# Time Coding OTDM MIMO System Based on Singular Value Decomposition for 5G Applications
## 4 Conclusions  
An STC OTDM architecture is proposed for enhancing the performance of the BER and increasing the diversity order. We considered a system with N = 16, 64, and 128. The modulation schemes QPSK, 64-QAM, and 256-QAM were investigated with a number of channel taps equaling 9, 12, and 15. For the sake of comparison, we also considered a standard OFDM system, STC OFDM, and standard OTDM with the same active sub-carriers, a cyclic prefix (CP) of length L for the OFDM and STC OFDM techniques, and simple zero-forcing equalization. The proposed system shows its superiority over the OFDM, STC OFDM, and OTDM in enhancing the performance of BER. The simulation results show that the SNR of the proposed system using QPSK modulation technique is equal to 10 dB at BER =\(10^{-3}\) when 16 subcarriers are used in a 9-tap Rayleigh fading channel. Also, the results show that the BER performance of the proposed technique is nearly constant for a different number of subcarriers. For example, the proposed technique using 64-QAM achieved the same BER performance, \(10^{-3}\) at \begin{table}
\begin{tabular}{c c c c c c c c c c} \hline \hline \multicolumn{10}{c}{**SNR (dB)**} \\ \hline
**L** & \multicolumn{3}{c}{**9**} & \multicolumn{3}{c}{**12**} & \multicolumn{3}{c}{**15**} \\ \hline
**N** & **16** & **64** & **128** & **16** & **64** & **128** & **16** & **64** & **128** \\ \hline \multicolumn{10}{c}{**QPSK**} \\ \hline
**OFDM** & 26.5 & 27 & 27 & 26.8 & 27 & 27 & 26.4 & 26.6 & 26.8 \\
**STC OFDM** & 10.7 & 11 & 11 & 10.7 & 10.9 & 10.9 & 10.9 & 11 & 11 \\
**OTDM** & 16 & 22 & 24 & 14 & 21 & 23.2 & 13.4 & 20 & 22.4 \\
**STC OTDM** & 10 & 10.1 & 10.1 & 10 & 10.01 & 10.01 & 10 & 10.01 & 10.01 \\ \hline \multicolumn{10}{c}{**64-QAM**} \\ \hline
**OFDM** & 34 & 35 & 35 & 35 & 35.2 & 35.1 & 35.2 & 35.3 & 35.4 \\
**STC OFDM** & 23 & 23 & 23 & 23.2 & 23.15 & 23.1 & 23.2 & 23 & 23 \\
**OTDM** & 27.5 & 31 & 31.4 & 26.4 & 32.7 & 32.7 & 25.4 & 31.5 & 33 \\
**STC OTDM** & 22.3 & 22.4 & 22.4 & 22.2 & 22.4 & 22.4 & 22 & 22.3 & 22.4 \\ \hline \multicolumn{10}{c}{**256-QAM**} \\ \hline
**OFDM** & 37.7 & 38.5 & 39 & 38.5 & 39 & 39.3 & 39.8 & 39.9 & 38.6 \\
**STC OFDM** & 28.3 & 28.5 & 28.7 & 28.2 & 28.4 & 28.29 & 29 & 28.89 & 28.96 \\
**OTDM** & 32.5 & 37 & 37.4 & 31 & 36.8 & 37 & 32 & 36 & 37 \\
**STC OTDM** & 28.2 & 28.3 & 28.32 & 28 & 28.2 & 28.28 & 28.1 & 28.12 & 28.2 \\ \hline \hline \end{tabular}
\end{table} 
Table 2: The SNR (dB) simulation results at BER = \(10^{-3}\) for different modulation schemes, different subcarriers, and channels models. Figure 7: BER of STC OTDM at different channel taps L using QPSK. SNR = 22.5 dB, for the different subcarriers 64 and 128. Thus, the required system performance can be obtained with less number of subcarriers and thus less system complexity for the different modulation techniques. When using 64-QAM and 256-QAM the performance of BER is nearly the same and the proposed system achieves high performance at high data rates. Simulations also showed that the STC OTDM improves the security of the wireless communication system, where only the desired user can decode the transmitted data. The proposed technique is basically composed of a linear equalizer and SVD algorithm which is widely used in different present wireless communication systems. The complexity of the SVD computation is of order O(\(mm^{2}\)) where m and n are the matrix dimensions that will apply the SVD on it. Thus, the proposed system is applicable and can be practically deployed. Conceptualization, A.Z. and W.K.B. ; Methodology, R.M.A., A.Z. and W.K.B. ; Software, R.M.A., A.Z. and W.K.B. ; Validation, A.Z., W.K.B. and M.H.A. ; Formal Analysis, A.Z. and W.K.B. ; Investigation, R.M.A. ; Resources, R.M.A., A.Z. and W.K.B. ; Data Curation, R.M.A. ; Writing--Original Draft Preparation, R.M.A. ; Writing--Review & Editing, A.Z., W.K.B. and M.H.A. ; Visualization, R.M.A., A.Z. and W.K.B. Supervision, A.Z., W.K.B. and M.H.A. ; Project Administration, R.M.A., A.Z. and W.K.B. This research has no external funding.