# Study of 5G-NR-MIMO Links in the Presence of an Interferer
## 4 Numerical Results
### Partial Band Noise Jammer  
Next, we simulated the case described in Section 3.3. For this, we used a 50% PBN jammer. Figure 10 shows the constellation of the transmitted symbols in blue and the received symbols in orange when sending 1000 bits with 4, 8, 16-PSK modulations with no AWGN and SIR = 10 dB. As expected, the received symbols are scattered randomly around the transmitted symbols as a result of adding PBN. The scattering distance from the transmitted symbols depends on the SIR. The lower its value is, the wider the scatter will be, and vice versa. The results are similar to the case of the general interferer. The difference between the general case and the PBN case is in the ML estimator processing or the SD block. If we have a symbol \(s_{2}\) that satisfies the necessary condition search, we construct a sufficient condition for symbol \(s_{1}\). In the general case, we have a greater minimization problem from the PBN case because symbol \(s_{2}\) affects whether symbol \(s_{1}\) can be found. If there is an impairment in the orthogonality between the channel-matrix columns, as described in the general interferer case, and also in the Appendix A, then the symbol \(s_{2}\) will depend on finding the symbol \(s_{1}\). In ML and SD, the search terms are defined by a circle equation. When there is a violation of the orthogonality, a circle in the \(s_{1}\) plane is built with a center and radius that depend on \(s_{2}\). Figure 9: Alamouti \(2\times 2\) with the presence of the smart jammer. BER as a function of the SIR. Different modulation orders 2, 4, 8, 16–PSK and SNR = 15 dB. Figure 11 shows the BER graphs as a function of the SIR when SNR = 15 dB. Several PSK constellation orders, M = 2, 4, 8, 16, were considered, \(10^{5}\) bits were transmitted, and \(\Delta\)SIR = 0.2 dB. Figure 11: Alamouti \(2\times 2\) with the presence of the partial band noise (PBN) jammer. BER as a function of the SIR. Different modulation orders 2, 4, 8, 16–PSK and SNR = 15 dB. Figure 10: A constellation of transmitted symbols (blue) and received symbols in the presence of the partial band noise (PBN) jammer (orange), for (**a**) 4–PSK, (**b**) 8–PSK, (**c**) 16–PSK modulations, no AWGN, and SIR = 10 dB. As in the case of the general interferer, the results show that a higher modulation order leads to lower BER. Finally, and most importantly, in Figure 12, we compared the different types of interferers concerning the 4-PSK modulation case. For SIR values smaller than 2 dB, the most destructive is the smart jammer due to duplicate symbols, followed by a general interferer and finally the PBN jammer. As mentioned, the PBN we used is of the 50% type, so its BER outperforms that of the general jammer. For SIR values greater than 2 dB, the smart jammer's performance is the most reliable, and the performance of the general interferer and the PBN jammer becomes similar. As we have seen, the smart jammer graphs are horizontal when the SIR values are negative. In this range, even if we increase the SIR value by, for example, a null space direct to the smart jammer to achieve selectivity in the space domain, performance will not improve, unlike the other interferer. Simulation parameters of all the above figures of the BER performances as a SIR function are summarized in Table 6.  
From the BER results depending on the SIR obtained in this chapter, the Channel Quality Indicator (CQI) value can be estimated for the different cases [46]. This value, at 5G-NR, keeps the BER below a pre-defined threshold for each user by determines the order and type of modulations, the code rate and the spectral efficiency of the base station downlink transmission.