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



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).


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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


    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