# Collision Detection Method Using Self Interference Cancelation for Random Access Multiuser MIMO
## 2 Proposed Method
### Detailed Principle of Proposed Method  
Figure 3 shows the waveforms before and after applying the proposed method. As can be seen in Figure 3, the preamble signals are transmitted for synchronization and estimation of CSI before transmitting the data signals; the short preamble signal is utilized for detecting the initial timing of the data packet.  
From Figure 4, it is seen that the short preamble signal is adopted in the IEEE802.11n-based wireless LAN system. At the transmitter, the signals are mapped for only twelve subcarriers in order to generate a periodic signal in the time domain [6]; following this IFFT processing, the signal is transmitted. At the receiver, timing synchronization based on the calculated correlation value between the received signal, \(y(t)\), and the short preamble signal in the time domain between the known transmitted and received signals, \(s_{p}(t)\), is employed. Note that the correlation calculation is completely different from that in [12], because this calculation is employed for finding the initial timing of the data packet. The correlation between these signals, \(\rho\), is denoted as  
\[\rho = \frac{\left|\sum_{t=1}^{L}s_{p}^{*}(t)y(t)\right|}{\sqrt{\sum_{t =1}^{L}\left|s_{p}(t)\right|^{2}}\sqrt{\sum_{t=1}^{L}\left|y(t)\right|^{2}}}, \tag{1}\]  
where \(L\) is the number of symbols for which correlation calculation is conducted (for IEEE802.11n-based OFDM signals, \(L=160\)) [6]. The correlation value, \(\rho\), is maximized at the initial timing of the short preamble signals.  
Figure 2: Concept of the proposed method.  
In a typical wireless LAN system, the short preamble is not used after timing synchronization. In contrast, in the proposed method, the short preamble is used after FFT processing. When the interference signals arrive at the AP, the received signal at the \(k\)-th subcarrier after FFT, \(r_{p}(k)\), is denoted as  
\[r_{p}(k) = \sum_{i=1}^{M}h_{s_{i}}(k)x_{i}(k)+h_{I}(k)s_{I}(k)+n(k), \tag{2}\]  
where \(h_{s_{i}}(k)\) is the self-interference channel response between the \(i\)-th transmit and the receive antenna of the AP at the \(k\)-th subcarrier. \(h_{I}(k)\) is the channel response between IT and the receive antenna of the AP at the \(k\)-th subcarrier. \(x_{i}(k)\) is the product of the transmitted signal of the \(i\)-th transmit antenna of the AP and the weight vector, which is generated by block diagonalization algorithm. \(s_{I}(k)\) and \(n(k)\) denote the interference signal, which assumes the short preamble signal, and the thermal noise at the \(k\)-th subcarrier, respectively. \(M\) is the number of self-interference signals at the receive antennas. Here, the transmitted signals, which are short preamble signals, are already known, and \(\tilde{h}_{s_{i}}\) denotes the estimated channel response of \(h_{s_{i}}\). The channel response, \(h_{s_{i}}(k)\), can be assumed to be obtained between the idle time at the AP in advance, because the propagation characteristic between the Antenna #1 and #2 at the AP could be not changed and \(h_{s_{i}}(k)\) will be regarded as the static channel. The channel response of the interference signal, \(h_{I}(k)\), is estimated as  
\[r_{p}(k)-\sum_{i=1}^{M}\tilde{h}_{s_{i}}(k)x_{i}(k)\approx h_{I}(k)s_{I}(k)+n( k). \tag{3}\]  
The interference detection can be realized by using Equation (3) while the transmission is employed.  
Figure 4: Short preamble signal.  
Figure 3: Waveforms before and after applying the proposed method.