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In this paper, a novel method is constructed to estimate the time delay. The purpose of this article is to deal with the lack of measurement data in small sample (single snapshot) and low signal to noise ratio environment during wireless location. First, the sparse representation model of received signals is established. And then the measurement matrix is proofed to achieve the restricted isometry property. The idea of subspace pursuit is to find the subspace which consist of the received signal. Therefore, the delay estimation can be achieved using the corresponding relation between the time delay and the measurement matrix. Finally, simulations show that the subspace pursuit algorithm is suitable for small sample environment. The method can achieve a higher precision than greedy algorithms such as orthogonal matching pursuit and Regularized orthogonal matching pursuit algorithm. Furthermore, the subspace pursuit algorithm has a better performance in anti-multi channels. Introduction The delay estimation is widely applied to radar, sonar, wireless location [1] and other fields, which is the research emphasis on this field in complex environment. In order to solve the insufficiency of the current algorithm in the conditions of small sample and the low signal-to-noise ratio, many new methods are introduced into the delay estimation problem. The classification method of rooting multiple signal is applied to the two-dimension parameter estimation to solve the parameter directly so that the arrival time of the pulse wireless system is achieved with combined estimation for the arrival direction, which the performance is still qualified in the condition of low signal-to-noise ratio, but the method require smooth frequency domain, so the estimation accuracy is reduced much in the condition of single-snapshot [2]. The Markov chain Monte Carlo method is applied to the passive radar location, which the mean square error still approaches the CRB in the conditions of single-snapshot and low signal-to-noise ratio, but this method is easily into stable condition in process of Markov chain sampling [3]. At the same time, that the compressed-sensing sparse-reconstruction method was proposed in recent years is widely applied to the signal processing field [4]. After processing of the time domain interference elimination and related issues, the DOA super resolution estimation is obtained by sparse-reconstruction method in the condition of single-snapshot [5]. The optimal sparse model of equal sine space based on source signal is proposed, in which the signal reconstruction and DOA estimation are achieved [6]. The measurement matrix obtained from the decomposition of Gauss random matrix's orthogonal triangle and the reception matrix of low-dimensional data obtained from the singular value decomposition are reconstructed by the formed algorithm based on compression of sensing beam, which 155 Advances in Computer Science Research (ACRS), volume 54 International Conference on Computer Networks and Communication Technology (CNCT2016)

Delay Estimation Based on Compressed Sensing Subspace Pursuit Algorithm