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SCIENCE CHINA Information Sciences, Volume 63 , Issue 8 : 180303(2020) https://doi.org/10.1007/s11432-020-2937-y

Multitask deep learning-based multiuser hybrid beamforming for mm-wave orthogonal frequency division multiple access systems

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  • ReceivedJan 2, 2020
  • AcceptedJun 3, 2020
  • PublishedJul 15, 2020

Abstract

Multiuser hybrid beamforming of a wideband millimeter-wave (mm-wave) system is a complex combinatorial optimization problem. It not only needs large training data, but also tends to overfit and incur long run-time when multiple serial deep learning network models are used to solve this problem directly. Preferably, multitask deep learning (MTDL) model could jointly learn multiple related tasks and share their knowledge among the tasks, and this has been demonstrated to improve performance, compared to learning the tasks individually. Therefore, this work presents a first attempt to exploit MTDL for multiuser hybrid beamforming for mm-wave massive multiple-input multiple-output orthogonal frequency division multiple access systems. The MTDL model includes a multitask network architecture, which consists of two tasks- user scheduling and multiuser analog beamforming. First, we use the effective channel with a low dimension as input data for the two parallel tasks to reduce the computational complexity of deep neural networks. In a shallow shared layer of the MTDL model, we utilize hard parameter sharing in which the knowledge of multiuser analog beamforming task is shared with the user scheduling task to mitigate multiuser interference. Second, in the training process of the MTDL model, we use the exhaustive search algorithm to generate training data to ensure optimal performance. Finally, we choose the weight coefficient of each task by traversing all weight coefficient combinations in the training phase. Simulation results prove that our proposed MTDL-based multiuser hybrid beamforming scheme could achieve better performance than traditional algorithms and multiple serial single tasks deep learning scheme.


Acknowledgment

This work was supported by National Natural Science Foundation of China (Grant Nos. 61871321, 61901367), National Science and Technology Major Project (Grant No. 2017ZX03001012-005), and Shaanxi STA International Cooperation and Exchanges Project (Grant No. 2017KW-011).


References

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  • Figure 1

    The structure of multi-user hybrid beamforming scheme.

  • Figure 2

    The structure of multitask deep learning-based multiuser hybrid beamforming scheme.

  • Figure 3

    The structure of single task deep learning-based multiuser hybrid beamforming scheme.

  • Figure 4

    The sum-rate cumulative distribution function (CDF) of different schemes with SNR = 0 dB. (a) ${{N}_{\rm~RF}}=2$, ${{N}_{\rm~RB}}=2$; (b) ${{N}_{\rm~RF}}=2$, ${{N}_{\rm~RB}}=4$.

  • Figure 5

    The sum-rate of different scheme versus SNR. (a) ${{N}_{\rm~RF}}=2$, ${{N}_{\rm~RB}}=2$; (b) ${{N}_{\rm~RF}}=2$, ${{N}_{\rm~RB}}=4$.

  • Figure 6

    The elapsed time of different schemes.

  •   

    Algorithm 1 Generation of the training data

    Require:${\boldsymbol~x}_{\rm~in}$.

    Output:$\mathcal{R}$, $\mathcal{B}$. Initialization: $~\mathcal{M}\in~O\left(~{{K}_{\rm~all}}\times~{{N}_{c}}~\right)$, $~\mathcal{U}\in~O\left(~{{N}_{c}}\times~{{N}_{\rm~RB}}~\right)$, $\mathcal{R}\in~O\left(~{{K}_{\rm~all}}\times~{{N}_{\rm~RB}}~\right)$, $\mathcal{B}\in~O\left(~{{K}_{\rm~all}}\times~{{N}_{c}}~\right)$, the selected MU-MIMO user set ${{\Omega~}_{S}}={{\emptyset}}$.

    According to the best beam index of each user, set the corresponding element of $\mathcal{M}$ to 1, e.g., if ${{\boldsymbol~B}_{k}}=n_c$, then $\mathcal{M}(k,n_c)=1$.

    Assume there are $Q_{{n}_{c}}$ possible schemes of resource allocation for users with the same best beam. Exploiting the exhaustive search algorithm to find the user scheduling scheme with the maximum sum rate. for ${{n}_{c}}=1:{{N}_{c}}$ for ${q}=1:{Q_{{n}_{c}}}$ $\left~\{~k^*~\right~\}=~{\mathop~{\arg~\max~}\nolimits_{q}}~{\sum_{n=1}^{N_{\rm~RB}}}~\Big(~{\frac{{{{\left\|~{{{\overline~{\boldsymbol~H}~}_{k,n}}}~\right\|}^2}}}{{{\sigma~^2}}}}~\Big)$, $\mathcal{U}({{n}_{c},n})={{k}^{*}}$ and ${\mathcal~R}({n_c},n)~=~1$, end end

    After resource allocation, each beam is regarded as a virtual OFDMA user multiplexing the whole frequency resource. Then, the integrated channel of each virtual OFDMA user is merged as follows, $\Omega~=\{~{{\tilde{\boldsymbol~H}}_{{{n}_{1}}}},{{\tilde{\boldsymbol~H}}_{{{n}_{2}}}},\ldots,{{\tilde{\boldsymbol~H}}_{{{N}_{c}}}}~\}$ and ${{\tilde~{\boldsymbol~H}}_{{n_c}}}~=~{[~{{{\boldsymbol~H}_{{\cal~U}({n_c},1)}}|{{\boldsymbol~H}_{{\cal~U}({n_c},2)}}|\cdots~|{{\boldsymbol~H}_{{\cal~U}({n_c},{N_{\rm~RB}})}}}~]_{{N_r}~\times~{N_{{t}}}}}$ is the channel matrix of a user allocated in the $n$th RB for the ${n}_{c}$th virtual OFDMA user. When a frequency resource is not been allocated to any user, ${\boldsymbol~H}_{\mathcal{U}({{n}_{c}},{n}})$ is equal to zero matrix.

    Select ${N}_{\rm~RF}$ virtual OFDMA users to maximizes sum-rate. for ${{n}_{c}}=1:{{N}_{\rm~RF}}$ if $~{n_c}~=~\mathop~{\max~}\nolimits_{{{\tilde~H}_{{n_c}}}~\in~\Omega~}~{\log~_2}\Big(~{1~+~\frac{{{{\|~{{\boldsymbol~U}_{{n_c}}^{\rm~H}{{{\tilde~{\boldsymbol~H}}}_{{n_c}}}{{\boldsymbol~V}_{{n_c}}}}~\|}^2}}}{{{\delta~^2}~+~\sum\nolimits_{j~\in~{\Omega~_s},{n_c}~\in~\Omega~}~{{{\|~{{\boldsymbol~U}_j^{\rm~H}{{{\tilde~{\boldsymbol~H}}}_{{n_c}}}{{\boldsymbol~V}_j}}~\|}^2}}~}}} +~\sum\nolimits_{j~\in~{\Omega~_s}}~{\frac{{{{\|~{{\boldsymbol~U}_j^{\rm~H}{{{\tilde~{\boldsymbol~H}}}_j}{{\boldsymbol~V}_j}}~\|}^2}}}{{{\delta~^2}~+~{{\|~{{\boldsymbol~U}_{{n_c}}^{\rm~H}{{{\tilde~{\boldsymbol~H}}}_j}{{\boldsymbol~V}_{{n_c}}}}~\|}^2}~+~\sum\nolimits_{i~\in~{\Omega~_s},i~\ne~j}~{{{\|~{{\boldsymbol~U}_i^{\rm~H}{{{\tilde~{\boldsymbol~H}}}_j}{{\boldsymbol~V}_i}}~\|}^2}}~}}}~~\Big)$, where ${\boldsymbol~U}$ and ${\boldsymbol~V}$ are the left unitary matrix and the right unitary matrix of the singular value decomposition of virtual OFDMA user ${{\tilde~{\boldsymbol~H}}}_{n_c}$, respectively. then ${\cal~B}(:,{n_c})~=~1$, $\Omega~~\leftarrow~\Omega~\backslash~\{~{{\tilde~{\boldsymbol~H}}_{{n_c}}}\}$, ${\Omega~_s}~\leftarrow~{\Omega~_s}~\cup~\{~{{\tilde~{\boldsymbol~H}}_{{n_c}}}\}~$. end

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