Systems and methods for efficient antenna weight vector tables in phased array antennas

Decomposing the AWV table into elevation and azimuth components addresses the large size issue, achieving efficient beamforming and switching with reduced computational and storage needs in phased array antennas.

JP2025542347APending Publication Date: 2025-12-25KYOCERA INTERNATIONAL INC
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Patent Information

Application Number
JP2025536640
Authority / Receiving Office
JP · JP
Patent Type
Applications
Current Assignee / Owner
Priority Date
2023-12-21
Filing Date
2023-12-21
Publication Date
2025-12-25

AI Technical Summary

Technical Problem

The size of antenna weight vector (AWV) tables in phased array antennas is excessively large, particularly in applications requiring numerous beams to cover a wide field of view, which affects the size of integrated circuits.

Method used

Decompose the AWV table into a first AWV table and a second AWV table, where the first AWV table is a function of only the elevation angle and the second AWV table is a function of both elevation and azimuth angles, reducing the overall table size by combining these tables for beamforming control and incorporating phase shift and delay values.

Benefits of technology

Reduces the size of the AWV table from N*M to Nv*Nh*(Mv+Mh), enabling efficient beamforming and beam switching with reduced computational and storage requirements.

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Abstract

A method and system for reducing the size of an AWV table for a phased array antenna is provided. In one novel aspect, the AWV table is decomposed into a combination of a first AWV table and a second AWV table, where the combined size is smaller than the size of the AWV table. In one novel aspect, groups of decomposable AWVs are identified and each is decomposed into a decomposed first AWV and a decomposed second AWV. In one embodiment, a W that is a function of both the elevation angle θ and the azimuth angle φ is used. h and W, which is a function of only the elevation angle θ v In one novel aspect, the decomposable weight W is decomposed into M v Weight and horizontal direction M h The AWV table for a phased array antenna having N antenna elements with weights and is given by N*(M v +M h ) into a first AWV table and a second AWV table with a combined size of 1 / 2.
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Description

[Technical Field]

[0001] CROSS-REFERENCE TO RELATED APPLICATIONS This application claims the benefit under 35 U.S.C. §119 of U.S. Provisional Application No. 63 / 434,830, entitled "SYSTEM AND METHOD FOR EFFICIENT ANTENNA WEIGHT VECTOR TABLES WITHIN PHASED-ARRAY ANTENNAS," filed December 22, 2022, the subject matter of which is incorporated herein by reference. This application claims the benefit under 35 U.S.C. §119 of U.S. Provisional Application No. 63 / 450,738, entitled "SYSTEM AND METHOD FOR EFFICIENT ANTENNA WEIGHT VECTOR TABLES WITHIN PHASED-ARRAY ANTENNAS," filed March 8, 2023, the subject matter of which is incorporated herein by reference.

[0002] The disclosed embodiments relate generally to phased array antennas, and more particularly to efficient antenna weight vectors (AWVs) in phased array antennas. [Background technology]

[0003] Phased array antennas represent a sophisticated and versatile type of antenna system gaining popularity in a variety of applications, from radar and communications systems to satellites and wireless networks. Phased array antennas offer several advantages, including high-speed beam agility, improved signal quality, and the ability to handle multiple tasks simultaneously. Unlike traditional antennas that rely on mechanical steering for beam direction, phased array antennas achieve beam control through electronic means, providing rapid and precise adjustments. The core of a phased array antenna contains multiple independent antenna elements, each connected to a phase shifter. By manipulating the phase of the signal applied to these elements, the antenna system can shape and control the electromagnetic waves being radiated or received. This electronic beam steering capability increases agility and responsiveness, enabling functions such as beamforming, beam scanning, and null interference.

[0004] Antenna weight vector (AWV) tables play an important role in the operation and optimization of phased array antennas. In the context of phased array systems, the term "weight vector" refers to a set of complex weights assigned to each antenna element. These weights determine the amplitude and phase of the signals fed to each individual element, affecting the direction and characteristics of the emitted or received beam. The antenna weight vector table serves as a comprehensive reference that specifies the optimal weighting for each antenna element in various scenarios. These tables are generated through a rigorous calibration process, simulation, or measurement, taking into account factors such as the desired beam direction, signal-to-noise ratio, and interference mitigation. However, in practice, each antenna has a corresponding AWV table. An array of n antenna elements has n AWV tables. The size of the AWV table affects the size of the integrated circuit (IC). In some applications for larger arrays, the beamwidth is very small. Therefore, many beams are required to cover the field of view. This results in a very large AWV table.

[0005] Reducing the size of the AWV table for phased array antennas requires refinements and improvements. Summary of the Invention

[0006] A method and system for reducing the size of an AWV table for a phased array antenna is provided. In one novel aspect, the AWV table is decomposed into a combination of a first AWV table and a second AWV table, and the sum of the size of the azimuth AWV table and the size of the elevation AWV table is smaller than the size of the AWV table. In one novel aspect, a group of resolvable AWVs is identified and decomposed into a decomposed first AWV and a decomposed second AWV, respectively, where the first AWV table includes the decomposed first AWV and the unrecomposed AWV, and the azimuth AWV table includes the decomposed second AWV and the unrecomposed AWV. In one embodiment, the group of resolvable AWVs and the group of non-resolvable AWVs are formed based on a determined elevation angle. The group of resolvable AWVs has an elevation angle close to 0°. In one embodiment, the resolvable AWVs are formed based on a determined elevation angle. h and W v and a weight W, where W v is a function of only the elevation angle θ, and W his a function of both the elevation angle θ and the azimuth angle φ. In one embodiment, the azimuth AWV table further includes an active azimuth beam index, and the elevation AWV table further includes an active elevation beam index. In one embodiment, for beamforming control, the active azimuth beam index is indicated by an azimuth pointer, and the active elevation beam index is indicated by an elevation pointer. In one embodiment, the system combines the first AWV table and the second AWV table for beamforming control. In one embodiment, the phase shift values ​​in the first AWV table and the second AWV table are combined modulo 360 degrees. In one embodiment, when performing wideband phased array operation, delay values ​​are added to the first AWV table and the second AWV table. In one embodiment, the composite gain value is the sum of the gain adjustment values ​​in the first AWV table and the second AWV table.

[0007] In one novel embodiment, M v Weight and horizontal direction M h The AWV table for a phased array antenna having N antenna elements with weights and is given by N*(M V +M h ) into a first AWV table and a second AWV table having a combined magnitude of N=N v *N h The combined size of the decomposed first AWV table and second AWV table is N v *N h *(M v +M h In one embodiment, the second AWV table has a size of:

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[0008] Other embodiments and advantages are described in the following detailed description. This summary is not intended to define the invention, which is defined by the claims.

[0009] The accompanying drawings illustrate embodiments of the present invention, in which like reference numerals refer to like elements. [Brief explanation of the drawings]

[0010] [Figure 1] FIG. 1 illustrates an exemplary phased array antenna system using a reduced AWV table in accordance with an embodiment of the present invention. [Figure 2] FIG. 2 shows an exemplary diagram of an AWV for a transmit array, in accordance with an embodiment of the present invention. [Figure 3] FIG. 3 shows an exemplary diagram of an AWV for a receive array, in accordance with an embodiment of the present invention. [Figure 4] FIG. 4 shows an exemplary diagram of a uniform planar array using a reduced AWV table, according to an embodiment of the present invention. [Figure 5] FIG. 5 shows an exemplary diagram of a reduced AWV table using decomposable and non-decomposable AWVs, according to an embodiment of the present invention. [Figure 6] FIG. 6 shows an exemplary diagram of a reduced AWV table using equivalent azimuth angles to decompose the AWV table, according to an embodiment of the present invention. [Figure 7] FIG. 7 shows an exemplary diagram of beamforming / switching control using a reduced AWV table, according to an embodiment of the present invention. [Figure 8]FIG. 8 shows an exemplary flowchart for reducing the size of an AWV table using decomposable and non-decomposable AWVs, according to an embodiment of the present invention. [Figure 9] FIG. 9 shows an exemplary flowchart for reducing the size of an AWV table using equivalent azimuth angles to decompose the AWV table, according to an embodiment of the present invention. DETAILED DESCRIPTION OF THE INVENTION

[0011] Reference will now be made in detail to certain embodiments of the invention, examples of which are illustrated in the accompanying drawings.

[0012] FIG. 1 illustrates an exemplary phased array antenna system using a reduced AWV table in accordance with an embodiment of the present invention. The phased array antenna 100 has a plurality of N antenna elements 110, each fed by a plurality of phased array front-end processing units, such as front-end processing units 121, 122, and 123. The phased array front-end processing typically consists of a power amplifier (PA) and phase shifter for the transmit array and a low-noise amplifier (LNA) and phase shifter for the receive array. In the case of a TDD (time division duplex) array, the processing unit consists of an antenna switch, a PA, a TX phase shifter, an LNA, and an RX phase shifter. The phased array front-end processing unit may be an RFIC. The phased array antenna system 100 also includes a signal combiner / divider / distribution network 130 and a control and synchronization bus 140. The phased array antenna system 100 performs signal transmission and reception (150) via the signal combiner / divider / distribution network 130. An AWV table is stored for each antenna element in the antenna system 100. In one exemplary scenario 180, the AMV table for a phased array antenna with N antenna elements has a size of K*N, where K is the number of entries. h horizontal weights and M v For a table of vertical weights, the number of entries is K=M v*M h In one novel aspect, the size of the AWV table is N*M v *M h In one novel aspect, the system 100 includes a plurality of N h *N v The antenna element (110) includes a front-end processing unit (121, 122, 123), a digital controller, a phased array, a phase shifter, and a low noise amplifier, a signal combiner (130), and a control and synchronization bus 140, and the digital control of each antenna element is controlled by M v weights and M in the horizontal direction h The AWV table is decomposed into a combination of a first AWV table and a second AWV table, and the sum of the size of the first AWV table and the size of the second AWV table is N h *N v *M h *M v is smaller than.

[0013] In one embodiment 191, the system 100 determines a group of decomposable AWVs and h and W v Decompose the decomposable AWV with weight W, where W v is a function of only the elevation angle θ, and W h is a function of both the elevation angle θ and the azimuth angle φ. In another embodiment 192, the system 100

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[0014] FIG. 2 shows an exemplary diagram of an AWV for a transmit array in accordance with an embodiment of the present invention. TX array 200 has N antenna elements 210 configured with multiple phased array front-end processors, such as front-end processors 221, 222, and 223. The phased array front-end processors communicate with signal distribution network 230. Digital controllers, such as digital controllers 261, 262, and 263, each have an AWV table, such as AWV tables 271, 272, and 273. The array-wide variable amplifier and phase shifter settings corresponding to an antenna beam are called an AWV (Antenna Weight Vector). Digital controls, in conjunction with data, control, and synchronization bus 240, can provide the AWV for controlling phased array beam steering or beam shaping. Multiple AWV settings can be stored in a single AWV table within digital controls, such as digital controls 261, 262, and 263, for rapid beam steering or beam switching and synchronized control of the AWVs across the array. The central control of the array provides a pointer to a specific AWV stored in an AWV table to enable beam switching. This facilitates beam switching by eliminating the need to update the AWV for the entire array. In one embodiment, a pointer can be passed to each AWV table in advance. The beam switch pulse can be used to activate the pointer. This achieves simultaneous switching of the beams of the antenna array with precisely controlled timing (from the beam switch pulse).

[0015] FIG. 3 shows an exemplary diagram of an AWV for a receive array in accordance with an embodiment of the present invention. RX array 300 has N antenna elements 310 configured with multiple phased array front-end processors, such as front-end processors 321, 322, and 323. The phased array front-end processors communicate with a signal distribution network 430. Digital controllers, such as digital controllers 361, 362, and 363, each have an AWV table, such as AWV tables 371, 372, and 373. The array-wide variable amplifier and phase shifter settings corresponding to an antenna beam are called an AWV (Antenna Weight Vector). Digital controls, in conjunction with data / control / synchronization bus 340, can provide the AWV for controlling phased array beam steering or beam shaping. Multiple AWV settings can be stored in a single AWV table within digital controls, such as digital controls 361, 362, and 363, for rapid beam steering or beam switching and synchronized control of the AWVs across the array. In one embodiment, for a wideband phased array, the phase shifters should be replaced with variable delays.

[0016] 4 shows an exemplary diagram of a uniform planar array with a reduced AWV table according to an embodiment of the present invention. The illustrated planar structure of the phased array antenna is N v 411(N v =8) rows and N h 412(N h = 4) columns, totaling N (N = N v *N h =32) antenna elements. h ×N v In a uniform planar array of elements, the antenna elements m,n For each m,n ,m=0,1,…N v and n=0,1,…,N hThe AWV table size includes at least phase shifter settings and amplitude (gain) settings. Since each antenna has a corresponding AWV table, an array of n antenna elements will have n AWV tables. The size of the AWV table affects the size of the IC. In one novel embodiment 450, the size of the AWV table is reduced. For some applications or larger arrays, the beamwidth is very small. Therefore, many beams are required to cover the field of view. This results in a very large AWV table. The size of an AWV table with K entries is (phase shifter settings, amplitude (gain) settings) m,n ×N h ×N v is the size of K*.

[0017] As shown in the figure, the planar phased array antenna has a horizontal h 421 and vertically d v Assume that the antenna elements are structured with 422 between them. For the beam direction (θ, φ), when θ 431 is the azimuth angle and φ 432 is the elevation angle, d 1+m+nNv =[0,nd h ,md V ] where m=0,1,…,N v -1 n=0,1,…,N h -1 is. Alternatively, the position vector of antenna element (m,n) is d m,n =[0,nd h -O h ,md V -O V ] where m=0,1,…,N v -1,0 v =-(N v +1) / 2*d v n=0,1,…,N h -1,0 h =-(N h +1) / 2*d h is. The antenna amplitude pattern in the (θ,φ) direction is g AA (θ,φ)=a T (θ,φ)w It can be written (approximated) as follows: where the array response vector is [a(θ,φ)] 1+m+nNv =g(θ,φ)[e jd m,n * k(θ,φ) ] and w=[w m,n ]and

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[0018] In one novel aspect, the weight

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[0019] In one embodiment, a group of AWVs is determined to be a resolvable AWV. A resolvable elevation angle is determined, a resolvable θ is determined based on the resolvable elevation angle, and a resolvable group of AWVs is formed based on the resolvable θ. In one embodiment, a resolvable group of AWVs is a product of a resolvable first / elevation AWV and a resolvable second / azimuth AWV. A weight can be decomposed into a Kronecker product of v and h components,

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[0020] In one embodiment 462, the weight vector is:

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[0021] 5 shows an exemplary diagram of a reduced AWV table using resolvable and non-resolvable AWVs, in accordance with an embodiment of the present invention. In one novel aspect, the system generates and stores an elevation AWV table and an azimuth AWV table as an AWV table for each antenna element of a phased array antenna. In one embodiment, the elevation AWV table includes a resolved elevation AWV 511 and a non-resolvable AWV 512, and the azimuth AWV table includes a resolved azimuth AWV 516 and a non-resolvable AWV 517. In one embodiment, the resolvable AWVs are h and W v and a weight W, where W v is a function of only the elevation angle θ, and W h is a function of both the elevation angle θ and the azimuth angle φ. In one embodiment, the elevation AWV table contains the corresponding null weights W v,null 513, and the azimuth angle AWV table further includes the corresponding null weights W h,null 518. Null weight W v,null 513 and W h,null 518 has a phase shift of 0 and an amplitude equivalent to 1.

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[0022] As shown, the EL AWV table 510 is v,d The decomposed entries of and the indecomposable W of I502 v,nd entries and a null weight entry W v,null 513. AZ AWV table 520 is M506 W h,d The decomposed entries of and the indecomposable W of J507 h,nd entries and a null weight entry W h,null 518. The size of the EL AWV table is N+I+1, and the size of the EL AWV table is M+J+1. The total number of AWVs stored in the EL AWV table and the AZ AWV table is NxM+I+J. If N and M are large enough, the number of AWVs stored in the EL AWV table and the AZ AWV table is large. The actual size of the AWV table is M+N+I+J+2, which is the reduced size of the AWV table.

[0023] 6 shows an exemplary diagram of a reduced AWV table using equivalent azimuth angles to decompose the AWV table, according to an embodiment of the present invention. In one novel aspect, the system h Azimuth AWV table with azimuth AWV for weight and M at antenna boresight v Calculate the elevation AWV table with the elevation AWV for the weight to obtain the equivalent azimuth angle φ0′, where the equivalent azimuth angle φ0′ is the azimuth angle φ0 and the elevation angle

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[0024] In one setting, 601, M v Vertical weight and M h With horizontal weights, N v *N h For an antenna array with antenna elements, the AWV table is v *N h *M v *M h In one novel embodiment 610, the weight vector is N v *N h *(M v +M h ) direction

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[0025] In step 611, M at an elevation angle of 0 h An azimuth AWV table is generated having azimuth AWV versus weight. v An elevation AWV table is generated with elevation AWV versus weight. For each antenna element (m,n), the following equation is used to calculate the elevation AWV for the horizontal at an elevation of 0: h Calculate and store the beam table.

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[0026] 7 shows an exemplary diagram of beamforming / switching control using reduced AWV tables, according to an embodiment of the present invention. Beamforming (switching) control 700 includes azimuth AWV table 701 and elevation AWV table 702. Beam index increment 711 is passed to modulo 712, and beam index increment 721 is passed to modulo 722. Beam switch pulse 715 is received by azimuth pointer 713, and beam switch pulse 725 is received by elevation pointer 723. The active azimuth and elevation AWVs are in two AWV tables, azimuth AWV table 701 and elevation AWV table 702, and are indicated by active azimuth beam index 718 and active elevation beam index 728 in the azimuth AWV table and elevation AWV table, respectively. Azimuth pointer 713 indicates the active azimuth beam index and elevation pointer 723 indicates the active elevation beam index in azimuth beam index table 718 and elevation beam index table 728, respectively.

[0027] The beam vector combiner 750 combines the azimuth and elevation AWVs. In one embodiment, the composite antenna weights are:

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[0028] In one embodiment 751, phase combining is performed. v and W h The phase shifter values ​​of W are summed modulo 360 degrees. In one embodiment, for wideband phased array operation, v and W h The delay values ​​of W are summed. In one embodiment 752, amplitude (gain) adjustment is performed. Amplitude (gain) adjustment can be achieved by multiple amplifier stages, with each amplifier stage providing a limited range of gain adjustment. The total gain adjustment range is the sum of the gain adjustment ranges of all amplifier stages. When the composite gain value is W v and W hIf the gain adjustment exceeds the gain adjustment of a single stage of the amplifier, the remaining value is passed to a second amplifier for further gain adjustment, and so on, until the desired sum of the gain adjustment values ​​is achieved.

[0029] 8 shows an exemplary flowchart for reducing the size of an AWV table using decomposable and non-decomposable AWVs according to an embodiment of the present invention. In step 801, the system decomposes a decomposable group AWV into a decomposed first AWV and a decomposed second AWV for each antenna element, where a decomposable group of AWVs is a product of the decomposed first AWV and the decomposed second AWV. In step 802, the system generates and stores a first AWV table and a second AWV table as AWV tables for each antenna element of the phased array antenna, where the first AWV table includes the decomposed first AWV and the non-decomposable AWV, and the second AWV table includes the decomposed second AWV and the non-decomposable AWV.

[0030] 9 shows an exemplary flowchart for reducing the size of an AWV table using equivalent azimuth angles to decompose the AWV table, according to an embodiment of the present invention. In step 901, the system calculates M h Azimuth AWV table with azimuth AWV for weight and M at antenna boresight v In step 902, the system obtains an equivalent azimuth angle φ 0 ′, where the equivalent azimuth angle φ 0 ′ is the ratio of the azimuth angle φ 0 to the elevation angle AWV.

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[0031] Although the present invention has been described in connection with certain specific embodiments for purposes of illustration, the invention is not limited thereto. Accordingly, various modifications, adaptations, and combinations of the various features of the described embodiments can be made without departing from the scope of the invention as set forth in the claims.

Claims

1. 1. A method for reducing the size of an antenna weight vector (AWV) table for each corresponding antenna element of a phased array antenna, comprising: decomposing a decomposable group AWV for each antenna element into a first decomposed AWV and a second decomposed AWV, wherein the decomposable group AWV is a product of the first decomposed AWV and the second decomposed AWV; generating and storing, for each antenna element of the phased array antenna, a first AWV table and a second AWV table as the AWV tables, the first AWV table including the first decomposed AWV and an undecomposed AWV, and the second AWV table including the second decomposed AWV and an undecomposed AWV.

2. The decomposable AWV is W h and W v and W v is a function of only the elevation angle θ, and W h The method of claim 1 , wherein θ is a function of both the elevation angle θ and the azimuth angle φ.

3. The first AWV table and the second AWV table have corresponding null weights W that have a phase shift of 0 and an amplitude equal to 1. null The method of claim 2 further comprising:

4. determining a resolvable elevation angle; determining a resolvable θ based on the resolvable elevation angle; The method of claim 1 , further comprising forming decomposable groups of the AWVs based on the decomposable θ.

5. The method of claim 4 , wherein the resolvable θ is close to 90°.

6. The method of claim 1 , wherein each AWV includes at least a phase shifter setting and an amplitude gain setting.

7. The method of claim 6 , wherein the decomposition is applied to both amplitude and phase adjustments.

8. The method of claim 1 , wherein the first AWV table further includes an active elevation beam index and the second AWV table further includes an active azimuth beam index.

9. The method of claim 8 , wherein for the beamforming control, the active elevation beam index is indicated by an elevation pointer and the active azimuth beam index is indicated by an azimuth pointer.

10. The method further includes a step of performing beamforming control of the phased array antenna based on the first AWV table and the second AWV table, wherein the beamforming control is performed by combining the first AWV table and the second AWV table for the beamforming control. The method of claim 1.

11. 11. The method of claim 10, wherein the phase shift values ​​in the first AWV table and the second AWV table are combined modulo 360 degrees.

12. The method of claim 11 , wherein delay values ​​are added to the first AWV table and the second AWV table when performing wideband phased array operations.

13. The method of claim 10 , wherein a composite gain value is the sum of the gain adjustment values ​​in the first AWV table and the second AWV table.

14. 14. The method of claim 13, wherein the gain adjustment exceeds the range of a single stage amplifier and the remaining value is passed to a second amplifier for further gain adjustment.

15. The vertical M of each corresponding antenna element of the phased array antenna v Weight and horizontal M h 1. A method for reducing the size of an antenna weight vector (AWV) table having a weight, the method comprising: M at an elevation angle of 0 h An azimuth AWV table with azimuth AWVs for weights and M at antenna boresight v calculating an elevation AWV table having elevation AWVs for weights; Equivalent azimuth angle φ 0 ', wherein the equivalent azimuth angle φ 0 ' is the azimuth angle φ 0 and elevation angle [Equation 1] and the azimuth angle AWV (φ 0 ') and the elevation angle AWV [Equation 2] The product of [Equation 3] and wherein the value is an approximation of

16. The AWV table for each antenna element of the phased array antenna is v *N h *(M v +M h 16. The method of claim 15, wherein the phased array antenna has dimensions Nv x Nh in a uniform planar configuration.

17. The element (m, n) of the azimuth angle AWV table is [Equation 4] is calculated using The element (m, n) of the elevation angle AWV table is [Equation 5] is calculated using [Equation 6] is the wavelength, and d v is the vertical spacing of the antenna elements, and d h is the horizontal spacing of the antenna elements, and O v =-(N v +1) / 2*d v, O h =-(N h +1) / 2*d h The method of claim 15, wherein [Request Item 18] [Number 7] Using [Equation 8] The method of claim 15, wherein the calculation is

19. The method of claim 15 , wherein the azimuth AWV table further includes an active azimuth beam index and the elevation AWV table further includes an active elevation beam index.

20. 1. A system having a reduced size antenna weight vector (AWV) table, comprising: Multiple N h *N v antenna elements, each including a front-end processing unit and a digital controller; a signal combiner; a control and synchronization bus; The digital control of each antenna element is performed by M v weights and M in the horizontal direction h The AWV table is decomposed into a combination of a first AWV table and a second AWV table, and the sum of the size of the first AWV table and the size of the second AWV table is N h *N v *M h *M v Smaller than the system.

21. 21. The system of claim 20, wherein a group of decomposable AWVs is identified and decomposed into decomposed first AWVs and decomposed second AWVs, respectively, and wherein the first AWV table includes the decomposed first AWVs and undecomposed AWVs, and the second AWV table includes the decomposed second AWVs and undecomposed AWVs.

22. The decomposable AWV is W h and W v and W v is a function of only the elevation angle θ, and W h 22. The system of claim 21, wherein {overscore (θ)} is a function of both the elevation angle θ and the azimuth angle φ.

23. The AWV table for each antenna element of the phased array antenna is v *N h *(M v +M h 21. The system of claim 20, wherein the distance between the first and second electrodes is 1 / 2.

24. The element (m, n) of the second AWV table is [Equation 9] is calculated using The element (m, n) of the first AWV table is [Equation 10] is calculated using [0011] is the wavelength, and d v is the vertical spacing of the antenna elements, and d h is the horizontal spacing of the antenna elements, and O v =-(N v +1) / 2*d v, O h =-(N h +1) / 2*d h The system of claim 23, wherein [Request Item 25] [Number 12] Using φ 0 '.

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