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Low Sidelobes from Identically Thinned Subarrays Randy L. Haupt The Pennsylvania State University, Applied Research Laboratory, State College, PA 16801 Introduction Large phased array antennas have many desirable characteristics but are extremely expensive to build. The large array can be broken into smaller subarrays and the amplitude or phase weighting can be done at the subarrays to save the expense of placing them at every element. Unfortunately, this approach results in unacceptable grating lobes [1]. A tradeoff exists between sidelobe performance and simplicity of design. One approach amplitude tapers the subarray outputs and the element outputs in such a way that the element amplitude tapers are identical for every subarray of a linear array [2]. In this way, the resulting amplitude taper is a better approximation to the desired taper than subarray tapering alone. All the subarrays are identical, so the feed design remains very simple A genetic algorithm (GA) has been used to design optimum amplitude tapers for both the elements in the subarrays and the subarray outputs for linear and planar arrays [3]. This paper extends the previous work by amplitude tapering identically thinned subarrays to minimize the sidelobe level. A mixed integer genetic algorithm is used to find the optimum configuration. Cost Function Formulation The cost function returns the maximum sidelobe level of the array, and the GA minimizes the cost. Optimization variables are the subarray amplitude weights at the subarray outputs and the amplitude weights of the elements in the subarrays. All elements within a subarray have the same amplitude weights, other than half the subarrays are mirror images of the other half. In the previous papers, the amplitude weights assumed array values between zero and one. In this paper the amplitude weights are either zero or one. Figure 1 is a diagram of a 256 element square array divided into 16, 4x4 element subarrays. Dark circles indicate that the element has an amplitude of one, and white circles indicate that the element is terminated in a matched load and receives an amplitude of zero. Note that the subarrays are either identical or are mirror images. 1-4244-0123-2/06/$20.00 ©2006 IEEE 4217 Figure 1. Planar array with identically thinned subarrays. The cost is the maximum relative sidelobe level is calculated from the array factor given by Ne cost = ∑ an cos [ kxn sin θ cos ϕ ] cos [ kyn sin θ sin ϕ ] (1) n =1 where an = product of element weight and subarray weight for element n k = 2π / wavelength ( xn , yn ) = location of element n (θ , ϕ ) = look direction The example here has 6 × 6 = 36 subarrays with each subarray having 5 × 5 = 25 elements. The element spacing in both directions of the square lattice is one half wavelength. Results A GA is used to find the optimum weights. If the subarray weights are optimized with all the elements uniformly weighted, then the maximum sidelobe level is found to be -18.4 dB. The directivity is 28.3 dB with a taper efficiency of 75%. These results are relative to a uniform aperture with a directivity of 29.5 dB and a maximum sidelobe level of -13.2 dB. If the subarray weights are uniform and the elements of the subarray thinned, then the directivity is 27.3 dB, the maximum sidelobe level is -15.3 dB, and the taper efficiency 60%. When the element thinning and subarray weights are simultaneously optimized, then the optimized element weights are shown in Figure 2 and the optimized subarray weights are shown in Figure 3. When multiplied together, the effective element weights for one quadrant of the array are shown in Figure 4. This taper 4218 has an efficiency of 54.5%. The resulting array factor appears in Figure 5. Its directivity is 26.9 dB and the maximum sidelobe level is -22.9 dB. Sidelobes that are 4.5 dB lower than the optimized subarray weighting come at a cost in taper efficiency and loss in directivity. Figure 2. Optimized element weights in one subarray. Figure 3. Optimized subarray weights for one quadrant of the array. 4219 Figure 4. Optimized effective element weights in one quadrant of the array. Figure 5. Optimized array factor. Conclusions Using identical subarrays decreases the complexity and cost of construction and testing. Thinning has the advantage of a simple, uniform feed network. Obtaining slightly lower sidelobes comes at a cost in aperture efficiency. References: [1] R.J. Mailloux, Phased Array Antenna Handbook, Artech House, Boston, MA, 2005. R. Haupt, "Reducing grating lobes due to subarray amplitude tapering," [2] IEEE AP-S Trans., Vol 33, No. 8, Aug 1985, pp. 846-850. R. Haupt, "Optimization of subarray amplitude tapers," IEEE AP-S [3] Symposium, Jun 1995, pp. 1830-1833. 4220