Pixel-based reconfigurable antenna and design method

Abstract

The invention discloses a pixel-based reconfigurable antenna (PRA) and a method for designing the PRA, and particularly relates to a pixel-based reconfigurable antenna (PRA) and a method for designing the PRA. The PRA supports a total of N fluid antenna system (FAS) ports which are uniformly distributed on the linear length of the W [lambda]. The established physical model associates the correlation of the reconfigurable radiation pattern of the antenna with the spatial correlation of the physical displacement. A two-step search-optimization algorithm is provided to find the optimal configuration of the pixel layer of the PRA.

Description

[0001] Cross-reference to related applications

[0002] This application claims priority and benefit to U.S. Provisional Patent Application No. 63 / 655,830, filed June 4, 2024, the disclosure of which is incorporated herein by reference in its entirety. Technical Field

[0003] This invention relates to the field of antenna systems. Background Technology

[0004] The total mobile data traffic, including traffic generated by fixed wireless access, is expected to grow from 130 EB per month in 2024 to 403 EB per month in 2029[1]. To meet this demand, the development of the next generation of wireless communication—the sixth generation (6G)—is underway[2],[3],[4]. 6G is expected to utilize a range of technologies covering the basic electromagnetic structure, such as multiple-input multiple-output (MIMO) and reconfigurable smart surfaces (RIS), as well as artificial intelligence (AI), all of which are currently under investigation[5],[6],[7]. The development of 6G will also require the development of new technologies, and the Fluid Antenna System (FAS)[8],[9] is one such system with the potential for 6G applications, which is expected to enhance the performance of wireless systems and potentially reduce implementation costs

[10] . FAS uses liquid-based or reconfigurable antenna structures to dynamically change their physical or electrical characteristics, such as resonant frequency, radiation pattern, or polarization, to adapt to different communication scenarios. The system can use liquid metals (such as gallium-based alloys) or microfluidic technology to physically reshape the antenna. Alternatively, it can employ electronic reconfiguration techniques, such as adjustable components or software-defined controls, to adjust antenna characteristics without physical movement. While FAS uses the term "fluid," it should be noted that this term is used from a system perspective, and FAS designs can be implemented in any way, as long as it meets the system requirements of FAS.

[0005] The inspiration for FAS comes from the wireless system perspective, which has accumulated a large amount of achievements. However, so far, existing FAS implementations are still relatively scarce and mainly based on mechanical antennas, including liquid-based

[19] ,

[20] , surface wave-based

[21] , and programmable droplet-based

[22] . These schemes can achieve fine spatial sampling by moving the metal or liquid in the antenna, thus largely meeting the system specifications of FAS. However, since FAS design relies on physical fluid displacement, its reconstruction speed is inherently limited by mechanical motion, thus bringing significant performance constraints

[12] . Compared with the data packet transmission rate (about one millisecond per data packet), existing mechanical-based FAS designs are not fast enough [9] to provide packet-by-packet reconstruction capabilities.

[0006] Pixel-based Reconfigurable Antenna (PRA) is an advanced antenna system that uses a grid of small, individually controllable elements called pixels to dynamically change its radiation pattern, frequency, polarization, or other properties. This reconfigurability enables the antenna to adapt in real-time to different communication requirements or environmental conditions. The antenna is composed of a grid of small conductive elements (pixels) that can be electrically connected or disconnected using switches (e.g., PIN diodes, MEMS switches, or transistors). By controlling the state of these pixels, the physical or electrical structure of the antenna can be reconfigured. The development of PRA has a long history, dating back to its first proposal in 2004

[23] . Since then, numerous designs have been proposed that can reconfigure the mode

[24] ,

[25] ,

[26] , polarization

[27] , phase

[28] , and frequency

[29] ,

[30] . S. Song et al. proposed a method to optimize a frequency reconfigurable pixel antenna using a genetic algorithm, achieving a reconfigurable dual-band antenna that can reconfigure the 820-1140 MHz and 1720-1900 MHz frequency bands to the 860-1160 MHz and 1890-2300 MHz frequency bands on a 40 mm x 65 mm ground plane with only one switch

[30] . To obtain a wider bandwidth and enable FAS to handle stable correlations at a larger bandwidth, the number of switches needs to be increased. That is, more switch combinations need to be searched to find a combination with sufficient bandwidth. SUMMARY

[0007] The present invention aims to propose a PRA design that meets the requirements of FAS and the required switching speed. That is, the present invention proposes a new method of FAS system design using PRA design. One of the challenges of using PRA for FAS is that previous designs have not developed the ability to provide channel fine spatial sampling. Therefore, in the present disclosure, the inventors propose a new type of FAS based on PRA design, which successfully provides a method to solve channel fine spatial sampling.

[0008] In the present disclosure, PRA is also referred to as PRA-FAS or FAS throughout the specification. These names or the names of the ports named are only for the convenience of description and do not limit the scope of the claims. Other names that meet the same or similar structures or functions described in the claims can also be used to replace the equivalents. Unlike traditional FAS that relies on physical movement, the proposed FAS uses radio frequency (RF) switches to achieve the required adaptability. PRA uses electronic switching elements (such as PIN diodes) to achieve reconstruction speeds of μs, meeting the per-packet reconfigurability requirements necessary for FAS operation.

[0009] In one embodiment, the proposed design can provide 12 FAS ports in the 1 / 2 wavelength range, and is composed of an E-slot patch antenna and an upper reconfigurable pixel layer with 6 RF switches. The simulation and experimental results of a prototype based on a 2.5 GHz operating frequency show that the design can meet the requirements of FAS, including port correlation and matched impedance.

[0010] The inventors found that doubling the height of the radiating feed plate and increasing the number of switches to 7 can increase the bandwidth to 130 MHz, an increase of more than 5%. Future research on bandwidth expansion is still needed to consider other bandwidth expansion methods.

[0011] In one aspect of the present disclosure, a PRA is provided. The PRA includes a lower substrate, a ground plane attached to the bottom surface of the lower substrate, and a patch antenna attached to the top surface of the lower substrate, the patch antenna serving as a radiation source of the PRA. The radiation source is configured to be fed from the back of the ground plane by a probe. The PRA further includes a reconfigurable pixel layer disposed above the lower substrate and spaced apart from the lower substrate by a distance h airThe system comprises an upper substrate and a pixel layer consisting of multiple metal pixel patches attached to the top surface of the upper substrate. These metal pixel patches are arranged in a uniform grid pattern, with a constant spacing b between any two adjacent metal pixel patches. A patch antenna provides a reference electric field, which is then radiated after metal coupling through the pixel layer. The pixel layer structure is reconfigurable, with each reconfigurable state of the PRA corresponding to a FAS port. The PRA supports a total of N FAS ports uniformly distributed along a linear length Wλ, where λ is the wavelength, W is the number of wavelengths, and N / W > 1. The connection between any two adjacent metal pixel patches is configured as hardwired, open-circuited, or via an RF switch. The location selection of hardwired, open-circuited, and RF switch satisfies a first condition: the location selection of hardwired, open-circuited, and RF switch provides impedance matching over a specified bandwidth. N FAS ports are selected and ordered from the combinations of on / off states of the RF switch to satisfy a second condition: any two adjacent FAS ports among the N FAS ports are spatially dependent. The second condition is satisfied when the difference between the radiation mode covariance matrix of all reconfigurable states and the target covariance matrix is ​​minimized.

[0012] Alternatively, the connection between any two adjacent metal pixel patches in the uniform grid pattern constitutes a common... There are P internal ports, of which P internal ports are assigned to RF switches. Vector x represents the disconnected state (0) and connected state (1) between any two adjacent metallic pixel patches, and set S specifies the location selection of the RF switches. Thus, vector x and set S completely define the connection configuration of the pixel layer's PRA, given by the following formula.

[0013]

[0014] in,

[0015]

[0016] Where q1 to q P Specify The ordinal index in vector x of the selected positions of P RF switches in the internal ports.

[0017] Alternatively or alternatively, for all possible vectors x, the vector x is composed of... l The set S consisting of all possible sets S k , Define a 2 P A set of elements representing all combinations of on / off states of an RF switch. This set is defined in this way. The total number is gather It is a set The subsets that satisfy the first condition, the mathematical formula for the first condition is:

[0018]

[0019] Where st represents the constraint condition. It is a vector and set S k The reflection coefficient of PRA under a given connection configuration.

[0020] Alternatively, the set that satisfies the first condition. A portion of the data is selected as the candidate set for fulfilling the second condition, in order to reduce the search space.

[0021] Alternatively, the second condition may be used as the objective function δ of the genetic algorithm (GA). e The optimization objective of (D) is given by the following formula.

[0022]

[0023] st:D∈{1,2,…,M} N ,with[D] n ≠[D] n′ (30),

[0024] Where st represents the constraint condition, and the vector sequence d = [d1, d2, ..., d... N ] T Indicates from each candidate set The selection and sorting of N FAS ports from M matching patterns, and the objective function δ e (D) is given by the following formula.

[0025]

[0026] Where Δ(D) is the total absolute error given by the following formula.

[0027]

[0028] in, It is the radiation mode covariance matrix The (n, n′)th element, and It is the target covariance matrix The (n,n′)th element.

[0029] Alternatively, when frequency is taken into account to meet bandwidth requirements, formula (18) can be replaced with

[0030]

[0031] And formula (26) can be replaced with

[0032]

[0033] in, f l It is the lower limit, f u It is the upper limit, and T represents the sampling frequency.

[0034] Alternatively or optionally, Given by the following formula

[0035]

[0036] Where J0 is a first-order, zero-order Bessel function.

[0037] Alternatively or optionally, The impedance matrix Z represents the impedance matrix Z. Composed of an internal port and a single external power supply port The impedance of each port, and The impedance matrix Z is expressed as

[0038]

[0039] Among them, Z i,j (f) indicates The elements of the impedance matrix Z, where f is the frequency, 0 represents a single external feed port, and 1 to... yes There are internal ports, and among them, and yes The four submatrices of the impedance matrix Z.

[0040] Alternatively, the input impedance of the PRA can be calculated as follows:

[0041] Z in (x,S)=z E -Z EI [Z I +Z L (x,S)] -1 Z IE (15),

[0042] Among them, Z L (x,S) is A diagonal matrix, which represents the concatenation configuration determined by vector x and set S. The impedance of each internal port.

[0043] Alternatively or optionally, the reflection coefficient Given by the following formula

[0044]

[0045] Where Z0 represents the characteristic impedance, and It is made of vectors and set S k The input impedance of the PRA under a given connection configuration.

[0046] Alternatively or optionally, When The open-circuit radiation mode excited by the unit current at port q when all other ports in the q-th port are disconnected is given by the following equation.

[0047]

[0048] Where θ and φ represent the elevation and azimuth angles in spherical coordinates, respectively, and Ω = (θ, φ). For The combination consists of the open-circuit radiation mode matrix E OC It is expressed as given by the following formula.

[0049]

[0050] Alternatively, the radiation mode covariance matrix Represented as

[0051]

[0052] in, It's Hadamard division, a matrix. The average energy of all M matching patterns is represented and used for normalization, and the (i,j)th element of matrix G is represented as...

[0053]

[0054] Where matrix C is the absolute correlation matrix of all M matching patterns, defined as follows:

[0055]

[0056] in, It is the correlation matrix of all open-circuit radiation modes weighted by S(Ω), where S(Ω) is the power angular spectrum (PAS), and E... OC It is the open-circuit radiation mode matrix, and I = [i1, i2, ..., i M ] is the current matrix, where i1, i2, ..., i M It is the current vector of all M matching modes, each vector is given by the following equation.

[0057]

[0058] Alternatively or optionally, Given by the following formula

[0059]

[0060] Where S(Ω) is the power angular spectrum PAS, e n (Ω) represents the current vector i of the nth current vector. n The FAS radiation mode of the nth port of the N FAS ports is excited, and e n′ The complex conjugate of (Ω). n (Ω) is represented as

[0061]

[0062] Among them, E OC It is the open-circuit radiation mode matrix, and the nth current vector i n The following formula is derived

[0063]

[0064] Alternatively or optionally, P = 6, and the number of candidate sets that satisfy the second condition is approximately 100.

[0065] Alternatively or optionally, the upper substrate and the lower substrate are of size P. s ×P s A square prism of length ×h has a side length P. s With height h, each metal pixel patch is a square with side length a, arranged in a uniform grid pattern of N. s ×N s Square configuration, the number of internal ports is determined by Provided.

[0066] Alternatively, the patch antenna may be an E-slot patch having a first slot and a second slot, the first slot and the second slot respectively extending from the L-slot patch. p ×W p The long side of the rectangular radiating surface extends inward. Both the first and second slots are slender rectangles with dimensions L and L respectively. s ×W s .

[0067] Alternatively, the RF switch is controlled by a DC control line arranged around the boundary of the PRA, wherein capacitors replace a portion of the hardwired portion, and inductors occupy the feed point and open portion of the DC control line. These capacitors and inductors provide isolation between the DC control signal and the RF signal.

[0068] In another aspect of this disclosure, a method for designing a PRA is provided. The pixel layer structure of the PRA is reconfigurable, and each reconfigurable state of the PRA corresponds to a FAS port. The PRA supports a total of N fluid antenna system FAS ports uniformly distributed over a linear length of Wλ, where λ is the wavelength, W is the number of wavelengths, and N / W > 1. The method includes: selecting the positions of hardwired, open-circuited, or RF-switched contacts between any two adjacent metallic pixel patches in the pixel layer to satisfy a first condition, wherein the selection of hardwired, open-circuited, and RF-switched contacts provides impedance matching over a specified bandwidth; and selecting and sorting N FAS ports from combinations of on / off states of the RF switches to satisfy a second condition, wherein any two adjacent FAS ports among the N FAS ports are spatially dependent. The second condition is satisfied when the difference between the radiation mode covariance matrix of all reconfigurable states and the target covariance matrix is ​​minimized.

[0069] Alternatively or additionally, the method may also include selecting a set that satisfies the first condition. A portion of the data is used as a candidate set to achieve the second condition, thereby reducing the search space.

[0070] Other exemplary embodiments are discussed in this article. Attached Figure Description

[0071] Embodiments of this disclosure will now be described by way of example only with reference to the accompanying drawings, in which:

[0072] Figure 1A A typical FAS system with N FAS ports on Wλ is shown according to an embodiment of the present disclosure.

[0073] Figure 1B It shows according to Figure 1A Channel gain at different FAS ports of the system.

[0074] Figure 1C It shows according to Figure 1A The channel gain of the two base stations on different FAS ports of the system.

[0075] Figure 2 The configuration of PRA-FAS according to an embodiment of this disclosure is shown.

[0076] Figure 3 It shows the basis according to Figure 2 The configured pixel layer configuration includes the spacing between adjacent metal pixel patches. A potential connection.

[0077] Figure 4 An equivalent circuit model of the RF switch MA4AGP907 is shown.

[0078] Figure 5 An embodiment of the present disclosure is shown with a single external power supply port and Equivalent circuit model of PRA-FAS with internal ports.

[0079] Figure 6 An optimized configuration of PRA-FAS according to an embodiment of the present disclosure is shown.

[0080] Figure 7 It shows Figure 2 The simulation of the reflection coefficient of the 12 states of the PRA-FAS proposed in the paper varies with frequency.

[0081] Figure 8A It shows Figure 6 The ideal objective covariance matrix of the PRA-FAS proposed in the paper has N=12 states, where W=0.5.

[0082] Figure 8B It shows Figure 6 The covariance matrix of the N=12 states simulation of the proposed PRA-FAS is given, where W=0.5 and the average relative error is δ. e =0.063.

[0083] Figure 8C It shows Figure 8B The simulation results and Figure 8A The absolute error between the target covariance matrices.

[0084] Figure 9 The simulated pixel layer current distribution for PRA-FAS states numbered 1, 2, 11, and 12 at 2.5 GHz is shown.

[0085] Figure 10 Simulated radiation patterns for states 1, 2, and 12 at 2.5 GHz are shown, depicting e θ (Ω) and e φ (Ω) Two polarization components.

[0086] Figure 11 The maximum realized gain and total efficiency for all 12 states at 2.5 GHz are shown in the simulation and measurements.

[0087] Figure 12A A prototype of the proposed PRA-FAS according to an embodiment of the present disclosure is shown.

[0088] Figure 12B It shows Figure 12A A top view of the pixel layer of PRA-FAS in the image.

[0089] Figure 12CThe measurement setup is shown, which demonstrates... Figure 12A The PRA-FAS proposed in the paper is controlled by an FPGA.

[0090] Figure 13 It shows Figure 12A The measured reflection coefficient of the PRA-FAS prototype in 12 states varies with frequency.

[0091] Figure 14A The simulated and measured radiation pattern for state 1 at 2.5 GHz is shown, where the plane has the maximum e when φ = 40°. φ (Ω)(unit: dBi).

[0092] Figure 14B The simulated and measured radiation pattern for state 1 at 2.5 GHz is shown, where the plane has a maximum e when φ = 130°. θ (Ω)(unit: dBi).

[0093] Figure 15 The measurement covariance matrix for the 12 PRA-FAS states is shown.

[0094] Figure 16 The evolution of time-varying signals received by 12 PRA-FAS ports, obtained through simulation, is shown.

[0095] Figure 17 The simulation ensemble average port correlation of PRA-FAS is shown by formulas (7) and (8).

[0096] Figure 18A The setup for the proposed PRA-FAS FAS port correlation experiment is shown, and the transmitter of the MIMO test platform with two dipoles is displayed.

[0097] Figure 18B The setup for the FAS port correlation experiment of the proposed PRA-FAS is shown, and the receiver of the MIMO test platform, including the proposed PRA-FAS and the dipole, is shown.

[0098] Figure 18C The setup for the FAS port correlation experiment of the proposed PRA-FAS is shown, and the indoor testing environment scheme of the proposed PRA-FAS is illustrated.

[0099] Figure 19 The diagram shows 12 PRA-FAS states (ports) for three different stable channels. and (2 FAS channels)

[0100] Figure 20The theoretical Bezier curve in Equation (9) and the average port correlation of the measurement ensemble of PRA-FAS are shown.

[0101] Figure 21 A method for designing a PRA-FAS according to an embodiment of the present disclosure is shown.

[0102] In the accompanying drawings, similar reference numerals are used for similar elements to aid in understanding. Detailed Implementation

[0103] The present disclosure will now be described with reference to the following embodiments, which should be considered illustrative rather than restrictive in all respects. In the accompanying drawings, corresponding features in the same embodiment or corresponding features common to different embodiments have the same or similar reference numerals.

[0104] Throughout the specification and claims, terms such as "comprising" and "including" should be understood as inclusive rather than exclusive or exhaustive; that is, they should be understood as "including, but not limited to".

[0105] Furthermore, as used herein, unless otherwise stated, the use of ordinal adjectives such as “first,” “second,” etc., to describe common objects merely indicates different instances of similar objects referred to, and does not imply that the objects described must be in a given order (whether in time, space, ordering, or any other way).

[0106] The terms “upper,” “lower,” “top,” and “bottom” used in the specification and claims are used only to clearly describe the relative positions of the elements in the illustrated embodiments. These directional references are not intended to limit any element to being only above, below, top of, or bottom of another element. For example, a device including these elements may be inverted, rotated, or otherwise oriented such that a described “top” may become a “bottom,” and vice versa, without departing from the scope of this disclosure.

[0107] For the sake of brevity, unless otherwise specified, explicit dependencies of frequency on electromagnetic quantities such as impedance and radiation modes are omitted. Bold letters represent matrices or vectors, and non-bold letters represent scalars. θ and φ represent spherical coordinates, called elevation and azimuth, where... and This is a unit spherical coordinate vector. [A] i It is the i-th element of vector A, and [A] is... i,j A T and A H These are the (i,j)th element, transpose, and conjugate transpose of matrix A, respectively. The letters in mathematical calligraphy represent sets. Sets The cardinality is denoted as δ(·) represents the impulse function. UN It is an N×N identity matrix. diag(a1,a2,…,a…) N ) represents a diagonal matrix with diagonal elements a1, a2, ..., a3. N .

[0108] The theoretical basis, implementation method, device embodiments, simulation and experimental results of this disclosure are described in detail below.

[0109] The most straightforward form of FAS can be considered as a single antenna element that can be physically moved or reconfigured between N predefined port locations (referred to as FAS ports). Here, the term "FAS port" is used for descriptive purposes only, to distinguish it from other ports in the specification. In fact, the FAS ports in this disclosure embody certain FAS performance characteristics, but their implementation is not limited to FAS systems, nor are they explicitly designated as FAS-specific. These ports are uniformly distributed over a linear length Wλ, where λ is the wavelength and W is the number of wavelengths. Figure 1A The system diagram of its implementation is shown [8], [9]. At any given time, only one FAS port can be accessed. In a scattering-rich environment, the channel gain of each FAS port is expected to follow a Rayleigh distribution, exhibiting spatial correlation. Since the ratio N / W >> 1, the FAS port can finely sample Rayleigh fading spatial signals, such as Figure 1B The solid dots in the diagram are shown. In a preferred embodiment, N / W > 10. Due to fine spatial sampling, the spatial channel correlation between adjacent ports of the FAS port is readily apparent. FAS utilizes this channel correlation characteristic to enhance wireless communication performance.

[0110] Figure 1C An example of how fine spatial sampling can be performed using a channel is shown in a multi-user, scatter-rich environment where the FAS receives signals from two base stations

[11] . Since the base stations are far apart, the signal fading observed by the FAS will be different for each base station. Therefore, the FAS can select a spatial port where the signal from the desired base station is strong and the signal from the interfering base station is weak, such as... Figure 1C Point A is shown in the figure. That is, by carefully selecting the FAS port location, the signal-to-interference ratio (SIR) can be significantly improved, thereby enhancing communication performance. More generally, it has been proven that using FAS for multiple access (called Fluid Antenna Multiple Access (FAMA)) can bring the performance of two users close to optimal

[12] ,

[13] . In addition, FAMA can be used in combination with other communication technologies, including millimeter-wave (mmW) communication, RIS, MIMO and non-orthogonal multiple access (NOMA)[9],

[14] ,

[15] ,

[16] ,

[17] ,

[18] . FAMA is just one possible example of how FAS can be utilized, and other scenarios are also under investigation.

[0111] A. PRA-FAS design theory

[0112] A.1 Typical FAS statistical model

[0113] First, a statistical model of a typical wireless environment is introduced, defined as a scattering-rich environment in which there is no dominant line-of-sight (LoS) component

[31] ,

[32] . Figure 1A As shown, the FAS antenna consists of a single movable or shaped radiator capable of switching between N FAS ports (also referred to in the specification as N PRA-FAS ports, N PRA-FAS states, or N states) uniformly distributed along a linear length of Wλ. Consider the case of a single RF chain, where only one port can be activated at a time due to the necessary physical movement of the radiator elements.

[0114] To analyze the FAS antenna, the open-circuit voltage received at the nth FAS receiver port is represented as g. n It follows a circularly symmetric complex Gaussian distribution with a mean of zero and a variance of σ. 2 Because in a rich scattering environment, the channel follows Rayleigh fading. The open-circuit voltages received at all N ports are represented as a vector g = [g1, g2, ..., g N ] T .

[0115] To describe the characteristics of fine spatial sampling in FAS, it is necessary to obtain g. n The statistical relationship between them. To this end, a FAS channel model describing the correlation between ports in FAS is proposed

[33] . This model uses the spatial covariance matrix. This is implemented where each element quantifies the correlation between a pair of ports. For example, denoted as ρ i,j , representing the correlation between the i-th port and the j-th port, and is usually represented as

[0116]

[0117] Where J0 is a zero-order Bessel function of the first kind, and Cov(·,·) is the covariance between the two quantities. It can be regarded as a Clarke model that follows mobile radio propagation

[31] .

[0118] A.2 From traditional FAS to "fluid" radiation pattern

[0119] Traditional antenna arrays (FAS) that rely on physical motion are limited by slow port switching speeds when used in wireless communication. To address this issue, the physical model of FAS needs to be re-examined to establish a physical model that links the correlation of the antenna's reconfigurable radiation pattern with the spatial correlation of physical displacement. This relationship will guide the design of new FAS models that can achieve faster switching speeds.

[0120] In order to link the requirements specified in formula (1) with the radiation mode, it is necessary to define the electromagnetic environment.

[0121] The incident radiation at FAS is expressed as...

[0122]

[0123] Where Ω = (θ, φ). The corresponding polarization matrices are represented as

[32] and

[34] .

[0124]

[0125] in, And similarly applicable to Γ θ,θ (Ω,Ω′), Γ φ,θ (Ω,Ω′) and Γ φ,φ (Ω,Ω′).

[0126] In the scattering-rich scenario, the incident radiation is modeled where the two polarization components are uncorrelated and have equal power, therefore Γ φ,φ =Γ θ,θ , and Γ φ,θ and Γ θ,φ The polarization matrix is ​​zero. Γ(Ω,Ω′) is a diagonal matrix. Furthermore, it is assumed that the spatial components are also uncorrelated, and the resulting polarization matrix is ​​expressed as...

[0127] Γ(Ω,Ω′)=S(Ω)U2δ(Ω-Ω′) (4),

[0128] Where S(Ω) is the power angular spectrum (PAS).

[0129] By using formula (4), different ports g were obtained. n The statistical relationship between them. In the case of rich scattering, the i-th and j-th ports g i and g j The correlation coefficient of the open-circuit voltage can be expressed as:

[0130]

[0131] Wherein, we assume the expected value ε[g] nAll are zero. The voltage at the port can be represented by the FAS mode and incident radiation at the nth port, as shown in

[32] and

[34] .

[0132]

[0133] in, It is the FAS radiation mode of the nth port. The scaling constant a is given in

[34] and

[35] , but is not required as it will be removed later. Using (5) and (6), the correlation expression can be expressed as

[0134]

[0135] For convenience, formula (5) does not include a denominator term. Applying a rich scattering scenario

[31] ,

[32] , using formula (4) and swapping the order of the integral and expectation, the final expression for the port correlation is:

[0136]

[0137] Equation (8) implies that the correlation characteristics between two FAS ports depend only on the antenna mode and the scattering environment through its PAS. It also proposes an alternative interpretation of the FAS that captures the flexible definition of an antenna in terms of shape and location, namely, that a fluid antenna in the FAS can be considered equivalent to a “fluid” radiation mode. This provides the theoretical basis for the second condition to be discussed in subsequent chapters. Specifically, the radiation modes of different FAS ports can be converted or configured to satisfy the desired FAS port correlation relationship, such as the relationship given in Equation (1).

[0138] To provide an example of the equivalence between a shape- and position-flexible antenna and an antenna with a “fluid” radiation mode, a typical example of two vertically polarized dipoles (where incident radiation is confined to a two-dimensional (2D) plane) can be analyzed, such that S(Ω) = δ(θ). Assume that all ports of the FAS act as vertically polarized dipoles, spaced apart from each other in the horizontal plane. If the mode of the i-th port is defined as Then the j-th port can be obtained by phase shifting. Using (8), the correlation can be obtained as follows:

[0139]

[0140] For convenience, the denominator term in equation (8) is not included in the first row. It can be seen that the same result as equation (1) is obtained, indicating that changing the FAS radiation mode can achieve the same result as moving the dipole antenna in a scattering-rich environment.

[0141] Equation (8) and example (9) show that port correlations can be obtained using patterns, and these correlations depend on the specific scattering environment of the PAS used. More generally, Equation (8) applies to FAS ports with arbitrary radiation patterns. In summary, developing a PRA-FAS with a sufficient number of states, where the radiation pattern of each state follows a specific correlation relationship (5), can effectively meet the requirements of the FAS.

[0142] A.3 PRA-FAS design goals

[0143] Using formula (8) and example (9), the overall design objective of the PRA-FAS can now be defined. The objective is to design a FAS with n reconfigurable states such that the elements in formula (8) are identical to those specified in formula (1) for the desired FAS covariance given W. A subtle aspect of the design objective is that the selection of states must also be arranged in an appropriate order to satisfy formula (1). Furthermore, the state switching of the system must be electronically controlled to achieve the necessary packet-level switching speed required for a high-performance FAS.

[0144] This document discloses the aforementioned correlation requirements. It should be noted that other correlation functions are also within the scope of this disclosure. In one embodiment, the objective is to satisfy the conditions specified in formula (1). It is also worth noting that a significant advantage of the proposed design method is its versatility and its potential to match any desired FAS covariance.

[0145] In one embodiment, the specific objective is to design a PRA-FAS where N = 12 and W = 1 / 2. This means that it is necessary to design such a PRA-FAS using formula (8), which has an N = 12 radiation mode that satisfies the conditions specified in formula (1), where W = 1 / 2. Detailed implementation will be discussed in later chapters.

[0146] B. Proposed PRA-FAS geometry and model

[0147] To meet the design objectives, the proposed PRA-FAS geometry 200 is... Figure 2 As shown in the diagram, the PRA-FAS geometry 200 includes two dielectric substrates: a lower substrate 210 and an upper substrate 220 disposed above the lower substrate 210. In one embodiment, both the upper substrate 210 and the lower substrate 220 are made of Rogers 4003C material, with a dielectric constant of ∈ r =3.55 and the loss tangent is tanδ d =0.0027. In a preferred embodiment, the lower substrate 210 and the upper substrate 220 are P s ×P s ×h square prism, side length P s=80mm, height h = 1.524mm. The separation distance between the upper substrate 220 and the lower substrate 210 is h. air =12mm. Those skilled in the art should understand that the dimensions and shapes in this specification are illustrative and not restrictive. The ground plane 290 almost completely covers the bottom surface of the lower substrate 210. The patch antenna 230 is attached to the top surface of the lower substrate 210. The patch antenna 230, as a radiation source for the PRA, is configured to be fed from the back of the ground plane via a signal feed probe 280. The signal feed probe 280 is located on... Figure 2 The text is represented by grid lines.

[0148] Probe feeding is a common excitation method in antenna engineering, in which a conductive probe (typically the inner conductor of a coaxial cable) transmits an RF signal from a ground plane 290 to a radiating element, such as a patch antenna. The RF signal is transmitted through the coaxial cable, and its inner conductor (the probe) couples energy to the patch. The probe typically passes through a hole in the ground plane, but it remains electrically isolated from ground to avoid short-circuiting the signal.

[0149] In one embodiment, the patch antenna 230 is shaped like an E-slot patch 2300. From a top view, the first slot 231 and the second slot 232 extend inward from the long side 2301 of the rectangular radiating surface of the E-slot patch 2300, along a direction parallel to the short side of the rectangular radiating surface. The length of the rectangular radiating surface is L. p =50mm, width is W p = 30.6mm. Each slot 231, 232 is a long, narrow rectangle with a length L. s =12mm and width W s =2mm. The signal feed probe 280 is located at a distance d from the first long side 2311 of the first slot 231, which is away from the boundary of the E-slot patch 2300. p =19.4mm, and the distance d from the long side 2301 of the E-slot patch 2300. f =10.7mm.

[0150] Pixel layer 2200 is attached to the top surface of upper substrate 220 and includes a plurality of metal pixel patches 240 printed on pixel layer 2200. E-groove patches 2300 serve as radiation sources for pixel layer 2200. Different radiation characteristics can be obtained by employing different connection configurations among the metal pixel patches 240 in pixel layer 2200. Each metal pixel patch 240 is square in top view, with a side length a = 7 mm. The shape of the metal pixel patches can exceed square geometry, including non-square configurations arranged in a periodic pattern. In a preferred embodiment, the metal pixel patches 240 are arranged in N... P ×N PA uniform grid pattern, with a constant spacing b = 4mm between any two adjacent metal pixel patches 240, where N s =6. Therefore, there is a certain distance between any two adjacent metal pixel patches 240. Possible connection locations, and this can be referenced. Figure 3 As seen, patch antenna 230 provides a reference electric field, which is then radiated after being metal-coupled through pixel layer 2200. The structure of pixel layer 2200 is reconfigurable by different configurations at the aforementioned possible connection locations, and each reconfigurable state of PRA-FAS 200 corresponds to a FAS port.

[0151] To construct a complete PRA-FAS, ideally, all the metal pixel patches 240 between any two adjacent patches would be... Each connection should be controlled by an RF switch up to 250, thus allowing a maximum of Such a configuration (ignoring symmetry), and therefore has One radiation mode. However, controlling a large number of RF switches 250 would require a complex DC feed network

[24] , thus affecting the antenna's performance in terms of efficiency

[36] . To reduce complexity, a strategy has been proposed to deploy a limited number of An RF switch 250 is used, and other connections between pixels are fixed by hardwire 260 or open circuit 270. In this respect, the connection between any two adjacent metallic pixel patches is configured as hardwired, open circuit, or implemented via RF switch 250. For example... Figure 2 As shown, in a preferred embodiment, there are P=6 RF switches 250 between any two adjacent metal pixel patches 240, where the choice of P strikes a good balance between design flexibility and complexity. A more detailed discussion of how to choose the number of switches will be explained in later sections. Using P=6, this can provide a maximum of 2 P =64 radiation modes, of which 12 radiation modes must be selected as 12 FAS ports that are well matched and meet the spatial correlation requirements in formula (1).

[0152] Figure 2The described structure is proposed primarily for two reasons. First, PRA-FAS typically ensures good matching of various configurations of pixel layer 2200. Equation (8) can be used to select radiation modes that meet the correlation criteria specified in Equation (1). Second, since the size of a single metal pixel patch 240 is only one-tenth of the wavelength λ, the similarity of radiation modes can be controlled by controlling the shape and number of connections consisting of RF switch 250, hardwire 260, and open circuit 270, thereby allowing for the management of correlation coefficients. If the metal pixel patches 240 (pixel patterns) connected in two states have similar shapes and differ only slightly in number, they can achieve high correlation, making them suitable for adjacent FAS modes, such as ρ 1,2 As illustrated by ≈1. Conversely, significant differences in pixel patterns can achieve the low correlation required for spatially distant FAS patterns, such as close to zero (ρ). 1,N The correlation coefficient is shown as ≈0.

[0153] To obtain 250 RF switches with P units and The configuration of a PRA-FAS, which includes hard-wired 260 and open-circuit 270, should specify the connection status. Therefore, binary variables... Used to indicate whether the q-th connection is broken ("0") or connected ("1"). The states of each connection can be represented as a vector:

[0154]

[0155] Since the connection between any two metal pixel patches 240 can be a switch connection (via 250) or a fixed connection (via 260 or 270), it is also necessary to distinguish them in formula (10). This is needed later because the impedance of the switch is different from that of the hardwire. The most straightforward method is to specify which connections are RF switches 250. This can be achieved by specifying a set containing the number of connections for the number of RF switches 250. For P RF switches 250, these locations can be given by connection number P and specified by set S.

[0156]

[0157] Among them, elements q1 to q P This indicates the connection number of RF switch 250. That is, q1 to q... P Specify The ordinal index of the selected position of P RF switches 250 in the vector x in each connection. A connection is also defined as An internal port, such as Figure 3 As shown, and the The internal ports will be discussed later. The vector x and set S fully define the configuration of pixel layer 2200 in PRA-FAS.

[0158] The connection state between any two adjacent metal pixel patches 240 in this PRA-FAS can also be represented by an impedance matrix. For a specific x and S, the diagonal Impedance matrix Used to indicate connections. Off-diagonal elements are all zero because there is only a connection between two adjacent metallic pixel patches 240. (Regarding...) (i.e., those connections that are either hard-wired 260 short-circuited or open-circuited 270), impedance matrix elements Set it directly to zero or ∞, depending on x. q The value is either 1 or 0. For the six connections with RF switch 250, as specified in S, the on and off impedances of RF switch 250 are required. In a preferred embodiment, an RF PIN diode MA4AGP907

[37] is used. Figure 4 The equivalent circuit models for the on and off states are given. Therefore, for these connections q∈S, the elements... Set as Figure 4 The “on” or “off” impedance shown is represented by the corresponding element x. q Specify whether to use 1 or 0.

[0159] With the connection impedance between any two adjacent metal pixel patches 240 specified, a circuit model for PRA-FAS can be provided, such as... Figure 5 As shown. The technique utilizing this model was previously known as the Internal Multiport Method (IMPM)

[30] . In IMPM, it can be represented using the method of... Internal ports (representing) Composed of a load impedance connection and an external port (single external feed port) The PRA-FAS is a port numbered 1. The model is accurate as long as the coupling between loads is negligible, which is generally valid

[30] . (where 0 represents a single external power supply port, and 1 to...) (These are internal ports). The voltage at the q-th port is represented as V. q And it is related to its current i q Related. All v q and i q Grouped into vectors

[0160]

[0161] Where v0 and i0 are the voltage and current of a single external power supply port (port 0), and Defined respectively Voltage and current vectors of each internal port.

[0162] The impedance of a single external feed port and an internal port is denoted by Z, which is a... A matrix that gives these voltages and currents the following relationship

[0163]

[0164] in, and Is it like this? Figure 5 shown The impedance matrix Z has four submatrices. Specifically, the impedance matrix Z can be represented as...

[0165]

[0166] Among them, Z i,j (f) indicates The elements of the impedance matrix Z, where f is the frequency. The voltage and current at the q-th internal port can be derived using the corresponding load impedance: Therefore, the voltage and current on all internal ports can be expressed as

[0167] v I =-Z L i I (14).

[0168] For a given connection vector x and set S, the input impedance of PRA-FAS can be calculated as follows:

[0169] Z in (x,S)=Z E -Z EI [Z I +Z L (x,S)] -1 Z IE (15),

[0170] Among them, Z L (x,S) is the corresponding diagonal matrix representing the impedance of all internal ports, whether short-circuited (via hardwire 260), open-circuited (via open-circuit 270), or switched on / off in a certain configuration (via RF switch 250).

[0171] The subsequent radiation modes of PRA-FAS can also be directly found. Using the port current vectors, the open-circuit radiation modes caused by the current at each port can be summed to obtain the total radiation mode. Assuming that in the N operating states of PRA-FAS, the nth current vector i...n The nth radiation mode e n (Ω) is

[0172]

[0173] in, It is the open-circuit radiation mode excited by a unit current at the q-th port when all other ports are disconnected, and the open-circuit radiation mode matrix is... Indicates for of The combination of current vector i. n The following formula can be used to obtain

[0174]

[0175] Therefore, the covariance matrix of N states It can be calculated using formula (8), where the (i,j)th element

[0176] Using the proposed geometric and circuit model, equations (15) and (16) can be used to obtain the input impedance and radiation mode of the PRA-FAS for a given x and set S. The next step is to find the switching position S and state x that best meet the PRA-FAS design objectives defined at the end of Section A. This will be described in the next section.

[0177] C. PRA-FAS analysis and design

[0178] Using the expressions for impedance and radiation modes from the previous section, the antenna performance under all possible states x and switching positions S needs to be analyzed to obtain those that meet the PRA-FAS design objectives. However, the number of vectors x and sets S is enormous. Figure 2 Taking the PRA-FAS model in the example, for There are 2 possible internal ports. 60 There are several possible states x. Furthermore, if there are P = 6 switches, then the possible set S of switches or their positions has... There are several possibilities. Therefore, the total number of possible configurations that need to be analyzed is [number missing]. In other words, there is a huge number of possible configurations. Therefore, it is necessary to develop a method that can efficiently select the appropriate internal port state x and set S.

[0179] This disclosure employs a two-step approach. Specifically, it proposes a two-step search-optimization algorithm to find the optimal configuration of pixel layer 2200. The first step involves finding a set S and a subset of states x that provide necessary impedance matching over a specified bandwidth. That is, the location selection of hardwired 260, open-circuit 270, and RF switch 250 should provide necessary impedance matching over the specified bandwidth. In the second step, these subsets of sets S and states x are searched to find 12 switch states, and the optimal selection and ordering that satisfies the proposed design objective is determined. Specifically, the selection and ordering of N FAS ports from the combinations of on / off states of RF switch 250 should satisfy a second condition, which states that any two adjacent FAS ports among the N FAS ports are spatially correlated. This second condition is satisfied when the difference between the radiation mode covariance matrix of all reconfigurable states and the target covariance matrix is ​​minimized. Those skilled in the art will understand that other methods can also be considered to describe the correlation. Figure 2 and Figure 3 Taking the PRA-FAS design as an example, where P = 6, The following describes these two steps.

[0180] C.1 Step 1: Select matching states

[0181] For a given x l and S k The pixel surface is fully defined. However, the position S k The RF switch 250 at the location can be reconfigured into 2 6 x has 4 possible states, therefore x l It can be easily refactored into 2 6 Any one of these states. For convenience, define a state containing a given x. l and S k All 2 6 A set of states In other words, sets Including position S k The states x where the element at position x can take all possible values l (The size of the set is 2) 6 For a given x l have a set And across all possible states, there are a total of A possible set

[0182] gather Not all 2 6Each state will have the required impedance matching within the desired bandwidth. This is because the driving element can adversely affect the matching of certain pixel combinations. Therefore, in this step, the task is to select only those sets with sufficient matching states. for The set is considered the expectation set, and the number of matching states in the set should exceed N. With this in mind, the following is defined: As a set A subset of the matched states. Therefore, the first condition can be expressed as

[0183]

[0184] Where st represents the constraint condition. It is the reflection coefficient of the state.

[0185]

[0186] Where Z0 is the characteristic impedance.

[0187] Then, set In the remainder of this disclosure, those sets are formally defined as satisfying formula (18) and constraint (19).

[0188] gather The number can be very large. However, it is not necessary to find all of them that meet the matching requirements. Sets. Only a sufficient number of sets are needed to provide a sufficiently high chance of satisfying the selection and sorting objectives in the second step. Therefore, sets that satisfy the first condition... A portion of the selection is used as a candidate set to proceed to the next step, reducing the search space. Typically, inventors find only about 100 matching sets. This is sufficient to proceed to the next step. Therefore, the purpose of step 1 is not only to find a matching configuration, but also to reduce the search space for the next step. Reduced to 100. Those skilled in the art will understand that the choice of the number 100 in this document is purely exemplary and should not be construed as restrictive.

[0189] C.2 Step 2: Meet spatial covariance requirements

[0190] The set of matches obtained from step 1 The optimal set should be selected, and these sets should be chosen from... From the M matching states, N matching states are selected to satisfy the spatial correlation objective in formula (1). Furthermore, this step requires a sorting process, where the N states are mapped to the number of FAS ports that best conform to formula (1). That is, not only... From its M matching states, N matching states are selected, and the selected N states should be arranged in a specific order.

[0191] To begin step 2, we need to find each set. The correlation between states in the set. To perform this step, it is necessary to use formula (16) for each set. Obtain all M radiation modes. This will place a heavy burden on the computation, as it will also require applying Equation (8) to each Calculate M(M-1) / 2 times. To make this process more computationally efficient, we can utilize previous research—the relevant pattern correlation decomposition method (PCDM)

[38] .

[0192] In PCDM, all current vectors of M reconfigurable states can be collected in a matrix I = [i1, i2, ..., i...]. M The total radiation modes can be represented compactly as E = [e1, e2, ..., e] . M The relationship between E and I is given by the following formula:

[0193] E = E oc I (21).

[0194] E oc This is the open-circuit radiation mode matrix discussed in the previous section. This allows for the radiation mode covariance matrix of all M PRA-FAS states. (represented as) (For distinguishing purposes) as

[0195]

[0196] in, This is Hadamard division, and C is the absolute correlation matrix of all M matching patterns, defined as...

[0197]

[0198] in, This is the correlation matrix of all open-circuit radiation modes after PAS weighting. Let G represent the average energy of all M modes, used for normalization. The (i,j)th element of G is denoted as...

[0199]

[0200] Formulas (22) to (24) provide a direct method for finding pattern correlations, eliminating the need for formula (16). This is because K ocFor PRA-FAS, it only needs to be found once. Then, all spatial correlations of all searched pixel configurations can be found directly using formulas (22) to (24), since the current I has already been obtained when the PRA-FAS impedance is determined using formula (17).

[0201] The next task in step 2 is to find the possible From the available states M, N = 12 states are selected to best satisfy the spatial correlation objective (1). This task is complex because both the selection and ordering of states are crucial to satisfying the spatial correlation objective (1). Therefore, a vector sequence D = [d1, d2, ..., d...] is used. N ] T The goal is to capture and sort N states from M states. Each element in D is in the range 1 to M, and each value can only be used once. Therefore, the state sequence of D has N states! A combination. The nth element of D acts as [D] from the nth FAS port to the PRA-FAS state. n The mapping. It is recommended to search all possible D to find the sequence that produces the closest match to formula (1).

[0202] Matched quantization is performed by defining a function as the difference between the radiation mode covariance matrix generated by the proposed PRA-FAS design and the target covariance matrix. The target covariance matrix used here is defined as... Its (n,n′)th element is represented as

[0203]

[0204] Based on the given D, take the formula (22) The terms in the matrix form the radiation mode covariance matrix for N states. Since the phase of the FAS port correlation is not a term of interest, the absolute value of each term in the radiation mode covariance matrix for a given port order D is used. Therefore, the total absolute error in the covariance matrix can be expressed as...

[0205]

[0206] Explicitly including the frequency is also important, so that the bandwidth design specifications can be met. Assuming the target specification is a single frequency band, its lower limit is f. l The upper limit is f u Formula (26) with T as the sampling frequency can be evaluated, where Explicitly including frequency dependence in the expression of formula (18) will yield

[0207]

[0208] Where t = 1, 2, ..., T. Correspondingly, the total absolute error (26) also becomes

[0209]

[0210] To verify the design results and the ideal objectives The degree of matching can be determined by selecting the average error δ. e The objective function is defined as the total absolute error divided by the number of elements in the covariance matrix, taking into account the sampling frequency T. It is a measure of the average difference between the covariance of the elements and the expected value, and is always less than 1, and should be as small as possible, at least less than 0.1. The resulting objective function is given below:

[0211]

[0212] The optimization objective can then be expressed as

[0213]

[0214] st: D∈{1,2,…,M} N ,with [D] n ≠[D] n′ (30).

[0215] The combinatorial optimization (30) is an NP-hard problem. Therefore, this paper uses the heuristic algorithms GA

[30] ,

[39] ,

[40] to solve the problem. Table 1 gives the detailed parameters of using GA, in which the proposed method provides computational efficiency and can be optimized quickly.

[0216] Table 1 Parameters used in GA

[0217]

[0218] Algorithm 1: Non-repeating sequential decoding algorithm

[0219]

[0220]

[0221] Using GA, the optimal switch position can be found. Fixed hardwire configuration (excluding) (element used as a switch) and mapping D * Then, it can be used to design the required PRA-FAS.

[0222] When using GA to optimize state selection and sorting, it is important to carefully consider the crossover between chromosomes (variables). This is because repeated elements in sequence D cannot be directly used as new chromosomes. An encoding method is proposed here to convert the encoding vector B, which may contain repeated elements, into a corresponding non-repeating vector D. The decoding process is shown in Algorithm 1 to ensure that the generated sequence D remains valid and free of repetitions.

[0223] D. Simulation and measurement results

[0224] This section presents simulation and measurement results of the proposed PRA-FAS design operating at a center frequency of 2.5 GHz. To ensure unidirectional radiation of the PRA-FAS, PAS is chosen as S(Ω), where when When φ∈[0,2π), S(θ,φ)=S0, otherwise S(θ,φ)=0. All simulations were performed using CST Studio Suite

[41] for full-wave simulations of S-parameters, radiation patterns and efficiency.

[0225] It is necessary to define the design of the switch so that the simulation can cover its effects and that the PRA-FAS can be fabricated in practice. In the design example, the RF switch 250 uses a PIN diode, similar to other PRA design methods

[24] ,

[25] ,

[42] ,

[43] ,

[44] . The PIN diode MA4AGP907

[37] is used, and its equivalent circuit model for conduction and cutoff is as follows: Figure 4 As shown. The control of the PIN diode is accomplished by a DC signal, so it is necessary to isolate the DC signal from the RF signal. This can be achieved by using an auxiliary inductor and capacitor. The Coilcraft 0402DC-R10XJRW

[45] inductor is used as an RF choke, which is equivalent to the RF open-circuit impedance connected to the internal port. The Murata GJM1555C1H130GB01

[46] capacitor is used both as an RF short circuit for the internal port and as a blocker for the DC signal. In order to control the PIN diode without interfering with the operation of the PRA-FAS, the DC control feed is located around the boundary of the PRA-FAS. Considering that the DC feed is isolated from the inductance of the radiating structure (pixel) and its length is much smaller than the wavelength, the DC feed has a minimal impact on the RF current and radiation. Figure 6 The proposed PRA-FAS switch layout and corresponding auxiliary components are shown. This design and simulation will be discussed further in the next section. Figure 6 The PRA-FAS consists of the positions of six RF switches and short-circuited internal ports connected via hardwiring. Unconnected pixels in the corners cannot be removed because they form the Z-shape along with other pixels, and they are also part of the optimization process. Measurement results and system evaluation will follow.

[0226] D.1 Simulation results for PRA-FAS

[0227] In the first simulation, it was provided Figure 2 Referring to the PRA-FAS design results, the target operating frequency is a center frequency of 2.5 GHz. To clarify the basic design flow, T=1 is set, and complex bandwidth optimization is not required. Following the PRA-FAS design flow described above, a PRA-FAS design was obtained, in which the optimal switching position was found. Fixed hardwire configuration (excluding those located in) (the switching element at the location) and the corresponding mapping D * The resulting design is as follows: Figure 6 As shown in the diagram, the detailed structure and location of the RF switch, hardwired circuit, open circuit, DC control line of the RF switch, inductor (equivalent to RF open circuit), and capacitor (equivalent to RF short circuit or hardwired circuit) are illustrated.

[0228] refer to Figure 3 The internal port numbers shown are as follows: The six RF switches are located at internal port numbers 3, 8, 16, 25, 27, and 36. Hardwired connections are located at internal port numbers 7, 12, 21, 23, 32, 37-39, 41, 42, 44, 45, 51, 54, 59, and 60. Open circuits are located at internal port numbers 1, 2, 4-6, 9-11, 14, 15, 17, 19, 20, 28-31, 33-35, 40, 43, 46, 48-50, 53, and 55-58. Capacitors (equivalent to hardwired connections) are located at internal ports 18, 22, and 47. Inductors (equivalent to open circuits) are located at internal ports 13, 24, 26, and 52, as well as at the feed points for all DC control lines for the six RF switches and the GND feed point. The DC control lines for the six RF switches are all located near the boundaries of the PRA-FAS.

[0229] The states of each switch corresponding to the 12 states of PRA-FAS are shown in Table 2.

[0230] Table 2 Parameters used in GA

[0231]

[0232] Figure 7 Simulated S-parameters are provided to verify that the antenna functions correctly under all conditions. These show that the PRA-FAS matches the 2.5 GHz center frequency well, with a total bandwidth slightly above 50 MHz.

[0233] However, the key design parameter for FAS is its correlation characteristics. Figure 8AThis shows the target covariance objective specified by formula (25) when N=12 and W=1 / 2. This figure shows the ideal covariance matrix for n, n′∈{1,2,…,12}. As expected, the main diagonal is 1, and the matrix is ​​symmetric. Figure 8B The covariance matrices of the simulated radiation modes for the 12 states optimized by PRA-FAS are shown. All 12 radiation modes were obtained through full-wave simulation. Figure 8C The difference between the simulated covariance matrix and the target correlation is shown. It can be seen that the covariance values ​​between any pair of modes are very close to the expected target. Using the operating conditions in Table 2, the minimum mean relative error between the simulated covariance matrix and the target covariance is as low as δ from Equation (29). e =0.063, thus proving the accuracy of the proposed PRA-FAS design method.

[0234] The covariance matrix of PRA-FAS shows that adjacent FAS states (ports) are highly correlated, which means that, according to Equation (8), the radiation patterns of these adjacent states should exhibit a higher degree of similarity. Simulation results of pixel layer current distributions for four selected FAS states confirm this. Figure 9 The current distributions for states 1, 2, 11, and 12 are shown. Clearly, adjacent states (e.g., 1 and 2, or 11 and 12) have similar current distributions. Therefore, their radiation patterns are indeed similar. Conversely, states that are far apart, such as 1 and 11, or 1 and 12, exhibit significantly different current distributions, resulting in uncorrelated radiation patterns, consistent with theoretical predictions.

[0235] By examining the radiation pattern of PRA-FAS, we can gain further insight into the relevant covariance matrix of the radiation mode. Figure 10 The e-radiation modes of PRA-FAS states 1, 2, and 12 are shown. θ (Ω) and e φ (Ω) component. A comparison between states 1 and 2 reveals a striking similarity between the two components, which naturally leads to a high correlation coefficient ρ. 1,2 Approaching 1. Conversely, the radiation modes of states 1 and 12 are in their e θ (Ω) and e φ The (Ω) component exhibits orthogonality, and due to cross-polarization, ρ 1,12 The correlation is low if the value is approximately 0. Furthermore, Figure 10 The results show that the maximum gain direction of the radiation mode in all states is closely aligned with the center normal of the antenna aperture plane, which confirms that it is accurate to describe all 12 states as exhibiting approximately unidirectional radiation.

[0236] It is important to note that differences between radiation modes reduce the correlation when using Equation (8) to calculate signal correlation. Although the amplitudes of the simulated and measured radiation patterns are similar across all states, it is primarily the differences between phases that cause the correlation of changes between antenna states. An example of this effect can be seen in the dipole in Equation (9), where only the mode phase changes.

[0237] Figure 11 The implemented gain and efficiency for all 12 PRA-FAS states at a center frequency of 2.5 GHz are shown. It can be seen that the implemented gain for all states is greater than 6.6 dBi. Meanwhile, an average efficiency of approximately 80% is achieved, which is sufficient for practical applications considering the presence of the RF switch.

[0238] D.2 Measurement results for PRA-FAS

[0239] Experimental results are needed to validate the proposed PRA-FAS design and the recommended design flow. Figure 2 The measurement results of PRA-FAS are presented in the paper.

[0240] Figure 12A A photo of the experimental prototype. Figure 12B The pixel structure of the upper layer of PRA-FAS is presented. An FPGA AX7035 (0 / 3.3V output) is deployed to control the state of all 6 switches, enabling switching between 12 reconfigurable states. Figure 12C The test setup for PRA-FAS is shown, in which absorbing material shields the DC control lines to prevent interference with the radiation field. Figure 13 The reflection coefficient measurements for all 12 states of the PRA-FAS are presented, demonstrating successful impedance matching in all states and exhibiting an operating bandwidth exceeding 50MHz. Figure 7 The simulation results are similar to those in the literature.

[0241] In the correlation calculation, only the electric field component of the upper hemisphere space is used (see PAS at the beginning of Section D). Figure 14A and Figure 14B The radiation patterns for state 1 are shown, and these patterns are respectively located at e θ (Ω) component is most prominent and e φ The measurements were taken on the plane where the (Ω) component is most prominent. These two models agree very well with the simulation results. This consistency is also present in the other 11 PRA-FAS states, indicating the accuracy of the measurements. Furthermore, Figure 11 The measured values ​​of peak gain and total efficiency of the radiation pattern of the PRA-FAS under different states are shown. The test results are in excellent agreement with the simulation data, and the differences can be attributed to manufacturing variations.

[0242] Figure 15 The covariance matrix obtained from the measurements is shown. The mean relative error of all relevant terms is δ. e =0.108, calculated using formula (29). and Figure 8B (δ e Compared to the simulated covariance matrix (=0.063), the average error in the experimental results has increased. This is likely due to modeling errors in the PIN diodes, as discussed in the discussion section below. Despite the deterioration in the average error, each column or row of the measured covariance matrix still exhibits a clear Bézier curve trend, making it suitable for the FAS scenario.

[0243] D.3 System experiments for PRA-FAS

[0244] To demonstrate the practical applicability of the proposed PRA-FAS, system-level simulations and experiments were also conducted.

[0245] In the proposed simulation, Clarke's three-dimensional spatial model was used to evaluate the performance of the PRA-FAS

[31] . A scattering-rich mobile environment was simulated, in which the transmitter was stationary while the receiver's PRA-FAS moved at a speed of v = 60 km / h, and the transmitted signal was scattered by stationary objects around the moving receiver. Under these conditions, the incident radiation at any given moment is unique, thus determining h(Ω) in Equation (2). Given the radiation patterns of the 12 PRA-FAS states, the voltage of each PRA-FAS port can be calculated using Equation (6), and then the channel gain of each port can be calculated. Figure 16 The time-varying signals received at 12 PRA-FAS ports are shown, revealing a channel gain difference of up to 40 dB between the PRA-FAS ports. Furthermore, the port correlation can be calculated using formula (7) based on the FAS port voltages, as shown in the results. Figure 17 As shown. The results of formulas (7) and (8) are highly consistent, confirming the accuracy of the derivation in Section A of this disclosure.

[0246] The final verification of the proposed PRA-FAS scheme was to conduct experiments and measure the signal at the FAS port in a scattering-rich environment. For this purpose, a 4×4 MIMO test platform was used

[47] . It can provide measurements of 4×4 wireless channels every 0.01 seconds. In order to use this test platform for FAS measurements, it was configured as a 2×2 test platform, and its general test settings are as follows: Figure 18A , Figure 18B and Figure 18C As shown. Figure 18A As shown, both transmit ports (Tx1 and Tx2) are configured as dipoles and separated by more than two wavelengths to provide uncorrelated transmission channels. Figure 18BA schematic diagram of the receiver is shown, where receiver port 1 (Rx1) is configured as a dipole, and receiver port 2 (Rx2) is configured as a PRA-FAS. They are also separated by at least two wavelengths, therefore they are uncorrelated.

[0247] Configure both ports of the transmitter as dipoles, MIMO channel unit h 1,1 and h 1,2 Corresponding to a conventional antenna system, and can be used as a reference channel. Channel h 2,1 and h 2,2 The two channels corresponding to the receiver-side PRA-FAS are denoted as follows: and The PRA-FAS is configured using an FPGA and set to sequentially cycle through 12 FAS states. The FAS states can be synchronized with the test platform, thus identifying the channel corresponding to each FAS state. MIMO antenna channel measurements were conducted in the Wireless Communication Laboratory of the Hong Kong University of Science and Technology in China, in an indoor environment... Figure 18C As shown. The transmitter and receiver are configured in a non-line-of-sight (LOS) configuration, 5 meters apart, with a 2-meter-high cabinet blocking the LOS path.

[0248] First, the verification results of the PRA-FAS antenna diversity capability are presented. Since only one FAS port can be active at any given time, the proposed PRA-FAS cycles through its 12 configurations when the rich-scattering channel is in a steady state. The steady state of the channel can be determined using two reference channels h. 1,1 and h 1,2 To verify, these two channels h 1,1 and h 1,2 There was no change within the measurement intervals of the 12 configuration states. Figure 19 It shows the 12 FAS states, for and Three sets of channel samples were used for measurement. Figure 19 In the diagram, solid dots represent sampling points, and interpolation lines have been added for clarity. These three sets of measurements are for different stable channels, which can be determined by... Figure 18B The PRA-FAS achieves this by placing the receiver in different locations and blocking the Loss of Sight (LoS) path. It can be observed that the PRA-FAS can provide a channel that varies with its configuration state as needed. Specifically, with 12 cycles of PRA-FAS states, the signal variation reaches approximately 30 dB, while the reference channel remains stable. This demonstrates that the PRA-FAS achieves sufficient diversity by changing its radiation pattern. Furthermore, it can be observed that in a multi-user environment, a SIR exceeding 15 dB can be achieved through port switching, demonstrating the potential application of the proposed PRA-FAS in FAMA.

[0249] To measure the signal correlation between FAS ports, multiple channel samples can be averaged to obtain the experimental set average of the FAS port correlation. Based on the results, the measured average port correlation is... It can be represented as

[0250]

[0251] Where i,j∈{1,2,…,12}, This represents the measured channel between PRA-FAS and Tx1 when PRA-FAS is in the i-th state and under the k-th stable channel condition; other terms also apply. Then, calculate all terms with the same |ij| value. The set average of items, such as Figure 20 As shown, the correlation given by Equation (9) is provided. It can be observed that the experimental results are generally slightly smaller than those of Equation (9). This is because the scattering-rich environment in the proposed test is not constrained to a uniform distribution in the 2D plane. In practice, PAS will be more like a donut shape, thus experimentally obtaining a correlation smaller than that of Equation (9). Nevertheless, the final measurement results provide concrete evidence that PRA-FAS provides a fading signal with appropriate correlation between FAS ports.

[0252] Figure 21 A method for designing a PRA-FAS is illustrated. The PRA-FAS supports N FAS ports uniformly distributed along a linear length Wλ. In step 2110, the locations of hardwires, open circuits, or RF switches between any two adjacent metallic pixel patches in a pixel-based reconfigurable antenna pixel layer are selected to satisfy a first condition: the locations of hardwires, open circuits, and RF switches provide impedance matching over a specified bandwidth. In step 2130, N FAS ports are selected and sorted from the combinations of on / off states of the RF switches to satisfy a second condition: any two adjacent FAS ports among the N FAS ports are spatially dependent. The second condition is satisfied when the difference between the radiation mode covariance matrix of all reconfigurable states and the target covariance matrix is ​​minimized. In an optional step 2120, a set satisfying the first condition is selected. A portion of the data is used as a candidate set to achieve the second condition, thus reducing the search space. Other methods have been discussed above and will not be repeated here to avoid redundancy.

[0253] E. Future discussion

[0254] This paper will further discuss three issues in the PRA-FAS design process. The first issue to consider is the selection of the required number of switches in the PRA-FAS design. The second issue is explaining the small deviation in covariance error between simulation and experimental results. Finally, the bandwidth of the FAS needs to be considered.

[0255] E.1 Choice of number of switches

[0256] In the design of PRA-FAS, selecting the optimal number of RF switches is crucial to ensure a sufficient number of reconfigurable states. Finding the right balance between maintaining design simplicity and efficiency is essential for enabling flexible adjustment of the 3D radiation mode in all states.

[0257] To better understand the selection of the number of switches, this article provides the results of the design algorithm under different P values, in order to obtain... Figure 2 The average error δ corresponding to the geometry e For each P, a two-step PRA-FAS design method is used to obtain the optimal configuration. and and mapping order D * Minimum average error δ e As shown in Table 3.

[0258] Table 3 Average error of different switches in the two-step method with N=12

[0259]

[0260] As the number of switches P increases from 4 to 6, the minimum average error δ e The error gradually decreases. This trend suggests that increasing the number of switches can bring the covariance matrix closer to the target, consistent with the initial expectation. However, as P further increases, the minimum error begins to rise. This increase is attributed to the exponential growth of the number of possible states with increasing P, meaning that each time 100 sets are calculated... The current simulation is insufficient to explore potential PRA-FAS configurations, thus failing to achieve a global minimum error. Considering the efficiency of the simulation process, P=6 was chosen as the optimal number of switches for the proposed design, thereby balancing the complexity and performance of the PRA-FAS.

[0261] E.2 Covariance matrix error

[0262] To help identify the source of the covariance matrix error between the measured and simulated results of the proposed PRA-FAS, it is necessary to carefully observe the radiation pattern. The amplitudes of the measured and simulated modes remain consistent across all spatial angles Ω; however, subtle phase differences are observed. It can be inferred from Equation (8) that the effect of the phase difference is particularly significant. Even small phase changes can severely affect the correlation results. It is reasonable to believe that this phase difference between the simulated and experimental results is due to the inaccuracy of the equivalent model of the RF switch in the simulation, since the diode's operating conditions differ from those measured in

[37] . Since six switches are used, any small error will further accumulate. Despite the existence of accumulated phase error (from Figure 14A and Figure 14B As can be seen from the data, the amplitude error is not significant. The proposed PRA-FAS still exhibits significant antenna diversity in system-level evaluation, so these errors are considered acceptable.

[0263] A recommended approach to solving the switching modeling problem is to optimize the parameters of the equivalent switching model to minimize the error between the updated radiation pattern and the experimental results. Using the updated diode equivalent circuit model, PRA-FAS will be more accurate.

[0264] E.3 Bandwidth

[0265] The focus of this design is to demonstrate that a FAS can be constructed using PRA. The obtained prototype bandwidth is slightly higher than 50MHz. In wireless applications, a wider bandwidth will be required. Therefore, the method of increasing bandwidth is an important issue to consider. In principle, this can be achieved by increasing T in formula (28), but there are two limiting factors that need to be overcome. The first is due to the design of the PRA-FAS radiating feed E-slot patch. Its height from the ground plane is low, only 1.524mm, resulting in bandwidth limitation. The second is the limitation of using only 6 switches during pixel surface reconstruction.

[0266] To achieve wider bandwidth and enable the FAS to handle stable correlations across larger bandwidths, the number of switches needs to be increased. This means searching for more switch combinations to find one with sufficient bandwidth. Research shows that doubling the height of the radiating feed board and increasing the number of switches to seven can boost the bandwidth to 130MHz, an increase of over 5%. Further research is needed to further improve bandwidth and consider other bandwidth expansion methods.

[0267] E.4 Extension to millimeter-wave band

[0268] One concern is whether the proposed design approach can be extended to the millimeter-wave band. At millimeter-wave and higher frequencies, the impedance difference between the on and off states of a PIN diode is limited

[48] , resulting in poor reconfiguration performance. In this case, advanced materials such as vanadium dioxide (VO2)

[49] can be used to achieve the switching function, which is known for its phase transition properties in the high-frequency range (up to terahertz). Adding parasitic structures around the PIN diode, as described above

[48] , can also be considered to improve the switching performance in the millimeter-wave band.

[0269] This disclosure describes a novel approach to FAS design based on pixel reconstruction. In developing this approach, it can be seen that the FAS can be considered equivalent to a system with a “fluid” radiation pattern. To validate this design approach, simulation and experimental results of a PRA-FAS prototype controlled by an RF switch are provided, applicable to a typical FAS with W = 0.5 and N = 12 at a center frequency of 2.5 GHz. Since the PRA-FAS uses electronic switches for reconstruction, the packet-by-packet switching speed required by the FAS can be met.

[0270] Experiments show that when the underlying wireless channel is in a steady state, the 12 states of the PRA-FAS can provide significantly varied channels, demonstrating that the PRA-FAS can provide the necessary diversity. Furthermore, both simulations and experiments show that the radiation mode covariance matrix approximately conforms to the Clarke model. Internally, six RF switches are strategically placed among 60 internal ports, achieving a balance between complexity and performance. To realize the complex design of the PRA-FAS, a two-step optimization process was employed, sequentially optimizing the antenna configuration and the sequence of matching modes to approximate the ideal covariance matrix. Comprehensive system-level experiments were conducted in a fully scattering environment to verify the diversity and port dependence of the designed PRA-FAS.

[0271] Further research is needed. Methods to scale up the PRA size are required to accommodate large-scale FAS with W > λ / 2 and N > 12. For MIMO-FAS, multi-port PRA-FAS design also needs further investigation.

[0272] The main contributions of this disclosure are as follows:

[0273] 1) Radiation Mode Covariance Matrix Analysis: Signal correlation is related to the antenna's radiation pattern, indicating that FAS can also be explained by "fluid" radiation modes. A radiation mode covariance matrix is ​​introduced to describe the radiation mode correlation between any two PRA-FAS ports, thereby describing signal correlation.

[0274] 2) Ample FAS ports: The proposed PRA-FAS achieves equivalent port shift within a range of 0.5λ and implements 12 FAS ports in a compact volume of 0.67λ×0.67λ×0.125λ. This port density level is comparable to that of conventional FAS and provides finer channel spatial sampling compared to existing PRAs.

[0275] 3) High reconfigurable speed: By utilizing RF switches and software control mechanisms, PRA-FAS achieves port switching with a delay of μs, meeting the switching requirements of high-speed FAS

[11] ,

[12] .

[0276] 4) Two-step approach for PRA-FAS design: A random search and GA approach is designed to optimize PRA-FAS, thereby effectively reducing design complexity. First, pixel configurations that can provide impedance matching are found. Then, configurations that satisfy the spatial correlation of FAS are selected from these configurations.

[0277] 5) PRA-FAS Prototype and Experimental Results: A PRA-FAS prototype operating at a frequency of 2.5 GHz is provided to verify the feasibility of the proposed design. Furthermore, system-level simulations and experiments were conducted using the proposed PRA-FAS to verify the port correlation in wireless communication.

[0278] It will also be understood that any feature in the above embodiments of this disclosure can be combined together and does not necessarily have to be applied in isolation. Those skilled in the art can easily combine two or more features in the above embodiments or preferred forms of this disclosure in a similar way.

[0279] Unless otherwise defined, the technical and scientific terms used herein have the same ordinary meaning as commonly understood by one of ordinary skill in the art related to the exemplary embodiments. The embodiments are illustrated by way of non-limiting examples. Various modifications that may be conceived by those skilled in the art based on the disclosed embodiments fall within the spirit and scope of the exemplary embodiments.

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Claims

1. A pixel-based reconfigurable antenna (PRA) comprising: a lower substrate; a ground plane attached to the bottom surface of the lower substrate; a patch antenna attached to the top surface of the lower substrate, the patch antenna serving as a radiation source of the PRA, the radiation source being configured to be fed from the back of the ground plane by a probe; an upper substrate disposed above the lower substrate and spaced apart from the lower substrate by a distance h air ; and a pixel layer consisting of a plurality of metal pixel patches attached on the top surface of the upper substrate, the plurality of metal pixel patches being arranged in a uniform grid pattern with a constant spacing b between any two adjacent metal pixel patches, wherein: the patch antenna provides a reference electric field, which is re-radiated after coupling through the metal of the pixel layer, wherein the structure of the pixel layer has reconfigurability, each reconfigurable state of the PRA corresponds to one FAS port, and the PRA supports N fluid antenna system (FAS) ports uniformly distributed over a linear length of Wλ, where λ is a wavelength, W is a quantity of the wavelength, and N / W>1; the connection between any two adjacent metal pixel patches is configured to be hardwired, open-circuited, or implemented via a radio frequency (RF) switch, and the position selection of the hardwired, open-circuited, and RF switch satisfies a first condition, the first condition being that the position selection of the hardwired, open-circuited, and RF switch provides impedance matching over a specified bandwidth; and the selection and ordering of the N FAS ports from the on / off state combinations of the RF switches satisfy a second condition, the second condition being that any two adjacent FAS ports among the N FAS ports are spatially correlated, wherein the second condition can be satisfied when the difference between the radiation pattern covariance matrix of all reconfigurable states and a target covariance matrix is minimized. 2.The PRA of claim 1, wherein: the connection between any two adjacent metal pixel patches in the uniform mesh pattern forms a common P internal ports, P of which are assigned to the RF switch, and a vector x represents the disconnection state denoted by 0 and the connection state denoted by 1 between any two adjacent metal pixel patches, and a set S specifies the position selection of the RF switch, whereby the vector x and the set S completely define the connection configuration of the PRA of the pixel layer, given by the following formula where x q ∈{0,1}, S = {q1, q2,..., q P}, where where q1to q P specifying the The selected positions of the P RF switches in the K internal ports are ordinal indices in the vector x. 3.The PRA of claim 2, wherein: For all possible vectors x consisting of vectors x l and all possible sets S consisting of sets S k , a set of 2 P elements is defined, which represents all combinations of on / off states of the RF switch, and the total number of the defined set is and set is a subset of set that satisfies a first condition, the mathematical formula of which is where s.t. denotes the constraint condition, is the reflection coefficient of the PRA under the connection configuration determined by the vector and the set S k .

4. The PRA of claim 3, wherein, a set satisfying the first condition a portion of the set of the middle is selected as a candidate set for implementing the second condition to reduce the search space. 5.The PRA of claim 4, wherein: A second condition as a target function δ of the genetic algorithm GA e (D) is given by the following expression s.t.: D∈{1,2,…,M} N ,with [D] n ≠[D] n′ (30), where s.t. denotes the constraint condition, the vector sequence D = [d1, d2,..., d N ] T denotes the selection and ordering of the N FAS ports from the M matching patterns in each candidate set , the objective function δ e (D) is given by where Δ(D) is the total absolute error given by wherein is the (n,n')th element of the radiation pattern covariance matrix and is the (n,n')th element of the target covariance matrix Rn.

6. The PRA of claim 5, wherein, When frequencies are considered to meet the bandwidth requirement, formula (18) is replaced by and formula (26) is replaced by wherein, t = 1, 2,..., T, f l is a lower limit, f u is an upper limit, T represents a sampling frequency point. 7.The PRA of claim 5, wherein: is given by the formula where J 0 is the first kind, zero order Bessel function. 8.The PRA of claim 5, wherein: The impedance matrix Z represents the impedance of the The impedance matrix Z is represented as​​ wherein Z i,j (f) represents elements of the impedance matrix Z, where f is the frequency, 0 represents the single external feed port, 1 to are the internal ports, and wherein, and are four sub-matrices of the impedance matrix Z. 9.The PRA of claim 8, wherein: the input impedance of the PRA is calculated as follows Z in (x,S) = Z E -Z EI [Z I +Z L (x,S)] -1 Z IE (15), wherein Z L (x, S) is a diagonal matrix representing the impedance of the internal ports in the connection configuration determined by the vector x and the set S. 10.The PRA of claim 9, wherein: the reflection coefficient is given by the equation where Z0represents a characteristic impedance, and is the input impedance of the PRA under the connection configuration determined by the set and the set S k . 11.The PRA of claim 9, wherein: is when the open-circuit radiation mode excited by a unit current in the qth port when all other ports are disconnected, given by where θ and φ represent the elevation and azimuth angles in a spherical coordinate system, respectively, and Ω=(θ, φ); and For the combination of the open-circuit radiation pattern matrix E OC is given by 12.The PRA of claim 11, wherein: The radiation pattern covariance matrix is represented as wherein is the Hadamard division, the matrix denotes the average energy of all M matching patterns and is used for normalization, and the (i,j)-th element of the matrix G is denoted as where the matrix C is the absolute correlation matrix of all M matched patterns, defined as wherein is the correlation matrix of all open-circuit radiation modes weighted by S(Ω), S(Ω) is the power angular spectrum PAS, E OC is the open-circuit radiation mode matrix, and I = [i1, i2, …, i M ] is the current matrix, where i1, i2, …, i M are the current vectors of all M matched modes, each given by 13.The PRA of claim 11, wherein: is given by the formula where S(Ω) is the power angular spectrum, PAS, e n represents the FAS radiation pattern of the nth port of the N FAS ports excited by the nth current vector i n represents the FAS radiation pattern of the nth port of the N FAS ports excited by the nth current vector i represents e n′ the complex conjugate of e e n (Ω) represents is where E OC is the open-circuit radiation pattern matrix, the nth current vector in n is given by 14. The PRA of claim 4, wherein, P = 6, and the number of candidate sets that satisfy the second condition is about 100.

15. The PRA of claim 1, wherein, The upper substrate and the lower substrate are of size P. s ×P s A square prism of length ×h has a side length P. s With height h, each metal pixel patch is a square with side length a, and the uniform grid pattern is arranged in N. s ×N s Square configuration, the number of internal ports is determined by Provided.

16. The PRA of claim 1, wherein, The patch antenna is an E-slot patch having a first slot and a second slot each extending from an L p x W p The long side of the rectangular radiation surface extends inwardly, and wherein the first slot and the second slot are each an elongated rectangle with dimensions L s x W s .

17. The PRA of claim 1, wherein, the RF switches are controlled by direct current (DC) control lines arranged around the boundary of the PRA, wherein a capacitance replaces a part of the hardwired, and an inductance occupies a part of the open-circuited and the feeding point of the DC control line, the capacitance and inductance providing isolation between the DC control signal and the RF signal.

18. A method for designing a pixel-based reconfigurable antenna (PRA), wherein, The structure of the pixel layer of the PRA is reconfigurable, each reconfigurable state of the PRA corresponds to one FAS port, the PRA supports N fluid antenna system (FAS) ports uniformly distributed over the linear length of Wλ, where λ is the wavelength, W is the number of the wavelength, and N / W>1, the method comprises: selecting the position of hardwiring, open circuit or radio frequency (RF) switch between any two adjacent metal pixel patches in the pixel layer to meet a first condition, the first condition is that the position selection of the hardwiring, the open circuit and the RF switch provides impedance matching over a specified bandwidth; and selecting and ordering the N FAS ports from the on / off state combinations of the RF switches to meet a second condition, the second condition is that any two adjacent FAS ports in the N FAS ports are spatially correlated, wherein the second condition can be met when the difference between the radiation pattern covariance matrix of all reconfigurable states and the target covariance matrix is minimized.

19. The method of claim 18, wherein: the connection between any two adjacent metal pixel patches in the uniform grid pattern forms a common P internal ports, P of which are assigned to the RF switch, and a vector x representing the disconnection state denoted by 0 and the connection state denoted by 1 between any two adjacent metal pixel patches, and a set S specifying the position selection of the RF switch, whereby the vector x and the set S completely define the connection configuration of the PRA of the pixel layer, given by: where x q ∈{0,1}, S = {q1, q2,..., q P}, where where q1to q P specifying the The selected positions of the P RF switches among the K internal ports are ordinal indices in the vector x.

20. The method of claim 19, wherein: For all possible vectors x consisting of vectors x l The set S consisting of all possible sets S k , A set of 2 P elements is defined, which represents all combinations of on / off states of the RF switch, and the defined set has a total number of and set is a subset of set that satisfies a first condition, the mathematical formula of which is where s.t. denotes the constraint condition, is the reflection coefficient of the PRA under the connection configuration determined by the vector and the set S k .

21. The method of claim 20, further comprising: Select the set that satisfies the first condition. A portion of this is used as a candidate set to achieve the second condition, in order to reduce the search space.

22. The method of claim 21, wherein: A second condition as a target function δ of the genetic algorithm GA e (D) is given by the following expression s.t.: D∈{1,2,…,M} N ,with [D] n ≠[D] n′ (30), where s.t. denotes the constraint condition, the vector sequence D = [d1, d2,..., d N ] T denotes the selection and ordering of the N FAS ports from the M matching patterns in each candidate set , the objective function δ e (D) is given by where Δ(D) is the total absolute error given by wherein is the (n,n')th element of the radiation pattern covariance matrix and is the (n,n')th element of the target covariance matrix .

23. The method of claim 22, wherein, When considering the frequency to meet the bandwidth requirement, formula (18) is replaced by and formula (26) is replaced by wherein f l is a lower limit, f u is an upper limit, T represents a sampling frequency point.

24. The method of claim 22, wherein: is given by the formula where J0 is the first kind, zero order Bessel function.

25. The method of claim 22, wherein: The impedance matrix Z represents the impedance of the internal ports and a single external feed port, and the impedance of the The impedance matrix Z is represented as wherein Z i,j (f) represents the elements of the impedance matrix Z, where f is the frequency, 0 represents the single external feed port, 1 to are the internal ports, and wherein, and are the four sub-matrices of the impedance matrix Z.

26. The method of claim 25, wherein: The input impedance of the PRA is calculated as follows Z in (x,S) = Z E -Z EI [Z I +Z L (x,S)] -1 Z IE (15), wherein Z L (x, S) is a diagonal matrix representing the impedance of the internal ports in the connection configuration determined by the vector x and the set S.

27. The method of claim 26, wherein: the reflection coefficient is given by the equation where Z0represents a characteristic impedance, and is the input impedance of the PRA under the connection configuration determined by the set and the set S k .

28. The method of claim 26, wherein: is the open-circuit radiation pattern of the qth port when all other ports in the (Q+1) ports are disconnected, given by where θ and φ represent the elevation and azimuth angles in the spherical coordinate system, respectively, and Ω=(θ, φ); and For the combination of is represented by the open-circuit radiation pattern matrix E OC given by 29. The method of claim 28, wherein: The radiation pattern covariance matrix is represented as where is the Hadamard division, the matrix denotes the average energy of all M matching patterns and is used for normalization, and the (i, j)-th element of the matrix G is denoted as where the matrix C is the absolute correlation matrix of all M matched patterns, defined as wherein is the correlation matrix of all open-circuit radiation modes weighted by S(Ω), S(Ω) is the power angular spectrum PAS, E OC is the open-circuit radiation mode matrix, and I = [i1, i2, …, i M ] is the current matrix, where i1, i2, …, i M are the current vectors of all M matched modes, each given by 30. The method of claim 28, wherein: is given by the formula where S(Ω) is the power angular spectrum, PAS, e n represents the FAS radiation pattern of the nth port of the N FAS ports excited by the nth current vector i n represents the FAS radiation pattern of the nth port of the N FAS ports excited by the nth current vector i represents e n′ the complex conjugate of e e n (Ω) represents is where E OC is the open-circuit radiation pattern matrix, the nth current vector in n is given by 31. The method of claim 21, wherein, P = 6, and the number of candidate sets that satisfy the second condition is about 100.

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