# Compressive Sensing-Based Coding Iterative Channel Estimation Method for TDS-OFDM System
## 1 Introduction  
Satellite platforms, which feature wide coverage and little impact from ground, serve as the key nodes of integrated air-space-ground communication network in the future. With the rapid development of communication technologies in recent years, ground 5G network is integrated with satellite communication network to form a seamlessly connected and fully covered space-ground communication network. This is an important development direction for new-generation communication systems [1, 2, 3, 4, 5]. TDS-OFDM is a multi-carrier communication system that can solve the problems of multipath fading and high-bit-rate transmission in wireless channels [6]. Different from conventional OFDM systems, the TDS-OFDM system cancels pilot signals and uses all subcarriers to transmit data and improve spectrum efficiency [7]. Additionally, it adopts a pseudorandom PN sequence as the guard interval and utilizes its good autocorrelation to realize channel estimation and synchronization [8]. However, after time-domain signals pass through a multipath channel, data smearing occurs, which causes the aliasing between the PNsequence and its adjacent valid data. It affects the accuracy of channel estimation and restricts the extensive applications of the TDS-OFDM system [9]. The key issue in TDS-OFDM channel estimation lies in the processing of the PN sequence as the guard interval. A large number of domestic studies have been conducted and mainly focused on the design and extraction of interference-free regions in the PN sequence as well as the separation and reconstruction of PN sequence and transmission data. Since aliasing interference usually occurs at the head and tail of the PN sequence and does not cover the entire sequence, it is an effective technique to estimate the channel using the non-aliasing part of the PN sequence. Ref. [10] proposed a sparse channel estimation technique based on forward-backtracking orthogonal matching pursuit (OMP), which estimates the channel impulse response using the PN sequence in the inter-symbol interference-free (ISI-free) regions to reduce channel interference. However, when the delay spread of the channel impulse response is approximated using the duration of the guard interval, the number of samples in the ISI-free regions was insufficient, leading to incomplete channel information estimation. Ref. [11] introduced a dual PN sequence method in which the first PN sequence was used as the guard interval, and the part of the second PN sequence that was not interfered by the data blocks was used for channel estimation to reduce the complexity of eliminating inter-block interference (IBI) and to improve channel estimation efficiency. However, this was carried out at the expense of some spectrum resources to some extent. To solve the above problems and improve the spectrum efficiency of the system, researchers turned their attention to the separation and reconstruction of the PN sequence and transmission data. Ref. [12] proposed a compressive sensing-based iterative channel estimation method in which a sensing matrix was constructed using a PN sequence and data affected by ISI; high-accuracy channel estimation was realized by the iterative optimization of compressive sensing channel estimation. Ref. [13] combined the least squares estimation (LS) method and RefineNet neural network to design a channel estimator. This estimator can accurately learn the characteristics of time-varying channels, and its estimation accuracy is significantly better than traditional LS estimation. However, the training data for this algorithm are based on the specific basis expansion model (BEM), differing from the actual channel and consuming many resources.