# Singular Value Decomposition Channel Estimation in STBC MIMO-OFDM System
## 5 Simulation Results  
The BER performance of the proposed SVD channel estimation method is shown in this section. The simulation is performed in static multipath channel environments and adopts three constellation modulation modes of QPSK, 16 QAM, and 64 QAM, respectively. The Rayleigh fading multipath channel models are CDT1, CDT6, CDT8, Brazil A, and Brazil B channels [23; 25]. These channels have six paths. Each channel has a different delay time and power. These channels have different frequency-selectivity. The main simulation parameters based on the STBC MIMO-OFDM system are presented in Table 1. The profiles for the CDT1, CDT6, and CDT8 channel models are shown in Table 2. The profiles for the Brazil A and Brazil B channel models are shown in Table 3. \begin{table}
\begin{tabular}{c c} \hline \hline
**Parameters** & **Specifications** \\ \hline System model & STBC MIMO-OFDM \\ Modulation mode & QPSK, 16 QAM, 64 QAM \\ Number of transmit antenna & 2 \\ Number of receive antenna & 2 \\ Pilot interval (subcarrier) & 1 \\ CP length (subcarriers) & 256 \\ Subcarrier number & 2048 \\ OFDM block length & 10 \\ Pilot type & Comb-type \\ \(\varphi\) & 1, 17/9, 13/5 \\ \hline \hline \end{tabular}
\end{table} 
Table 1: Parameters for STBC-OFDM systems. Four channel estimation methods, LS, threshold, MMSE, and SVD, are presented in the STBC MIMO-OFDM system. As can be seen from Table 1, in the STBC MIMO-OFDM system, different modulation modes, such as QPSK, 16 QAM, and 64 QAM, are applied to test the system performance. There are two transmit antennas and two receive antennas in the STBC MIMO-OFDM system. The pilot interval is one subcarrier. The total number of subcarriers is 2048. The CP occupies 256 subcarriers. One OFDM block consists of 10 OFDM symbols. The comb-type pilot pattern in Figure 4 is used to estimate the CSI. Under the QPSK, 16 QAM, and 64 QAM modulation modes, the BER performance curves in the CDT1 channel are shown in Figures 5-7, respectively. \begin{table}
\begin{tabular}{c c c c c c c} \hline \hline \multirow{2}{*}{**Tap**} & \multicolumn{2}{c}{**CDT1**} & \multicolumn{2}{c}{**CDT6**} & \multicolumn{2}{c}{**CDT8**} \\ \cline{2-7}  & **Delay (\(\mu\)s)** & **Power (dB)** & **Delay (\(\mu\)s)** & **Power (dB)** & **Delay (\(\mu\)s)** & **Power (dB)** \\ \hline
1 & 0 & 0 & 0 & 0 & 0 & 0 \\
2 & \(-1.8\) & \(-20\) & \(-18\) & \(-10\) & \(-18\) & \(-1.8\) \\
3 & \(0.15\) & \(-20\) & \(-1.8\) & \(-20\) & \(-20\) & \(0.15\) \\
4 & \(1.8\) & \(-10\) & \(0.15\) & \(-20\) & \(-20\) & \(1.8\) \\
5 & \(5.7\) & \(-14\) & \(1.8\) & \(-10\) & \(-10\) & \(5.7\) \\
6 & \(18\) & \(-18\) & \(5.7\) & \(-14\) & \(0\) & \(30\) \\ \hline \hline \end{tabular}
\end{table} 
Table 2: Profiles for China DTV Test 1 st (CDT1), CDT6, and CDT8 multipath fading channels. Figure 5: Comparisons of bit error rate (BER) performance in the case of quadrature phase shift keying (QPSK) modulation at the static China DTV Test 1 st (CDT1) channel. \begin{table}
\begin{tabular}{c c c c c} \hline \hline \multirow{2}{*}{**Tap**} & \multicolumn{2}{c}{**Brazil A**} & \multicolumn{2}{c}{**Brazil B**} \\ \cline{2-5}  & **Delay (\(\mu\)s)** & **Power (dB)** & **Delay (\(\mu\)s)** & **Power (dB)** \\ \hline
1 & 0 & 0 & 0 & 0 \\
2 & 0.15 & \(-20\) & \(-18\) & \(-10\) \\
3 & 2.22 & \(-20\) & \(-1.8\) & \(-20\) \\
4 & 3.05 & \(-10\) & \(0.15\) & \(-20\) \\
5 & 5.86 & \(-14\) & \(1.8\) & \(-10\) \\
6 & 5.93 & \(-18\) & \(5.7\) & \(-14\) \\ \hline \hline \end{tabular}
\end{table} 
Table 3: Profiles for Brazil A and Brazil B multipath fading channels. As can be seen from Figure 5, the BER curves of four channel estimation methods show a downward trend. The LS method does not suppress the AWGN. Hence, its performance is the worst. Although the SVD method is a simplification of the MMSE method, its performance is very close to that of the MMSE method. Since the energy of the channel is mainly concentrated on the first \(l\) singular values of the channel autocorrelation matrix.