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Table 3 Algorithm to obtain the superframe sets \(\mathcal {U}^{S}_{I}\) and \(\mathcal {U}^{S}_{E}\)

From: User grouping and resource allocation in multiuser MIMO systems under SWIPT

1: Set a threshold 0≤α≤1

2: Order the users increasingly with the following rule:

\(\frac {C_{1}(t)}{C^{1}_{\max }} \le \frac {C_{2}(t)}{C^{2}_{\max }} \le \dots \le \frac {C_{K/2}(t)}{C^{K/2}_{\max }} \le \frac {C_{K/2+1}(t)}{C^{K/2+1}_{\max }}\le \dots \le \frac {C_{K}(t)}{C^{K}_{\max }}\)

3: if\(\alpha < \frac {C_{K/2}(t)}{C^{K/2}_{\max }}\)

4: Users {1,2,…,K/2} go to \(\mathcal {U}^{S}_{E}\)

5: Users {K/2+1,K/2+2,…,K} go to \(\mathcal {U}^{S}_{I}\)

6: else

7: Find the user m such that \(m=\arg \min _{i} \left |\frac {C_{i}(t)}{C^{i}_{\max }} - \alpha \right |\)

8: Users {1,2,…,m} go to \(\mathcal {U}^{S}_{E}\)

9: Users {m+1,m+2,…,K} go to \(\mathcal {U}^{S}_{I}\)

10: end if