## 4 Fairness-Aware Machine Learning Based Power and RB Allocation with Multiple Relays
### Relays Deployment and Users Association
This further reduces the required transmit power of the relay, hence a net increase in EE has been observed in \[K = \text{Total number of clusters being formed}.\]4 Addition of multiple relays slightly affect the SAMM NN and SAMM equal power in positive and negative way, respectively. The PF component of the SAMM forces the association of low throughput users to increase the fairness. This association goes in positive way for the SAMM NN due to the EE based power allocation, but goes in negative way for the SAMM equal power because of no compensation of the interference power. The increased fairness of SAMM NN is evident from the Figure 21, where, even the farthest users 9 and 10 have higher throughput. It can be seen that in LERPA, closer users get lower throughput but fairly large throughput is given to the farther users. This is because it uses max-min criterion for the RB allocation, which assigns the RB to the users who have lowest received SNR. \[K = \text{Total number of clusters being formed}.\]5 The error histogram. \[K = \text{Total number of clusters being formed}.\]6 The users’ throughput with neural network for SAMM along with LERPA of [11] in multiple relays scenario. \[K = \text{Total number of clusters being formed}.\]7 The system energy efficiency with neural network for SAMM which is trained on waterfilling based power allocation among users and BOPA based power allocation among subchannels in a single relay scenario. Table 3 summarizes simulation results. It can be seen that SAMM with BOPA and NN compete well in fairness with best EE. Tradeoff has to be done on system throughput. LERPA has better fairness performance but is less efficient in EE and system throughput, whereas, the hypothetical MT performs better in average system throughput. We say hypothetical because it only allocates the RB and power to the users with the highest SNR which can not be applicable on practical scenarios. ## 5 Complexity Analysis

The RB allocation scheme SAMM uses alternate MT and PF metrics to assign the \(N\) RBs to \(K\) users. MT assigns \(\frac{N}{2}\) RBs to \(K\) users and PF assigns \(\frac{N}{2}\) RBs to \(K-1\) users in alternate TTI. Therefore, the computational complexity of SAMM is \(\mathcal{O}\left(N(K-\frac{1}{2})\right)\). The BOPA Algorithm 1, first requires \(\lambda_{min}\) and \(\lambda_{max}\) in line 4 using water-filling algorithm for which the worse-case complexity is \(\mathcal{O}(2 NK)\). After that, BOPA uses binary search method to estimate the roots of Equation (17). In the worse case, with \(N_{p}\) points in the search space, binary search requires \(\log_{2}(N_{p})\) iterations to find the roots of polynomial. In our case, \(N_{p}=\frac{\lambda_{max}-\lambda_{min}}{\epsilon}\), where \(\epsilon\) is the error tolerance. Therefore, the overall complexity of the Algorithm 1 is \(\mathcal{O}(2 NK^{2}\log_{2}(N_{p}))\). In case of the optimal exhaustive search (\(K^{N}\)) RB allocation combining with the BOPA; the complexity is \(\mathcal{O}(2 NK^{N+2}\log_{2}(N_{p}))\), whereas, the complexity of SAMM-BOPA is \(\mathcal{O}((NK)^{2}(2K+1)\log_{2}(N_{p}))\). The running-time complexity of the K-mean algorithm is \(\mathcal{O}(kmdi)\)[31], where \(k\) is the number of clusters, \(m\) is the number of objects to be clustered, \(d\) is the dimension of objects, and \(i\) is the number of iterations. In our application of K-mean Algorithm 2, we use \(min_{k}<k<max_{k}\) and two-dimensional