# An Efficient Quantized Message Passing Receiver Design for SCMA Systems
## 4 Simulation Results
### BER Evolution for AWGN Channel  
In this subsection, we examine the validity of our proposed quasi-uniform quantizer for the SCMA system over the AWGN channel. In Figure 3, the bit error ratio (BER) performance of different SCMA detectors under the AWGN channel was observed for \(K=4\) and \(K=5\), respectively. The steps of the Sub-log MPA detector have been summarized in Algorithm 1, and the iteration number is set to 10. It is obvious that the BER performance gap between the original Log-MPA and the Max-log MPA can be neglected, but the Max-log MPA can achieve less computational complexity, which is essential to practical implementation. Note that the curve of the Sub-log MPA is overlapped with the Max-log MPA in bot cases, which in return verifies the effectiveness of the proposed Sub-log MPA.  
In the next stage, the convergence behavior of different SCMA detectors is shown in Figures 4 and 5 for \(K=4\), \(J=6\) and \(K=5\), \(J=10\), respectively, over the AWGN channel in the context of different SNRs. For the case of \(K=4\), SNR = 6 dB and SNR = 10 dB are taken into account, while SNR = 8 dB and SNR = 12 dB are considered. Based on Figures 4 and 5, it is obvious that both the original Log-MPA and the Max-log MPA need six iterations to converge, while only four iterations are enough for the Sub-log MPA. This is because the Sub-log MPA uses the latest updating message in the current iteration to exchange probabilities.  
\begin{table}
\begin{tabular}{c c c} \hline \hline
**Input Range** &
\begin{tabular}{c} **Quantized Value** \\ **(Decimal)** \\ \end{tabular} & **Binary Form** \\ \hline \([0,0.25)\) & 0 & 00000 \\ \([0.25,0.75)\) & 0.5 & 00001 \\ \([0.75,1.25)\) & 1 & 00010 \\ \([1.25,1.75)\) & 1.5 & 00011 \\ \([1.75,2.25)\) & 2 & 00100 \\ \([2.25,2.75)\) & 2.5 & 00101 \\ \([2.75,3.25)\) & 3 & 00110 \\ \([3.25,3.75)\) & 3 In the last set of simulations, we investigated the BER performance of different quantized schemes under the AWGN channel for \(K=4\) and \(K=5\), as shown in Figures 6 and 7, respectively, in terms of the Max-log MPA detector. The parameters of the quasi-uniform quantizer were set to \(\Delta=0.25\) and \(\mu=1.3\).The uniform and quasi-uniform quantizer were obtained according to Equations (19) and (21). Based on Figures 6 and 7, it is obvious that the BER performance suffers great degradation when the 4-bit, 5-bit, and 6-bit quantizers were considered. This is because the range of quantized messages is limited with the fixed step size \(\Delta\). Notably, the 8-bit uniform quantization of the messages can achieve almost the same BER performance as compared to the floating Max-log MPA, while the (5 + 1)-bit quasi-uniform quantization have nearly the same BER performance as that of the 8-bit uniform quantization. Moreover, the BER performance of the (5 + 1)-bit quasi-uniform quantizer under the AWGN channel for \(K=4\) and the Max-  
Figure 5: The convergence behavior of different SCMA detectors under the AWGN channel for \(K=5\).  
Figure 6: The BER performance of different quantized schemes under the AWGN channel for \(K=4\) and the Max-log MPA detector.  
Figure 7: The BER performance of different quantized schemes under the AWGN channel for \(K=5\) and the Max-log MPA detector.