# Joint Channel Estimation Algorithm Based on DFT and DWT
## 1 Introduction
In order to solve this problem, in papers [5; 12; 13], paths with a channel power component smaller than its noise power component are judged as valid paths, and these valid paths are retained as much as possible by a set threshold value. The ideal threshold selection principle should be to classify the samples where the noise component is larger than the channel power component as the noise taps and set them to zero, meanwhile the remaining samples are determined as the valid taps and reserved. However, since the exact percentage of the channel power component and noise component at each sample is not available, this method is still subject to misclassification. Although the above threshold-based DFT channel estimation algorithms can alleviate this by choosing the appropriate wavelet basis and wavelet decomposition layers, the wavelet-denoising algorithm can significantly improve the estimation performance floor problem of the DFT algorithm under high SNR. Under high SNR conditions, it still needs to be further improved. In addition, if the threshold setting is too conservative, fewer noise components will be removed, and the algorithm estimation performance will be degraded under low SNR. Some studies have applied wavelet-denoising to channel estimation algorithms [14; 15; 16; 17; 18]. The basic principle of the wavelet-denoising algorithm is to transform the CFR estimated by the LS algorithm to the wavelet domain, process the wavelet coefficients using the threshold method, and then reconstruct the signal to achieve noise cancellation. By choosing the appropriate wavelet basis and wavelet decomposition layers, the wavelet-denoising algorithm can significantly improve the estimation performance floor problem of the DFT algorithm under high SNR conditions. The main contributions of our work can be summarized as follows: For OFDM systems with virtual subcarriers, this paper first proposes the Segmented Threshold DFT-based (ST-DFT) channel estimation algorithm. By using the different distribution characteristics of the channel and noise components on the time-domain samples, a new CIR effective taps decision threshold is proposed to improve the estimation performance under the condition of channel energy dispersion. Then, motivated by the fact that the DWT algorithm and the ST-DFT algorithm have better detection performances under high and low SNR conditions, respectively, we further propose a joint channel estimation algorithm based on ST-DFT and DWT. The MSE estimation performance of the two algorithms under different channel conditions shows that the joint channel estimation algorithm can dynamically select the algorithm with the best estimation performance under different SNR conditions. The simulation results also show that, compared with the single estimation algorithm, the DFT channel estimation algorithm with an improved threshold produces better overall estimation performances. Furthermore, the proposed joint channel estimation algorithm can determine the optimal channel estimation solution under the full SNR range without any prior conditions. The remainder of this paper is organized as follows: Section 2 outlines the system model. Section 3 introduces the existing DFT algorithm and proposes the ST-DFT algorithm. Section 4 briefly describes the conventional DWT algorithm. Section 5 describes the proposed joint channel estimation algorithm based on ST-DFT and DWT in detail. In addition, Section 6 presents simulations and the discussion, and Section 7 gives the conclusions of this paper.