CN116244940A - Dual-beam ultra-wideband array antenna optimization layout method - Google Patents

Abstract

The invention belongs to the technical field of antennas, provides a double-beam ultra-wideband array antenna optimization layout method, and relates to array antenna pattern synthesis and antenna array element position optimization. The method comprises the following steps: step 1, initializing and laying out planar array antenna units by adopting a Fermat spiral array layout method; and 2, performing continuous perturbation optimization on the array element positions by adopting an iterative convex optimization method, and minimizing the maximum sidelobe level of the dual-beam with the beam pointing to different directions in the range of ultra-wideband working frequency (the ratio of the highest working frequency point to the lowest working frequency point is more than 3) to obtain an optimization target. And setting maximum sidelobe level constraint, array element position perturbation amplitude constraint and minimum unit spacing constraint in the optimization process. The invention can integrate the planar array with ultra-wideband and dual-beam scanning performance by optimizing the antenna unit layout, and can effectively control the minimum unit spacing to meet the practical application requirements.

Description

A dual-beam ultra-wideband array antenna optimization layout method

Technical Field

The invention belongs to the technical field of antennas, and in particular relates to a dual-beam ultra-wideband array antenna optimization layout method.

Background Art

Ultra-wideband array antennas can achieve effective radiation when the ratio of the highest operating frequency to the lowest operating frequency is greater than 3, so they are widely used in wireless communication systems and radar systems. However, the design of high-performance ultra-wideband array antennas usually faces a dilemma, that is, the choice of the minimum unit spacing. On the one hand, half the wavelength of the highest frequency point is selected as the minimum unit spacing, such as tight coupling technology. Although this technology can achieve a very large working bandwidth, it requires a large number of channels and has difficulty in suppressing the active standing wave ratio. On the other hand, half the wavelength of the lowest frequency point is selected as the minimum unit spacing, but this will cause high-frequency grating lobes to be introduced into the array radiation pattern. Therefore, most current methods use sparse array layout methods to further optimize the position of array antenna units. For example: Reference 1 uses the characteristics of the first-order Bessel function to represent the array factor, and proposes a design method for analytically calculating the ring radius and the number of elements in the ring. The experimental results show that this method can achieve a wide-bandwidth angular scanning sparse concentric ring array with low sidelobe level.

Although the above method can synthesize a dual-beam ultra-wideband array antenna that meets the design index requirements, it searches for parameters that affect the layout of the antenna units within a reasonable range of values to analytically find the antenna unit position that can achieve the best radiation performance. However, although the solution speed of the above method is fast, the limited solution range limits the optimization performance of the algorithm. At the same time, how to ensure broadband and beam scanning performance while considering the minimum unit spacing and avoiding physical overlap between antenna elements during the optimization process is also a great challenge. Finally, among the existing ultra-wideband array synthesis methods, only the sparse array layout method is used to synthesize single-beam linear arrays, and the sparse array layout method is used to synthesize dual-beam ultra-wideband planar arrays, and there are few methods to achieve minimum unit spacing control.

Chinese patent CN202110281818.5 discloses a method for arranging an array with large-angle scanning without grating lobes in an ultra-large-spacing array. The patent first divides the entire array antenna into three planar array areas, Ⅰ, Ⅱ, and Ⅲ, according to the x-axis, arranges the planar arrays in planar array area Ⅰ and area Ⅲ at an oblique angle, and adjusts the shape of the entire two-dimensional planar array to increase space utilization. Experimental results show that this method can achieve an ultra-wideband grating-free sparse array with a frequency of more than 3 times. However, the planar ultra-wideband array synthesized by this method analytically retrieves the parameters that affect the layout, and the optimized array element layout results still have room for further optimization.

Summary of the invention

In view of the deficiencies of the above-mentioned prior art, the present invention provides a dual-beam ultra-wideband array antenna optimization layout method, which adopts the Fermat spiral layout as the initial layout of the array and ensures that it meets the required minimum unit spacing; finally, the iterative convex optimization method is used to perform continuous perturbation optimization on the array element position, and within the ultra-wideband operating frequency (the ratio of the highest operating frequency to the lowest operating frequency is greater than 3), the dual-beam maximum sidelobe level with beams pointing in different directions is minimized as the optimization goal. During the optimization process, the maximum sidelobe level constraint, the array element position perturbation amplitude constraint and the minimum unit spacing constraint are set. The optimized array element layout can realize a dual-beam planar array with ultra-wideband and beam scanning performance, and meet the required minimum unit spacing to meet actual application needs.

In order to achieve the above technical objectives, the present invention adopts the following technical solutions:

A dual-beam ultra-wideband array antenna optimization layout method comprises the following steps:

(1) Determine the number of planar array antenna elements and the minimum element spacing, and use the Fermat spiral array layout method to initialize the layout of the planar array antenna elements;

(2) An iterative convex optimization method is used to perform perturbation optimization on the array element position. Within the ultra-wideband operating frequency range, the optimization goal is to minimize the maximum sidelobe level of the dual beams pointing in different directions. During the optimization process, the maximum sidelobe level constraint, the array element position perturbation amplitude constraint, and the minimum array element spacing constraint are set; the ultra-wideband operating frequency is the ratio of the highest operating frequency to the lowest operating frequency that is greater than 3.

Furthermore, in step 1, the Fermat spiral array layout method is used to initialize the layout of the planar array antenna elements, specifically:

In the polar coordinate system, the polar diameters and polar angles of the nth, n=1,...,Nth array elements based on the Fermat spiral plane array are

为黄金角，归一化因子

d_min为最小单元间距，即最低频点的半波长，N为平面阵列天线阵元数目，将天线阵元极坐标系下的位置信息通过式(3)和(4)转换为xoy面的直角坐标系位置信息；In the formula,

is the golden angle, normalization factor

_dmin is the minimum unit spacing, that is, the half wavelength of the lowest frequency point, N is the number of planar array antenna elements, and the position information of the antenna element in the polar coordinate system is converted into the rectangular coordinate system position information of the xoy plane through equations (3) and (4);

x _n =ρ _n cos(φ _n ) (3)

_yn = _ρn sin( _φn ) (4)

Based on the array element positions obtained from equations (3) and (4), the array factor expression of the dual-beam planar array at the k=1,...,Kth frequency point is shown in (5):

x_n和y_n分别表示位于阵列中第n个天线阵元在x轴和y轴的位置，

表示第n个天线阵元在第k个频点的有源单元方向图，θ和

分别表示从z和x轴测量的观测方向，β_k＝2πf_k/c表示在第k个频点自由空间的波数，且f_k＝f_L+(f_H-f_L)*k/K，f_L和f_H分别表示工作频点的最低和最高频点，

以及

和

和

分别表示两个波束的期望指向，u和v分别表示球坐标系投影到xoy面后的横坐标与纵坐标。in,

x _n and y _n represent the position of the nth antenna element in the array on the x-axis and y-axis respectively.

represents the active unit radiation pattern of the nth antenna element at the kth frequency point, θ and

denote the observation directions measured from the z and x axes, respectively; β _k =2πf _k /c denotes the wave number in free space at the kth frequency point; and f _k =f _L +(f _H -f _L )*k/K, where f _L and f _H denote the lowest and highest frequency points of the operating frequency points, respectively.

as well as

and

and

They represent the desired pointing directions of the two beams respectively, and u and v represent the horizontal and vertical coordinates after the spherical coordinate system is projected onto the xoy plane.

Furthermore, step 2 is specifically as follows:

The iterative convex optimization method is used to continuously perturb the element position. Within the ultra-wideband operating frequency range, the optimization goal is to minimize the maximum sidelobe level of the dual beams pointing in different directions. On the basis of controllable minimum spacing, the peak level of the grating lobe/sidelobe area is reduced to obtain the optimal planar array antenna element layout. The basic principle of the perturbation method is to transform the element positions _xn and _yn in equation (5) into _xn +Δxn and _{yn + Δyn} , where _Δxn and _Δyn represent the position perturbations of the element in the x and y directions, respectively, and expand them into linear expressions through first-order Taylor expansion. In the optimization process, the three constraints of the dual beam sidelobe level constraint, the position perturbation amplitude constraint and the minimum spacing constraint are guaranteed to be met. The specific constraints are set as follows:

的取值小于ε；1) Dual-beam sidelobe level constraint: In the ultra-wideband operating frequency range, an auxiliary variable ε is introduced to constrain the dual-beam pattern in the sidelobe area of the kth frequency point.

The value of is less than ε;

2) Position perturbation amplitude constraint: For n=1,…, _N , | _βHΔxn |≤μ and | _βHΔyn | _≤μ are satisfied, where _βH is the highest frequency free space wave number in the working frequency band and μ is the set value, which determines the amplitude of the position perturbation;

3) Minimum spacing constraint: During the perturbation process, for any two antenna elements p and q, the distance between them must be greater than the set minimum unit spacing _dmin , p&q＝1,…,N&p≠q and p≠q;

Finally, the array synthesis problem is expressed as Equation (6) and solved by an iterative convex optimization method. The optimization objective in the l=1,...,Lth iteration is to minimize the peak level in the grating\sidelobe region;

表示第k个频点的副瓣区域，双波束分别指向

和

(x_p，y_p)和(x_q，y_q)分别为天线阵元p和q的坐标，θ_a&θ_b∈{0°,θ_max}表示在优化过程中考虑的双波束分别指向的2个俯仰角为{0°,θ_max}，θ_max为考虑的最大俯仰角，

表示在优化过程中考虑的双波束分别指向的4个方位角为{0°,45°,90°,135°}；在满足以上约束条件，通过迭代凸优化法对阵元位置进行多步微扰，降低栅瓣/副瓣区域的峰值电平；在每一步迭代求解出x和y方向的位置微扰量Δx_n和Δy_n后，将x_n和y_n变成x_n+Δx_n和y_n+Δy_n以更新阵元位置，当新阵列的栅瓣/副瓣区域的峰值电平保持不变且阵列布局也不变时，即得到最优化阵列布局。Where ε is the auxiliary variable introduced to constrain the peak level of the array pattern.

Indicates the sidelobe area of the kth frequency point, and the dual beams point to

and

(x _p , y _p ) and (x _q , y _q ) are the coordinates of antenna elements p and q respectively. θ _a &θ _b ∈{0°,θ _max } means that the two elevation angles of the dual beams considered in the optimization process are {0°,θ _max } respectively. θ _max is the maximum elevation angle considered.

It indicates that the four azimuth angles pointed by the dual beams considered in the optimization process are {0°, 45°, 90°, 135°} respectively; when the above constraints are met, the array element position is perturbed in multiple steps through the iterative convex optimization method to reduce the peak level in the grating lobe/side lobe area; after solving the position perturbations _Δxn and _Δyn in the x and y directions in each iterative step, _xn and _yn are converted into _xn + _Δxn and _yn + _Δyn to update the array element position. When the peak level of the grating lobe/side lobe area of the new array remains unchanged and the array layout remains unchanged, the optimized array layout is obtained.

The present invention can synthesize a planar array with ultra-wideband and dual-beam scanning performance by optimizing the antenna unit layout, and can effectively control the minimum unit spacing to meet actual application requirements.

BRIEF DESCRIPTION OF THE DRAWINGS

FIG1 is a flow chart of the technical solution of the present invention.

FIG. 2 shows the initial antenna unit positions based on the Fermat spiral array layout method.

FIG3 shows the sidelobe peak levels during the process of optimizing the position of array antenna elements using iterative convex optimization.

FIG4 shows the position of the array antenna elements after iterative convex optimization.

Figure 5 shows the array radiation pattern of the dual-beam distribution pointing normal and elevation angles at 3 GHz frequency and when the azimuth angle is 45 degrees.

Figure 6 shows the array radiation pattern of the dual-beam distribution pointing to the normal direction, elevation angle and azimuth angle of 45 degrees at the 13 GHz frequency point.

DETAILED DESCRIPTION

In order to make the objectives, technical solutions and advantages of the present invention more clearly understood, the present invention is further described in detail below in combination with specific implementation cases and with reference to the accompanying drawings.

The present invention is further explained below with reference to an example. Design objectives: operating frequency range between 3 Hz and 13 GHz, minimum frequency f _L =3 GHz and f _H =13 GHz; considering two frequency points K=2, and the maximum angle of the dual beam at the elevation angle is θ _max =45°; sparse planar array with the peak level of the grating lobe/side lobe region remaining unchanged.

As shown in Figure 1, follow the steps below:

Step 1: Use the Fermat spiral array layout method to perform initial layout. In the polar coordinate system, the polar diameters and polar angles of the nth, n＝1,...,Nth array elements based on the Fermat spiral plane array are respectively

为黄金角，归一化因子

时，d_min＝λ_L/2＝0.05m为最小单元间距(最低工作频点波长的一半)。将天线阵元极坐标系下的位置信息通过式(3)和(4)转换为xoy面的直角坐标系位置信息。图2给出了基于费马螺旋线阵列布局方法完成的天线单元位置。The number of array elements N = 140,

is the golden angle, normalization factor

When d _min = λ _L /2 = 0.05 m is the minimum unit spacing (half the wavelength of the lowest operating frequency). The position information of the antenna element in the polar coordinate system is converted into the rectangular coordinate system position information of the xoy plane through equations (3) and (4). Figure 2 shows the antenna element position completed based on the Fermat spiral array layout method.

x _n = p _n cos(φ _n ) (3)

_yn = _pn sin( _φn ) (4)

Based on the array element positions obtained from equations (3) and (4), the array factor expression of the dual-beam planar array at the k=1,...,Kth frequency points is shown in (5).

x_n和y_n分别表示位于阵列中第n个天线阵元在x轴和y轴的位置，

表示第n个天线阵元在第k个频点的有源单元方向图，θ和

分别表示从z和x轴测量的观测方向，β_k＝2πf_k/c表示在第k个频点自由空间的波数，且f_k＝f_L+(f_H-f_L)*k/K，f_L和f_H分别表示工作频点的最低和最高频点，

以及

和

和

分别表示两个波束的期望指向，u和v分别表示球坐标系投影到xoy面后的横坐标与纵坐标。in,

x _n and y _n represent the position of the nth antenna element in the array on the x-axis and y-axis respectively.

represents the active unit radiation pattern of the nth antenna element at the kth frequency point, θ and

denote the observation directions measured from the z and x axes, respectively; β _k =2πf _k /c denotes the wave number in free space at the kth frequency point; and f _k =f _L +(f _H -f _L )*k/K, where f _L and f _H denote the lowest and highest frequency points of the operating frequency points, respectively.

as well as

and

and

They represent the desired pointing directions of the two beams respectively, and u and v represent the horizontal and vertical coordinates after the spherical coordinate system is projected onto the xoy plane.

Step 2: Use the iterative convex optimization method to continuously perturb the array element position, with the optimization goal of minimizing the maximum sidelobe level of the dual beams pointing in different directions within the ultra-wideband operating frequency (the ratio of the highest operating frequency to the lowest operating frequency is greater than 3). On the basis of controllable minimum spacing, the peak level of the grating lobe/sidelobe area is minimized to obtain the optimal planar array antenna unit layout. The basic principle of the perturbation method is to transform the array element positions _xn and _yn in equation (5) into _xn + _Δxn and _yn + _Δyn , where _Δxn and _Δyn represent the position perturbations of the array element in the x and y directions, respectively, and expand them into linear expressions through the first-order Taylor expansion. In addition, during the optimization process, it is necessary to ensure that the three constraints of the dual beam sidelobe level constraint, position perturbation amplitude constraint and minimum spacing constraint are met. The specific constraints are set as follows:

的取值小于ε。1) Dual-beam sidelobe level constraint: In the ultra-wideband operating frequency range (the ratio of the highest operating frequency to the lowest operating frequency is greater than 3), in order to ensure that the peak level of the dual beams pointing at different angles in the grating lobe/side lobe area is minimized during the optimization process, an auxiliary variable ε is introduced to constrain the dual-beam pattern in the sidelobe area of the kth frequency point.

The value of is less than ε.

2) Position perturbation amplitude constraint: In order to ensure the approximate accuracy of the position perturbation, for n = 1, 2, …, N, |β _H Δx _n | ≤ μ and |β _H Δy _n | ≤ μ are satisfied, where β _H is the highest frequency free space wave number in the working frequency band, and the size of μ determines the amplitude of the position perturbation, which is set to μ = 1.4 mm.

3) Minimum spacing constraint: In order to reduce the difficulty of antenna unit design, improve the practicality of antenna array layout, and to minimize the coupling of antenna units within the working frequency band, the array element spacing needs to meet the minimum spacing constraint during the actual antenna array layout. Therefore, when the minimum unit spacing d _min = 50 mm (half wavelength of the lowest working frequency) between array elements is set, for any two antenna units p and q during the perturbation process, the distance between them needs to be greater than the set minimum unit spacing d _min (half wavelength of the lowest working frequency), p&q = 1,…, N&p≠q and p≠q.

Finally, this array synthesis problem can be expressed as Equation (6), which is solved by an iterative convex optimization method. The optimization goal in the l=1,...,Lth iteration is to minimize the peak level in the grating\sidelobe region;

表示第k个频点的副瓣区域，双波束分别指向

和

(x_p，y_p)和(x_q，y_q)分别为天线阵元p和q的坐标，θ_a&θ_b∈{0°,θ_max}表示在优化过程中考虑的双波束分别指向的2个俯仰角为{0°,θ_max}，θ_max为考虑的最大俯仰角，

表示在优化过程中考虑的双波束分别指向的4个方位角为{0°,45°,90°,135°}；在满足以上约束条件，通过迭代凸优化法对阵元位置进行多步微扰，降低栅瓣/副瓣区域的峰值电平；在每一步迭代求解出x和y方向的位置微扰量Δx_n和Δy_n后，将x_n和y_n变成x_n+Δx_n和y_n+Δy_n以更新阵元位置，当新阵列的栅瓣/副瓣区域的峰值电平保持不变且阵列布局也不变时，即得到最优化阵列布局。图3给出了每步微扰结果的栅瓣/副瓣区域的峰值电平值，大约70次迭代后，栅瓣/副瓣区域的峰值电平降到大约-15.43dB，随后基本保持不变，通过迭代凸优化之后栅瓣/副瓣区域的峰值电平总共降低了4.26dB。图4给出了迭代凸优化之后的阵列位置。图5和图6分别给出了3GHz和13GHz频点时双波束分别指向法向以及

的平面阵列方向图，此时栅瓣/副瓣区域的峰值电平分别为-14.28dB和-10.68dB。Where ε is the auxiliary variable introduced to constrain the peak level of the array pattern.

Indicates the sidelobe area of the kth frequency point, and the dual beams point to

and

(x _p , y _p ) and (x _q , y _q ) are the coordinates of antenna elements p and q respectively. θ _a &θ _b ∈{0°,θ _max } means that the two elevation angles of the dual beams considered in the optimization process are {0°,θ _max } respectively. θ _max is the maximum elevation angle considered.

Indicates that the four azimuth angles of the dual beams considered in the optimization process are {0°, 45°, 90°, 135°}; Under the above constraints, the array element position is perturbed in multiple steps by the iterative convex optimization method to reduce the peak level of the grating lobe/side lobe area; After solving the position perturbation values _Δxn and _Δyn in the x and y directions in each iteration, _xn and _yn are converted into _xn + _Δxn and _yn + _Δyn to update the array element position. When the peak level of the grating lobe/side lobe area of the new array remains unchanged and the array layout remains unchanged, the optimal array layout is obtained. Figure 3 shows the peak level value of the grating lobe/side lobe area of each perturbation result. After about 70 iterations, the peak level of the grating lobe/side lobe area drops to about -15.43dB, and then remains basically unchanged. After iterative convex optimization, the peak level of the grating lobe/side lobe area is reduced by 4.26dB in total. Figure 4 shows the array position after iterative convex optimization. Figures 5 and 6 show the dual beams pointing to the normal and

The planar array radiation pattern, at this time the peak levels of the grating lobe/side lobe area are -14.28dB and -10.68dB respectively.

Claims (3)

1. A dual-beam ultra-wideband array antenna optimization layout method, characterized in that it includes the following steps: (1) Determine the number of planar array antenna elements and the minimum element spacing, and use the Fermat spiral array layout method to initialize the layout of the planar array antenna elements; (2) An iterative convex optimization method is used to perform perturbation optimization on the array element position. Within the ultra-wideband operating frequency range, the optimization goal is to minimize the maximum sidelobe level of the dual beams pointing in different directions. During the optimization process, the maximum sidelobe level constraint, the array element position perturbation amplitude constraint, and the minimum array element spacing constraint are set; the ultra-wideband operating frequency is the ratio of the highest operating frequency to the lowest operating frequency that is greater than 3. 2. The method for synthesizing an ultra-wideband sparse planar array according to claim 1, characterized in that in step 1, the Fermat spiral array layout method is used to initialize the layout of the planar array antenna elements, specifically: In the polar coordinate system, the polar diameters and polar angles of the nth, n=1,...,Nth array elements based on the Fermat spiral plane array are

In the formula,

is the golden angle, normalization factor

_dmin is the minimum unit spacing, that is, the half wavelength of the lowest frequency point, N is the number of planar array antenna elements, and the position information of the antenna element in the polar coordinate system is converted into the rectangular coordinate system position information of the xoy plane through equations (3) and (4); x _n =ρ _n cos(φ _n ) (3) _yn = _ρn sin( _φn ) (4) Based on the array element positions obtained from equations (3) and (4), the array factor expression of the dual-beam planar array at the k=1,...,Kth frequency point is shown in (5):

in,

x _n and y _n represent the position of the nth antenna element in the array on the x-axis and y-axis respectively.

represents the active unit radiation pattern of the nth antenna element at the kth frequency point, θ and

denote the observation directions measured from the z and x axes, respectively; β _k =2πf _k /c denotes the wave number in free space at the kth frequency point; and f _k =f _L +(f _H -f _L )*k/K, where f _L and f _H denote the lowest and highest frequency points of the operating frequency points, respectively.

as well as

and

and

They represent the desired pointing directions of the two beams respectively, and u and v represent the horizontal and vertical coordinates after the spherical coordinate system is projected onto the xoy plane. 3. The dual-beam ultra-wideband array antenna optimization layout method according to claim 2, wherein step 2 specifically comprises: The iterative convex optimization method is used to continuously perturb the element position. Within the ultra-wideband operating frequency range, the optimization goal is to minimize the maximum sidelobe level of the dual beams pointing in different directions. On the basis of controllable minimum spacing, the peak level of the grating lobe/sidelobe area is reduced to obtain the optimal planar array antenna element layout. The basic principle of the perturbation method is to transform the element positions _xn and _yn in equation (5) into _xn +Δxn and _{yn + Δyn} , where _Δxn and _Δyn represent the position perturbations of the element in the x and y directions, respectively, and expand them into linear expressions through first-order Taylor expansion. In the optimization process, the three constraints of the dual beam sidelobe level constraint, the position perturbation amplitude constraint and the minimum spacing constraint are guaranteed to be met. The specific constraints are set as follows: 1) Dual-beam sidelobe level constraint: In the ultra-wideband operating frequency range, an auxiliary variable ε is introduced to constrain the dual-beam pattern in the sidelobe area of the kth frequency point.

The value of is less than ε; 2) Position perturbation amplitude constraint: For n=1,…, _N , | _βHΔxn |≤μ and | _βHΔyn | _≤μ are satisfied, where _βH is the highest frequency free space wave number in the working frequency band and μ is the set value, which determines the amplitude of the position perturbation; 3) Minimum spacing constraint: During the perturbation process, for any two antenna elements p and q, the distance between them must be greater than the set minimum unit spacing _dmin , p&q＝1,…,N&p≠q and p≠q; Finally, the array synthesis problem is expressed as Equation (6) and solved by an iterative convex optimization method. The optimization objective in the l=1,...,Lth iteration is to minimize the peak level in the grating\sidelobe region;

Where ε is the auxiliary variable introduced to constrain the peak level of the array pattern.

Indicates the sidelobe area of the kth frequency point, and the dual beams point to

and

(x _p , y _p ) and (x _q , y _q ) are the coordinates of antenna elements p and q respectively. θ _a &θ _b ∈{0°,θ _max } means that the two elevation angles of the dual beams considered in the optimization process are {0°,θ _max } respectively. θ _max is the maximum elevation angle considered.

It indicates that the four azimuth angles pointed by the dual beams considered in the optimization process are {0°, 45°, 90°, 135°} respectively; when the above constraints are met, the array element position is perturbed in multiple steps through the iterative convex optimization method to reduce the peak level in the grating lobe/side lobe area; after solving the position perturbations _Δxn and _Δyn in the x and y directions in each iterative step, _xn and _yn are converted into _xn + _Δxn and _yn + _Δyn to update the array element position. When the peak level of the grating lobe/side lobe area of the new array remains unchanged and the array layout remains unchanged, the optimized array layout is obtained.

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