## 3 Proposed Scheme
### Metaheuristic-tabu Search Algorithm
However, the computational complexity of the optimization

Figure 6: (a) Power consumption of the overall system as a function of the distance between the D2D transmitter and D2D receiver; (b) fairness as a function of the distance between the D2D transmitter and receiver. Figure 7: (a) Cumulative distribution of the spectral efficiency of an M-D2D user; (b) cumulative distribution of the spectral efficiency of a cellular user. problem was high due to the large number of iterations. To achieve low computational complexity, we introduced a metaheuristic-tabu search algorithm. Moreover, the fairness of the resource allocation was analyzed by using an efficient Jain's fairness index, which maintained a level of the required SINR. For analysis, we assumed the optimal value of the fairness index as 1. We performed extensive simulations in terms of the target SINR, the distance between the D2D transmitter and receiver, threshold SINR, and number of successful D2D receivers in an M-D2D group. We compared our proposed scheme with the RRA scheme with and without the metaheuristic-tabu search algorithm. The results demonstrated that our proposed scheme provides a good tradeoff between the interference mitigation and required throughput, thus it effectively increases overall system throughput and spectral efficiency. As a future work, this approach can be extended by assuming a resource reuse factor more than 1 for the M-D2D communications. **Author Contributions:** [PERSON] organized and developed the proposal of the study, carried out the mathematical analysis, and performed simulations using Monte Carlo. S.S. provided guidance, key suggestions, and finalized the paper. **Funding:** This research is partly supported by Basic Science Research Program through the National Research Foundation of Korea (NRF) funded by the Ministry of Education with Grant NRF-2018R1D1A1B07048338 and a part of the project titled 'Development of Automatic Identification Monitoring System for Fishing Gears', funded by the Ministry of Oceans and Fisheries, Korea with Grant No. 20170388. **Conflicts of Interest:** The authors declare no conflict of interest. ## Appendix A

For uplink interference region analysis, the general expressions of the received SINRs of a cellular user, \(c^{in}\), and the D2D group, \(g\), are calculated as follows:

\[\frac{P_{B}\cdot l_{c^{in},B}^{-\alpha}}{P_{g^{edge}}\cdot l_{g^{edge},B}^{- \alpha}+\sigma_{n}^{2}}\geq\ \gamma_{Th}\ \text{and}\ \frac{P_{g^{edge}}\cdot l_{g^{edge}_{t},g^{edge}_{t}}^{-\alpha}}{P_{B}\cdot l _{c^{in},g^{edge}_{t}}^{-\alpha}+\sigma_{n}^{2}}\geq\ \gamma_{Th} \tag{1}\]

Neglecting the noise power from Equation (1), we have:

\[\frac{P_{B}\cdot l_{c^{in},B}^{-\alpha}}{P_{g^{edge}}\cdot l_{g^{edge},B}^{- \alpha}}\geq\ \gamma_{Th}\ \text{and}\ \frac{P_{g^{edge}}\cdot l_{g^{edge}_{t},g^{edge}_{t}}^{-\alpha}}{P_{B}\cdot l _{c^{in},g^{edge}_{t}}^{-\alpha}}\geq\ \gamma_{Th} \tag{2}\]

Solving Equation (2), \(l_{c^{in},g^{edge}_{t}}^{\alpha}\) can be expressed as:

\[\frac{\gamma_{Th}\ l_{g^{edge}_{t}}^{-\alpha}}{l_{c^{in},B}^{- \alpha}}=\frac{l_{g^{edge}_{t}}^{-\alpha}}{\gamma_{Th}l_{c^{in},g}^{-\alpha}} \tag{3}\] \[l_{c^{in},g^{edge}_{t}}^{-\alpha}=\frac{l_{g^{edge}_{t}}^{-\alpha} \gamma_{Th}^{-\alpha}}{l_{c^{in},g^{edge}_{t}}^{-\alpha}+\sigma_{Th}^{-\alpha }}\] Figure 4:0 Figure 4:1

Since the uplink interference region is defined by the distance between the cellular user and M-D2D receiver, we have:

Figure 4:2

This completes the proof. Figure 4:3

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