# Cognitive Interference Cancellation with Digital Channelizer for Satellite Communication
## 4 Cognitive Interference Cancellation
### Improved Interference Detection  
To improve the interference detection performance, the previous method is modified using an FFT operation. Because the FFT is one of the simplest filter banks, we can use it as a simple digital channelizer even though it has poor stopband attenuation and passband flatness. These characteristics of the FFT channelizer are not a significant problem in detecting CW tone interference. On the other hand, the low complexity and flexibility of FFT is an advantage in interference detection. In the process of the 1024-point FFT with a radix-2 algorithm, we can automatically obtain two 512-point FFT outputs with even- and odd-indexed input of 1024 input samples in the time domain. In Figure 5, the structure of the 1024-point FFT including two 512-point FFT with even- and odd-indexed input samples is shown. Therefore, the output of the 512-point FFT represents the spectrum of the lower half band of the total bandwidth which consists of the 1024-point FFT input signal. Because the input of the 512-point FFT consists of every second sample, i.e., even- and odd-indexed samples, the bandwidth of each subchannel for the 512-point FFT is identical to that of the 1024-point FFT. However, the number of subchannels for the 512-point FFT is half of that of the 1024-point FFT. To obtain the spectrum of the upper half band, i.e., subchannels of the upper half band, a frequency up-shift of the 1024 input samples is adopted by using a numerical oscillator, \(\exp(j\pi k)\) for \(k=0,1,\cdots\). The overall structure of the proposed interference detector is illustrated in Figure 6. The detailed block of CW interference detection in the lower and upper bands is shown in Figure 7. As shown in the figure, two output samples  
where \(\tilde{y}_{e}(i,m)\) and \(\tilde{y}_{o}(i,m)\) denote the \(m\)-th FFT output sample (\(m\)-th subchannel) in the \(i\)-th block of the even- and odd-indexed input signals. For the lower band, the range of \(m\) is given by \(m=0,\cdots,255,768,\cdots,1023\). For the upper band, \(m=256,\cdots,767\). To detect the subchannel corrupted by interference, the decision statistics for the subchannels are compared with the threshold. The condition for the interference detection existing in the \(n\)-th subchannel is given by  
\[\left\{ \begin{array}{ll}T_{im}(n)\geq\lambda,\\ T_{im}(m)<\lambda,&m\
eq n.\end{array} \right. \tag{9}\]  
Similar to (7), the condition for the no false alarm event is given by  
\[T_{im}(m)<\lambda,\text{ for all }m\in\{0,\cdots,1023\}. \tag{10}\]  
The improved method provides two 512-subchannel outputs but the bandwidth of all 512 subchannels is half of the total signal bandwidth. Because the range of the frequency detection in the improved method is just half of the total bandwidth, the frequency ambiguity problem cannot be avoided. This means that tone interference in the higher band is also detected in the lower band interference detection process and vice versa. For example, if the \(n\)-th subchannel in the higher band (\(n\geq 512\)) is assumed to be corrupted with interference, the interference is also detected in the \((n-512)\)-th subchannel in the lower band. However, this frequency ambiguity is simply overcome with the output of the 1024-point FFT. In the above example, the actual interfered subchannel can be identified by comparing the \(n\)-th and \((n-512)\)-th subchannels in the 1024-point FFT output. As mentioned previously, two 512-point FFTs with even- and odd-indexed samples are by-products of the 1024-point FFT. Therefore, the complexity of the additional process required to solve the frequency ambiguity is much smaller than that of the other processes in the interference detection. Note that the FFT is used to detect a subchannel with interference, and channelization is performed by an NPR polyphase filter bank for enhancement of both the stopband attenuation and passband flatness of the subchannels. Figure 5: Structure of fast Fourier transform (FFT) using radix-2 algorithm.