# Precoder and Decoder Co-Designs for Radar and Communication Spectrum Sharing +
## 4 Simulation Examples
The interference experienced by different receivers will increase with signal power. The probability of detection as a function of SNR curves is drawn considering 500 radar pulses. Figure 4a shows that the proposed max-SINR joint precoder-decoder design leads to a significant performance gain in target detection because interference from the communication system is almost completely eliminated. Even in a low-SNR regime where the SNR is below 0 dB, the proposed design still provides some performance gain in target detec  
Figure 4: The radar’s ROC curve comparison between the proposed max-SINR joint precoder-decoder design (**a**) and SSSVSP (**b**) in \(-10\), \(-5\), 0 and 5 dB SNR. Figure 3: The total SINR, which is the sum of SINR values at all receivers for the proposed design, DoF bound, SSSVSP, and original signal for coexistence between the radar and communication network. tion. The SSSVSP method is not able to suppress interferences caused at communication transmitters due to the limitations of the precoder-only design. Consequently, the performance of the radar subsystem is severely degraded, as shown by the probability of detection as a function of SNR in Figure 4b, where the radar signal is overwhelmed by interference such that the target cannot be reliably detected using SSSVSP. Increased signal power at the transmitters will further reduce the performance. In Figure 5, the difference in radar performance between the proposed max-SNR joint precoder-decoder design and SSSVSP is shown. A Neyman-Pearson detector is applied with false alarm constraints \(P_{fa}=10^{-2},P_{fa}=10^{-4}\), and \(P_{fa}=10^{-6}\). The performances of pulse numbers \(k=1\) and 500 are also compared in this simulation as a function of the number of pulses. At this time, the SINR value of SSSVSP is always below 0 dB. However, by using the proposed precoder-decoder with IA, the detectors achieve \(P_{d}=1\) at a much lower SNR than by any other method. By increasing the number of pulses, the radar detection performance improves because the radar performance benefits from coherent signal processing. A large gap in performance between the proposed design and SSSVSP is observed. In the proposed design, the radar detection probability is above 0.85 when the SNR is above 0. In Figure 6, the SINR performance is studied as a function of the number of users. In this simulation, the DoF of each user is 1. The results show that total system SINR increases as the number of users increases. An additional user may add a useful signal to the system. However, it will cause interference for the other users. The proposed design can successfully remove interference for the entire system. The higher SNR at each receiver could also increase the system SINR. The proposed design avoids performance loss when the number of users increases. Figure 5: Detection performance difference comparison between proposed max-SINR joint precoder–decoder design and SSSVSP at \(P_{fa}=10^{-2},P_{fa}=10^{-4}\), and \(P_{fa}=10^{-6}\). A single pulse \(k=1\) and multi-pulse \(k=500\) are considered in this comparison.