# Fast Converging Gauss-Seidel Iterative Algorithm for Massive MIMO Systems
## 4 Simulation Results and Analysis
### BER Performance  
A comparison and analysis of the BER performance of different iterative algorithms with different antenna configurations is shown in Figure 3. The channel matrix is independent and identically distributed, that is \(\zeta_{r}=0\), \(\zeta_{t}=0\). Signal modulation is 16-QAM. In Figure 3a, it is clear that all schemes have excellent BER performance after a modest quantity of rounds, and that the CJGS scheme has improved BER performance over the other repetition methods for the identical number of rounds. The BER of the CJGS and JAGS iterative algorithms is \(2.604\times 10^{-6}\) after two iterations, but the gap between them is 8 dB. Therefore, the CJGS iterative method is better. From Figure 3b, it can be noticed that the CJGS iterative scheme requires three iterations, while the other four iterative schemes require more than seven iteration cycles to achieve the ability of the MMSE scheme when the MIMO antenna configuration is \(128\times 32\). If the signal-to-noise ratio (S/N) is 20 dB, the BER achievable via the CJGS iterative method is \(1.302\times 10^{-5}\) after three iterations, and the BERs achievable via GS, CPGS, JAGS, and PGS after seven iterations are \(3.906\times 10^{-5}\), \(8.073\times 10^{-5}\), \(0.0001172\), and \(7.031\times 10^{-5}\), respectively. In Figure 3c, it can be seen that with the MIMO antenna configuration of \(128\times 32\), CJGS, GS, and JAGS can achieve better BER performance after two iterations, but the BER performance of CPGS and PGS is not very good. Furthermore, by keeping \(U\) at a fixed value and increasing \(B\), all algorithms can gain an identical BER in a fraction of the repetitions from Figure 3a,b. Conversely, if \(B\) remains fixed and \(U\) increases, all algorithms need a higher signal-to-noise ratio to obtain identical results, and the quantity of receptions required increases from Figure 3b,c. Figure 4 is a comparison and analysis of the BER behavior of different iterative algorithms. The antenna configurations are different. The channel matrix satisfies \(\zeta_{r}=0.3\), \(\zeta_{t}=0\). Signal modulation is 16-QAM. In Figure 4a, with the MIMO antenna configuration of \(256\times 64\), the performance of the other four iterative algorithms after running five iterations is still worse than that of the CJGS iterative algorithm in one iteration. The minimum BER achieved via MMSE detection is \(7.813\times 10^{-6}\), while the BER of the CJGS iteration is \(5.208\times 10^{-6}\) after one iteration. From Figure 4b, the CJGS iterative scheme provides a much more superior performance when the MIMO antenna configuration is \(128\times 64\), which converges faster than the remaining  
Figure 3: BER performance for independent and identically distributed channels. iterative methods. In Figure 4c, it can be seen that the CJGS iterative algorithm after three iterations can achieve effects identical to those of the MMSE detection scheme if the S/N is 16 dB. A comparison and analysis of BER performance for different algorithms with different antenna configurations is shown in Figure 5. The channel matrix satisfies \(\zeta_{r}=0\), \(\zeta_{t}=0.3\). Signal modulation is 16-QAM. The detection performance of the GS, CPGS, JAGS, and PGS iterative algorithms is less satisfactory for an iteration number of one in Figure 5, while the CJGS iterative algorithm achieves a desirable performance close to MMSE detection. All iterative algorithms become better in detection performance as the number of iterations increases. As shown in Figures 3 and 5, all algorithms require more iterations to achieve optimal performance when the transmit-side antenna is correlated. If the MIMO antenna configured is set to 128 \(\times\) 64 and the BER reaches 5.208 \(\times\) 10\({}^{-6}\), the required S/N ratio for CJGS is 20 dB, while the S/N ratio requirement for PGS and JAGS iterations is 24 dB. Therefore, the proposed algorithms are more suitable for channel scenarios where correlation exists on the transmit side of large-scale MIMO systems.