# Cognitive Interference Cancellation with Digital Channelizer for Satellite Communication
## 6 Numerical Results  
For the evaluation of the cognitive interference detection and cancellation performance, and verification of analytical results, we conduct computer simulations under various conditions. First, the minimum interference power that should be cancelled out is evaluated. As mentioned previously, interference with a power lower than a certain level does not need to be cancelled because its cancellation causes higher degradation of the desired wideband signal than the interference. For example, Figure 8 shows constellation of the desired wideband signal with and without interference cancellation when the CW tone interference power is -25 dB and -5 dB lower than the desired wideband signal. The wideband signal is modulated by quadrature phase shift keying (QPSK) and uses single carrier transmission. The number of subchannels is set to be 1024 and a single tone interference with a normalized frequency of \(\frac{200}{1024}\pi\) radians/sample is added. The frequency of the interference is not changed in this study. In a subchannel with interference, the power of AWGN is much lower than the power of the interference and desired signal components, i.e., \(|[\tilde{s}(\cdot,\cdot)|^{2}]\gg\mathbb{E}[|[\tilde{w}(\cdot,\cdot)|^{2}]]\) and \(\mathbb{E}[|\tilde{x}(\cdot,\cdot)|^{2}]\gg\mathbb{E}[|\tilde{w}(\cdot,\cdot) |^{2}]\) in Equation (2). Therefore, we neglect the AWGN term, i.e., \(\tilde{w}(\cdot,\cdot)=0\). Additionally, we normalize the desired signal in the whole band. Therefore, the power of the desired signal component in each subchannel becomes 1/1024, i.e., -30 dB. Assuming that the subchannel index corrupted by interference is perfectly known, Figure 8a-c show the constellation with interference cancellation with different interference power. The proposed method cancels the interference by omitting the corrupted subchannel. This means that one of the 1024 components of the desired signal is also omitted in the cancellation process. Even though the interference is correctly cancelled out, we cannot obtain the ideal QPSK constellation as shown in Figure 8a-c. The error vector magnitude (EVM), i.e., the inverse of the effective SNR, is -30 dB because \(1/1024\) of the desired signal along with the CW tone interference is cancelled out. The definition of EVM is the ratio of the mean square of the error vector to the power of the reference constellation, i.e., ideal constellation. That is, the EVM in dB scale is as follows:  
\[EVM(dB)=10\log_{10}\left(\frac{\mathbb{E}[|C_{mean}-C_{ref}|^{2}]}{\mathbb{E}[ |C_{ref}|^{2}]}\right), \tag{23}\]  
where \(C_{mean}\) and \(C_{ref}\) denote the measured and reference constellations, respectively. The numerator and denominator in Equation(23) stand for the error caused by noise and interference in signal constellations and the power of the ideal signal, respectively. Therefore, the EVM is regarded as the inverse of the signal-to-noise (-plus-interference) ratio. On the other hand, Figure 8b and Figure 8d show the constellation of the desired signal without interference cancellation under low and high interference conditions. The EVM of the constellation in Figure 8c is -25 dB because the CW tone interference power is -25 dB lower than the desired wideband signal. Figure 8d shows the constellation without cancellation of the higher interference, i.e., -5 dB lower than the desired wideband signal, and the EVM of this case is -5 dB. Figure 9 shows the EVM results with and without interference cancellation when the CW tone interference power varies from -40 to -20 dB (lower than the desired signal power in the whole bandwidth). In this simulation, we use the same condition as in Figure 8. The desired signal is modulated with a single carrier QPSK, 1024 subchannels are used, and a single tone interference at \(\frac{200}{1024}\pi\) radians/sample frequency is added. When the interference is cancelled, the EVM of the desired signal is about -30 dB regardless of the interference power.