# A Pilot-Pattern Based Algorithm for MIMO-OFDM Channel Estimation
## 5 Simulations and Results  
To verify the efficiency of the configuration, a simulation platform is established as shown in Figure 3.  
In the simulation model, the channel is designed as a pseudo-static Rayleigh channel in which all of the parameters follow the specification of ITU-R M.1225 for a channel B model [22; 23], as listed in Table 1. The MIMO-OFDM system for simulation is constructed to form the scenario in which the number of antennas in the transmitter and receiver are set as NT = 2, NR = 2, respectively, the number of the sub-carrier is configured as \(N\) = 128, the length of cyclic prefix (CP) is set to 16; and the sampling cycle is Ts = 2 \(\times\) 10\({}^{-7}\) s. Quadrature phase shift keying (QPSK) is chosen as the modulation scheme, while the hard decision criteria is adopted for signal detection on the receiver side [21].  
Figure 4 shows the performance of the LS algorithm used for a single-symbol scheme. It can be concluded that the single-symbol scheme, compared with non-channel estimation, can really improve bit error rate (BER), while reducing computation complexity. Figure 5 shows the performance comparison between single-symbol and double-symbol scheme when using two antennas to transmit the same pilot data alternatively within a training block. It can be seen that the double-symbol scheme performs better than the single-symbol scheme for the reason that the double-symbol scheme need not the computation of interpolation so that it avoids interpolation error. However, the double-symbol scheme needs more pilot signals, which increases the system complexity and frequency overhead. The curves of BER versus SNR plotted in Figure 6 correspond to three cases of the single-symbol scheme, double-symbol scheme, and the improved scheme regarding performance trade-off.  
\begin{table}
\begin{tabular}{c c c c c c c} \hline \hline
**Taps** & **1** & **2** & **3** & **4** & **5** & **6** \\ \hline Relative time Delay & 0 & 100 & 200 & 300 & 500 & 700 \\ Average power (dB) & 0 & \(-\)3.60 & \(-\)7.20 & \(-\)10.8 & \(-\)18.0 & \(-\)25.0 \\ \hline \hline \end{tabular}
\end{table}
Table 1: Indoor model of ITU-R M.1225 Channel B.  
Figure 3: System simulation platform.  
Figure 4: Performance of channel estimation based on the LS method with one symbol.  
Figure 5: Performance comparison of pilot pattern with one symbol and two symbols.  
Figure 6: Performance of channel estimation using a double-symbol pilot pattern.  
The simulation results can be summarized thusly:  
1. Since the number of pilot signals of the double-symbol scheme is four times that of the single-symbol scheme, the interpolation is unnecessary. Thus, the interpolation error can be avoided. From this view, the double symbol-scheme is better than the single-symbol scheme, which has the advantage of more effective overhead.
2. The tradeoff scheme also does not need interpolation anymore; thus, it is better than the single-symbol scheme. Owing to the number of pilot signals being just half of that in the double-symbol scheme, the performance of tradeoff method is worse than the double-symbol scheme. However, the tradeoff method achieves an optimized balance between system performance and the overhead of the pilot pattern.