# An Improved Orthogonal Matching Pursuit Algorithm for CS-Based Channel Estimation
## 1 Introduction  
Channel estimation is among the key technologies in modern wireless communication systems, and data-assisted channel estimation offers remarkable advantages, such as low errors and low complexity, and it is extensively applied to modern wireless transmission systems. Conventional channel estimation methods do not use priori information while transmission channels have sparse properties but focus only on the maximum delay spread of the channel, so they lead to the overuse of bandwidth and energy due to the large overhead of the reference signal. Compressed-sensing (CS)-based methods take advantage of the fact that the propagation multipath of wireless broadband channels usually has time-domain sparsity characteristics [1] and adopt a parametric estimation method to complete channel state detection. By estimating the path delay, path gain, and phase parameters of each propagation path, the parametric estimation method is able to achieve superior channel estimation performance with fewer reference signals, and thus, it improves the effectiveness and reliability of the system. Currently, CS-based sparse channel estimation is among research hotspots. Sparse signal reconstruction is the core of CS theory [2, 3]. References [4, 5, 6] provided reviews of the CS technique and also a comprehensive overview of various applications of sparse representation in wireless communications. Reference [4] focused on the sparse recovery algorithms and discussed some comparisons among them, and it also presented several applications of compressed sensing, such as images and videos, compressed transmission data, systems communication, and detection and recognition systems. Reference [5] identified the potential applications and research challenges of sparse representation in fifth-generation (5G) and Internet-of-Things (IoT) networks. Reference [6] listed some futureresearch directions for CS techniques in wireless applications. Reference [7] investigated the application of a CS technique and an OMP algorithm to reconfigurable-intelligent-surface (RIS)-assisted wireless communication systems. There are two main types of methods for signal reconstruction algorithms for CS: convex optimization methods and greedy algorithms. Because of the unacceptable computation time and complexity of convex optimization algorithms, greedy algorithms are more commonly applied. A greedy algorithm is not an optimization algorithm, and unlike convex optimization algorithms, it does not have an objective function and does not minimize it, but it finds the positions and coefficients of the non-zero elements of the sparse signal through several iterations to achieve sparse signal recovery [8]. As an important greedy algorithm, the orthogonal matching pursuit (OMP) algorithm is more commonly applied to CS-based channel estimation [9]. Reference [10] used the OMP algorithm to estimate sparse channels with more accuracy than conventional algorithms. Reference [11] provided a detailed description and summary of different CS-based channel estimation methods. The OMP algorithm can cause reconstructed results to fall into a local optimum. In order to improve estimation accuracy, reference [12] proposed the A*OMP pseudo-greedy algorithm, which utilized the backtracking feature of the A* algorithm. Compared with the OMP algorithm, it had higher accuracy and reconstruction probability. Reference [13] developed an improved A*OMP algorithm and verified its performance in orthogonal frequency division multiplexing (OFDM) systems. The obtained results showed that the proposed method effectively improved the accuracy of channel estimation. The improved algorithm optimized path initialization; meanwhile, in order to avoid unknown errors caused by too many iterations, the difference between the residuals of two adjacent iterations was applied as a condition for the termination of iteration, which resulted in higher estimation accuracy.