Random Projection and Truncated SVD for Estimating Direction of Arrival in Antenna Array

Abstract

Introduction. The need to solve inverse problems arises in many areas of science and technology in connection with the recovery of the object signal based on the results of indirect remote measurements. In the case where the transformation matrix has a high conditional number, the sequence of its singular numbers falls to zero, and the output of the measuring system contains noise, the problem of estimating the input vector is called discrete ill-posed problem (DIP). It is known that the DIP solution using pseudoinverse of the input-output transformation matrix is unstable. To overcome the instability and to improve the accuracy of the solution, regularization methods are used. Our approaches to ensuring the stability of the DIP solution (truncated singular decomposition (TSVD) and random projection (RP)) use the integer regularization parameter, which is the number of terms of the linear model. Regularization with an integer parameter makes it possible to provide a model close to the best in terms of the accuracy of the input vector recovery, and also to reduce the computational complexity by reducing the dimensionality of the problem. The purpose of the article is to develop an approach to estimating the direction of arrival of signals in the antenna array using the DIP solution, to compare the results with the well-known MUSIC method, to reveal the advantages and disadvantages of the methods. Results. Comparison of TSVD and MUSIC (implemented in real numbers) when working with correlated sources and five snapshots showed the advantage of TSVD in terms of the power of the useful signal P ratio by 2.2 times with the number of antenna elements K = 15 and by 4.7 times with K = 90. The advantage of TSVD in P ratio is by 3.7 times for K = 15 and by 4.2 times for K = 90. Comparison of RP and MUSIC (implemented in real numbers), when working with correlated sources and five snapshots, showed the advantage of RP in P ratio by 3

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