# A Haar Wavelet Decision Feedback Channel Estimation Method in OFDM Systems
## 1 Introduction  
Orthogonal frequency division multiplexing (OFDM) system [1; 2; 3; 4; 5] has been widely used in modern wireless communication systems due to its high spectrum efficiency and strong multipath fading resistance ability. The cyclic prefix (CP) is used as the guard interval in each OFDM symbol to reduce the inter-symbol interference (ISI) and inter-carrier interference (ICI) greatly. At the same time, the OFDM system utilizes the time delay characteristics of multipath fading channel which greatly simplifies the equalizer design. The OFDM technology can also combine with the multiple-input multiple-output (MIMO) technology to enhance the channel capacity [6]. The wireless channel is an important part in OFDM systems. But when the signal passes through the wireless fading channel, it will be disturbed by the additive white Gaussian noise (AWGN) which affects the quality of signal transmission and the performance of the system. Some papers [7; 8] use Turbo coding with code rate of \(1/3\) and \(1/2\) respectively at the transmitter in OFDM system to suppress the effect of noise in wireless channel. It can obtain good performance in bit error rate (BER). To further improve the OFDM system performance, channel estimation is a key technology, and an efficient channel estimation method can greatly improve the system performance. To estimate the characteristics of the channel, some conventional channel estimation methods are often performed in frequency-domain using pilots [9], such as least square (LS) method [10; 11; 12], minimum mean square error (MMSE) method [13], linear MMSE (LMMSE) method [14], singular value decomposition (SVD) method [15], noise suppression threshold method [16; 17], and so on. The LS channel estimation method has the advantage of low complexity and easy implementation. But thismethod does not consider any noise effect in obtaining its solutions and has poor performance [10; 11]. In [12], LS channel estimation method is applied on the space-time block-code based MIMO-OFDM system. It also designs a new pilot pattern to further improve the accuracy of the channel estimation. This method has low complexity, but it may has poor performance in dynamic channel which restrains the application. The MMSE channel estimation method has good performance because of utilizing the channel statistics and the signal-to-noise ratio (SNR) to suppress the effect of noise. However this method requires a large amount of calculations concerning the inverse operation of the matrix, and the hardware implementation is relatively hard [13]. To further reduce the calculation complexity, the LMMSE channel estimation method is proposed in [14]. But the disadvantage of this method is that much priori information is required to calculate the autocorrelation matrix about the channel. Hence, the application of this method will be restrained in complicated fading channel conditions. In [15], the discrete cosine transform-SVD (DCT-SVD) based channel estimation technique was presented in IEEE 802.16e downlink partially used sub channelization system. This channel estimation method has a low calculation complexity. However, it just utilizes the outer coding technology in downlink partially used sub channelization system, and the channel estimation accuracy is decreased in fast fading environment. A time-domain threshold channel estimation method for OFDM systems was proposed in [16]. This method is based on a time-domain threshold which is a standard deviation of noise obtained by wavelet decomposition. To obtain a good performance, the time-domain threshold decreases with the increase of SNR. But the disadvantage of this method is that it uses comb pilots to estimate the channel state information which greatly reduces the spectrum efficiency. In [17], the linear filter least square channel estimation method was proposed in OFDM systems. This method can effectively suppress the AWGN by the linear filter in time-domain.