# Regularized Zero-Forcing Dirty Paper Precoding in a High-Throughput Satellite Communication System
## 4 Simulation Verification and Analysis
Moreover, the regularized zero-forcing dirty paper precoding algorithm can achieve the largest throughput, which is further improved by about 5% compared with regularized zero-forcing precoding. Figure 5 is the comparison of the influence of beam number on the throughput per beam of four precoding schemes. A random order regularized zero-forcing dirty paper precoding algorithm is added, which aims to reduce the complexity and analyze its advantages and disadvantages. It can be seen that the average achievable throughput of all four precoding schemes decreases with the increase in the number of beams. Especially in the process of changing the number of beams from 7 to 19 to 37, the decreasing trend is obvious because the increased number of beams will bring more co-channel interference. Figure 4: Performance diagram of each beam throughput of four precoding schemes. The average beam throughput of zero-forcing precoding is most affected by the increase in the number of beams because it does not consider the suppression of the noise in the system. With the increase in the number of beams, the noise in the system is greater, and the impact is more prominent. The other three precoding schemes are basically the same, as they are affected by the increase in the number of beams, and the regularized zero-forcing dirty paper precoding scheme with a determined coding sequence has the best performance. Figure 6 shows the influence of the 3 dB angle on the throughput performance of the precoding schemes with random user location. It can be seen that in a certain range of beam coverage, given the beam radius, when the 3 dB angle of the beam increases, the system's achievable throughput increases first and then decreases, and the maximum extreme point is the edge of the beam, which is a 3 dB power attenuation. It can be concluded that when selecting the beam coverage form, it is best to select the 3 dB beam width as the beam edge. Moreover, it is found that the performance of the regularized zero-forcing dirty paper precoding algorithm is the best, as it is far less affected by the 3 dB angle than is the zero-forcing precoding, and there is little difference between the performance of the two dirty paper regularized zero-forcing precoding algorithms with two coding sequences. Figure 7 shows the influence of 3 dB angle on throughput performance of precoding schemes with users distributed at the edge of the beam. In the satellite communication system, the performance of the worst external conditions should be considered when measuring the system performance; in other words, the situation where users are distributed at the edge of the beam. It can be seen that when users are arranged at the edge of the beam and the 3 dB angle of the beam is small, the achievable throughput of the system is much different from that with a random user arrangement. However, when the 3 dB width of the beam exceeds the beam diameter, the user arrangement basically does not affect the system throughput performance. Figure 5: Influence of beam number on throughput per beam of four precoding schemes. Figure 8 shows the influence of the size of the beam overlap area on the system performance with random user location. The overlap factor is defined as the ratio of the beam radius to the radius when there is no overlap between beams. It is assumed that the edge power attenuation of each beam is 3 dB, and the beam center position is given. It can be seen that when there is no beam overlap and the user random distribution model is adopted, the achievable throughput performance curves of the four precoding schemes basically coincide. When the beam overlap factor is larger than 1.2, the performance of the zero-forcing precoding algorithm decreases significantly. Figure 6: Influence of the 3 dB angle on the throughput performance of precoding schemes with random user location. Figure 7: Influence of 3 dB angle on throughput performance of precoding schemes with users distributed at the edge of the beam.