# Collision Detection Method Using Self Interference Cancelation for Random Access Multiuser MIMO
## 3 Effectiveness of the Proposed Method by Computer Simulation  
Through this computer simulation, in which IEEE802.11n/ac-based OFDM signal is assumed, the effectiveness of the proposed method is verified by evaluating the characteristics of self-interference reduction and detection of interference from ITs. Table 1 shows the simulation parameters. As can be seen in Table 1, when considering the self-interference signal between AP antennas, the average signal to noise power ratio (average SNR) is set to be 45 dB from the previous measurement [7], and we confirmed that the fading caused by self-interference between AP antennas can be negligible due to its large power, even if people work around the AP [8]. On the other hand, the propagation of interference signal is assumed to be Rayleigh fading. In the simulation, the signal to interference power ratio (SIR) is changed from 0 to 50 dB. The other basic parameters are the same as that for the IEEE802.11n/ac standard with 20 MHz mode. When \(\tilde{h}_{s_{i}}(k)\) denotes the estimated channel response between the AP antennas and \(\rho_{h}(t)\) denotes the time variation of channel response, \(h_{s_{i}}\), the channel response between the \(i\)-th transmit and a receive antenna of the AP is denoted as  
\[h_{s_{i}}(k)=\rho_{h}(t)\tilde{h}_{s_{i}}(k)+\sqrt{1-\rho_{h}^{2}(t)}h_{iid}(k). \tag{4}\]  
From the results in [8], \(\rho_{h}(t)\) is set to be 0.9999 in the evaluation. The simulation process is summarized as follows:  
* [Step (1)] The desired signal and the interference signal with the OFDM signal format are created and added. * [Step (2)] The short preamble signal is detected from the signal by the sliding correlation. * [Step (3)] The interference signal is estimated and detected. Figure 5 and 6 show the received power of interference from IT in the frequency domain, and these are estimated by the proposed method by assuming that the SIR is 10 and 45 dB. The received power is not transmitted when there is self-interference between the AP antennas; only the interference signal from the IT arrives at the receiver of the AP. The estimated and ideal interfering powers are plotted in these figures. When considering low SIR, as shown in Figure 5, the interference power versus subcarrier number for the estimated interfering power is almost identical to that for the ideal interfering power. Although the estimation seems to be possible when the SIR is 10 dB (in Figure 5), we can observe that the estimation error with SIR = 45 dB is much larger than that with SIR = 10 dB. \begin{table}
\begin{tabular}{c c} \hline \hline
**Number of Trial** & **10001** \\ \hline Number of transmit antennas (\(N_{T}\)) & 2 \\ Number of receive antennas (\(N_{R}\)) & 1 \\ Number of desired user terminals (\(N_{UJ}\)) & 2 \\ Number of interference user terminals (\(N_{IT}\)) & 1 \\ Average SNR & 45 dB \\ Average SIR & 0\(\sim\)50 dB \\ Propagation path of interference signal & Rayleigh fading \\ Bandwidth & 20 MHz \\ Number of FFT points & 64 \\ \hline \hline \end{tabular}
\end{table} 
Table 1: Simulation parameters. In order to evaluate how to estimate the interference signal when considering low SIR, the interference channel response is estimated by using Equations (2) and (4). If the multiplication of interference signal and short preamble signal is denoted as \(\tilde{h}_{I}(k)\tilde{s}_{p}(k)\), the estimated equation is denoted as  
\[\tilde{h}_{I}(k)\tilde{s}_{p}(k)\approx r_{p}(k)-\sum_{i=1}^{M}\tilde{h}_{s_{i} }(k)s_{i}(k). \tag{5}\]  
The estimation error on the interference power by the proposed method is evaluated. The estimation error is denoted as  
\[Estimation\ Error=\left|20\log_{10}\frac{|h_{I}(k)s_{p}(k)|}{|\tilde{h}_{I}(k) \tilde{s}_{p}(k)|}\right|, \tag{6}\]  
where \(|h_{I}(k)s_{p}(k)|^{2}\) and \(|\tilde{h}_{I}(k)\tilde{s}_{p}(k)|^{2}\) denote the ideal and estimated interference power, respectively. In this study, the number of trials was 10,001. Figure 7 shows the estimation error versus SIR.