THE growing number of sensor and communication systems

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1 2858 IEEE TRANSACTIONS ON ANTENNAS AND PROPAGATION, VOL. 53, NO. 9, SEPTEMBER 2005 Interleaved Thinned Linear Arrays Randy L. Haupt, Fellow, IEEE Abstract This paper presents three approaches to improving the efficiency of an array aperture by interleaving two arrays in the same aperture area. The interleaved arrays have aperiodic spacings that are integer multiples of a set minimum spacing and are optimized to reduce the maximum sidelobe level. Fully and partially interleaved sum arrays operating at the same frequencies are demonstrated as well as interleaved sum and difference arrays for a monopulse system. A genetic algorithm is used to optimize arrays of isotropic point sources as well as arrays of dipoles modeled using the method of moments. Narrow beamwidths are possible while avoiding high sidelobes. The available aperture area is efficiently used. Index Terms Antenna arrays, antenna array feeds, genetic algorithms (GAs), monopulse antennas, phased arrays. I. INTRODUCTION THE growing number of sensor and communication systems on vehicles increases the demand for antenna real estate. A number of interesting antenna layouts have resulted from efforts to place several antennas in a confined area. Having one antenna perform multiple functions like detection, location, and communications saves space on a ship, satellite, or airplane. Two or more antennas that occupy the same area are known as shared aperture or common aperture antennas. When elements dedicated to different array antennas appear intermixed in a shared aperture, then the array is called interleaved, interlaced, or interspersed. In [1], the authors advocate random interleaving of elements in adjacent subarrays in order to disrupt the grating lobes that result when only one phase shifter per subarray is used to steer the beam. The random assignment of elements to subarrays reduced the peak sidelobe level. Interleaved arrays of waveguide radiators operating at different frequencies are analyzed in [2]. It was found that the low-frequency elements induce grating lobes that do not appear in the high frequency array. An aperture with three arrays of interleaved elements operating in the L, S, and C bands was successfully built and measured to demonstrate the feasibility of interleaving three arrays on the same aperture [3]. A dual-band phased array using interleaved waveguides (C band) and printed dipoles on a high dielectric substrate (S band) has been developed. The element spacings for both arrays were equal, so no grating lobes formed in either band [4]. A phased array antenna with interleaved waveguide elements and wide-band tapered elements was shown to operate over at least three frequency bands [5]. A dual-band/dual-polarization array had an interleaved cross-dipole radiator and a Manuscript received September 22, 2004; revised February 25, The author is with the Applied Research Laboratory, The Pennsylvania State University, State College, PA USA ( haupt@ieee.org). Digital Object Identifier /TAP Fig. 1. Diagram of the interleaved array concept. cavity-backed disk radiator in the same lattice structure [6]. In all but [1], the interleaved arrays operate at different frequencies. The interleaving was done with equal spacing between elements. The interleaving ideas presented in this paper take advantage of the inefficient use of space in thinned arrays. A thinned array turns elements off in a uniform array in order to obtain a spatial taper that results in low sidelobes [7]. The elements that are turned off are connected to a matched load and deliver no signal to form a beam. If the elements that are turned off in the first thinned array could be used by a second array, then the entire aperture would be more efficiently used. This paper reports on an investigation to use the elements turned off in a thinned array for another array operating at the same frequency. Three approaches to efficient interleaving thinned linear arrays are presented here. The first forms two sum beams from the same aperture. Since two arrays compete for the same desirable elements, this approach has a narrow main beam but not low sidelobes. The second method partially overlaps two apertures. This approach is shown to make more efficient use of a given space than two separate thinned arrays. The final technique interleaves a sum array with a difference array. In this approach, low sidelobe sum and difference patterns are created without having to introduce power splitters at each element in the array. Fig. 1 shows the interleaved concept with a dipole array. All the dipoles are identical and equally spaced. The output of an element either goes to array #1 or array #2 or to a matched load. This paper demonstrates the possibility of interleaving thinned arrays in order to efficiently and effectively make use of a given aperture size. The unique contributions reported here are 1) interleaved arrays with nonuniform spacing; 2) low sidelobe thinned difference arrays; 3) interleaved low sidelobe sum and difference arrays; 4) high aperture efficiency thinned arrays. The first section provides background on thinning and introduces thinning to difference patterns. The next three sections demonstrate interleaving thinned arrays in several different ways X/$ IEEE

2 HAUPT: INTERLEAVED THINNED LINEAR ARRAYS 2859 Fig. 2. Array factor for a 120-element uniform sum array that has been optimally thinned using a GA. The maximum sidelobe level is db. II. THINNED ARRAYS This section reviews thinning arrays for low sidelobe sum patterns and introduces thinned arrays for low sidelobe difference patterns. The examples shown are for comparison with optimized interleaved arrays presented in later sections. Amplitude weights are either a 1 or a 0. A 1 indicates that the element is connected to a matched feed network and a 0 indicates the element is connected to a matched load. A symmetric linear array with an even number of elements lying along the -axis has an array factor given by where ; angle measured from -axis; element spacing; 2 ; wavelength; sum amplitude weight for element ; 2 number of elements in the array. The array taper efficiency for a thinned array can be calculated from [8] number of elements in the array turned on total number of elements in the array An example of an array factor for an optimally thinned 120 element array with and is shown in Fig. 2. Its peak sidelobe level is 21.0 db below the main beam and has. As reported in [9], a genetic algorithm (GA) was used to perform the thinning in order to minimize the maximum sidelobe level. The ones and zeros at the top of the graph represent the array elements that are turned on and off. The top left 1 corresponds to element 1, while the bottom right 1 corresponds to element 2. The top right 1 and bottom left 1 are the weights for the two center elements. This means that the (1) (2) Fig. 3. Gain pattern for a 120-element uniform sum array of dipoles that has been optimally thinned using a GA. The maximum sidelobe level is db below the peak of the main beam. left side of the array is on the first line and the right side of the array is on the second line. In this instance, the end elements were forced to be on, so a chromosome in the GA had 59 bits. This optimization was repeated for an array of 120 dipoles (Fig. 1) that are spaced 0.6 apart. The dipoles are parallel to the -axis. Each dipole has a radius of and is broken into segments that are 0.05 long for a method of moments solution [10]. A matched load is 77. In this example, the GA found the same thinning configuration as for the isotropic point sources. The maximum sidelobe level for the pattern in Fig. 3 is 21.2 db and. This author was unable to find a reference to creating low sidelobe difference arrays through thinning. One of the reasons for the lack of information is probably due to the fact that sum and difference beams tend to be formed simultaneously through separate beam forming networks that share common elements. Since a low sidelobe difference amplitude taper looks considerably different from a low sidelobe sum amplitude taper, thinning has not been used for monopulse arrays. Since this paper addresses interleaving sum and difference arrays, a thinned difference array is of importance. The array factor for a symmetric linear difference array lying along the -axis is given by where difference amplitude weight for element.ina similar manner to the sum array, it is possible to thin an array to get a low sidelobe difference pattern by setting the to either 0 or 1. An example of an array factor for a thinned 120 element difference array with and is shown in Fig. 4. The maximum sidelobe level relative to the difference pattern peak is 19.9 db below the peak difference lobes and. Again, a GA was used to perform the thinning in order to minimize the maximum sidelobe level. The ones and zeros at the top of the graph represent the array elements that are turned on and off. (3)

3 2860 IEEE TRANSACTIONS ON ANTENNAS AND PROPAGATION, VOL. 53, NO. 9, SEPTEMBER 2005 The optimization of the thinned difference array was repeated for an array of 120 dipoles. The GA found the same thinning configuration as for the isotropic point sources. The maximum sidelobe level for the pattern in Fig. 5 is 19.8 db and. Note that the sum pattern has the highest density of ON elements near the center, while the center density of the difference pattern is low. Both arrays have decreasing numbers of ON elements near the edges. These characteristics suggest the possibility of using the elements turned OFF by the thinned sum array for the thinned difference array. The objective of the research reported in this paper is to make more efficient use of the thinned arrays by interleaving thinned sum arrays or thinned sum and difference arrays. Similar maximum sidelobe levels and thinning configurations were obtained for the arrays of isotropic point sources and arrays of dipoles. Mutual coupling is not important in the optimization and modeling, because the coupling is well behaved. Unlike some other interleaving concepts, all the arrays in this paper operate at the same frequency. When assembling these arrays, all the elements would be identical and have the same impedance (except for the edge elements). Since all the elements are identical, we have the following: 1) the element spacing over the aperture is periodic; 2) no amplitude or phase weights are imposed; 3) the elements are connected to matched loads; 4) the arrays are large. As a result, mutual coupling will be the same as for a uniform array of the same overall aperture size. In other words, all the element patterns can be reasonably represented by the element pattern of a center element. These arrays look like a single uniform linear array. In reality, there are multiple arrays with an element connected to either a matched feed network or a matched load. Fig. 4. Array factor for a 120-element uniform difference array that has been optimally thinned using a GA. The maximum sidelobe level is db. Fig. 5. Gain pattern for a 120-element uniform difference array of dipoles that has been optimally thinned using a GA. The maximum sidelobe level is db below the peak of the main beam. III. FULLY INTERLEAVED SUM ARRAYS Suppose that two uniformly weighted arrays at the same frequency must exist within the same aperture extent. One approach is to divide the aperture in two. The array on the left side forms one beam and the array on the right side forms the other beam. This arrangement appears at the top of Fig. 6 and the pattern of one array is the dashed line in Fig. 7. Another approach is to interleave the two arrays where every other element belongs to one array and the remaining belongs to the other array. This arrangement appears in the center of Fig. 6 and the pattern of one array is the dotted line in Fig. 7. As seen in Fig. 7, the side-by-side arrays have the advantage of lower average sidelobe levels while the interleaved arrays have the advantage of narrower beamwidth. Each array in the aperture has. This number seems low until the whole aperture is taken into account. Defining an aperture efficiency as number of elements in the aperture turned on total number of elements in the aperture shows that in both cases. A GA was used to optimize the placement of the elements to minimize the sidelobe level of the interleaved arrays. The two arrays each have 60 elements and are antisymmetric in that, when one array has an element on/off, the other array has it off/on. The GA found the optimum thinning that appears at the bottom of Fig. 6, and the pattern of one of these arrays is the solid line in Fig. 7. The amplitude weights are represented as (4) (5) (6) Adding and yields a vector of all ones, which implies %. Each array has %. The symmetry associated with and insures that 50% of the elements will be turned on for each thinning. Array factors for the two arrays are found from (7)

4 HAUPT: INTERLEAVED THINNED LINEAR ARRAYS 2861 Fig. 6. Two arrays occupying the same aperture size. The top arrays are two 30-element uniformly spaced arrays placed side-by-side (d =0:5). The center two arrays have every other element turned on, resulting in two arrays with d =0:5. The bottom two arrays were optimized to create the lowest maximum sidelobe. Fig. 7. Array factor for an optimized fully interleaved array is compared to the array factors for a side-by-side array (d =0:5) and every other element interleaved array (d =1:0) when there are 60 total elements with 30 turned on. This optimized array has the narrow beamwidth of the full aperture and has the same peak sidelobe level of a uniform array. Thus, it is a compromise between the side-by-side uniform array and the every other element interleaved array. IV. PARTIALLY INTERLEAVED SUM ARRAYS Fully interleaving two arrays limits the peak sidelobe reduction. The top of Fig. 8 shows an example of two fully interleaved sum arrays. They make use of 100% of the aperture, so peak sidelobes are on the same order as a uniform array. Looking at the thinned aperture in Fig. 2 spawns the idea of shifting one array half an aperture to the right and then interleaving the two arrays. In this manner, the heavily populated center of one array overlaps with the lightly populated edge of the other array. The resulting arrays are no longer 100% efficient, though. Both arrays operate at the same frequency and elements not connected to one of the matched array feed networks are terminated in a matched impedance. The center of Fig. 8 shows the first approach to partially interleaved arrays. Two arrays are interleaved over 50% of their elements. In other words, the right half of one array is interleaved with the left half of the other array. The center third of Fig. 8. This diagram compares the fully interleaved concept with the two partially interleaved concepts. Partially interleaved 1 is asymmetric and works with two arrays. Partially interleaved 2 is symmetric and can work with many arrays. the aperture is 100% efficient. The end thirds are thinned. This array is not symmetric and has element weights given by where means the element is connected to feed network #1 and means the element is connected to feed network #2. The first elements have no overlap or The remaining 2 elements are interleaved with the adjacent array. The adjacent array has element weights given by The array factor is calculated using (7). Fig. 9 is the resulting array factor for both of these arrays when there are a total of 60 elements spaced 0.5 apart. Its maximum sidelobe level is 19.4 db with and. Optimizing two 120-element interleaved arrays produces the array factor (8) (9)

5 2862 IEEE TRANSACTIONS ON ANTENNAS AND PROPAGATION, VOL. 53, NO. 9, SEPTEMBER 2005 Fig. 9. Array factor for a 60-element array using asymmetric partial Fig. 11. Array factor for a 60-element array using symmetric partial Fig. 10. Array factor for a 120-element array using asymmetric partial Fig. 12. Array factor for a 120-element array using symmetric partial in Fig. 10. The maximum sidelobe level is 19.8 db with and. This array has higher sidelobes than the 120-element thinned array in Fig. 2 but has the ability to be interleaved at a very high efficiency. The bottom of Fig. 8 is an example of three symmetric partially interleaved arrays. Mathematically, is given by and by (10) (11) Note that (10) differs from (8) in that (10) are the weights for a symmetric array while (8) are not. The purpose of considering symmetric partial tapered arrays is that many of these arrays can be cascaded together whereas the asymmetric partially tapered arrays are limited to two interleaved arrays. The array factors for the two symmetric interleaved arrays are found from (1) and (12) The sum pattern for a 60-element array with appears in Fig. 11. The peak sidelobe level is 13.1 db below the main beam. All of the center elements are ON while all of the edge elements are OFF. This array has and. Increasing the number of elements to 120 results in the array factor in Fig. 12. The peak sidelobe level in this case is 15.3 db with and. More elements result in lower sidelobes.

6 HAUPT: INTERLEAVED THINNED LINEAR ARRAYS 2863 Fig. 13. Sum array factor for a 60-element aperture that has sum and difference arrays interleaved. Fig. 15. Sum array factor for a 120-element aperture that has sum and difference arrays interleaved. Fig. 14. Difference array factor for a 60-element aperture that has sum and difference arrays interleaved. V. INTERLEAVED SUM AND DIFFERENCE ARRAYS The array thinnings in Figs. 2 and 4 show that arrays have elements turned on in the center while the difference arrays do not. Also, the edges of both arrays appear randomly thinned. This observation led to the idea of using the elements that are turned off in the sum array to form a difference pattern. This idea does not result in an acceptable difference pattern, because the difference pattern has high sidelobes, wide beamwidth, and low gain. A better approach is to define the aperture size and element spacing and let a GA decide which elements should be on/off for the sum and difference arrays. The difference pattern consists of the elements turned off in the sum pattern or, where and are either zero or one. Since an element is connected to either the sum feed or the difference feed, then the array looks like a uniform array as far as mutual coupling is concerned. The resulting optimized sum and difference patterns for the 0.6 spaced dipole array are shown in Figs. 13 and 14, respectively. The peak sidelobe level of the sum pattern is 12.3 db below its Fig. 16. Difference array factor for a 120-element aperture that has sum and difference arrays interleaved. main beam, and the peak sidelobe level of the difference pattern is 12.1 db below its main beam. The sum array has and the difference array has. Increasing the number of elements to 120 and optimizing the dipole model results in peak sum sidelobes of 13.1 db and peak difference sidelobes of 13.3 db. Efficiency for the sum array is and for the difference array is. The array factors appear in Figs. 15 and 16. The entire aperture is 100% efficient, so optimum use is made of the available space. VI. CONCLUSION Two arrays at the same frequency can be interleaved in such a way that their array factors have narrow beamwidths and do not have high sidelobe levels. These thinned arrays make efficient use of the available aperture space. Two sum patterns can be interleaved within the same aperture areas. Low sidelobe difference patterns can be obtained through thinning the elements. Optimizing the thinning of interleaved sum and difference arrays produces array factors with a narrow beam, low sidelobes, and high space efficiency.

7 2864 IEEE TRANSACTIONS ON ANTENNAS AND PROPAGATION, VOL. 53, NO. 9, SEPTEMBER 2005 There is no reason that the interleaving cannot be extended to two dimensions. The cost function becomes much more time consuming and difficult to calculate. Including mutual coupling effects as was done with the dipole array is straightforward, but time consuming. Since the arrays are relatively large, equally spaced, and uniformly weighted, the environment of each element is the same. Consequently, the results obtained from the array factor optimization are sufficient to validate the concept. REFERENCES [1] J. Stangel and J. Punturieri, Random subarray techniques in electronic scan antenna design, in Proc. IEEE AP-S Symp., vol. 10, Dec. 1972, pp [2] J. Hsiao, Analysis of interleaved arrays of waveguide elements, IEEE Trans. Antennas Propag., vol. AP-19, no. 6, pp , Nov [3] J. Boyns and J. Provencher, Experimental results of a multifrequency array antenna, IEEE Trans. Antennas Propag., vol. AP-20, pp , Nov [4] K. Lee et al., A dual band phased array using interleaved waveguides and dipoles printed on high dielectric substrate, in Proc. IEEE AP-S Symp., vol. 2, Jun. 1984, pp [5] R. Chu, K. Lee, and A. Wang, Multiband phased-array antenna with interleaved tapered-elements and waveguide radiators, in Proc. IEEE AP-S Symp., vol. 3, Dec. 1996, pp [6] K. Lee, A. Wang, and R. Chu, Dual-band, dual-polarization, interleaved cross-dipole and cavity-backed disc elements phased array antenna, in Proc. IEEE AP-S Symp., vol. 2, Jul. 1997, pp [7] R. Willey, Space tapering of linear and planar arrays, IEEE Trans. Antennas Propag., vol. AP-10, pp , [8] Phased Array Antenna Handbook, Artech House, Boston, MA, R. J. Mailloux. [9] R. L. Haupt, Thinned arrays using genetic algorithms, IEEE Trans. Antennas Propag., vol. 42, no. 7, pp , Jul [10] FEKO Suite 4.1, EM Software and Systems (2003). [Online]. Available: Randy Haupt (M 82 SM 90 F 00) received the B.S. degree in electrical engineering from the U.S. Air Force Academy, U.S. Academy, CO, the M.S. degree in engineering management from Western New England College, Springfield, MA, in 1981, the M.S. degree in electrical engineering from Northeastern University, Boston, MA, in 1983, and the Ph.D. degree in electrical engineering from the University of Michigan, Ann Arbor, in He was a Professor of electrical engineering at the U.S. Air Force Academy and Professor and Chair of Electrical Engineering at the University of Nevada - Reno. In 1997, he retired as a Lt. Col. in the U.S. Air Force. He was a Project Engineer for the OTH-B radar and a Research Antenna Engineer for Rome Air Development Center. From 1999 to 2003, he was Professor and Department Head of Electrical and Computer Engineering at Utah State University, Logan. He is currently a Senior Scientist at the Applied Research Laboratory, Pennsylvania State University, State College. He has many journal articles, conference publications, and book chapters on antennas, radar cross section and numerical methods and is coauthor of the book Practical Genetic Algorithms, 2nd edition (New York: Wiley, May 2004). He has eight patents in antenna technology. Dr. Haupt is a Member of Tau Beta Pi, Eta Kappa Nu, International Scientific Radio Union (URSI) Commission B, and the Electromagnetics Academy. He was the Federal Engineer of the Year in 1993.