Abstarct: The issue of estimation of direction of arrival (DOA) has long been an important issue in the field of signal array processing. Among the systems that use array sensors, in our country, due to the proximity to the three seas and the growing need for underwater science, sonar systems can be considered one of the most widely used systems. According to studies, methods baxsed on compressed sensing or sparse signal representation have the greatest advantage in terms of accuracy and resolution. However, one of the main challenges of these methods is their high computational time. One of the most common ways to reduce computation time is realizing the equations of DOA estimation. This is often done in methods that use symmetric linear arrays. However, realizing equations in non-uniform arrays, especially nested arrays, which have many advantages over linear arrays, is very difficult due to the special form of their data model. To solve this problem, in this dissertation, using a new method, a matrix is designed that by multiplying it in a complex data model, a real data model can be obtained. With this data model, all equations of DOA estimation will also become real, which solves the computational time problem to an acceptable level. The results of the simulations show an improvement of at least 35% of the computation time in the proposed model compared to the complex model while maintaining its performance baxsed on the criteria of accuracy and resolution.