## 4 Simulation Results and Complexity Analysis
### Simulation Results and Discussion
\begin{table}
\begin{tabular}{c c} \hline \hline
**Parameter** & **Value** \\ \hline Modulation & 1024-QAM \\ Amount of data & 512 \\ Pilot Length & 52 \\ Number of transmitting antennas & 16 \\ Number of receiving antennas & 64,128,192,256 \\ Channel type & Rayleigh fading channel \\ Spatial-correlation coefficient (Tx, Rx) & (0.3, 0.4) \\ Noise & AWGN \\ Number of paths & 2 \\ The maximum SNR & 50 \\ Channel estimation & LS \\ Monte Carlo times & 500,000 \\ \hline \multicolumn{2}{c}{**OFDM parameters**} \\ \hline CP Length & 128 \\ \hline \multicolumn{2}{c}{**UFMC parameters**} \\ \hline Number of subcarriers & 1024 \\ Number of sub-bands & 16 \\ Number of subcarriers in each sub-band & 32 \\ Number of zero-padding & 256 \\ Filter type & Chebyshev FIR filter \\ Filter length & 43 \\ Filter sidelobe attenuation & 40 \\ \hline \hline \end{tabular}
\end{table} 
Table 2: Parameters used in simulation scenarios. Figure 7: BER performance comparison for OFDM vs. UFMC with \(N_{R}\times N_{T}=64\times 16\). when the number of receive antennas \(N_{R}\) is 64 and 128; thus, better performance at higher \(N_{R}\) is unlikely. Based on these results, GS and CG are excluded from the subsequent figures for visual conciseness and to avoid clutter. On the other hand, Figure 9a,b shows that when \(N_{R}\times N_{T}=64\times 16\) and the number of iterations is 4, the BER performance curves of the proposed CHSOR method almost overlap with the MMSE detector. In particular, in Figure 9a for the OFDM system, when the SNR is 35 dB, the BER numerical results of the proposed and CSOR methods are \(1.620\times 10^{-3}\) and \(1.934\times 10^{-2}\), respectively, which is an improvement of 91.624%. For the UFMC system in Figure 9b, the results show that the BER of the proposed and CSOR methods are \(5.324\times 10^{-5}\) and \(1.469\times 10^{-2}\), respectively, which is an improvement of 99.638%. Therefore, the proposed CHSOR detector provides a significant improvement compared to the CSOR method, especially for the UFMC system. To observe the impact of M-MIMO on the BER performance of different detectors, we increased the number of receiving antennas from 128 to 192, and then to 256, as shown in Figures 10-12, respectively. Our proposed CHSOR detector still provides superior BER performance compared to the others. It is worth mentioning that when the number of receiving antennas is 128, the BER performance curve of the proposed CHSOR method remains very close to the MMSE detection method after two iterations. When the number of antennas \(N_{R}\) is increased to 192 and then again to 256, the BER performance of our proposed CHSOR method still maintains the same trend, only needing one iteration for both OFDM and UFMC. It can be seen that increasing the number of receiving antennas can speed up the convergence of the receiver without exception. These represent promising results for the application of M-MIMO to B5G applications. For more clarity, Table 3 enumerates the detailed BER results of the proposed CHSOR scheme and the Chebyshev-MAOR scheme. The improvement rate of the proposed CHSOR scheme is compared to the Chebyshev-MAOR scheme at SNR = 30 dB for \(N_{R}\times N_{T}=128\times 16\) and \(N_{R}\times N_{T}=192\times 16\) under both the OFDM and UFMC systems. Examining the numerical data in the CHSOR scheme in Table 3. when \(N_{R}\) increases, in addition to the decrease in BER and enhancement of the improvement rate relative to other detectors, the application of UFMC for B5G systems is especially powerful. Figure 8: PSD comparison for OFDM vs. UFMC. Figure 10: Cont. Figure 9: BER performance comparison for different detection methods with \(N_{R}\times N_{T}=64\times 16\) and number of iterations = 4 for (**a**) OFDM and (**b**) UFMC. Figure 11: BER performance comparison for different detection methods with \(N_{R}\times N_{T}=192\times 16\), and number of iterations = 1 for **(a)** OFDM and **(b)** UFMC.