matches its Crossref record; 68 of the 70 references it cites were found in a registry or an index.
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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Cites
Adam: A Method for Stochastic Optimization
Kingma, D. P., & Ba, J. (2014) · arXiv · doi:10.48550/arxiv.1412.6980 · Cited by 98,946 · cited 1×
“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…”
MethodBatch Normalization: Accelerating Deep Network Training by Reducing Internal Covariate Shift
Ioffe, S., & Szegedy, C. (2015) · arXiv · doi:10.48550/arxiv.1502.03167 · Cited by 27,818
Multilayer feedforward networks are universal approximators
Hornik, K., Stinchcombe, M., & White, H. (1989) · Neural Networks · doi:10.1016/0893-6080(89)90020-8 · Cited by 21,728 · cited 4×
“Thus, we can use a neural network to approximate the mapping function from h to q [43].”
BackgroundMethodResultInfluential(2010) · Cited by 14,134
Multilayer feedforward networks are universal approximators
HornikK., StinchcombeM., & WhiteH. (1989) · Neural Networks · doi:10.5555/70405.70408 · Cited by 9,266
Semidefinite Relaxation of Quadratic Optimization Problems
Luo, Z.-Q., Ma, W.-K., So, A., Ye, Y., & Zhang, S. (2010) · IEEE Signal Processing Magazine · doi:10.1109/msp.2010.936019 · Cited by 3,715 · cited 2×
“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].”
Shi, Q., Razaviyayn, M., Luo, Z.-Q., & He, C. (2011) · IEEE Transactions on Signal Processing · doi:10.1109/tsp.2011.2147784 · Cited by 2,129 · cited 6×
“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].”
BackgroundMethod
Research works printed but not linked: 1
- grant, 2014, CVX Matlab Software for Disciplined Convex Programming Version 2 1
Cited by
Sorted by citations
Noor-A-Rahim, M., Liu, Z., Lee, H., Khyam, M. O., He, J., Pesch, D., Moessner, K., Saad, W., & Poor, H. V. (2022) · Proceedings of the IEEE · doi:10.1109/jproc.2022.3173031 · Cited by 737
“Adaptive beamforming in a vehicular communication scenario [139] and [140] is possible, but frequent beam training may be needed.”
BackgroundQuantum Machine Learning for 6G Communication Networks: State-of-the-Art and Vision for the Future
Nawaz, S. J., Sharma, S. K., Wyne, S., Patwary, M. N., & Asaduzzaman, M. (2019) · IEEE Access · doi:10.1109/access.2019.2909490 · Cited by 658
“In this context, a DL based framework for optimization of downlink beamforming is proposed in [92].”
MethodShen, Y., Shi, Y., Zhang, J., & Letaief, K. B. (2021) · IEEE Journal on Selected Areas in Communications · doi:10.1109/jsac.2020.3036965 · Cited by 367
“Most of the existing works adopt MLPs [7], [9], [11], [21] or convolutional neural networks (CNNs) [8], [12].”
BackgroundSelf-citationMismar, F. B., Evans, B. L., & Alkhateeb, A. (2019) · IEEE Transactions on Communications · doi:10.1109/tcomm.2019.2961332 · Cited by 285
“The performance of deep neural networks on beamforming was studied in [20] but without the use of reinforcement learning.”
BackgroundFast Beamforming Design via Deep Learning
Huang, H., Peng, Y., Yang, J., Xia, W., & Gui, G. (2019) · IEEE Transactions on Vehicular Technology · doi:10.1109/tvt.2019.2949122 · Cited by 282
“Hence, it is a natural way to adopt DL for fast beamforming design and the DL based beamforming design method has been studied in mmWave systems [24], [25] and MISO systems [26], [27].”
MethodSelf-citation
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
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