## 4 Simulation Results and Complexity Analysis  
### Simulation Results and Discussion  
Some numerical simulations are conducted to evaluate the performance of the proposed two-stage receiver. Consider an \(N_{R}\times N_{T}\) uplink MU M-MIMO OFDMA systems as depicted in Section 2, where \(N_{R}\) and \(N_{T}\) are the numbers of the antennas at the base station side and total user side, respectively. As in Table 1, simulation scenarios are 1024-quadrature amplitude modulation (QAM) and the number of subcarriers as 256, 100 OFDM symbols, cyclic prefix (CP) length is 64, each symbol has pilots as 20. In addition, assume that the channels are two-ray flat Rayleigh fading with additive white Gaussian noise (AWGN) and channel state information (CSI) is available at the receiver by LS estimation. Five receivers, including the SOR [27], the modified SOR [28], the SSOR [29], the AOR [30], and the proposed two-stage receiver, are conducted for comparison in terms of the bit error  
Figure 1: The block diagram of the proposed two-stage detection scheme. rate (BER) performance. Moreover, to accentuate the novelty of our proposed scheme, we briefly describe the characteristics of previously published work and our proposed scheme in Table 2.  
First, we use Equations (16) and (17) to gain the appropriate relaxation parameter \(\omega\) and the acceleration parameter \(\gamma\), respectively, within the first stage. Apart from this, we show the BER performance of the proposed CAOR scheme against \(\gamma\) and \(\omega\) for different relaxation parameter \(\omega\) values and acceleration parameter \(\gamma\) values in Figures 2 and 3, respectively, when the number of iterations \(i\) is 4, \(N_{R}\times N_{T}=64\times 16\) and the SNR level is set to 40 dB. We can observe that if \(\omega\) approaches 1.1 or so, the BER performance will improve; otherwise, BER performance will decrease. Thus, we believe that the choice of \(\omega\) close to 1.1 and \(\gamma\) close to 1.0 will yield the best parameter estimate. Simultaneously, the inferences from Figures 2 and 3 are consistent with the calculated values of Equations (16) and (17), respectively. \begin{table}
\begin{tabular}{c c} \hline \hline
**System** & **Parameter** \\ \hline Number of data subcarriers & 256 \\ Number of OFDM symbols & 100 \\ Modulation scheme & 1024-QAM \\ CP Length & 64 \\ Number of pilot data in one OFDM symbol & 20 \\ The maximum SNR & 60 \\ Channel & Rayleigh fading channel \\ Number of channel taps & 2 \\ Noise & AWGN \\ Channel estimation & LS \\ Monte Carlo (times) & 10,000 \\ \hline \hline \end{tabular}
\end{table} 
Table 1: Simulation scenarios. \begin{table}
\begin{tabular}{c l} \hline \hline
**Scheme** & **Brief Description** \\ \hline SOR [27] & SOR is a method of solving a linear system of equations derived by extrapolating the Gauss–Seidel method. \\ modified SOR [28] & Modified SOR is a variant of SOR, which changes certain parameters in the SOR algorithm and is nearly unaffected by the relaxation factor \(\omega\) in lower modulation order. \\ SSOR [29] & SSOR combines two SOR sweeps in such a way that the resulting iteration matrix is similar to a symmetric matrix. \\ AOR [30] & The AOR iterative algorithm can be regarded as an extension of the SOR iterative algorithm, which is a two-parameter generalization of the SOR method. \\ CAOR & The CAOR method combines the AOR iterative algorithm and the recursive characteristics of the Chebyshev polynomials.