## 3 Proposed Scheme
### Metaheuristic-tabu Search Algorithm
the fact that the larger the distance, the lower the aggregate uplink interference from cellular users to M-D2D receivers. As observed from Figure 5a, our proposed resource allocation and metaheuristic-tabu search scheme has the best performance compared with other schemes. The variation of the received SINR of cellular users with respect to the distance between the M-D2D transmitter and eNB is plotted in Figure 5b. As can be seen, the received SINR increases as the distance increases and, compared with the RRA scheme, our proposed scheme can accommodate high SINR. The total power consumption as a function of the distance between the D2D transmitter and its corresponding receivers in an M-D2D group is shown in Figure 6a. It is seen from Figure 6a that as the distance increases, the link quality decreases, therefore, the M-D2D transmitter must transmit data to its corresponding receivers with a higher transmission power. However, the overall power consumption of our proposed scheme is much lesser than the RRA scheme with and without the metaheuristic-tabu search algorithm. This is due to the fact that the metaheuristic-tabu search algorithm ignores certain repetitions while finding best resource reuse partners. Figure 6b shows the fairness of resource distribution against the distance between the D2D transmitter and receiver. For simple analysis, we assumed the optimal fairness index as 1. It can be seen from Figure 6b that as the distance between the D2D transmitter and receiver of a multicast group increases, the fairness index decreases drastically. We observe that our proposed scheme obtains a nearly optimal fairness index as compared with the existing scheme. Figure 7a plots the spectral efficiency distribution of M-D2D users. Observed from Figure 7a, our proposed joint resource allocation and metaheuristic-tabu search algorithm has the best performance compared with other schemes. This is due to the fact that our proposed metaheuristic-tabu search algorithm finds the most promising resource sharing partner between cellular users and M-D2D users, which can reduce the total uplink interference. On the other hand, the RRA scheme without the metaheuristic-tabu search algorithm experiences lowers spectral efficiency; this is due to the interference from cellular users to nearby M-D2D receivers. Finally, we notice that 70% of M-D2D users in our proposed scheme achieved a spectral efficiency of 71.08 bits/sec/Hz. The spectral efficiency distribution of cellular users is shown in Figure 7b. We can observe that our proposed scheme has the best throughput performance compared with existing schemes. This is because our proposed scheme aims at maximizing the user's throughput based on the resource partition technique. Also, from Figure 7b, it is seen that in the proposed communication scenario, 60% of users achieved

Figure 5: (**a**) Received SINR of M-D2D as a function of the distance between M-D2D receivers and the cellular user; (**b**) received SINR of a cellular user as a function of the distance between the M-D2D transmitter and eNB. a spectral efficiency of 72.51 bps/Hz. Finally, we notice that the spectral efficiencies of M-D2D users are greater than those for cellular users, due to generally smaller communication distances in M-D2D communications. ## 6 Conclusions

In this paper, we have considered joint resource allocation and the metaheuristic-tabu search algorithm for M-D2D communications reusing uplink cellular resources. The main drawback of M-D2D communications underlaying a cellular network is the interference caused by D2D users to conventional cellular networks. To mitigate the interference, we proposed a spectrum reuse method based on the FFR technique. Then, to achieve higher system performance, we formulated a sum throughput optimization problem.