Sparse phased array antennas on planar and conformal platforms based on low-discrepancy sequences

Abstract

Numerous applications in sensing, radar, and long-distance communication require antenna arrays with very directive beams. In order to achieve the high directivity, the array aperture size has to be very large, which significantly drives the cost due to the large number of elements needed on the aperture with traditional Nyquist sampling. The cost-effective solution to this problem is by using sparse arrays, i.e. a reduced number of elements that undersample the aperture. These sparse arrays have an average element spacing larger than 1 wavelength, and significantly reduce the cost of the antenna array. The biggest issue with sparse arrays however is that due to undersampling, grating lobes appear in the visible region which degrade the array performance. To mitigate this issue, synthesis approaches for sparse arrays work to spread the energy of the grating lobes in space in order to reduce the sidelobe levels of the antenna. In addition to the grating lobe issue, many applications in defense and first responder operations also require real-time techniques for sparse array synthesis. Despite decades of work on sparse antenna arrays, a cost-effective and time-efficient solution for synthesis of large sparse arrays was not available. Random element spacing removes the grating lobes but produces large variations in element density across the aperture. In fact, some areas are so dense that the elements will overlap. This work presents the first solution to this problem by using low discrepancy sequence (LDS) sampling. Analytical methods, numerical methods, statistical and probabilistic approaches, have been studied over the years, and it is shown that none of these methods can yield a solution even close to the true optimum. The difficulty is due to the fact that side lobe level depends on the element spacing in a highly nonlinear manner, and in general there is no analytical method to determine the highest side lobe level or the angular direction where the highest side lobe may occur, unless an entire three dimensional pattern is computed. As such, the only adopted solution thus far is based on optimization approaches which are: 1) computationally slow, 2) not hierarchical, and 3) typically require amplitude and phase control over the elements which significantly increase the cost. A cost effective sparse array uses elements with unity amplitude and zero phase. This significantly simplifies the feed network and amplification circuits, which reduce the cost. The only existing work that is comparable are thinned arrays. However, we show that thinned arrays cannot achieve a low side lobe performance once average element spacing exceeds one wavelength. Moreover, our proposed approach is directly applicable to non-planar surfaces without the need for any modifications. In this dissertation, a complete analysis of LDS methods for synthesis of large planar and cylindrical sparse arrays is presented. In summary the primary intellectual merits of this work are: 1) The first cost-effective and time-efficient solution to synthesis of large sparse arrays, with the elements having a unity amplitude and zero phase, 2) The synthesis algorithm is based on mathematical sequences that are hierarchical, enabling real-time synthesis of sparse arrays over planar and non-planar apertures, 3) The approach is transformative as it promises revolutionary improvements over existing sparse analog techniques, and it applies to a broad range of applications in electromagnetics including measurements, sensing, and communications.