## 5 Time Frequency Distribution Based Co-Channel Interference Suppression  
The time frequency distribution of the pulse shaping signal has low energy characteristics at the edge of each symbol period. Based on this feature, if the energy center of the co-channel interference is located at the edge of the desired signal's symbol period, then the interference could be suppressed by the time varying filter of which the pass region is generated according to the energy distribution of the desired signal.  
Assume that the desired signal is \(s_{i}^{c}(t)\), and the co-channel interference signal is denoted as \(s_{i}^{d}(t)=s_{i}^{c}(t-T_{b}/2)\), where \(T_{b}\) is the symbol period. The interference has half symbol period time difference from the desired signal. Figure 14 shows the time frequency distributions of the desired signal and the interference. It indicates that the high energy of the interference just locates at the low energy area of the desired signal, and vice versa. If apply the time varying filter according to the energy distribution of the desired signal, more co-channel interference can be suppressed.  
The simulation parameters are listed in Table 2.  
Figure 14: Time frequency distributions of the desired and co-channel interference signals.  
Figure 13: The pass regions with different window lengths. **(a)** The pass region with \(L_{h}\) = 10; **(b)** The pass region with \(L_{h}\) = 20; **(c)** The pass region with \(L_{h}\) = 30; **(d)** The pass region with \(L_{h}\) = 40.  
Figure 15a shows how the BER performance varies with SIRs with the LPF and the LTV filters, respectively. It indicates that the LTV filter provides better BER performance when the interference power is strong. Since the proposed time varying filter aims at mitigating the high energy area of the interference, the suppression ability is more obvious with stronger interference. Take \(E_{b}/N_{0}=10\) dB for example, it shows that the LTV filter achieves better BER performance than the LPF filter, with an SIR gain of about 3 dB for strong co-channel interference (SIR \(<4\) dB), and 2.5 dB for moderate co-channel interference (SIR \(>4\) dB). However, when the interference is weak, the BER with the LTV filter is high, which is because that the distortion of the desired signal overwhelms the suppression to the interference in this case. Figure 15a plots three groups of curves that BER varies with SIRs when \(E_{b}/N_{0}\)s are set to be 5 dB, 8 dB and 10 dB, respectively. It shows that the performance crossing point varies with different \(E_{b}/N_{0}\)s. The three performance crossing points are 8.5 dB, 11 dB and 13 dB, respectively. The complexity of LTV filter is O(\(N^{3}\)), and the complexity of LPF filter is O(N), which is shown in Table 3.  
Figure 15b shows how the BT value affects the filter effect. It indicates that the performance crossing points are 8.5 dB and 9 dB, when the BTs are 0.3 and 0.35, respectively. When the BER is \(2\times 10^{-2}\), the SIR gain for the three groups of curves are 0.5 dB, 1.5 dB and 3 dB, respectively. As shown in Figure 2, the low energy characteristic of the desired signal at the edge of each symbol period is more obvious with bigger BT, hence more advantages could be obtained with the LTV filter.  
\begin{table}
\begin{tabular}{c c} \hline \hline
**Parameters** & **Values** \\ \hline Gaussian pulse parameter BT & 0.4 \\ Truncated length of the Gaussian pulse & \(6T_{b}\) \\ Center frequency of the expected signal & 800 MHz \\ Center frequency of the interference signals & 800 MHz \\ Symbol time period \(T_{b}\) & 0.26042 \(\mu\)s \\ \hline \hline \end{tabular}
\end{table}
Table 2: Simulation Parameters.  
Figure 15: The BER performance with the proposed co-channel interference suppression method. (a) BER varies with different SIRs; (b) BER varies with SIRs with different BTs.