As location tracking technology has developed, reliance on global positioning system (GPS) communication has increased. Currently, anti-jamming is researched as protection against environmental factors such as distortion, interferences caused by multipath propagation, and jamming signals that intentionally disrupt communication. The controlled reception pattern antenna (CRPA) array is used to control nulling in the direction of a jamming signal and increase gain in the direction of the satellites [1–3]. It is advantageous to design many radiating elements to protect GPS communications against jamming signals because the number of nulls (N–1) is dependent on the number of radiating elements (N). Thus, it is essential to design a miniaturized radiating element for multiple nulls.

There are various numerical methods to achieve null steering in a specific direction [3, 4]. However, null steering using numerical methods is both inaccurate and time-consuming if cost function is not elaborated. On the other hand, a total radiation pattern can be obtained from an active element pattern (AEP) multiplied by the array factor (AF). Using an AF, the input phases of radiating elements can be simply calculated to obtain nulls in the directions of jamming signals.

In this letter, the AF of a circular array should be modified because the radiating elements are arranged toward the center. In addition, the radiating elements are designed using mu-zero resonance (MZR), which is suitable for a miniaturization to implement the seven elements in a 5-inch circle space [5]. Since the radiating elements have a CP characteristic for GPS communication, the AF of the seven radiating elements can be modified considering the rotation angle of the n^th radiating element. From the modified AF, the phases of input ports can be obtained to achieve pattern nulling at a certain angle. The one CRPA circular array and the two kinds of power dividers used to inject calculated input phases were fabricated to verify the modified AF. The modified AF is described in Section II, and the simulated and measured far-field radiation pattern with a null are compared in Section III.

Fig. 1(a) and (b) show the geometry of the CRPA circular array with and without consideration for the rotation angle of the n^th radiating element. A total radiation pattern can be obtained from an AEP multiplied by the AF. In this paper, the rotation angles of the radiating elements are considered in the AF instead of the AEP to expect the input phases for a radiation pattern’s null before the design of radiating elements. The AF, having seven radiating elements without considering the rotation angle of the nth radiating element, can be expressed by Eq. (1):

Above, a, Φ_n, and β_n are at a distance between the center and the radiating element, an angle of the n^th element from x-axis, and an input phase of nth element, respectively. When the seven radiating elements are arranged toward the center and have CP characteristics, the AF of Eq. (1) can be modified as Eq. (2), because the rotation angle (ψ_n) of the nth element can be expressed as the phase difference:

where ψ_n is 2(n-1)π/7 because the seven radiating elements are oriented toward the center. To achieve the pattern null at (θ₀, Φ₀), Eq. (2) should be zero. Then, the input phase (β_n) of the n_th port can be derived as Eq. (3):

The input phase (β_n) of each port is calculated to achieve null steering in two directions (Case I: θ₀ = 0°, Φ₀ = 0° and Case II: θ₀ = 55°, Φ₀ = 150°). Table 1 shows the calculated input phase (β_n) from the modified AF. Fig. 2(a) and (b) show the CRPA array, which is introduced in [5] using seven MZR radiating elements. To obtain the CP characteristic, two orthogonal MZR antennas realized by a gap and a shorting via are employed and have dual feeding structures with a phase difference of 90°. Fig. 3(a) and (b) present feeding networks using a power divider for Case I and Case II, respectively. To approach the same power at each port, the dividers, including a 50-Ω termination port with eight output ports, are designed despite the seven radiating elements. The substrate utilized for the power dividers has a thickness of 1.6 mm and the permittivity of 10.2. The power dividers are designed using a quarter-wave transformer composed of 50 Ω and 70 Ω lines, which have a width of 1.404 mm and 0.485 mm. Fig. 4 shows simulated and measured radiation patterns with a nulling at Case I and Case II. The results were obtained using the ANSYS HFSS and the full anechoic chamber. As shown in Fig. 4(a) and (b), the measured results are in agreement with the simulated results, except for a difference of 5° in the θ of Case II. The minor null points of the measured radiation patterns are generated by coaxial cables for the other ports.

In this letter, a method to calculate the input phase of each port of radiating elements for a GPS anti-jam using a modified AF was presented. The modified AF considers both a rotation and an arrangement of radiating each element designed with circular array implemented by a MZR antenna with a CP characteristic. In addition, the power divider is employed to approach the calculated phases at each port. Null steering in a specific direction (Case I: θ₀ = 0°, Φ₀ = 0° and Case II: θ₀ = 55°, Φ₀ = 150°) is confirmed by a simulated and measured radiation pattern with a null.