# An Enhanced Precoder for Multi User Multiple-Input Multiple-Output Downlink Systems
## 5 Simulation Results
### MGBD Precoder  
The MGBD precoder is compared to the conventional precoders in terms of BER and throughput performances. The Figures 4 and 5 show the BER performance for the MGBD precoder, RBD precoder and GBD precoder according to SNR. Also, Figure 4 shows the BER performance when each of the 3 UEs has 3 receive antennas and BS has 9 transmit antennas and Figure 5 is BER performance when each of the 4 UEs has 3 receive antennas and BS has 16 transmit antennas. In Figures 4 and 5, the BER performance for the proposed scheme increases compared with the GBD precoder at all SNRs and all cases except for minimum data streams (\(r=3\) or \(r=4\)). Compared to GBD, the performance gain of the MGBD precoder is about 3 dB (\(r=6\)) to 15 dB (full streams) when each of the 3 UEs has 3 receive antennas and BS has 9 transmit antennas according to Figure 4. In Figure 5, the MGBD precoder obtains about 2 dB (\(r=8\)) to 5 dB (full streams) gain in comparison with GBD precoder when each of the 4 UEs has 3 receive antennas and BS has 16 transmit antennas. This advantage is obtained by optimizing with a modified MMSE criterion like Equation (12). If the BS transmits minimum data stream, the extra BER gain that the modified MMSE criterion provides is negligible in comparison with diversity gain. Thus, the BER performance for the MGBD precoder is equal to the BER performance for the GBD precoder when BS transmits minimum data streams. The degrees of freedom for MGBD and GBD precoder increases as the data streams decrease. Therefore, the BER performance is maximized when BS transmits 1 data stream to each UE and is minimized when BS transmits full data streams by consuming all ranks for the channel. In this case, the MGBD precoder does not obtain extra diversity gain; thus, the BER performance for the proposed scheme is the same as the BER performance for the RBD precoder. \begin{table}
\begin{tabular}{c c} \hline \hline
**Parameters** & **Values** \\ \hline Number of simulation iterations & 100,000 \\ Data size & 512 \\ Number of receive antennas & 3 \\ Number of transmit antennas & 16, 9 \\ Number of UEs & 4, 3 \\ Channel & Complex Rayleigh flat fading \\ Modulation order & 16-quadrature amplitude \\  & modulation (QAM) \\ Decoder & Zero forcing (ZF) \\ \hline \hline \end{tabular}
\end{table} 
Table 1: The simulation parameters. The gap for BER performance between MGBD and GBD precoder in Figure 5 decreases more than the gap for BER performance in Figure 4. Because extra BER gain is obtained by increasing the number of transmit antennas relative to the number of receive antennas, the gap for BER performance decreases in both precoders. Figures 6 and 7 represent normalized throughput performance for the modified GBD precoder, RBD precoder and GBD precoder according to SNR. Also, the throughput performances for the proposed scheme are compared with Tomlinson-Harashima precoding (THP), which is well known as a suboptimal precoder in the MU-MIMO system [23] to show the superiority of the proposed scheme. Both figures show that peak value for normalized throughput is enhanced as the number of data streams increases. However, the required SNR where a peak value for normalized throughput is achieved rises as the number of data streams increases. First, in the both cases, THP reaches maximum throughput rapidly when BS transmits data with full streams. However, the throughput performance for the MGBD outperforms the THP when BS transmits data with lower than the maximum streams (\(r=3\), \(r=6\) in Figure 6 and \(r=4\), \(r=8\) in Figure 7). Also, the GBD obtains more gain than the THP in minimum streams, and the gap between these precoders decreases as the number of streams reduces. These results are effected by the MGBD and GBD obtaining more diversity gain than the THP since the partial nulling is used. Additionally, the gap of throughput performance between the MGBD and THP is large when the SNR is low since the proposed scheme obtains additional SNR gain by mitigating noise components.