On design of a small-sized arrays for direction-of-arrival-estimation taking into account antenna gains

In the paper a technique for designing antenna arrays composed of directional elements for direction-of-arrival (DOA) estimation is proposed. Especially this approach is applied for developing hybrid antenna arrays with increased accuracy which features digital spatial spectral estimation after preliminary analog beamforming. The earlier obtained explicit formula for calculating the Cramér–Rao lower bound (CRLB) which determines the relationship between the variance of the DOA-estimation and antenna elements' radiation patterns, array geometry, has been used. Main idea of the proposed technique is that it takes into account spatial pattern and gain of the antenna elements. The high gain unlike the number of the antenna elements or interelement distance is the most important factor which allows reducing the value of the DOA-estimation errors. A couple of the examples of calculating radiation patterns of antenna elements improving accuracy of DOA-estimation with super-resolution are provided in the paper. Proposed antenna arrays are modeled according to the method of moments (MoM). The values of the root mean square error after the DOA-estimation are obtained. It is shown that the resulting hybrid systems can reduce the error value in DOA-estimation with super-resolution.