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Table 2 Low-complexity suboptimal two-step algorithm

From: Joint user clustering and resource allocation for device-to-device communication underlaying MU-MIMO cellular networks

Two-step algorithm

1.

Initialization: S = ∅, K = ∅, L = ∅

2.

     Clustering Procedure:

3.

         For each resource pattern with only one RB rb ∈ {1,2,…,K rb }

4.

            Find the CUE sub-cluster and DUE sub-cluster \( \left\{\overline{k},\overline{l}\right\}= \arg \underset{\left\{k,l\right\}}{ \max }{t}_{k,l,rb} \)

5.

              \( K=K{\displaystyle \cup}\kern0.5em \overline{k} \)

6.

              \( L=L\;{\displaystyle \cup}\kern0.5em \overline{l} \)

7.

          End

8.

Searching Space Reduction Procedure:

9.

     For each \( \widehat{k}\in K;\widehat{l}\in L \) sets

10.

\( {s}_0=\left\{i\Big|\left(\widehat{k}-1\right)*{N}_{all,d}{N}_{all,rb}+\left(\widehat{l}-1\right)*{N}_{all,rb}+1\le i\le \left(\widehat{k}-1\right)*{N}_{all,d}{N}_{all,rb}+\widehat{l}*{N}_{all,rb}\right\} \)

12.

   S = S ∪ s 0

13.

     End

14.

Joint Solution Procedure:

15.

            Obtain the reduced-dimension optimization problem

16.

                  \( {x}_s=\underset{{\mathbf{x}}_S}{ \min}\left\{-{\mathbf{t}}_{\boldsymbol{S}}^{\boldsymbol{T}}{\mathbf{x}}_S\right\} \), s.t. \( {\mathbf{R}}_{:,S}{\mathbf{x}}_S={\mathbf{1}}_{\left({N}_c{N}_d{N}_{rb}+{K}_c+{K}_d\right)\times 1} \)

17.

            Find its solution based on the BBS algorithm

18.

Return \( {x}_s \)

19.

End