Ultra-wideband high-isolation transceiver array

Abstract

This application discloses an ultra-wideband high-isolation transceiver array, belonging to the field of antenna technology. The ultra-wideband high-isolation transceiver array embeds a dual-polarized transmitting array and a dual-polarized receiving array within a first metal cavity and a second metal cavity, respectively. The surface of the metal platform is provided with multiple metamaterial absorber groups with multi-layered multi-resonant unit structures, wherein each metamaterial absorber group is periodically arranged. The apertures of both the dual-polarized transmitting and receiving arrays are chamfered at 45° to concentrate the energy of the sidelobes of each array onto the diagonally opposite region of the array aperture, thereby improving the isolation between the dual-polarized transmitting and receiving arrays.

Description

Technical Field

[0001] This application relates to the field of antenna technology, and in particular to an ultra-wideband high-isolation transceiver array. Background Technology

[0002] In traditional ships, each electronic device performs a relatively independent function. Antennas are arranged discretely, designed according to several principles of isolation control. This allows for the shielding and isolation of electromagnetic waves by the superstructure, eliminating interference between related devices and enhancing the system's electromagnetic compatibility. However, when ships adopt integrated radio frequency (RF) technology, using planar phased array antennas instead of separate mast antennas, the receiving and transmitting arrays are arranged coplanarly. The usable spatial isolation distance decreases from tens of meters to just a few meters, necessitating a rational array layout to avoid direct beam penetration. Furthermore, end-fire interference between arrays still exists, requiring isolation control measures in the corresponding directions. Therefore, improving the isolation of coplanar transmitting and receiving arrays becomes crucial for the successful implementation of integrated RF technology.

[0003] Existing technologies disclose a method for improving isolation by rotating a coplanar dual-polarization array by 45°. This method designs the array's 0° / 90° polarization arrangement as a 45° / 135° polarization arrangement, resolving the mismatch in isolation between the E-plane and H-plane of the array and resulting in an average improvement of 20dB in isolation between array planes. However, this method alters the array's polarization direction, thus limiting its application scope.

[0004] Existing technologies also disclose methods to improve the isolation of antennas in co-frequency transceiver units. These methods involve placing a periodic metal plate between two antennas, optimizing the size and spacing of the periodic metal plate, and adjusting the amplitude and phase of the leaked and reflected signals to achieve anti-cancellation. This method provides isolation performance in the 1.5GHz-2GHz operating frequency band, but this periodic structure cannot achieve amplitude and phase anti-cancellation over a wider frequency range, and its isolation effect on array antennas needs further verification.

[0005] Furthermore, existing technologies also disclose transmit / receive isolation systems where the transmitting antenna employs a cosine square distribution to weight the antenna array column amplitudes, thereby achieving a low sidelobe design. The low sidelobe pattern achieved by this method is symmetrically distributed from left to right. Summary of the Invention

[0006] The main objective of this application is to provide an ultra-wideband high-isolation transceiver array, which aims to improve the isolation between transceiver arrays.

[0007] To achieve the above objectives, this application provides an ultra-wideband high-isolation transceiver array, comprising: a metal platform and a first metal cavity and a second metal cavity located on both sides of the metal platform; the dual-polarized transmitting array and the dual-polarized receiving array are respectively embedded in the first metal cavity and the second metal cavity; the surface of the metal platform is provided with a plurality of metamaterial absorber groups with multilayer multi-resonant unit structures, wherein each metamaterial absorber group is periodically arranged; wherein the array apertures of the dual-polarized transmitting array and the dual-polarized receiving array are each chamfered at 45°, so that the energy of the sidelobe regions of the dual-polarized transmitting array and the dual-polarized receiving array is concentrated to illuminate the diagonally opposite region of the array aperture.

[0008] Optionally, the array elements of the dual-polarized transmitting array and the dual-polarized receiving array are arranged in the same direction, and each has a size of 2N columns. In the first N columns, the number of array elements in each column increases sequentially, and in the last N columns, the number of array elements in each column decreases sequentially. The dual-polarized transmitting array and the dual-polarized receiving array arranged by the array elements are both parallelograms.

[0009] Optionally, the cavity opening of the first metal cavity is enlarged proportionally to the array aperture of the dual-polarized transmitting array, and the cavity opening of the second metal cavity is enlarged proportionally to the array aperture of the dual-polarized receiving array. Both the first metal cavity and the second metal cavity are trapezoidal cavities, and their respective cavity tilt angles are not less than 5 degrees and not more than 15 degrees. The inner wall of the first metal cavity near the cavity opening is provided with a plurality of first metal semi-circular serrations, and the inner wall of the second metal cavity near the cavity opening is provided with a plurality of second metal semi-circular serrations.

[0010] Optionally, the metamaterial absorbers in the metamaterial absorber group are arranged at equal intervals and their height decreases sequentially from the middle to both sides.

[0011] Optionally, each of the metamaterial absorbers includes a first conductive layer, a first dielectric layer, a first unit structure layer, a second unit structure layer, and a second dielectric layer stacked sequentially; wherein, an air layer is filled between the first unit structure layer and the second unit structure layer, and between the first conductive layer and the first dielectric layer; the first unit structure layer includes at least two concentric square rings, and the at least two concentric square rings are etched on the surface of the first dielectric layer away from the first conductive layer; the second unit structure layer includes at least four uniformly distributed circular rings, and the at least four circular rings are etched on the surface of the second dielectric layer near the first dielectric layer.

[0012] Optionally, each of the square rings includes four first lumped resistors connected by multiple first conductive lines, and each of the circular rings includes four second lumped resistors connected by multiple second conductive lines.

[0013] Optionally, the array apertures of the dual-polarized transmitting array and the dual-polarized receiving array are phase-weighted using a modified Taylor distribution algorithm to obtain an asymmetric sidelobe distribution, thereby correcting the radiation pattern of the sidelobes.

[0014] Optionally, the formula used in the modified Taylor distribution algorithm is:

[0015]

[0016] Where F is the pattern function, z is the normalized independent variable, and A L A represents the inverse hyperbolic cosine function value corresponding to the level of the first sidelobe on the left side of the radiation pattern. R This represents the inverse hyperbolic cosine function value corresponding to the level of the first sidelobe on the right side of the radiation pattern. This represents the level of the left sidelobe of the radiation pattern. σ represents the level of the right sidelobe of the radiation pattern. L σ is the left lobe broadening factor of the radiation pattern. R This is the right lobe broadening factor of the radiation pattern.

[0017] This application proposes an ultra-wideband high-isolation transceiver array, in which a dual-polarized transmitting array and a dual-polarized receiving array are embedded in a first metal cavity and a second metal cavity, respectively. The surface of the metal platform is provided with multiple metamaterial absorber groups with multi-layer multi-resonant unit structures, wherein each metamaterial absorber group is periodically arranged. The array apertures of the dual-polarized transmitting array and the dual-polarized receiving array are each chamfered at 45°, so that the energy of the sidelobe regions of the dual-polarized transmitting array and the dual-polarized receiving array is concentrated to illuminate the diagonally opposite region of the array aperture, thereby improving the isolation between the dual-polarized transmitting array and the dual-polarized receiving array. Attached Figure Description

[0018] Figure 1 This is a schematic diagram of the structure of the ultra-wideband high isolation transceiver array provided by the present invention;

[0019] Figure 2 These are schematic diagrams of the chamfered rectangular array and the conventional rectangular array provided by this invention;

[0020] Figure 3 This is a comparison diagram of the three-dimensional radiation patterns at the center frequency point between the chamfered rectangular array of the present invention and the conventional rectangular array;

[0021] Figure 4This is a schematic diagram of the metal trapezoidal cavity of the ultra-wideband high isolation transceiver array provided by the present invention;

[0022] Figure 5 This is a schematic diagram of the metamaterial absorber unit structure of the ultra-wideband high isolation transceiver array provided by the present invention;

[0023] Figure 6 This is a comparison diagram of the aperture amplitude and phase distribution of the modified Taylor distribution of the present invention and the conventional Taylor distribution;

[0024] Figure 7 This is a comparison diagram of the two-dimensional scanning pattern of the modified Taylor distribution of the present invention and the conventional Taylor distribution at the center frequency.

[0025] Figure 8 This is a comparison chart of the isolation of the transmit and receive separate dual-polarization array before and after the implementation of this invention;

[0026] The realization of the purpose, functional features and advantages of this application will be further explained in conjunction with the embodiments and with reference to the accompanying drawings. Detailed Implementation

[0027] It should be understood that the specific embodiments described herein are merely illustrative of this application and are not intended to limit this application.

[0028] Reference Figure 1 The ultra-wideband high isolation transceiver array provided in the first embodiment of this application may include:

[0029] The system comprises a metal platform 1 and a first metal cavity 2 and a second metal cavity 3 located on either side of the metal platform 1. The dual-polarized transmitting array 4 and the dual-polarized receiving array 5 are respectively embedded within the first metal cavity 2 and the second metal cavity 3. The surface of the metal platform 1 is provided with multiple metamaterial absorber groups 6 having a multi-layered multi-resonant unit structure, wherein each metamaterial absorber group 6 is periodically arranged. The array apertures of the dual-polarized transmitting array 4 and the dual-polarized receiving array 5 are each chamfered at 45° to concentrate the energy of the sidelobe regions of the dual-polarized transmitting array 4 and the dual-polarized receiving array 5 onto the diagonally opposite region of the array aperture.

[0030] Specifically, the ultra-wideband high-isolation transceiver array proposed in this application includes a first metal cavity 2 and a second metal cavity 3 arranged on both sides of a metal platform 1. A dual-polarized transmitting array 4 and a dual-polarized receiving array 5 (hereinafter referred to as dual-polarized dual-polarized transmitting / receiving array or transceiver array) are respectively embedded in the first metal cavity 2 and the second metal cavity 3. The first metal cavity 2 and the second metal cavity 3 are conformally aligned with the dual-polarized transmitting array 4 and the dual-polarized receiving array 5, respectively. An ultra-wideband dual-polarized spatial isolation device is placed on the middle surface of the metal platform 1. The ultra-wideband dual-polarized spatial isolation device is a metamaterial absorber group 6 with a multi-layer multi-resonant unit structure. Both the dual-polarized transmit array 4 and the dual-polarized receive array 5 have their aperture faces cut at 45°. This ensures that the energy of the sidelobes of both arrays is concentrated in the diagonally opposite region of the aperture face. Specifically, the rectangular aperture formed by the dual-polarized transmit / receive arrays is cut at 45°, creating a 45° oblique rectangular aperture. This ensures that the point of maximum sidelobe energy is located in the diagonally opposite region of the array face, preventing the energy from concentrating along the line connecting the array faces, thus significantly improving the isolation between the transmit and receive arrays. (Reference) Figure 3 , Figure 3 (b) is the chamfered rectangular array of the present invention. Figure 3 (a) A comparison of the three-dimensional radiation patterns of a conventional rectangular array at the center frequency f0. In the figure, the antenna aperture fields of the dual-polarized transmitting array 4 and the dual-polarized receiving array 5 are uniformly distributed according to the aperture amplitude, and the beam directions are all normal. The three-dimensional radiation pattern at the center frequency f0 is as follows. Figure 3 As shown, the array gain and beamwidth are the same for the two array arrangement methods, but the sidelobe energy distribution is different. The sidelobe energy of the rectangular aperture with a 45° chamfer is mainly distributed in the diagonal 45° / 135° direction.

[0031] In one embodiment of this application, the array elements of the dual-polarized transmitting array 4 and the dual-polarized receiving array 5 are arranged in the same direction, and each has a size of 2N columns. In the first N columns, the number of array elements in each column increases sequentially, and in the last N columns, the number of array elements in each column decreases sequentially. The dual-polarized transmitting array 4 and the dual-polarized receiving array 5 arranged by the array elements are both parallelograms.

[0032] Specifically, the dual-polarized transmit / receive array adopts a rectangular array arrangement with a 45° angled chamfer. The dual-polarized transmit / receive array antenna has 2N columns in the azimuth direction. The number of array elements in each column from left to right forms an arithmetic sequence, namely 1, 3, 5, 7, ..., 2N-3, 2N-1, 2N-1, 2N-3, ..., 7, 5, 3, 1. The total number of array elements is N*N / 2.

[0033] For example, refer to Figure 2 , Figure 2 (b) shows the array arrangement of rectangular apertures with a 45° oblique angle. Figure 2 (a) is a conventional rectangular aperture. For a rectangular aperture with a 45° chamfer, the dual-polarized transmit / receive array antenna has 24 columns in the azimuth direction. Each column, from left to right, has an arithmetic sequence of array elements: 1, 3, 5, 7, ..., 21, 23, 23, 21, ..., 7, 5, 3, 1, for a total of 288 elements. In contrast, a conventional rectangular aperture transmit / receive array antenna has 17 columns in the azimuth direction, with 17 elements in each column, for a total of 289 elements.

[0034] In one embodiment of this application, the cavity opening of the first metal cavity 2 is enlarged proportionally to the array aperture of the dual-polarized transmitting array 4, and the cavity opening of the second metal cavity 3 is enlarged proportionally to the array aperture of the dual-polarized receiving array 5. Both the first metal cavity 2 and the second metal cavity 3 are trapezoidal cavities, and their respective cavity tilt angles are not less than 5 degrees and not greater than 15 degrees. The inner sidewall of the first metal cavity 2 near the cavity opening is provided with a plurality of first metal semi-circular serrations 8, and the inner sidewall of the second metal cavity 3 near the cavity opening is provided with a plurality of second metal semi-circular serrations 9.

[0035] refer to Figure 4 The dual-polarized transmit / receive array is embedded in two metal trapezoidal cavities. The openings of the trapezoidal cavities are conformal to the array aperture, with rectangular windows at a 45° angle. Specifically, the tilt angle of the trapezoidal cavities is not less than 5 degrees and not more than 15 degrees, preferably 10°. The tilted trapezoidal cavities improve the horizontal polarization isolation of the transmit and receive arrays. The edges of the trapezoidal cavities are provided with metal semi-circular sawtooth structures, which can reduce mutual interference between the sidelobes of the transmit and receive arrays, thereby reducing the energy of electromagnetic waves directly coupled to the receive array, thus increasing the electromagnetic blocking effect. The diameter of the metal semi-circular sawtooth structure can be 10mm-25mm, preferably 20mm.

[0036] In one embodiment of this application, the metamaterial absorbers 7 in the metamaterial absorber group 6 are arranged at equal intervals and their height decreases sequentially from the middle to both sides.

[0037] Specifically, each of the metamaterial absorbers 7 includes a first conductive layer 701, a first dielectric layer 702, a first unit structure layer 703, a second unit structure layer 704, and a second dielectric layer 705 stacked sequentially; wherein, an air layer is filled between the first unit structure layer 703 and the second unit structure layer 704, and between the first conductive layer 701 and the first dielectric layer 702; the first unit structure layer 703 includes at least two concentric square rings, and the at least two concentric square rings are etched on the surface of the first dielectric layer 702 away from the first conductive layer 701; the second unit structure layer 704 includes at least four uniformly distributed circular rings, and the at least four circular rings are etched on the surface of the second dielectric layer 705 near the first dielectric layer 702.

[0038] Furthermore, each of the square rings includes four first lumped resistors connected by multiple first conductive lines, and each of the circular rings includes four second lumped resistors connected by multiple second conductive lines.

[0039] In other words, an ultra-wideband dual-polarized spatial isolation device based on metamaterial absorbers 7 is arranged between the transceiver arrays. This device consists of several metamaterial absorber groups 6 erected at different heights and arranged at certain intervals, which can efficiently absorb electromagnetic waves incident on the surface of the metamaterial absorber 7. The metamaterial absorber 7 uses a multilayer printed circuit board with etched metal patterns and loaded with lumped resistors. The size of the etched metal patterns in each layer is different to form a multi-resonant structure to expand the bandwidth. The top layer pattern consists of four circular rings with equal radii, and the bottom layer pattern consists of two square rings of different sizes. The pattern has a central rotational symmetry structure and has dual-polarized absorption capability. When the array antenna performs beam scanning, the isolation is also significantly improved.

[0040] For example, the unit structure of the metamaterial absorber 7 constituting the ultra-wideband dual-polarization space isolation device is as follows: Figure 5 As shown, Figure 5 (a) is a side view. Figure 5 (b) is a top view. Figure 5 (c) is a bottom view. Figure 5 (d) is a sectional view. Figure 5(e) shows the equivalent circuit diagram. It consists of a top printed circuit board (second dielectric layer 705), a bottom printed circuit board (first dielectric layer 702), and a metal backplate (first conductive layer 701), with air gaps separating each layer. Four identical circular rings are etched on the lower surface of the top printed circuit board, and two square rings of different sizes are etched on the upper surface of the bottom printed circuit board. The remaining surfaces are unpatterned. Each circular and square ring is fitted with four lumped resistors. The dielectric of the printed circuit board is F4B (relative permittivity 2.2, loss tangent 0.001). The printed pattern is symmetrical, effectively absorbing both horizontally and vertically polarized electromagnetic waves. The pattern arrangement period can be p = 8 mm, the air gap thickness h1 = 2 mm, and the printed circuit board thickness h2 = 1.524 mm.

[0041] Continue to refer to Figure 1 The ultra-wideband dual-polarization spatial isolation device is formed by periodically arranging several metamaterial absorbers 7 units. Preferably, it consists of 10 groups of metamaterial absorbers 7, each group having heights of 125mm, 150mm, 175mm, 200mm, 225mm, 225mm, 200mm, 175mm, 150mm, and 125mm, respectively. The interval between each group of metamaterial absorbers 7 is 50mm, and they are arranged sequentially along the center of the transceiver array.

[0042] In one embodiment of this application, the array apertures of the dual-polarized transmitting array 4 and the dual-polarized receiving array 5 are phase-weighted using a modified Taylor distribution algorithm to obtain an asymmetric sidelobe distribution, thereby correcting the radiation pattern of the sidelobes.

[0043] The dual-polarized transmit / receive array employs a modified Taylor distribution on its aperture surface, which simultaneously weights the amplitude and phase of the dual-polarized transmit / receive array. This modified Taylor distribution is derived from the conventional Taylor distribution. It does not alter the amplitude distribution of the transmit / receive array aperture surface but controls the left and right sidelobes separately through phase weighting, resulting in an asymmetric sidelobe distribution. This allows for lower sidelobes on one side of the array coupling direction over an ultra-wide bandwidth, thereby further improving the isolation between the transmit and receive arrays.

[0044] The pattern function corresponding to the modified Taylor distribution algorithm is:

[0045]

[0046] Where F is the pattern function, z is the normalized independent variable, and A L A represents the inverse hyperbolic cosine function value corresponding to the level of the first sidelobe on the left side of the radiation pattern. R This represents the inverse hyperbolic cosine function value corresponding to the level of the first sidelobe on the right side of the radiation pattern. This represents the level of the left sidelobe of the radiation pattern. σ represents the level of the right sidelobe of the radiation pattern. L σ is the left lobe broadening factor of the radiation pattern. R This is the right lobe broadening factor of the radiation pattern.

[0047] Figure 6 This is a comparison diagram of the aperture amplitude and phase distribution of the modified Taylor distribution of the present invention and the conventional Taylor distribution. Figure 7 This is a comparison diagram of the two-dimensional scanning pattern of the modified Taylor distribution of the present invention and the conventional Taylor distribution at the center frequency.

[0048] This application presents simulation and experimental studies on an ultra-wideband, high-isolation, dual-polarized transceiver array designed based on the method of this invention. The isolation between the dual-polarized transceiver arrays before and after implementation is shown below. Figure 8 The comparative results show that the design of the present invention significantly improves the array isolation between the two polarizations. In the 3rd octave band, the average vertical polarization isolation is increased from 90dB to 140dB, and the average horizontal polarization isolation is increased from 100dB to 145dB.

[0049] The significant advantages of this invention compared to existing technologies are:

[0050] (1) Cut the existing rectangular aperture at a 45° angle without changing the array polarization, azimuth, and elevation beamwidth, which can significantly reduce the coupling energy between the transceiver arrays in a wide frequency band.

[0051] (2) Embed the transceiver array into a metal cavity and optimize the cavity structure. Set a metal semi-circular sawtooth structure at the edge of the cavity to block or reduce the direct rays between the transceiver antennas and further improve the isolation of the transceiver array.

[0052] (3) Compared with the interference cancellation method, the metamaterial absorber 7 with multi-layer multi-resonant unit structure can achieve efficient absorption of electromagnetic waves with arbitrary polarization and large angle of incidence in a wide frequency band, avoiding diffraction waves and surface waves caused by traditional metal isolation plates, while improving the jitter of the antenna pattern. Moreover, the metamaterial broadband absorber is more flexible in preparation and design than traditional metal isolation plates and absorber materials, and can be optimized according to actual needs. Therefore, the metamaterial-based broadband absorber can effectively reduce the electromagnetic waves directly coupled from the transmitting array to the receiving array, and can also reduce the creeping wave coupling and diffraction coupling mutual interference signals to a certain extent.

[0053] (4) Modified Taylor distribution controls the left and right sidelobes separately by phase weighting on the basis of amplitude weighting of conventional Taylor distribution. Without changing the main beam energy of the transmit / receive array, it can achieve a lower sidelobe on one side of the array coupling direction in the ultra-wide bandwidth, thereby further improving the isolation between the transmit and receive arrays.

[0054] The above are merely preferred embodiments of this application and do not limit the patent scope of this application. Any equivalent structural or procedural transformations made using the content of this application's specification and drawings, or direct or indirect applications in other related technical fields, are similarly included within the patent protection scope of this application.

Claims

1. A high-isolation, ultra-wideband transceiver array, characterized in that, include: A metal platform and a first metal cavity and a second metal cavity located on both sides of the metal platform, respectively; The first metal cavity and the second metal cavity are respectively provided with a dual-polarized transmitting array and a dual-polarized receiving array. The surface of the metal platform is provided with a plurality of metamaterial absorber groups with multi-layer multi-resonant unit structures. The metamaterial absorber groups are arranged periodically. The array apertures of the dual-polarized transmitting array and the dual-polarized receiving array are each chamfered at 45° so that the energy of the sidelobe regions of the dual-polarized transmitting array and the dual-polarized receiving array is concentrated to irradiate the diagonal region of the array aperture. The dual-polarized transmitting array and the dual-polarized receiving array each have the same array element arrangement direction, and each has a size of 2N columns. In the first N columns, the number of array elements in each column increases sequentially, and in the last N columns, the number of array elements in each column decreases sequentially. Both the dual-polarized transmitting array and the dual-polarized receiving array are parallelograms. The opening of the first metal cavity is proportionally enlarged based on the array aperture of the dual-polarized transmitting array, and the opening of the second metal cavity is proportionally enlarged based on the array aperture of the dual-polarized receiving array. Both the first metal cavity and the second metal cavity are trapezoidal cavities, and the tilt angle of each trapezoidal cavity is not less than 5 degrees and not more than 15 degrees. The inner wall of the first metal cavity near the cavity opening is provided with a plurality of first metal semi-circular serrations, and the inner wall of the second metal cavity near the cavity opening is provided with a plurality of second metal semi-circular serrations.

2. The ultra-wideband high-isolation transceiver array as described in claim 1, characterized in that, The metamaterial absorbers in the metamaterial absorber group are arranged at equal intervals and their height decreases from the middle to both sides.

3. The ultra-wideband high-isolation transceiver array as described in claim 2, characterized in that, Each of the aforementioned metamaterial absorbers comprises a first conductive layer, a first dielectric layer, a first unit structure layer, a second unit structure layer, and a second dielectric layer stacked sequentially. Air is filled between the first unit structure layer and the second unit structure layer, and between the first conductive layer and the first dielectric layer. The first unit structure layer includes at least two concentric square rings, and the at least two concentric square rings are etched on the surface of the first dielectric layer away from the first conductive layer; the second unit structure layer includes at least four uniformly distributed circular rings, and the at least four circular rings are etched on the surface of the second dielectric layer near the first dielectric layer.

4. The ultra-wideband high-isolation transceiver array as described in claim 3, characterized in that, Each of the square rings includes multiple first conductive lines and four first lumped resistors connected by the multiple first conductive lines, and each of the circular rings includes multiple second conductive lines and four second lumped resistors connected by the multiple second conductive lines.

5. The ultra-wideband high-isolation transceiver array as described in claim 1, characterized in that, The array apertures of both the dual-polarized transmitting array and the dual-polarized receiving array employ a modified Taylor distribution algorithm to perform phase weighting on the sidelobes, resulting in an asymmetric sidelobe distribution to correct the radiation pattern of the sidelobes.

6. The ultra-wideband high-isolation transceiver array as described in claim 5, characterized in that, The pattern function corresponding to the modified Taylor distribution algorithm is: in, F For pattern functions, z To normalize the independent variable, A L This represents the inverse hyperbolic cosine function value corresponding to the level of the first sidelobe on the left side of the radiation pattern. A R This represents the inverse hyperbolic cosine function value corresponding to the level of the first sidelobe on the right side of the radiation pattern. This represents the level of the left sidelobe of the radiation pattern. This represents the level of the equal sidelobes on the right side of the radiation pattern. This is the left lobe broadening factor of the radiation pattern. This is the right lobe broadening factor of the radiation pattern.

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