# A Haar Wavelet Decision Feedback Channel Estimation Method in OFDM Systems
## 5 Simulation Results  
This section presents the BER and NMSE performance comparisons between LS, DFT, DF, and the proposed Haar wavelet decision feedback method. The simulation is performed in static and dynamic multipath environments, respectively. The multipath channel models are China DTV Test 1 st (CDT1) and China DTV Test 6 st (CDT6). CDT1 and CDT6 channels are from the field tests for digital television terrestrial broadcasting standard [37]. Both CDT1 and CDT6 channels are belong to the Rayleigh fading channel. Under Rayleigh fading channel environment, the received signals suffer from the effect of multipath propagation. The received signals come from the different paths and have different delay time before arriving at the receiver. It is assumed that the components of the received waveform obey  
Figure 4: The proposed Haar wavelet channel estimation method in wavelet-OFDM system. the Gaussian distribution with a mean value of zero and standard deviations \(\sigma_{\rm R}^{2}\), and the probability density function of the Rayleigh fading amplitude is presented as [8]  
\[f(a)=\left\{ \begin{array}{cc}\frac{a}{\sigma_{\rm R}^{2}}\exp(-\frac{a}{2 \sigma_{\rm R}^{2}}),&a\geq 0,\\ 0,&a<0,\end{array} \right. \tag{11}\]  
where \(a\) is the amplitude of the received signal. CDT1 is a typical multipath broadcasting channel model which has slight frequency-selectivity. CDT6 channel has stronger frequency-selectivity than CDT1 channel. These two channels are used to verify the effectiveness to channel characteristics of the proposed Haar wavelet method. The profiles for the CDT1 and CDT6 channel models are shown in Table 1. The main simulation parameters based on wavelet-OFDM system and CP-OFDM system are presented in Table 2.  
The conventional LS, DFT, and DF channel estimation methods are presented in CP-OFDM system. The proposed Haar wavelet method is proposed in wavelet-OFDM system. In the wavelet-OFDM and CP-OFDM systems, the modulation mode is the QPSK scheme. The total number of data subcarriers is 512. The CP occupies 128 subcarriers in the simulation of CDT1 channel. Due to CDT6 channel has stronger frequency-selectivity than CDT1 channel, this paper adds the length of CP under CDT6 channel environment. The CP occupies 140 subcarriers in the simulation of CDT6 channel. One OFDM block consists of 10 OFDM symbols. In LS and DFT channel estimation methods, 5 block type pilots are inserted into the OFDM symbols uniformly. In DF and the Haar wavelet methods, one block pilot symbol is inserted into the front of the first OFDM symbol. This paper utilizes the Doppler spread equivalent to 20 Hz in dynamic multipath channel environment. The threshold \(\hat{\sigma}\) obtained in the proposed Haar wavelet method under CDT1 and CDT6 channels are presented in Figure 5.  
As can be seen from Figure 5, with the increase of SNR, the threshold \(\hat{\sigma}\) under both CDT1 and CDT6 channels are decreasing, respectively. Under low SNR conditions, noise has larger energy than the useful signal. Hence, the threshold \(\hat{\sigma}\) is set to be large to suppress the noise to the maximum extent. According to Equation (9), when SNR = 10 dB, the thresholds \(\hat{\sigma}\) are 0.0268 and 0.0281 in CDT1 and CDT6 channels, respectively. When SNR = 14 dB, the thresholds \(\hat{\sigma}\) are 0.0148 and 0.0164 in CDT1 and CDT6 channels, respectively. The changing threshold can filter the noise effectively and improve the accuracy of channel estimation, reducing the system BER at the same time.