# Compressive Sensing-Based Coding Iterative Channel Estimation Method for TDS-OFDM System
## 1 Introduction
The compressive sensing reconstruction algorithm is used to solve the L1 norm minimum solution, which can be mainly divided into three categories based on the type of reconstruction:  
Convex optimization algorithm or optimal approximation algorithm: Converting non-convex problems into convex problems to find the approximation of the signal, such as the Basic Pursit (BP) algorithm. Bayesian algorithm: First, determine the sparse prior distribution of the signal, and reconstruct the signal that satisfies this partition from the randomly observed data information using Bayesian probability distribution criteria, such as Bayesian Compressed Sensing (BCS) and Variational Bayesian Compressed Sensing (VBCS). Among the two algorithms mentioned above, convex optimization method and Bayesian algorithm require complex matrix operations and have strong dependence on parameters, resulting in high hardware resource consumption. To avoid such problems, this article uses the greedy iterative algorithm, iteratively finding the support set of sparse vectors, i.e., directly selecting the most relevant atoms in the perception matrix to form new samples, and using constrained support least squares estimation to reconstruct the signal. Examples include Matching Pursuit (MP), Orthogonal Matching Pursuit (OMP), Compressed Sampling Matching Pursuit (CoSaMP), etc. Among them, the MP algorithm converges slowly and may repeatedly select the same atoms. OMP is sensitive to noise and requires precise knowledge of sparsity. The CoSaMP algorithm has strong noise resistance and can adapt to sparsity. Therefore, in the case of accurately reconstructing the original sparse signal while balancing computational complexity and noise environment, the CoSaMP algorithm in greedy iterative algorithms is a good choice. To sum up, the channel estimation method based on the interference-free region in the PN sequence is limited by the short PN data length, which easily leads to incomplete channel information estimation. The channel estimation method based on the separation and reconstruction of a complete PN sequence has a better channel estimation capability. However, this method brings noise interference during data reconstruction in this method, which increases the errors in channel estimation. To solve the above problems, this paper proposes a cyclic compressive sensing channel estimation algorithm based on channel coding. It combines cascaded channel coding technology with compressive sensing channel estimation to realize channel estimation through the iterative optimization of compressive sensing and an equalization feedback loop. After cascaded channel coding is employed to correct the data errors, compressive sensing is iterated again to further improve the accuracy of channel estimation. This paper attempts to make the following contributions:  
1. There is a problem of insufficient samples when using PN sequences without IBI regions for wireless sparse channel reconstruction. This article utilizes the CoSaMP algorithm in greedy algorithms to construct an equilibrium feedback loop, achieving sparse channel iterative estimation using all PN sequences. It solves the limitation of small non-IBI areas in PN sequences, and improves channel estimation accuracy in multipath fading environments. 2. In this paper, RS-LDPC cascaded coding is introduced, and the accuracy of decoded data is improved through the correction of received data errors. Moreover, the accuracy of the sensing matrix is effectively improved by designing the recoding link of error-corrected data, and the accuracy of channel estimation in a multipath fading environment is improved through repeated iterative optimizations. Meanwhile, RS-LDPC cascaded coding enhances the anti-interference of data and improves the bit error rate (BER) of the system.