## 3 Fairness-Aware Power and Resource Block Allocation with Single Relay LTE-A Network
### Performance Evaluation  
A single cell is considered for generating simulations results. The cell consists of a BS, RN and UEs equipped with Omni-directional antennas. The throughput, energy and spectral efficiency is averaged over 1000 TTIs, with the duration of a TTI being 0.5 ms. The channel involves Raleigh fading and distance based path loss as shown in Figure 1. BS is located in the center of the cell coverage and most distant user is 1 Km distant from BS with RN in between at 0.55 Km. RN are In-band full duplex relays and bit error rate (BER) considered for MQAM modulation is \(10^{-3}\). Table 2 below summarizes all simulation parameters used to derive results shown next.  
Figure 2 shows the result of average throughput for MT and SAMM with equal power and BOPA based power allocation. It can be seen that SAMM curves remain on top of MT curves for most of the users due to inherent fairness which ensures all users get due share of RBs. However as evident from Figure 3 Sum throughput of MT is higher as compared to SAMM for overall averaged throughput of sum users due to channel exploitation of users with good channel conditions. This makes MT better than SAMM as BOPA has proportional rate constraint set for  
\begin{table}
\begin{tabular}{c c} \hline \hline
**Parameter** & **Value** \\ \hline Cell Radius & 1 Km \\ Noise Density (\(\sigma\)) & \(-171\) dBm/Hz \\ No of users (K) & 10 \\ Bandwidth (B) & 5 MHz \\ Number of resource blocks (RB) (N) & 25 \\ No of subcarriers per RB & 12 \\ Subcarrier bandwidth & 15 KHz \\ BS Transmitter Power & 46 dBm \\ Relay Power & 34 dBm \\ TTI duration & 0.5 ms \\ Relay distance from BS & 0.55 Km \\ Bit Error Rate (BER) & \(10^{-3}\) \\ OFDM symbols per TTI & 7 \\ Relay Type (In-band / Out-band Type 1 / Type 2) & In-band with Type 1b (full duplex) \\ \hline \hline \end{tabular}
\end{table}
Table 2: Simulation Parameters.  
Figure 3: Sum throughput of all users.  
Figure 2: User vs. Throughput averaged over thousand times for SAMM and MT with equal power and BOTA.  
Figure 4 shows energy efficiency per user in bits per seconds per watts. SAMM BOPA outperforms for initial users and remains considerably lower for rest of the users. Whereas MT BOPA compared to all other schemes performs better for every user of the system with consistency due to convergence of BOPA to maximize throughput and minimize energy.  
Figure 5 shows fairness Index using [PERSON]'s fairness Index [25] using below equation  
\[FI=\frac{\left(\sum\limits_{k=1}^{K}r_{k}\right)^{2}}{K\sum\limits_{k=1}^{K}{r^ {2}}_{k}}, \tag{19}\]  
where \(r_{k}\) can be throughput or EE. Figure 5 shows SAMM has better fairness in terms of throughput due to PF in its algorithm. Figure 6 depicts the system's energy efficiency EE with and without power allocation. The BOPA-based power allocation algorithm allocates the available power to the RB to maximize the energy efficiency EE, therefore, both MT-BOPA and SAMM-BOPA outperforms their corresponding MT and SAMM schemes with equal power allocation.  
Figure 4: Users vs. Energy Efficiency (bits per second per watts) for all four schemes.  
Figure 5: [PERSON]'s fairness Index for Throughput.