# Topological Interference Management for K-User Downlink Massive MIMO Relay Network Channel
## 7 Numerical Results  
The proposed three-user MIMO interference channel model with a shared relay as shown in Figure 2. In this section, we consider \(K=3\) users, where two symbols are transmitted on each sub-carrier over the time slots. We also assume that the transmitters and relay each with two antennas \((M=2)\) and a receiver equipped with single antenna \((N=1)\). The MMSE linear precoder with 256 quadrature amplitude modulation (QAM) is used in the simulation. The channel vector of each transmitter and relay is considered as an i.i.d complex Gaussian with zero mean and unit variance MIMO space-time-correlated Rayleigh fading channels. We also considered that the transmit power for each transmitter \((P)\) and relay \((P_{R})\) are 50 mW are fixed throughout the simulation. In Figure 7, the BER performance is compared in two main scenarios: with limited CSIR knowledge and with perfect CSIR knowledge [18]. Thus, the proposed scheme relies on a limited CSIR knowledge because, over a time slot, only two transmitters are active; whereas, with a perfect CSIR, the relay knows all the channel state information. At BERs of \(10^{-3}\) and \(10^{-4}\), in the perfect CSIR case the SNR increases from 20 dB to 21.3 dB respectively, whereas, in the proposed limited CSIR case, the SNR varies from 18.6 dB to 21.3 dB. The simulation result shows that the perfect CSIR case performance is 1.5 dB better than the proposed limited CSIR case. This result is predictable, since the relay has only limited channel state information over the time slots. Figure 8 displays the power allocation strategy versus the computed achievable sum-rate [17; 22]. We mainly focus on three major schemes; in the proposed R-STIA technique, the sum-rate is computed for \(K=3\) users, under an average power constraint. The R-STIA technique is compared with the MIMO broadcast channel and the interference channel schemes, where at  
the sum-rate increases from 17.5 bps/Hz to 30 bps/Hz, respectively; the MIMO broadcast channel achieves an increase from 15.7 bps/Hz to 27.4 bps/Hz and the interference channel scheme from 8.5 bps/Hz to 15.5 bps/Hz. This drastic variation in the sum-rate is predicted because, in the proposed scheme, the additional receiver and limited CSIR information enable an increase in the sum-rate compared to the MIMO broadcast and interference channel schemes. Figure 9 presents the bit error rate versus the SNR (dB) [18]. The proposed R-STIA technique is compared with the QO-STIA and the distributed R-STBC techniques. At BERs of \(10^{-2}\) and \(10^{-3}\), in the proposed technique, the SNR increases from 10.8 dB to 16.3 dB, respectively, whereas the relay QO-STIA technique achieves an SNR increase from 2.5 dB to 18 dB and the distributed STIA technique from 14 dB to 21 dB. This extreme variation is predictable because the proposed techniques relies on the MMSE linear precoder, which, in turn, helps to improve the BER performance. In Figure 10, we plot the average run-time (seconds) versus the number of users (\(K\)). The proposed R-STIA technique average run-time (seconds) is compared with the distributed STIA and QO-STIA techniques. At \(K=16\) users case, the proposed R-STIA technique for \(M=2\), \(N=1\) antenna settings average run-time is 60 s. However, the QO-STIA and distributed STIA techniques average run-time is 90 s and 100 s, respectively. The simulation results show that the proposed R-STIA technique enhances the average run-time performance (seconds) compared to the distributed STIA and QO-STIA techniques. This result is predictable, since the proposed R-STIA technique reduces the decoding complexity due to the presence of additional receiver and less interference misalignment at the intended receiver-end. Moreover, the cooperation between the intended and unintended receivers also helps to reduce the decoding complexity of the proposed scheme.