# Computationally Efficient Soft Detection Schemes for Coded Massive MIMO Systems +
## 4 Simulation Results  
We simulated the performance of the coded MIMO system with 16 quadrature amplitude modulation (QAM) over a frequency-flat Rayleigh fading channel. As a forward error correction (FEC) scheme, low density parity check (LDPC) code with a length of 16,200 bits and a code rate of 1/3 was used. We first compare the bit error rate (BER) performance of various coded MIMO systems at the first iteration of MMSE-PIC detection. This is to see the performance behavior by the number of iterations inside of the LDPC decoder, before we investigate the performances of JIDD based detection schemes.  
Figure 2 compares the BER performance of the proposed method with that of the conventional scheme for \(M\times N\) MIMO systems. The maximum number of iterations inside the LDPC decoder is denoted by \(\alpha\). As shown in the figure, the performance of both methods improves as \(\alpha\) increases, regardless of the number of antennas. The performance gap between the conventional and proposed methods at a given \(M\times N\) MIMO system with \(\alpha\) of 20 is almost the same as the one with \(\alpha\) of 30. Henceforth, the maximum number of iterations inside the decoder was limited to 20 for the remaining simulations. This is because we are mainly targeting to see the performance behviour of the proposed detection schemes, not that of the decoder.  
Figure 3 compares the BER performance of the \(16\times 128\) MIMO system for different \((\eta,l)\), where \(\eta\) and \(l\) denote the number of joint iterations and the number of detector iterations, respectively. From the simulation results in Figure 3, we can find that BER performance of the proposed method approximates to that of the conventional method as \(\eta\) increases when \(l=1\). In addition, two iterations inside the detector, i.e., \(l=2\), are shown to be sufficient to produce approximating performance to that of the conventional method when \(\eta=4\). Hereafter, the maximum number of joint iterations and detector iterations were limited to 4 and 2, respectively.  
\begin{table}
\begin{tabular}{c c c c} \hline \hline \(K\) & **(2), (3)** & **(19)+(20), (23)+(24)** & \(\widetilde{s}_{i}\)**, \(E_{i}\) in Table 1** \\ \hline
4 & 96, 82 & 24, 10 & 6, 5 \\
6 & 512, 450 & 64, 26 & 12, 11 \\
8 & 2560, 2306 & 160, 66 & 20, 23 \\ \hline \hline \end{tabular}
\end{table}
Table 3: Complexity of estimating \(\widetilde{s}_{i}\) and \(E_{i}\) in terms of the number of multiplications.  
Figure 2: BER performance comparison according to \(\alpha\) at the first iteration.  
Figure 4 compares the BER performance between the proposed and conventional methods with various numbers of antennas. As shown in the figure, the performance of the proposed method slightly degrades when the number of antennas is comparatively small. On the other hand, the proposed method achieves an approximating performance to the conventional methods as the number of antennas increases. We note that we can achieve greater reduction in computational complexity with a larger number of antennas, as shown in Table 2.  
Figure 4: BER performance comparisons with various numbers of antennas when \((\eta,l)=(4,2)\).  
Figure 3: BER performance comparison with various \((\eta,l)\) for \(16\times 128\) system.