3-Faceted Array With Low Side Lobe Levels Using Tuneable Windows

2013 7th European Conference on Antennas and Propagation (EuCAP) 3-Faceted Array With Low Side Lobe Levels Using Tuneable Windows Nurul H. Noordin, Tughrul Arslan, Brian Flynn Advanced Smart Antenna Technologies Research Group, School of Engineering, The University of Edinburgh, EH9 3JL, UK (N.Noordin, Brian.Flynn, Tughrul.Arslan)@ed.ac.uk eight left-hand circularly polarized (LHCP) microstrip antennas is synthesised for low SLL using tuneable Kaiser, Chebychev, and Taylor windows. The antenna has a beamwidth of 87.9° and resonates at 2.4 GHz [18]. The resulting radiation patterns are then compared to those synthesised using the Binomial, Blackman and Hamming window functions. Abstract—In this paper, a 3-faceted phased array antenna synthesised for low side lobe levels using a tuneable window is presented. The array consists of eight left hand circularly polarised antennas. The phase difference of the antennas on the faceted structure is first compensated for and then an amplitude tapering method is used to synthesise the array to have a low sidelobe level, (SLL). The effect of the phase compensation on the angular scanning range of the 3-faceted array is then investigated. Simulation results show that the radiation patterns generated with tuneable windows, such as Kaiser, Chebyshev and Taylor, have a similar profile to the uniform amplitude distribution but with a much lower SLL and broader main beam. This technique enables the faceted structure to be synthesised for low SLL and at the same time retain its radiation pattern profile. Prior to the low SLL synthesis, the effect of using the phase compensation for the beamforming of the 3-faceted array is analysed. This includes the effect of phase correction on the scanning range of the array. This paper is divided into five sections. Section II presents the array geometries and techniques used for SLL reduction. The effect of the compensated phase difference on the angular-scanning-range of the 3-faceted array is analysed in Section III. In section IV, the tapered 3-faceted array performance is discussed and finally, Section V concludes the paper. Index Terms—Low Side-lobe level synthesis, amplitude tapering I. INTRODUCTION II. The scanning range of an adaptive phased array antenna can be increased by providing some degree of curvature to the array. In the literature, faceted and curved arrays were shown to provide a wide scan range [1-5]. However, these arrays suffer from a high sidelobe level (SLL), especially for end-fire beams [4, 6]. Methods to synthesise phased arrays for low SLLs include genetic algorithms (GA) [7], particle swarm optimization (PSO) algorithms [8, 9] and amplitude tapering using windowing techniques [10, 11]. In this section, the 3-faceted array geometry, the phase compensation technique and the low SLL synthesis techniques are described. A. 3-faceted array geometry The geometry of the 3-faceted array is illustrated in Fig.1. The radiation pattern for the array with elements distributed in a 3-dimensional space is described by Equation (1), which is based on the array factor derived in [5]. APfaceted (θ , φ ) = ∑ EPcirc ( n ) wn e jk [ x n ( u − u s ) + y n ( v − v s ) + z n cos θ ] The procedure to synthesise a phased array antenna for low SLL using windowing is identical to the design process for a FIR filter in digital signal processing (DSP) [12, 13].The SLL of an adaptive phased array antenna is reduced by increasing the radiation intensity from the elements in the centre and simultaneously reducing the radiation intensity from the elements at the edges [13]. The intended radiation intensity can be achieved by controlling the amplitude excitation of the array elements. Several windowing techniques for filter design such as Dolph-Chebychev, Gaussian, Kaiser, Hamming and Blackman have been previously used in synthesising the phased array antenna for low SLLs [11-16]. However, this approach applies only to 1-Dimensional (1-D) and 2Dimensional (2-D) arrays. N (1) n =1 where EPcirc(n) is the patch radiation pattern of nth element, (xn, yn, zn) is the position of the nth element on the array and (θs, Øs) is the steering angle. B. Phase compensation The compensation is obtained by calculating the phase delay of the elements that have the longer radiation paths as shown in Fig. 2. The phase delay is calculated using Equation (2) [19]. Unlike 1-D and 2-D arrays, variations in the radiation pattern of the elements of the array have a greater effect in a faceted array, due to the 3-D nature of the antenna structure. In [17] a technique to synthesise faceted arrays for low SLLs was presented. By compensating for the phase difference, the windowing technique, which was previously used in uniform linear arrays, can be used to synthesise a faceted array for low SLLs. In this paper, a 3-faceted antenna array consisting of 978-88-907018-3-2/13 ©2013 IEEE METHOD corr _ a = k ⋅ dist _ a ⋅ (sin θ ) ; k = 2π λ (2) where k is the wave number, λ is the wavelength, dist_a is the distance between an element and the tilting point and θ is the tilting angle. 600 2013 7th European Conference on Antennas and Propagation (EuCAP) 2 ⎤ ⎡ ⎛n⎞ I 0 ⎢α 1 − ⎜ ⎟ ⎥ ⎢ ⎝ N ⎠ ⎥⎦ w(n) = ⎣ I 0 [α ] where Io is a modified Bessel function of first kind and zeroth order. The tuning elements for Kaiser Windows are α dB, the sidelobe level attenuation. θa = 50° III. Figure 1. corr_a corr_b θ, tilting angle Phase delay due to the conformal structure PHASE CORRECTION INFLUENCE A. Angular Scanning Range The scanning range is defined from boresight to the scan angle where the directivity of the antenna array is 3 dB below the maximum directivity. This means that in this range, the array directivity is maintained within 50 % from the maximum directivity achieved by the array. By incorporating the radiation patterns of the left-hand circularly polarised (LHCP) microstrip antennas, the 3 dB scanning ranges for both 3-facted and flat surface arrays over the scan angle are calculated and plotted in Fig. 3. The main beam of the array is steered to a scan angle by adjusting the phase excitation of the array elements. The amplitude excitation is uniform across the array. The excitation values are obtained by calculating the difference between the desired scan angle and the boresight of the array. The geometry of the 3- faceted array dist_a (5) Array elements radiation Figure 2. Phase delay due to the 3-faceted array structure C. Windowing Techniques As mentioned previously, the side-lobe levels of the array can be reduced by compressing the radiation of elements in the edge. There are many possible windowing techniques that can be used for this purpose, such as; Kaiser, Blackman, Hanning and Hamming. However, low SLLs come at the expense of a wider main beamwidth [20, 21]. In filter design, the Blackman window has the lowest SLL but a wide main lobe width. On the other hand, the Kaiser and Dolph-Chebyshev windows are tuneable, which allows the main lobe width and the SLL to be customised. However, these windows require complex calculation [22]. Thus, the choice of the windowing technique is a trade-off between SLL reduction, main beam width and calculation complexity. For the flat surface linear array, the main beam is steered from boresight by exciting the array elements with progressive phase shifts. However, for the 3-faceted array, the phase difference of the elements on the tilted facets is first compensated and progressive phase shifts are then applied to the elements in order to steer the main beam towards a desired angle. At boresight, the linear array achieves the highest directivity whereas the directivity of the faceted array is approximately 3 dB less. However, as the main beam is steered away from boresight, the directivity of both arrays degrades, especially for the linear array. Interestingly, the 3-faceted array achieves the widest scanning range, 69°, while for the flat surface array, it only reaches ±57°. 3 dB Scanning Range a) Blackman Window Blackman weights can be described by (3) [12]. 20 linear 3-faceted ( θa = 50o ) 18 2πn 4πn ) + 0.08 cos( ) N −1 N −1 (3) Directivity (dBi) w(n) = 0.42 − 0.5 cos( In symmetrical cases, the Blackman weight is obtained by flipping the first half around the midpoint. b) Hamming Window The Hamming weights are computed from the following equation (4) [12]. w( n) = 0.54 − 0.46 cos( 2πn ) N 16 14 12 10 (4) 8 0 10 20 30 40 50 60 70 80 Scanning Angles (θ°) Figure 3. The Scanning range of the faceted arrays c) Kaiser Window Kaiser weighting is obtained using (5) [13]. 601 90 2013 7th European Conference on Antennas and Propagation (EuCAP) IV. LOW SIDELOBE LEVEL SYNTHESIS Kaiser Window 20 After the phase difference is compensated, the 3-faceted array is then synthesised for low SLL using amplitude weighting techniques. The radiation patterns and corresponding amplitude distributions for the 3-faceted array using Blackman, Binomial and Hamming windows are shown in Fig. 4. The amplitude and phase excitation of the array elements are listed in Table 1. As observed from Fig. 4 (a), the narrowest main beam is obtained with the uniform weighting but at the expense of increased SLL. On the contrary, the Blackman weighting produces a radiation pattern with the lowest SLL but with the widest main beam. Directivity (dBi) 10 0 -10 uniform α=1 α=2 α=3 -20 -30 Another class of amplitude tapering technique is using Kaiser, Taylor and Chebyshev windows. These windows have variable input parameters with which the SLL can be customised. The amplitude and phase excitations of the array elements are listed in Table 1. In Fig. 5, the resulting radiation patterns of the 3-faceted array using the Kaiser Window with different α values are plotted. It can be seen that lowest SLL is obtained with α = 3. On the other hand the narrowest main beamwidth is obtained when α = 1. -90 -60 -30 0 30 60 90 o θ (a) Classical Weighting 20 (b) Figure 5. Low SLL synthesis using Kaiser Window with different α values. (a) Radiation pattern, (b) Amplitude Distribution 0 Taylor Window -10 20 Uniform Weighting Blackman Weighting Hamming Weighting Binomial Weighting -20 -30 -90 -60 -30 0 30 10 60 Directivity (dBi) Directivity (dBi) 10 90 o θ (a) 0 -10 uniform SLL = -30 SLL = -20 SLL = -10 -20 -30 -90 -60 -30 0 30 60 90 o θ (a) (b) Figure 4. Low SLL technique with Binomial, Blackman and Hamming Windows.(a) Radiation pattern, (b) Amplitude Distribution The radiation patterns of the 3-faceted array using Taylor and Chebyshev Windows are shown in Fig. 6 and Fig. 7, respectively. In both simulations, similar trade-offs are observed, where lower SLLs are obtained at the expense of a broader main beamwidth. The amplitude and phase excitations of the array elements are also listed in Table I. (b) Figure 6. 602 Low SLL synthesis using Taylor Window with different SLL. (a) Radiation pattern, (b) Amplitude Distribution 2013 7th European Conference on Antennas and Propagation (EuCAP) 3-faceted Array (Boresight) 20 10 10 0 Directivity (dBi) Directivity (dBi) Chebyshev Window 20 -10 uniform SLL = -10 SLL = -20 SLL = -30 -20 -30 0 -10 Uniform Blackman Taylor Kaiser Chebyshev -20 -30 -90 -60 -30 0 30 60 90 -90 o -60 -30 0 θ θ (a) (a) 30 60 90 o o 3-faceted Array (θ=60 ) 20 Directivity (dBi) 10 (b) Figure 7. Low SLL synthesis using Chebyshev Window with different SLL. (a) Radiation pattern, (b) Amplitude Distribution TABLE I. 0 -10 Uniform Blackman Taylor Kaiser Chebyshev -20 -30 ELEMENT EXCITATION FOR THE 3-FACETED ARRAY WITH LOW SIDE-LOBE LEVELS (AMP < Ø°) -90 -60 -30 0 30 60 90 o 1&8 2&7 3&6 4&5 θ (b) 1.00 < 287 1.00 < 168 1.00 < 0 1.00 < 0 Figure 8. Low SLL Synthesis with Windowing Techniques (a) θ = 0° (b) θ = 60° 0.03 < 287 0.20 < 168 0.60 < 0 1.00 < 0 Blackman 0.01 < 287 0.09 < 168 0.46 < 0 0.92 < 0 Hamming Kaiser (α = 3) Chebychev [17] (SLL = -30dB) Taylor [17] (SLL = -30dB) 0.08 < 287 0.25 < 168 0.64 < 0 0.95 < 0 0.20 < 287 0.26< 287 0.50 < 168 0.52< 168 0.79 < 0 0.81< 0 0.97 < 0 1<0 0.28< 287 0.53< 168 0.81< 0 1<0 Weight / Element Uniform Binomial [17] Fig. 8 shows the radiation pattern of the 3-faceted array at two different scan angles; 0° and 60°. The array is synthesised for low SLL using four different windows; Blackman, Kaiser (α = 3), Taylor (SLL = -30) and Chebyshev (SLL = -30). The directivity of the array decreases as the main beam is steered away from boresight. When the main beam is steered further away from boresight, the grating lobes begin to appear. The grating lobe occurrence degrades the peak directivity of the main beam as power is transferred from the main beam to the grating lobes [23-25]. The lowest SLL is achieved with Blackman window, but at the expense of wide beam width. The Kaiser, Taylor, and Chebyshev tuneable windows give radiation patterns that have lower SLLs than the uniform distribution. With these tuneable windows, the 3-faceted array is able to generate radiation patterns with low SLLs and narrow main lobe width. V. CONCLUSION Due to the degree of curvature of the 3-faceted array, a wider scanning range can be achieved. However, this comes at 603 2013 7th European Conference on Antennas and Propagation (EuCAP) [9] the cost of high sidelobe levels. The tilt in the structure causes the elements of the array to have different far-field radiation path lengths. By compensating for the phase delays arising from these different paths, the conventional amplitude tapering method that is normally used for 1-D and 2-D arrays can be applied to the 3-faceted array. It was shown that with phase compensation, the 3dB scanning range of the 3-faceted array could reach up to ± 69° from boresight. On the other hand, the 3dB scanning range of the flat linear array is only ± 56°. The use of a window function with tuneable properties, such as Kaiser, Chebyshev or Taylor allows the SLL of the array to be customised. The radiation pattern generated by these tuneable windows also has a similar profile to the uniform amplitude distribution but with a much lower SLL and broader main beam. Overall, Blackman weighting produces the lowest SLL but with the widest beam width, while uniform weighting produces the narrowest beam width but has the highest SLL. The Kaiser window with weighting (α=3) is the best one as it balances the SLL and the main beam width and allows a tradeoff between them. [10] [11] [12] [13] [14] [15] ACKNOWLEDGMENT [16] The authors acknowledge financial support from the Universiti Malaysia Pahang and the Government of Malaysia. 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