## 4 Simulation Results  
In this section, we firstly compare the achievable DoF and sum-rate performance between TPIA and other conventional schemes. Then, the average rate performance of the CCU and CEU are simulated and analyzed to support the explanation of the system model. The simulation parameters are listed in Table 1. Specifically, the signal to noise ratio (SNR) in the simulation is defined as the ratio of transmit power to the power of noise. The transmit power at each BS and relay is set to the maximum value (i.e., the simulation parameters in Table 1), and the power of noise at CCU and CEU vary according to \(P_{N(CCU)}=P_{BS}-SNR(dB)\) and \(P_{N(CEU)}=P_{relay}-SNR(dB)\), respectively. Furthermore, the lower complexity and ease of deployment make the relays with fixed amplification factors attractive from a practical standpoint. Hence, the influence of fixed amplification factor is analyzed and three fixed values of relay amplification factors are selected for simulation simplicity in this section. It should be noted that the power of noise at the CEU varies according to \(P_{N(CEU)}=P_{relay}(\rho)-SNR(dB)\), since the transmit power of the relay is decided by the fixed amplification factor. The channels among different nodes are assumed to be uncorrelated and the average simulation results are computed under 1000 channel instances. The achievable SDoF and sum-rate comparison of different schemes are shown in Table 2 and Figure 2, respectively. We assumed the amplification factor to be variable to maintain the maximum transmit power of relay. It can obviously be seen that the TPIA scheme utilizes less sub-time slots than others and obtains the highest SDoF and sum-rate performance. That is because both intra-cell and inter-cell interference are simultaneously mitigated in only two sub-time slots per transmission period while other schemes need an extra sub-time slot to avoid the intra-cell interference caused by the BS. Furthermore, our method can effectively decrease the cost caused by synchronization because of the smaller number of time partition. In Figure 3, we plot the average rate comparison between CCU and CEU to analyze the proposed TPIA scheme based on the system model. As can be seen from the figure, the average rate curve of the CCU is obviously higher than that of the CEU, especially at the high SNR region. That is because the data transmission from BS to CCU is performed in both two sub-time slots (i.e., Formulas (5) and (7) in Section 2), while the relay only transmits a signal to the CEU in the second sub-time slot (i.e., Formula (6) in Section 2). Additionally, the average rate increase is faster than that of the CEU, since part of the intra-cell interference is aligned to the desired signal subspace and both the two aligned signals to CCU increase with SNR, which results in a significant improvement of receive power at each CCU. Furthermore, the combined signal forwarded by the relay to the CEU in each cell contains inter-cell interference and more kinds of noise (details are given in Formula (6) in Section 2), all of which increase with the SNR. Hence, the average rate of the CEU gradually approaches the ceiling with increasing SNR. \begin{table}
\begin{tabular}{c c} \hline \hline
**Parameter** & **Assumption** \\ \hline Radius of cell (\(r\)) & 500 m \\ Radius of center area (\(r_{1}\)) & 250 m \\ Distances among nodes (\(d_{1}\), \(d_{2}\), \(d_{R}\), \(d_{\bar{r}_{1}}\), \(d_{\bar{r}_{2}}\)) & 200 m, 30 m, 400 m, 300 m, 50 m \\ Carrier frequency / Bandwidth & 2 GHz/10 MHz \\ Maximum transmit power of base station (BS) & 46 dBm \\ Maximum transmit power of relay & 18 dBm \\ The number of antennas at BS & 2 \\ The number of antennas at Relay & 2 \\ The number of antennas at user equipment (UE) & 3 \\ degrees of freedom (DoF) of each transmission link & 128.1 + 37.6 log10R [dB], R in km \\ Path loss from BS to user & 140.7 + 36.7 log10R [dB], R in km \\ Antenna pattern & 0 dB (omni-directional) \\ \hline \hline \end{tabular}
\end{table} 
Table 1: Simulation Configurations.