The algorithm of combined zeros of radiation patterns for constructing an angular spectrum with super resolution

An efficient source direction finding algorithm is proposed, which combines computational simplicity and high angular resolution. To construct a angular spectrum, the sum of several amplitude radiation patterns is used, which are formed on the basis of the Winer-Hopf solutions. These solutions are obtained by inverting the same covariance matrix of the signals. Directional patterns differ in the position of the maxima, which are located outside the direction finding area and are offset relative to each other. This avoids the occurrence of common matching zeros in the sum of the amplitude diagrams in the absence of signal sources in the direction finding area. However, if there are sources in the corresponding directions of space, zeros are formed in all radiation patterns. Combining these zeros makes it possible to construct angular spectra.. The algorithm is based on the criterion of minimizing the RMS deviation between the reference signal and the output signal of the antenna array. The signal of a fictitious source with a given position in space is used as a reference for each generated directional pattern. The proposed algorithm differs from well-known direction finding algorithms such as Capon and MUSIC in that it does not require the preliminary formation of hypothesis vectors and their sequential iteration. This allows for a significant increase in computational efficiency. The high angular resolution of the algorithm is provided due to the significant steepness of the radiation pattern in the area close to zero, as well as the absence of main lobes in the direction finding zone. Numerical studies have compared the proposed algorithm with the algorithms of Capon, MUSIC, and maximum entropy. It was found that the Capon algorithm demonstrates a significant decrease in angular resolution compared to other algorithms in the conditions of the interference environment under consideration. The proposed algorithm, although inferior in computational efficiency to the maximum entropy algorithm, is capable of resolving two closely spaced sources at the same level as the MUSIC algorithm. At the same time, the proposed algorithm is characterized by simplicity of implementation, since it does not require the definition of eigenvalues and eigenvectors. It has been shown that the limiting resolution of the algorithm deteriorates significantly when the rays of the generated radiation patterns fall into the direction finding area.