# Channel Estimation Based on Statistical Frames and Confidence Level in OFDM Systems
## 6 Simulation Results
### The Performance in Dynamic Multipath Channels  
Figures 6 and 7 present the SER performance in 16 QAM-modulated CP-OFDM systems over dynamic Brazil B and Brazil D, respectively. As shown in Figure 6, the gap of the SNR gain among \(T_{1}=5\), \(T_{2}=7\), \(T_{3}=9\) and \(T_{4}=11\) is about 3 dB, 2 dB and 1.2 dB at the SER of \(5\times 10^{-2}\), respectively. In Figure 7, the gap of the SNR gain among \(T_{1}=5\), \(T_{2}=7\), \(T_{3}=9\) and \(T_{4}=11\) is about 4 dB, 1.8 dB and 0.5 dB at the SER of \(8\times 10^{-2}\), respectively. Therefore, \(T_{1}=5\) is a suitable value, which can be chosen for the dynamic multipath channels. Figure 5: SER performance of the 16 QAM-modulated CP-OFDM system over static CDT1. LS: least square; IMMSE: improved minimum mean square error. In Figure 8, under the maximum Doppler spread of 20 Hz, the proposed confidence level method can provide 0.4 dB, 1.0 dB and 1.2 dB SNR improvements compared with the IMMSE method, the LS method and the Chi-distribution method at the target SER of 2 \(\times\) 10\({}^{-2}\), respectively. The IMMSE method has bad SER performance when the SNR is higher than 19 dB. The confidence level method has the best SER performance except the ideal estimation and threshold value methods. As shown in Figure 8, the proposed confidence level method and threshold value method have almost the same SER performance in the lower SNR range. Compared with the ideal channel estimation method, the proposed confidence level method has 2.2 dB SNR degradation at the target SER of 2 \(\times\) 10\({}^{-2}\). Figure 6: SER performance of the 16 QAM-modulated CP-OFDM system over Brazil B with a Doppler spread of 20 Hz. Figure 7: SER performances of the 16 QAM-modulated CP-OFDM system over Brazil D with a Doppler spread of 20 Hz. Under the Brazil B channel with a Doppler spread of 60 Hz, as shown in Figure 9, the proposed confidence level method provides the SNR gains of 0.6 dB, 2.0 dB and 4.5 dB at the SER of \(2\times 10^{-2}\) compared with the LS, IMMSE and Chi-square distribution methods, respectively. The IMMSE method has bad SER performance when the SNR is higher than 19 dB. The confidence level method has the best SER performance except the ideal estimation and threshold value methods. Compared with the threshold value method, the proposed confidence level method has 0.4 dB SNR degradation at SER of \(2\times 10^{-2}\). Compared with the ideal channel estimation, the proposed confidence level method has 1.9 dB SNR degradation at the target SER of \(2\times 10^{-2}\). Furthermore, the SNR gap between the SER performance curves of ideal channel estimation and the proposed confidence level methods is about 1.8 dB at the SER of \(2\times 10^{-2}\). Figure 8: SER performance of the 16 QAM-modulated CP-OFDM system over Brazil A under \(T_{1}=5\). Figure 9: SER performance of the 16 QAM-modulated CP-OFDM system over Brazil B under \(T_{1}=5\). As shown in Figure 10, compared with the IMMSE method, the Chi-square distribution method and the LS method, the proposed confidence level method provides the SNR gains of 1.3 dB, 1.5 dB and 2.5 dB at the SER of 3 \(\times\) 10\({}^{-2}\) when the maximum Doppler spread equals 80 Hz. The confidence level method has the best SER performance except the ideal estimation. The IMMSE estimation method has worse SER performance in the high SNR region, and the Chi-square distribution method has the worst SER performance. Compared with the ideal channel estimation, the proposed confidence level method has 2.3 dB SNR degradation at the target SER of 3 \(\times\) 10\({}^{-2}\). Moreover, compared with the threshold value method, the proposed confidence level method provides the SNR gains of 0.05 dB at the SER of 10\({}^{-2}\) with the maximum Doppler spread equal to 80 Hz. The proposed confidence level method can suppress the noise effectively based on the statistical frames buffer, which reduces the noise.