Periodic template compensation wave control algorithm for improving beam pointing accuracy of phased array antenna

Abstract

The application discloses a periodic template compensation wave control algorithm for improving beam pointing accuracy of a phased array antenna. u 、 v The quantization error of the four-round wave control algorithm digital phase shifter in the four-round wave control algorithm is derived for a phased array antenna wave control system, and is recorded as P u 、 P v Then, a two-dimensional beam pointing area is divided into units of u v P u P v In the first phase quantization error period u , v}∈{[0, P u ),[0, P v}, a compensation matrix template is constructed by using a sequential phase feeding method based on a minimum beam pointing error criterion. In the PTC algorithm, a corresponding compensation vector is periodically selected from the compensation matrix template according to the beam pointing, a wave control code of the four-round wave control algorithm is added to the compensation vector to obtain a wave control code of the PTC algorithm, and the method can effectively reduce the beam pointing error of the phased array antenna, has low calculation amount and is easy to implement.​​​

Description

Technical Field

[0001] This invention relates to the field of radar information technology, specifically a Periodic Template Compensation (PTC) beam control algorithm. Background Technology

[0002] In phased array antenna systems, phase shifters are key components in the transceiver module, used to control beam direction and enable radar and communication systems to perform rapid spatial scanning. Phase shifters adjust the phase of the input radio frequency signal based on the applied control signal. Based on the type of control signal, phase shifters are mainly divided into two categories: analog and digital phase shifters.

[0003] Analog phase shifters utilize variable capacitors or Schottky diodes to achieve continuous phase shifting, providing high-precision phase control and reducing beam pointing errors for phased array antennas. However, they suffer from complex control circuitry and low reliability. Digital phase shifters are mainly divided into three types: switch-line, load-line, and reflective phase shifters. They utilize microelectromechanical systems (MEMS), transistors, and PIN diodes as switches, and can achieve discrete phase shifting based on a control bus.

[0004] Compared to analog phase shifters, digital phase shifters offer advantages such as simpler structure, more stable phase shifts, and easier control by digital signal processors, leading to their widespread use in phased array systems. However, because digital phase shifters provide discrete phase states, the required phase shift must be quantized to an integer multiple of the minimum phase shift through rounding, carry-over, or rounding. Phase quantization errors cause beam pointing deviations, which in turn degrade the angle measurement or angle tracking performance of the radar system.

[0005] For rounding, the beam pointing deviation can be as high as about half the beamwidth. Q The value is 10 times, where Q represents the number of bits in the digital phase shifter. To improve the beam pointing accuracy of planar phased array antennas, proposed beam control algorithms based on intelligent optimization algorithms, such as simulated annealing, genetic algorithms, and particle swarm optimization, have a large computational load. Two-dimensional quantization methods improve beam pointing accuracy by independently adjusting the phase of each element in a plane perpendicular to the scanning plane, but they lack universality for planar arrays. Summary of the Invention

[0006] The purpose of this invention is to reduce beam pointing error caused by quantization error of digital phase shifters in phased array antenna systems, and to provide a periodic template compensation beam control algorithm to improve the beam pointing accuracy of phased array antennas.

[0007] The technical solution to achieve the purpose of this invention is: a periodic template compensation beam control algorithm for improving the beam pointing accuracy of a phased array antenna. First, the phase quantization error period of the rounding beam control algorithm in the uv dimension is derived, denoted as P. u and Pv Then the UV beam is pointed at the region with P. u ×P v Divide the system into units. Using the sequential feed method, in {u,v}∈{[0,P} u ),[0,P v A beam control code compensation matrix template is constructed for the region. Based on the beam pointing, the PTC algorithm periodically selects the corresponding beam control code compensation vector from the compensation matrix template. The beam control code is the sum of the rounded beam control code and the beam control code compensation vector. This beam control algorithm can significantly reduce the beam pointing error caused by the digital phase shifter.

[0008] The specific steps include:

[0009] (1) Derive the phase quantization error period P in the uv dimension of the digital phase shifter of the phased array antenna when using the rounding wave control algorithm for quantization. u and P v .

[0010] (2) The beam pointing region is in the u and v dimensions with P u ×P v Divide into multiple regions based on the unit Δu = P. u / 2 N and Δv=P v / 2 N Quantization is performed for the beam pointing quantization unit, within the phase quantization error period {u,v}∈{[0,P} u ),[0,P v The result obtained from )} is of size 2 N ×2 N The beam pointing matrix S.

[0011] (3) For the beam pointing matrix S, the sequential phase feeding method is used to construct the beam control code compensation template matrix C. In the sequential phase feeding method, the relationship between beam pointing error and phase quantization error is derived. Taking the minimum beam pointing error as the criterion, the beam control code of each array element is determined according to the arrangement order of the antenna elements. For {u,v}∈{[0,P u ),[0,P v For each quantized beam pointing in the region, the beam control code compensation template is calculated to form the beam control template matrix C.

[0012] (4) For beam pointing in the entire space, the corresponding wave control code compensation vector is periodically selected from the compensation matrix template, and the rounded wave control code is added to the wave control code compensation vector as the wave control code for the phased array antenna configuration.

[0013] Compared with the prior art, the present invention has the following significant advantages:

[0014] (1) This invention utilizes the periodicity of phase quantization error in the rounding beam control algorithm to construct a beam control code compensation template within one quantization error cycle and apply it to the entire beam pointing region, thereby reducing the beam pointing error in the entire spatial domain with a lower computational load.

[0015] (2) The calculation of the present invention is very simple, involving only multiplication, addition and shifting, and is easy to implement in a phased array system.

[0016] (3) The present invention significantly reduces the beam pointing error caused by the digital phase shifter and improves the beam pointing accuracy. Attached Figure Description

[0017] Figure 1 It is a rectangular planar phased array antenna composed of M1×M2 array elements.

[0018] Figure 2 This describes the PTC algorithm flow.

[0019] Figure 3 The beam pointing error of a 10×8 rectangular planar phased array is calculated using the rounding method.

[0020] Figure 4 The rounding quantization error of the wave control code for array elements No.1,3,7 when u∈[0,0.08] and v=0.

[0021] Figure 5 The rounding quantization error of the wave control code for array elements No.10,30,70 when u=0, v∈[0,0.08].

[0022] Figure 6 The beam pointing error within the phase quantization error period {u,v}∈{[0,0.026),[0,0.026)} of a 10×8 planar phased array.

[0023] Figure 7 For a 16×16 planar phased array with phase quantization error period {u,v}∈{[0,1 / 2} 5 ),[0,1 / 2 5 Beam pointing error within )}.

[0024] Figure 8 The phase quantization error is calculated by rounding at beam pointing k = 495, p = 17.

[0025] Figure 9 C is the wave control code compensation vector for the PTC algorithm. 495,17 Values.

[0026] Figure 10 The antenna pattern is shown when the beam direction is k = 495 and p = 17.

[0027] Figure 11 The antenna pattern is shown when the beam direction is k = 2543 and p = 4113.

[0028] Figure 12 The antenna pattern is given when the beam direction is k = -4625 and p = -3567.

[0029] Figure 13 C is the wave control code compensation vector for the PTC algorithm. 257,254 Values.

[0030] Figure 14 Let be the beam pointing error for beam pointing u,v∈[-0.5,0.5].

[0031] Figure 15 This is a physical image of a 172-element triangular mesh phased array antenna.

[0032] Figure 16 This is the azimuth measurement result when the azimuth angle changes from 0° to 10°.

[0033] Figure 17 for Figure 16 The angular measurement error of the azimuth angle in the middle. Detailed Implementation

[0034] This invention discloses a Periodic Template Compensation (PTC) beam control algorithm, which mainly involves deriving the quantization error period of the digital phase shifter in the u and v dimensions of the rounding beam control algorithm for a phased array antenna system, denoted as P. u P v Then the UV beam is pointed to the region with P u ×P v Divide into units. In the first phase quantization error period {u,v}∈{[0,P] u ),[0,P v In this paper, a sequential phase-feed method based on minimizing beam pointing error is used to construct the beam control compensation matrix template. In the PTC algorithm, a corresponding compensation vector is periodically selected from the compensation matrix template according to the beam pointing. The rounded beam control code of the beam control algorithm is added to the compensation vector to obtain the PTC algorithm's beam control code, thereby reducing the beam pointing error caused by the digital phase shifter. The PTC method has the advantages of low computational cost and ease of engineering implementation.

[0035] The present invention will now be further described with reference to the accompanying drawings.

[0036] Rectangular planar phased array antenna arrangement as follows Figure 1 As shown, the isotropic antenna radiating elements are divided into M1 rows and M2 columns, with a horizontal spacing of d between the antenna elements. xThe vertical spacing is d y Ignoring the mutual coupling effect of antenna elements, the coordinates of the m-th element are (m... x ,m y ),Right now:

[0037] m = m x +m y M1 (1)

[0038] Where m x ,m y ∈N, 0≤m x ≤M1-1,0≤m y ≤M2-1, 0≤m≤M1M2-1, the coordinates of the m-th element are (m x d x ,m y d y ).

[0039] The basic process of the proposed PTC algorithm is as follows: Figure 2 As shown.

[0040] Step 1: First, derive the quantization error period P of the uv-dimensional wave control code when the digital phase shifter of the phased array antenna uses the rounding method. u and P v The array factor of a planar phased array antenna is

[0041]

[0042] Where λ represents the operating wavelength and θ represents the off-axis angle. Indicates the rotation angle, I m and φ m Let represent the amplitude and phase shift of the m-th element, respectively. Definition:

[0043]

[0044] When the quantization bit depth of the digital phase shifter is Q Figure 1 The beam pointing is (00, φ0), and the precise wave control code for the m-th element is...

[0045]

[0046] in Δ=2π / 2 Q This represents the phase quantization unit of a digital phase shifter.

[0047] To reduce computational complexity, rounding is often used in phased array antennas. The quantized wave control code is:

[0048]

[0049] The `round()` function performs rounding operations, which have a rounding error compared to precise wave control codes.

[0050] c r,m (u0,v0)=c pre,m (u0,v0)+δ r,m (u0,v0) (6)

[0051] Where δ r,m (u,v) represents the quantization error of the wave control code after rounding and quantization of the m-th array element.

[0052] Because of phase quantization errors in the wave control algorithm, such as Figure 1 As shown, this causes the beam pointing to deviate from (00,φ0) to (00',φ0'), where

[0053]

[0054] definition and The unit vectors representing the theoretical and actual beam pointing directions are expressed as follows:

[0055]

[0056]

[0057] The antenna beam pointing error is defined as the angle between the actual beam pointing direction and the binding beam pointing direction, denoted as γ:

[0058]

[0059] According to equation (5), the quantization error of the rounding method has periodicity, with periods in the u-dimensional and v-dimensional dimensions as follows:

[0060]

[0061] Therefore, the beam points to (u,v) and (kP). u +u,pP v The relationship between the wave control codes of +v) is as follows:

[0062] c r,m (k·P u +u,p·P v +v)=c r,m (u,v)+m x k+m y p,k,p∈Z (12)

[0063] Step 2: Point the beam in the u and v dimensions with P u ×P vDivide into multiple regions based on the unit Δu = P. u / 2 N and Δv=P v / 2 N Quantization is performed for the beam pointing quantization unit, within the phase quantization error period {u,v}∈{[0,P} u ),[0,P v The result obtained from )} is of size 2 N ×2 N The beam pointing matrix S.

[0064] In a phased array antenna, the beam scanning region is quantized into discrete beam pointing for implementation in a digital signal processor. In the PTC algorithm, the beam pointing quantization unit is:

[0065] Δu=P u / 2 N

[0066] Δv=P v / 2 N (13)

[0068] In a quantization error period {u,v}∈{[0,P} u ),[0,P v Within )}, there exist 2 N ×2 N A discrete beam pointing matrix S is defined as a beam pointing matrix.

[0069]

[0070] Combining equations (4), (11), and (13), the precise beam control code for beam pointing to S(k,p) in matrix S is obtained as follows:

[0071]

[0072] The rounding control code is:

[0073]

[0074] To simplify, c pre,m (kΔu, pΔv) and c r,m (kΔu, pΔv) is represented as c pre,m (k,p) and c r,m (k,p).

[0075] Step 3: For the beam pointing matrix S, construct the beam control code compensation template matrix C using the sequential phase feeding method. In the sequential phase feeding method, the relationship between beam pointing error and phase quantization error is derived. Taking the minimum beam pointing error as the criterion, the beam control code for each element is determined according to the arrangement order of the antenna elements, for {u,v}∈{[0,P u ),[0,P v For each quantized beam pointing in the region, the beam control code compensation template is calculated to form the beam control template matrix C.

[0076] Step 3-1: Construct the beam control code compensation matrix C of the beam pointing matrix S;

[0077] Since the rounding method has a large beam pointing error, a beam control code compensation vector is constructed for the beam pointing S(k,p). To reduce beam pointing error, the new beam control code is a rounded beam control code combined with the compensation vector C. k,p The sum, that is:

[0078] c m (k,p)=c r,m (k,p)+C k,p (m) (17)

[0079] C k,p The value of (m) can be +1, 0, or -1. For matrix S, 2... N ×2 N Given discrete beam directions, construct a wave control code compensation matrix C, where each element is C0. k,p Specifically, it is expressed as follows:

[0080]

[0081] Select vector C from C. k,p The new beam control code for the beam pointing S(k,p) can be calculated using equation (17). Where vector C... k,p The value of each element is selected from three candidate values: -1, 0, and 1, based on the criterion of minimizing the beam pointing error caused by rounding. The formula is as follows:

[0082]

[0083] The value of the compensation matrix C is calculated using the sequential feed method.

[0084] Step 3-2: Derive the relationship between pointing error γ and phase quantization error in the sequential phase feeding method;

[0085] First, the relationship between the pointing error γ and the phase quantization error in the sequential phase feeding method is derived. For a beam pointing (00, φ0), its quantized beam pointing is (k0Δu, p0Δv). The wave control code c of the m-th element in the sequential phase feeding method... SPF,m (k0, p0) is selected from the following three candidate values:

[0086]

[0087] like Figure 1 As shown, the antenna array factor in equation (2) reaches an extreme value at (00′,φ0′). Therefore, AF(0,φ) with respect to θ and The partial derivative of is 0 at (00′, φ0′), that is:

[0088]

[0089] Substituting equation (2) into equation (21), we get:

[0090]

[0091] Where φ SPF,m (k0,p0)=c SPF,m (k0,p0)·α, since the phase quantization error is small, therefore:

[0092]

[0093] According to the approximate formula sina≈a, when a→0, equation (22) can be written as:

[0094]

[0095] Substituting equation (7) into equation (24), we get:

[0096]

[0097] Where φ SPF,m (k0,p0)=φ pre,m (k0,p0)+δ SPF,m (k0,p0), φ pre,m =c pre,m (k0,p0)·Δ.

[0098] Because the beam direction deviates slightly from the theoretical direction, sin(00+δ) θ cos(φ0+δ) φ ) and sin(00+δ θ sin(φ0+δ) φ It can be approximated as:

[0099]

[0100]

[0101] Substituting equations (26) and (27) into equation (25), we get:

[0102]

[0103] Define s1, s2, t1, and t2 as:

[0104]

[0105] As shown in equation (29), for a given beam pointing (00, φ0), s1, s2, t1, and t2 are constants. Equation (28) can be simplified to:

[0106]

[0107] Solving equation (30) yields:

[0108]

[0109] Substituting equation (31) into equation (10), we can obtain the value of beam pointing error γ caused by phase quantization error in sequential phase feeding method, that is, the relationship between beam pointing error and phase quantization error.

[0110] Step 3-3: Determine the wave control code compensation vector C using the sequential phase feeding method. k,p The value of .

[0111] Based on the minimum beam pointing error γ criterion, the beam control code for each array element is determined sequentially. According to the derivation, the sequential phase feeding method specifically consists of the following three steps:

[0112] Step 3-3-1: For the beam pointing (kΔu,pΔv) corresponding to (0,φ), use Equation (29) to calculate s1, s2, t1, and t2.

[0113] Step 3-3-2: Determine the wave control code c of the No.i array element sequentially from i=0 to M1M2-1. SPF,i (k,p), the specific steps are as follows:

[0114] Step 3-3-2-1: Calculate the precise wave control code c of element No.i using equation (15). pre,i (k,p).

[0115] Step 3-3-2-2: Calculate the three cs using equation (20). SPF,i (k,p) candidate values ​​and corresponding phase quantization errors.

[0116] Step 3-3-2-3: Calculate the beam pointing error γ corresponding to the three candidate values of the No. i array element using Equation (32) and Equation (33), and determine the wave control codes of the No. 0 to No. i-1 array elements. SPF,i Candidate value corresponding to the beam pointing error γ i , and determine the wave control codes of the No. 0 to No. i-1 array elements.

[0117]

[0118]

[0119] Step 3-3-2-4: Select the value with the smallest beam pointing error from the three candidate values as the final wave control code c SPF,i .

[0120] Step 3-3-3: If i < M1M2 - 1, then set i = i + 1, and then go to Step 3-3-2. Otherwise, the wave control codes of all array elements are determined.

[0121] The wave control code compensation vector C calculated by the sequential phase feeding method is: k,p For:

[0122] C k,p (m) = c SPF,m (k,p) - c r,m (k,p), 0 ≤ m ≤ M1M2 - 1 (34)

[0123] Step Four: For the beam pointing in the entire airspace, periodically select the corresponding wave control code compensation vector from the compensation matrix template, and add the wave control code obtained by the rounding method and the wave control code compensation vector as the wave control code for the phased array antenna configuration.

[0124] Divide the beam pointing area into multiple P u ×P v , and add the wave control code obtained by the rounding method and the corresponding compensation vector periodically selected from the compensation matrix template to obtain the wave control code of the PTC algorithm. For the beam pointing (kΔu, pΔv) that satisfies 0 ≤ k, p ≤ 2 N -1, Equation (17) gives the calculation method of the wave control code. Next, discuss the case where k > 2 N -1 or p > 2 N -1. Set

[0125]

[0126] According to Equation (12), for the rounding method, the phase quantization error of the beam pointing (kΔu, pΔv) is the same as that of (k2Δu, p2Δv). Therefore, in the PTC algorithm, the wave control code compensation vector can be selected from the compensation matrix template C To compensate for the phase quantization error in beam pointing (kΔu, pΔv), the PTC algorithm wave control code for element No.m is:

[0127]

[0128] k2 and p2 are calculated from equation (35).

[0129] The present invention will be further described below with reference to embodiments.

[0130] This invention uses two planar phased array antennas as examples to simulate and verify the performance of the PTC algorithm. Table 1 shows the parameters of the first 10×8 rectangular planar phased array antenna.

[0131] Table 1 Parameters of a 10×8 planar phased array

[0132]

[0133] Figure 3 The beam pointing error of the rounding method in the uv dimension is given when u,v∈[-0.5,0.5]. As can be seen from the figure, the rounding method has obvious pointing errors in multiple beam directions. For example, the beam pointing error γ is the largest when u=0.39 and v=0.44, reaching γ=0.197°.

[0134] Figure 4 The wave control code quantization error of array elements No.1, No.3 and No.7 is given when u∈[0,0.08] and v=0. Figure 5 The wave control code quantization errors of array elements No.10, No.30, and No.70 are given when u = 0 and v ∈ [0, 0.08]. The figure shows that the phase quantization error period of the array elements in the uv dimension is 0.026, consistent with the period calculated by equation (11). The maximum phase quantization error is close to 0.5Δ, which is 0.049 rad for a 6-bit digital shifter.

[0135] For the 10×8 rectangular planar phased array in Table 1, with N=9, the phase quantization error period {u,v}∈{[0,0.026),[0,0.026)} has 512×512 discrete beam pointing units, and the beam pointing quantization unit is Δu=Δv=5.09×10 -5 Within the range {u,v}∈{[0,0.026),[0,0.026)}, Figure 6 (a) and Figure 6 (b) The beam pointing error of the rounding method and the proposed PTC algorithm is given. Figure 6As shown, the rounding method has the largest beam pointing error of 0.191° when k=28 and p=246, while the maximum beam pointing error of the PTC algorithm is 0.070°, which is 37% lower than that of the rounding method.

[0136] The parameters of the second 16×16 rectangular planar phased array are shown in Table 2, with an element spacing of 0.5λ along the x and y axes. According to equation (11), the phase quantization error period is P. u =P v =1 / 2 5 Set N=9, and in the phase quantization error period {u,v}∈{[0,P} u ),[0,P v The memory contains 512×512 discrete beam pointing units, with beam pointing quantization units of Δu = Δv = 1 / 2. 14 .

[0137] Table 2 Parameters of a 16×16 rectangular planar phased array

[0138]

[0139] In the phase quantization error period {u,v}∈{[0,P u ),[0,P v Within the range, the beam pointing errors of the rounding method and the PTC algorithm are respectively as follows: Figure 7 (a) and Figure 7 As shown in (b). In Figure 7 In (a), the rounding method results in the largest beam pointing error of 0.082° at k=495 and p=17. Meanwhile... Figure 7 In (b), the maximum beam pointing error of the PTC algorithm is 0.022°, which is 27% lower than that of the rounding method.

[0140] Next, the beam pointing performance at beam direction k=495, p=17 was analyzed. For k=495, p=17, the phase quantization error of 256 elements in the planar phased array using rounding is as follows: Figure 8 As shown. From Figure 8 It can be seen that the rounding method has a high phase quantization error. After adopting the sequential phase feeding method, the wave control code compensation vector C of the 256 array elements in the PTC algorithm is... 495,17 Values ​​such as Figure 9 As shown, vector C k,p The value of an element in the middle is -1, 0, or 1.

[0141] For a beam direction k = 495, p = 17, the theoretical beam pointing is u = 0.0302, v = 0.0010 (θ = 1.732°). ). Figure 10The u-dimensional radiation pattern is given using the rounding method and the PTC algorithm. The u-dimensional radiation pattern is shown below. Figure 10 As shown in (a). Figure 10 (a) A magnified view of the main lobe as shown in Figure Figure 10 As shown in (b), the v-dimensional radiation pattern is as follows Figure 10 As shown in (c) Figure 10 (c) A magnified view of the main lobe is shown below. Figure 10 As shown in (d), the beam pointing performance of these two algorithms is shown in Table 3.

[0142] Table 3 Beam pointing performance at k=495, p=17

[0143]

[0144] like Figure 10 As shown in Table 3, the beam pointing using the rounding method is u = 0.0312, v = 0, corresponding to θ = 1.788°. The proposed PTC algorithm has a beam pointing of u = 0.0301, v = 0.0010, corresponding to θ = 1.726°. The beam pointing error of the rounding method is 0.082°, while that of the PTC algorithm is 0.007°. Therefore, the beam pointing accuracy of the PTC algorithm is far superior to that of the rounding method.

[0145] Next, it was verified that when k>2 N -1 or p>2 N Beam pointing performance at -1. For beam direction k = 2543, p = 4113, the predetermined beam pointing is u = 0.1552, v = 0.2510 (θ = 17.166°). For the PTC algorithm, according to equation (35), we can obtain k1 = 4, k2 = 495, p1 = 8 and p2 = 17. The beam control code compensation vector pointing to k = 2543 and p = 4113 is C. 495,17 ,like Figure 9 As shown.

[0146] For the beam direction k = 2543, p = 4113 Figure 11 (a) shows the u-dimensional radiation pattern. Figure 11 (a) is a magnified view of the part. Figure 11 As shown in (b) Figure 11 (c) shows the v-dimensional radiation pattern. Figure 11 (c) is a magnified view of the part. Figure 11 As shown in (d), the beam performance of the rounding method and the PTC algorithm is shown in Table 4. Figure 11As shown in Table 4, the beam pointing error of the PTC algorithm is 0.007°, while the beam pointing error of the rounding method is 0.082°. This demonstrates that the beam pointing error of the proposed PTC algorithm is significantly lower than that of the rounding method.

[0147] Table 4. Beam pointing performance at beam direction k = 2543, p = 4113

[0148]

[0149] For beam directions k = -4625, p = -3567, the predetermined beam pointing is u = -0.2823, v = -0.2177 (θ = 20.885°). For the PTC algorithm, according to equation (35), we can obtain k1 = -10, k2 = 495, p1 = -7 and p2 = 17, and the wave control code compensation vector is also C. 495,17 ,like Figure 9 As shown. For beam pointing k = -4625, p = -3567, Figure 12 (a) shows the u-dimensional radiation pattern. Figure 12 (a) is a magnified view of the part. Figure 12 As shown in (b) Figure 12 (c) is the v-dimensional radiation pattern. Figure 12 (c) is a magnified view of the part. Figure 12 As shown in (d), the beam performance of the rounding method and the PTC algorithm is shown in Table 5. From Figure 12 As can be seen from Table 5, the beam pointing error of the PTC algorithm is 0.009°, while the beam pointing error of the rounding method is 0.088°.

[0150] Table 5 Beam pointing performance at beam direction k = -4625, p = -3567

[0151]

[0152] For the three beam pointing methods (1) k = 257, p = 254 (2) k = 4353, p = -2306 (3) k = -3839, p = 2814, the beam control code compensation vector of the PTC algorithm is the same, which is C. 257,254 ,like Figure 13 As shown in Table 6, the beam pointing performance of the rounding method and the PTC algorithm in these three directions is as follows. In Table 6, for the three beam pointing directions, the beam pointing errors of the PTC algorithm are 0.002°, 0.003°, and 0.004°, respectively, while the beam pointing errors of the rounding method are 0.060°, 0.061°, and 0.057°, respectively. The PTC algorithm effectively reduces the beam pointing error in different beam directions by periodically using the compensation matrix template C.

[0153] Table 6 uses the compensation matrix C 257,254 Beam pointing performance in three beam directions

[0154]

[0155] Figure 14 (a) and Figure 14 (b) The beam pointing errors of the rounding method and the PTC algorithm on beam pointing u,v∈[-0.5,0.5] are given respectively. Figure 14 In (a), the maximum beam pointing error using the rounding method is 0.088°, located at beam pointing k = 3113, p = -7700 (u = 0.1900, v = -0.4700). The average beam pointing error across all beam pointing directions is 0.006°. Figure 14 In (b), the maximum beam pointing error of the PTC algorithm is 0.023°, located at k = 510, p = -4096 (u = 0.0311, v = -0.2500), and the average beam pointing error is 0.003°. The maximum beam pointing error of the PTC algorithm is 26% of the rounding error.

[0156] Next, the angle measurement performance of the PTC algorithm in a phased array radar system was evaluated. The X-band phased array antenna in the radar system is shown below. Figure 15 As shown, it is a triangular grid array consisting of 172 elements with an element spacing of 0.56λ. The radar is mounted on a turntable in an anechoic chamber, and the azimuth angle between the radar and the target is controlled by the turntable, while the elevation angle is 0°.

[0157] When the azimuth angle changes from 0° to 10° at a speed of 1° / s, the azimuth angle measurement results using the rounding method and the PTC algorithm are as follows: Figure 16 (a) and Figure 16 As shown in (b), Figure 16 The x-axis represents the radar coherent processing interval (CPI). Figure 16 The measurement errors of the two algorithms are as follows: Figure 17 As shown. In Figure 16 (a) and Figure 17 In (a), the azimuth measurement results obtained by rounding show significant fluctuations around azimuth angles of 3.065° and 8.133°, with a maximum fluctuation of 0.190°. Figure 16 (b) and Figure 17 In (b), the PTC algorithm exhibits smaller fluctuations, with a maximum value of 0.079°, which is 41% of the rounding method. This demonstrates that, compared to the rounding method, the PTC algorithm possesses superior beam pointing accuracy and angle measurement performance.

Claims

1. A periodic template compensation beam control algorithm for improving the beam pointing accuracy of a phased array antenna, characterized in that: For phased array antenna wave control system, first deduce the phase quantization error period of rounding wave control algorithm digital phase shifter in u-v dimension, denoted as P u and P v ; then divide the u-v dimension beam pointing area into units of P u ×P v ; Using the sequential phase feeding method based on the minimum beam pointing error criterion, in the first phase quantization error cycle The region constructs a beam control code compensation matrix template; in the PTC algorithm, the corresponding beam control code compensation vector is periodically selected from the compensation matrix template according to the beam direction, and the rounded beam control code of the beam control algorithm is added to the compensation vector to obtain the beam control code of the PTC algorithm; The specific steps include: (1) For the phased array antenna beam control system, the phase quantization error period P in the uv dimension when the digital phase shifter of the phased array antenna is quantized using the rounding beam control algorithm is derived. u and P v ; (2) Point the beam in the u and v dimensions with P u ×P v Divide the unit into multiple regions; With Δu=P u / 2 N and Δv=P v / 2 N Quantization is performed for the beam pointing quantization unit, within the phase quantization error period {u, v}∈{[0, P u ), [0, P v The result obtained from )} is of size 2 N ×2 N The beam pointing matrix S; (3) For the beam pointing matrix S, the beam control code compensation template matrix C is constructed using the sequential phase feeding method; in the sequential phase feeding method, the relationship between beam pointing error and phase quantization error is derived, and the beam control code of each element is determined according to the order of antenna element arrangement, taking the minimum beam pointing error as the criterion. For {u, v}∈{[0, P u ), [0, P v For each quantized beam pointing in the region, the beam control code compensation template is calculated, forming a beam control template matrix C; (4) For the beam pointing in the full airspace, periodically select the corresponding wave control code compensation vector from the compensation matrix template, and add the round-off wave control code and the wave control code compensation vector as the wave control code configured for the phased array antenna.

2. The periodic template compensation beam control algorithm for improving beam pointing accuracy of phased array antennas according to claim 1, characterized in that: In the arrangement of rectangular planar phased array antennas, the isotropic antenna radiating elements are divided into... lines and The horizontal spacing between antenna elements is [number]. Vertical spacing is Ignoring the mutual coupling effect of antenna elements, the first The coordinates of each array element are ,Right now: （1） in ,0≤m x ≤M1-1,0≤m y ≤M2-1, 0≤m≤M1M2-1, the coordinates of the m-th element are (m x d x ,m y d y ).

3. The periodic template compensation beam control algorithm for improving beam pointing accuracy of phased array antennas according to claim 2, characterized in that, The specific implementation process of step (1) is: The array factor of the planar phased array antenna is (2) in Indicates the operating wavelength. Indicates the off-axis angle. Indicates the rotation angle. and They represent the first The amplitude and phase shift of each array element; Definition: (3) When the digital phase shifter has quantization bits of When the beam direction is (θ0, φ0), the precise wave control code for the m-th element is: (4) in , Δ=2π / 2 Q This represents the phase quantization unit of a digital phase shifter; In the phased array antenna, the round-off method is adopted, and the quantized wave control code is: (5) where round() represents the round-off operation, and there is a rounding error between it and the exact wave control code, that is: (6) Where δ r,m (u,v) represents the quantization error of the wave control code after rounding and quantization of the m-th array element; There is a phase quantization error in the wave control algorithm, resulting in the beam pointing deviating from (θ0, φ0) to (θ0', φ0'), where (7) definition and The unit vectors representing the theoretical and actual beam pointing directions are expressed as follows: (8) (9) The antenna beam pointing error is defined as the angle between the actual beam pointing and the bound beam pointing, denoted as . : (10) According to Equation (5), the quantization error of the round-off method is periodic, and the periods in the u dimension and v dimension are respectively: (11) Therefore, beam pointing and The relationship between the wave control codes is as follows: (12)。 4. The periodic template compensation beam control algorithm for improving beam pointing accuracy of phased array antennas according to claim 2, characterized in that, The specific implementation process of step (2) is: In the phased array antenna, the beam scanning area is quantized into discrete beam pointings. In the PTC algorithm, the beam pointing quantization unit is: (13) In a quantization error period Inside, there are 2 N ×2 N A discrete beam pointing matrix S is defined as a beam pointing matrix. (14) Combining equations (4), (11), and (13), we obtain the matrix. The precise beam control code for mid-wave beam pointing to S(k,p) is: (15) The wave control code of the round-off method is: (16) Will and Represented as and .

5. The periodic template compensation beam control algorithm for improving beam pointing accuracy of phased array antennas according to claim 2, characterized in that, The specific implementation process of step (3) is: Step 3-1: Construct the wave control code compensation matrix C of the beam pointing matrix S; Construct a beam control code compensation vector for the beam pointing S(k,p) To reduce beam pointing error, the new beam control code is a rounded beam control code combined with the compensation vector C. k,p The sum, that is: (17) The value can be +1, 0, or -1; for matrix S, 2 N ×2 N Given discrete beam directions, construct a wave control code compensation matrix C, where each element is C0. k,p Specifically, it is expressed as follows: (18) Select vector C from C. k,p The new beam control code for beam pointing S(k,p) can be calculated using equation (17); where vector C k,p The value of each element is selected from three candidate values: -1, 0, and 1, based on the criterion of minimizing the beam pointing error caused by rounding. The formula is as follows: (19) The value of the compensation matrix C is calculated by the sequential phase feeding method; Step 3-2: Deriving the pointing error in the sequential phase feeding method Relationship with phase quantization error; First, the pointing error in the sequential phase feeding method is derived. The relationship with phase quantization error; for beam pointing (θ0, φ0), its quantized beam pointing is (k0Δu, p0Δv), and the wave control code c of the m-th element in the sequential phase feeding method. SPF,m (k0, p0) is selected from the following three candidate values: (20) The antenna array factor in equation (2) reaches an extreme value at (θ0´, φ0´), and AF(θ,φ) with respect to and The partial derivatives are 0 at (θ0´, φ0´), that is: (21) Substituting Equation (2) into Equation (21) gives: (22) in ,have: (23) According to the approximate formula ,when Then, equation (22) can be written as: (24) Substituting Equation (7) into Equation (24) gives: (25) in , ; sin(θ0+δ θ )cos(φ0+δ φ ) and sin(θ0+δ θ )sin(φ0+δ φ ) approx. (26) (27) Substituting Equation (26) and Equation (27) into Equation (25) gives: (28) Define s1, s2, t1, and t2 as: (29) As shown in Equation (29), for the specified beam pointing (θ0, φ0), s1, s2, t1, and t2 are constants; Equation (28) is simplified to: (30) Solving Equation (30) gives: (31) Substituting equation (31) into equation (10), we obtain the beam pointing error caused by the phase quantization error of the sequential phase feeding method. The value of is obtained, which gives the relationship between beam pointing error and phase quantization error; Step 3-3: Determine the wave control code compensation vector C using the sequential phase feeding method. k,p The value of .

6. The periodic template compensation beam control algorithm for improving beam pointing accuracy of a phased array antenna according to claim 5, characterized in that, The specific implementation process of step 3-3 is: Step 3-3-1: For the beam pointing (kΔu, pΔv) corresponding to (θ, φ), calculate s1, s2, t1, and t2 using Equation (29); Step 3-3-2: Determine the wave control code c of the No.i array element sequentially from i=0 to M1M2-1. SPF,i (k,p), the specific steps are as follows: Step 3-3-2-1: Calculate the precise wave control code c of element No.i using equation (15). pre,i (k,p); Step 3-3-2-2: Use formula (20) to calculate the three cs. SPF,i (k,p) candidate values ​​and corresponding phase quantization errors; Step 3-3-2-3: Use equations (32) and (33) to calculate the three c values ​​of the No.i array element. SPF,i Beam pointing error corresponding to candidate values And determine the wave control codes for array elements No.0 to No.i-1; (32) (33) Step 3-3-2-4: Select the value with the smallest beam pointing error from the three candidate values ​​as the final beam control code c. SPF,i ; Step 3-3-3: If i < M1M2 - 1, then set i = i + 1, and then go to step 3-3-2. Otherwise, the wave control codes of all array elements are determined; The wave control code compensation vector C calculated using the sequential phase feeding method k,p for: (34)。 7. The periodic template compensation beam control algorithm for improving beam pointing accuracy of phased array antennas according to claim 2, characterized in that, The specific implementation process of step (4) is: Divide the beam pointing region into multiple P u ×P v The wave control code obtained by rounding is added to the corresponding compensation vector periodically selected from the compensation matrix template to obtain the wave control code of the PTC algorithm; for the condition 0≤k, p≤2 N The beam pointing (kΔu, pΔv) is -1, and Equation (17) gives the calculation method of the beam control code; for k>2 N -1 or p>2 N In the case of -1, set (35) According to equation (12), for the rounding method, the phase quantization error of the beam pointing (kΔu, pΔv) is the same as that of (k2Δu, p2Δv). Therefore, in the PTC algorithm, the beam control code compensation vector can be selected from the compensation matrix template C. To compensate for the phase quantization error in beam pointing (kΔu, pΔv), the PTC algorithm wave control code for element No.m is: (36) where k2 and p2 are calculated by Equation (35).

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