# A Haar Wavelet Decision Feedback Channel Estimation Method in OFDM Systems
## 1 Introduction
But the suppression factor of the linear filter in this paper is usually utilized in time-domain synchronous-OFDM (TDS-OFDM) systems. Hence, other communication systems, such as underwater acoustic communication and MIMO-OFDM systems, may require choosing a new suppression factor to effectively suppress the AWGN. The pilot-based channel estimation method is relied on the pilot symbols to estimate the channel state information which reduces the data transmission rate and spectrum efficiency. Another channel estimation method which has been extensively studied is called blind channel estimation method [18; 19; 20]. The blind channel estimation method presented in [21; 22] requires no pilots to estimate the channel state information. Hence, the blind channel estimation method has higher spectrum and data transmission efficiency than the pilot-based channel estimation methods. But at the same time, the blind channel estimation method requires calculating the statistical properties between the transmitted symbols and received symbols to estimate the channel impulse response (CIR). Hence, this method has high computational complexity which restrains the application in the OFDM systems. To further reduce the computation complexity of blind channel estimation method, a precoding-assisted blind channel estimation algorithm was proposed in [23]. This algorithm designs a non-redundant linear pre-coder based on auto-correlation matrix at the transmitter. This method has low complexity than conventional subspace-based blind channel estimation method. But this algorithm cannot be applied in MIMO system which is widely used today. The semi-blind channel estimation method is a tradeoff between computational complexity and spectrum efficiency [24; 25; 26]. Compared with the pilot-based channel estimation method, the semi-blind method uses less pilots to estimate the channel state information which improves the data transmission rate and spectrum efficiency. At the same time, the computational complexity is further reduced compared with the blind channel estimation method. In [27], a quasi-Newton method for semi-blind estimation is derived for channel estimation in uplink cloud radio access networks. Firstly, the initial channel state information is provided by LS channel estimation. Then, the maximum-likelihood principle is used to improve the estimation performance in the semi-blind channel estimation. Simulation results show that semi-blind channel estimation decreases the overhead of bandwidth without sacrificing the mean square error (MSE). In [28], an iterative space-alternating generalized expectation maximization (SAGE) based semi-blind channel estimation method was presented in massive MIMO systems. This method updates the pilot-based channel estimate errors with the help of SAGE algorithm. It first uses a few pilots to obtain the initial channel parameters. Then, the iteratively SAGE algorithm is used to improve the accuracy of the initial channel parameters. The advantage of this method is that it saves the additional pilot overhead and achieves convergence in almost one iteration. But the disadvantage of this method is that the SAGE algorithm increases the system complexity. An optimized semi-blind channel estimation method in OFDM systems was presented in [29]. This method uses the scaled LS technique to estimate channel state information and further eliminate the subspace decomposition estimation error which is caused by the noise in the channel. Due to using a few pilots, this method improves the spectrum efficiency. But the disadvantage of this method is that it cannot suppress the ICI and ISI effectively due to using the zero prefix (ZP) as the guard interval. In paper [30], a semi-blind algorithm that uses the linear prediction as the blind channel estimation, in combination with some training data to further improve the channel estimation accuracy, yielding a better estimation performance.