A joint analog-digital beamforming method

Abstract

The present invention discloses an analog-digital joint beamforming method. The analog-digital joint beamforming theory and method include two parts: the design of a 3D stereo super-directional antenna and the analog-digital joint beamforming design. The 3D stereo super-directional antenna includes at least one column with multiple radiation units, and the array is used to generate a radiation field. The analog-digital joint beamforming design includes two parts: an analog excitation design and a digital beamforming matrix. The analog excitation design adjusts the antenna radiation pattern in real time based on the electromagnetic coupling effect, generates a super-directional beam, adapts to the communication environment, and improves the performance gain of the communication system. The digital beamforming matrix designs the optimal digital beamforming according to the antenna pattern and the characteristics of the wireless link, and combines the analog beamforming to iteratively improve the system performance.

Description

Technical Field

[0001] The present invention relates to the field of beamforming, including an analog-digital joint beamforming method. Background Art

[0002] With the development of wireless communications, multiple-input multiple-output (MIMO) technology has shown a very powerful ability to improve spectrum efficiency and wireless communication system capacity, and has become a key technology for improving 5G communication rates. However, the theoretical capacity analysis of traditional MIMO arrays is based on the condition that there is no coupling between antennas. The physical implementation of this mathematical condition is that the antenna elements of the MIMO array need to be at least half a wavelength (λ / 2) apart. Therefore, the spatial aperture area required for large-scale MIMO array deployment will also be larger. In actual base station deployment of antennas, due to restrictions such as scenarios and costs, there is often only a fixed total array area. Therefore, the number of available antennas in the MIMO array in actual use is also limited.

[0003] Based on the above practical background, a natural technical exploration direction is to arrange more antenna elements on a given total antenna aperture area and explore whether there is gain relative to the traditional MIMO antenna array. At the same time, due to the advancement of antenna manufacturing technology, antenna arrays are no longer limited to planes. Since the spacing between the emerging 3D stereoscopic super-directional antenna array elements is narrower and there is electromagnetic coupling between the array elements, the beam vector generated by traditional beamforming methods (such as Zero-forcing algorithm, MMSE algorithm, etc.) will be distorted after antenna coupling and cannot achieve the expected effect of aligning to the user.

[0004] In terms of super-directivity, existing studies have shown that when the spacing between antenna elements is less than half a wavelength, electromagnetic coupling can be used to generate super-directional beams by properly setting beamforming excitation. However, in the case of linear arrays, only the end-fire direction can generate super-directional beams. Therefore, we considered 3D super-directional antennas. The purpose is to generate super-directional beams in any direction in space.

[0005] In addition, the traditional beamforming method does not take into account the radiation pattern of the antenna element. It assumes that the radiation of a single antenna element is isotropic. This radiation pattern is difficult to produce in actual antenna elements. The energy radiation of commonly used actual antenna elements (such as dipole antennas) is uneven in space. This inherent uneven distribution of antenna radiation energy in space is not considered in the current beamforming algorithms. Furthermore, the spatial characteristics of the 3D stereoscopic super-directional antenna radiation pattern generated by the three characteristics of non-isotropic radiating array elements, antenna simulation excitation coefficient vectors, and electromagnetic coupling are not considered in traditional communication models and algorithms.

[0006] In summary, it is a challenge to perform low-complexity beamforming while considering the actual radiation pattern of the antenna array in the presence of coupling and the actual scattering communication environment, and to use 3D stereo super-directional antenna coupling to generate a super-directional beam to aim at the user. Summary of the invention

[0007] Based on the above problems, in order to incorporate the antenna array radiation pattern including electromagnetic coupling into the communication modeling, and at the same time improve the beamforming gain of the 3D stereo super-directional antenna, so as to extend the algorithm's applicable scenarios to more common and practical communication scenarios, the present invention proposes an analog-digital joint beamforming method.

[0008] In one aspect, the present invention provides an analog-digital joint beamforming method, the method comprising:

[0009] S1. Acquire communication scenario information and establish a 3D super-directional antenna array through a dense array of radiation units and an analog excitation circuit;

[0010] S2, record the radiation field generated when there is no coupling in the array and the radiation field of the uniquely excited different antenna elements when there is coupling;

[0011] S3, performing spherical wave coefficient expansion on the radiation fields before and after coupling, establishing the connection between the coupled electromagnetic field and the uncoupled electromagnetic field, and obtaining a coupling matrix;

[0012] S4. The coupling matrix is ​​integrated with the communication model to calculate the optimal analog beamforming and the optimal digital beamforming, wherein the communication model is divided into a single-user reception model and a multi-user reception model. Specifically:

[0013] Under the single-user receiving model, an optimal analog beamforming vector under a fixed digital beamforming condition and an optimal digital beamforming vector under a fixed analog beamforming condition are obtained by derivation and iterative optimization;

[0014] Under the multi-user receiving model, when analog beamforming is fixed, the sum rate maximization problem is converted into an SDP problem through variable conversion, and the optimal antenna array analog excitation current vector under the fixed digital beamforming condition is solved by using a convex optimization toolkit as the optimal analog beamforming; when digital beamforming is fixed, the sum rate maximization problem is converted into an SDP problem through variable conversion, and the optimal digital beamforming matrix under the fixed analog beamforming condition is solved by using a convex optimization toolkit; and iterative optimization is performed during the solution;

[0015] S5. Geometry adjustment: Find the optimal antenna element spacing that best balances the radiation efficiency and directivity of the 3D super-directional antenna through simulation.

[0016] Furthermore, the communication scenario information includes: an elevation angle and a horizontal angle of a scatterer in a communication environment relative to a base station.

[0017] Furthermore, the 3D super-directional antenna array is established as follows: the array is N t The densely distributed antenna array elements are evenly spaced in a plane, where the interval between the elements is less than half a wavelength.

[0018] Furthermore, in S2, the radiation field generated when there is no coupling is recorded using the actual spatial position, the elevation angle and the horizontal angle of the spherical coordinates are evenly divided, the space is discretized into P directions, and the electric field strength in the theta direction and the phi direction of each direction is recorded as the radiation field of the array element currently being solved; recording the radiation field of different antenna array elements that are uniquely excited when coupling exists is specifically: when setting the excitation of the array, only the antenna array element unit that needs to be solved is excited to generate electromagnetic radiation, and the other antenna array elements are connected to the matching impedance network as a load, and the space is also discretized into P directions, and the electric field strength in the theta direction and the phi direction of each direction is recorded.

[0019] Furthermore, the establishment of the connection between the coupled electromagnetic field and the uncoupled electromagnetic field is specifically as follows: the coupled radiation electric field of a single element is represented as a linear combination of the uncoupled radiation electric fields of multiple elements. If the total number of transmitting antennas is M, the uncoupled radiation field is The coupled radiation field is denoted by The linear representation is:

[0020]

[0021] The electric field coefficient e is introduced by using the actual recorded radiation electric field parameters or the spherical wave expansion coefficient, and the number of expansion items is adjusted according to the required accuracy; the linear combination coefficient c nm The physical meaning of is the influence of the radiation field of the nth antenna element on the radiation field of the mth antenna when there is coupling;

[0022] The coupled field is represented by a linear combination of several uncoupled fields, and the above formula is simplified in matrix form as follows:

[0023]

[0024] in is the recorded coupled electric field, is the recorded uncoupled electric field, C is given by the above coupling coefficient c nm The coupling matrix composed of and In the case of a matrix, the calculation formula of the C matrix is:

[0025]

[0026] Furthermore, the coupling matrix and the communication model are integrated as follows:

[0027] The radiation pattern of the uncoupled antenna array is expressed as:

[0028]

[0029] in is the radiation pattern of a single antenna element without coupling, κ is the wave number, is a unit vector pointing in the direction of the user, r m is the spatial position of the mth antenna;

[0030] The antenna radiation pattern is sampled and recorded to obtain the radiation intensity of the array at different angles in space. matrix, L is the number of scatterers, N is t is the number of antenna elements; each column represents the radiation pattern of different antennas for a single scattering direction, and each row represents the radiation intensity of the same antenna for different directions; when a single antenna element is excited by current, its radiation pattern becomes where i is a complex excitation containing amplitude and phase; therefore, the uncoupled array radiation after excitation is IR, where I = diag(i) represents the simulated excitation vector of the antenna array; finally, the actual array radiation pattern after coupling is CIR, which is multiplied by the channel matrix S of dimension L × K, and the received signal vector can be written as y = (CIRS) T W BB x+n; where x is the signal vector, K is the number of users, W BB is the digital beamforming matrix, y is the receive vector, and n is the noise vector.

[0031] Furthermore, the optimal analog beamforming and the optimal digital beamforming are calculated under the single-user model as follows:

[0032] The SNR for single-user reception is expressed as

[0033]

[0034] Since both analog excitation and digital beamforming have energy constraints in actual transmission, it is actually necessary to maximize the corresponding received signal-to-noise ratio under fixed transmission energy conditions, specifically:

[0035]

[0036] The optimal analog beamforming vector under fixed digital beamforming conditions: By taking the derivative of the antenna array excitation vector i through the objective formula (*) and setting the result equal to 0, the optimal analog beamforming expression is obtained:

[0037]

[0038] Among them A * and A H denote the conjugate matrix and conjugate transposed matrix of matrix A respectively, w BB is the digital beamforming vector, s is the multipath channel scattering coefficient, C, R, i represent the coupling matrix, array radiation matrix and array excitation vector respectively, i t-1 represents the simulated stimulus obtained in the previous iteration, i t Represents the simulated excitation vector obtained in the current t-th cycle;

[0039] The optimal digital beamforming vector under fixed analog beamforming conditions: The antenna array excitation vector w is determined by the objective formula (*) BB Taking the derivative and setting the result equal to 0, the optimal digital beamforming expression is obtained:

[0040]

[0041] where w BB,t-1 represents the digital excitation vector obtained in the previous iteration, w BB,t Represents the digital excitation vector obtained in the current t-th cycle.

[0042] Furthermore, the optimal analog beamforming and the optimal digital beamforming are calculated under the multi-user model as follows:

[0043]

[0044] The corresponding optimization problem is

[0045]

[0046] &s.tP T,analog +P T,digital ≤P T

[0047] where e rad is the antenna array radiation efficiency, X = RS obtained by multiplying two matrices, W BB,k is the digital beamforming matrix corresponding to the kth user, σ is the standard deviation of the channel additive Gaussian noise; P T,analog , P T,digital and P T They represent the analog beamforming energy limit, the digital beamforming energy limit and the total energy limit of the transmitter respectively;

[0048] Solve the optimal antenna array analog excitation current vector under fixed digital beamforming conditions as the optimal analog beamforming: By variable substitution, it is transformed into the following optimization problem

[0049]

[0050]

[0051]

[0052] stTr(G)≤P T，analog

[0053] s.trank(G), G ≥ 0

[0054]

[0055] After removing the rank 1 constraint, the problem becomes SDP. The optimal analog beamforming matrix is ​​solved by convex optimization. The Lagrange multiplier method is used to prove that the convex optimization solution must satisfy the rank = 1 condition. Finally, the optimal analog beamforming vector is obtained by eigenvalue decomposition.

[0056] Solve the optimal digital beamforming matrix under the fixed analog beamforming condition and transform it into the following optimization problem through variable substitution:

[0057]

[0058]

[0059]

[0060]

[0061] strank(F k )=1,F k ≥0

[0062]

[0063] Where G = ii H represents the rank 1 matrix composed of the simulated excitation vector multiplied by its own conjugate transpose, Q i represents the rank 1 matrix composed of the interference vector of the i-th user to the k-th user multiplied by its own conjugate transpose; t k represents the lower limit of the signal-to-noise ratio of the kth user, u k represents the upper limit of the interference plus noise term of the kth user;

[0064] After removing the rank-1 constraint, the problem becomes the SDP problem. The optimal digital beamforming matrix is ​​solved by convex optimization. The Lagrange multiplier method is used to prove that the convex optimization solution must satisfy the rank-1 condition. Finally, a column of the optimal digital beamforming matrix is ​​obtained by eigenvalue decomposition. The above process is repeated to obtain the complete optimal beamforming matrix.

[0065] Furthermore, the goal of the geometric structure adjustment is to achieve the maximum achievable gain Realized Gain; wherein Realized Gain = efficiency * Directivity. As the spacing between antenna elements decreases, the directivity that the array can achieve increases, but as the element spacing d decreases, the coupling effect increases and the radiation efficiency of the antenna decreases. The maximum achievable gain Realized Gain is obtained through simulation.

[0066] On the other hand, the present invention provides an analog-digital joint beamforming device, including a memory and one or more processors, wherein the memory stores executable code, and when the one or more processors execute the executable code, they are used to implement the steps of the analog-digital joint beamforming method.

[0067] The beneficial effects of the present invention are as follows:

[0068] By incorporating the actual array radiation pattern taking into account the electromagnetic coupling characteristics into the modeling of the communication system, the analog-digital joint beamforming method based on the super-directional heterogeneous holographic MIMO antenna array takes into account the electromagnetic characteristics more comprehensively than the traditional method, combining the communication information theory and the actual physical transmission environment. In addition, by utilizing the super-directional beam generated by electromagnetic coupling, the antenna radiation energy is more focused at the user, improving the communication quality of each user while reducing the signal interference between different users, ultimately achieving higher communication and speed.

[0069] In the novel analog-digital joint beamforming theory and method, the analog excitation design adjusts the antenna radiation pattern in real time based on the electromagnetic coupling effect, thereby generating a super-directional beam, adapting to the communication environment, and improving the performance gain of the communication system; the digital beamforming matrix designs the optimal digital beamforming according to the antenna pattern and the characteristics of the wireless link, and combines the analog beamforming to iteratively improve the system performance.

[0070] For joint beamforming in a single-user scenario with a 3D stereo super-directional antenna, analog beamforming can achieve highly directional beam alignment based on the spatial azimuth of the user, and digital beamforming can adapt to random channels. As the user's position changes, it only requires estimating the user's azimuth to quickly iterate and generate the optimal super-directional beam aligned with the user's position.

[0071] For beamforming in multi-user scenarios with 3D stereo super-directional antennas, the proposed joint beamforming method can achieve super-directional beam alignment for multiple users and reduce interference between users, thereby reducing interference between users while improving energy efficiency and communication rate, which is a significant improvement compared to traditional MIMO array implementations.

[0072] In order to solve the problem that the radiation efficiency of 3D stereo super-directional antennas with electromagnetic coupling may be low, we made a trade-off between the antenna array structure design and the coupling effect strength, and made a compromise between the theoretical directional gain and the practical achievable gain, thus realizing a 3D stereo super-directional antenna with actual energy gain. BRIEF DESCRIPTION OF THE DRAWINGS

[0073] Figure 1 It is a communication scenario diagram of the research problem of the present invention;

[0074] Figure 2 It is a schematic diagram of a multi-directional super-directional beam generated by a 3D stereoscopic super-directional antenna of the present invention;

[0075] Figure 3 It is a schematic diagram showing the variation of the single-user communication rate of the single-layer 3D stereoscopic super-directional antenna according to the present invention with the spacing of antenna elements;

[0076] Figure 4 It is a schematic diagram showing the variation of multi-user communication rate of a single-layer 3D stereoscopic super-directional antenna according to the present invention with the spacing of antenna elements;

[0077] Figure 5 It is a schematic diagram showing the variation of the communication rate of the single-layer 3D stereoscopic super-directional antenna according to the present invention with respect to the SNR;

[0078] Figure 6 It is a schematic diagram showing the variation of the communication rate of a single user of the multi-layer 3D stereoscopic super-directional antenna according to the present invention with the spacing of antenna elements;

[0079] Figure 7 It is a schematic diagram showing the variation of the multi-user communication rate of the multi-layer 3D stereoscopic super-directional antenna according to the present invention with the spacing of antenna elements;

[0080] Figure 8 It is a schematic diagram showing the variation of the communication rate of the multi-layer 3D stereoscopic super-directional antenna according to the present invention with respect to the SNR;

[0081] Fig. 9 It is a structural diagram of an analog-digital joint beamforming device of the present invention. DETAILED DESCRIPTION

[0082] The specific implementation modes of the present invention are further described in detail below with reference to the accompanying drawings.

[0083] The present invention describes an example of a novel analog-digital joint beamforming theory and method. The disclosed analog-digital joint beamforming method includes the design of a 3D stereo super-directional antenna and analog-digital joint beamforming. The disclosed 3D stereo super-directional antenna includes a dense array of radiation units and an excitation circuit, and there is a coupling effect between the radiation units. The analog-digital joint beamforming design includes two parts: an analog excitation design and a digital beamforming matrix. The analog excitation design adjusts the antenna radiation pattern in real time based on the electromagnetic coupling effect, thereby generating a super-directional beam, adapting to the communication environment, and improving the performance gain of the communication system; the digital beamforming matrix designs the optimal digital beamforming according to the antenna pattern and the characteristics of the wireless link, and combines the analog beamforming to iteratively improve the system performance.

[0084] In an embodiment of the present invention, the design of a 3D stereoscopic super-directional antenna including a plurality of radiating elements includes: the array includes at least one column including a plurality of radiating elements, and the array is used to generate a radiation field.

[0085] In any of the above aspects / embodiments, an electromagnetic coupling effect is included between the multiple radiation units.

[0086] In any of the above aspects / embodiments, the array comprises a single column of radiating elements.

[0087] In any of the above aspects / embodiments, the array comprises a plurality of columns of radiating elements in the same plane.

[0088] In any of the above aspects / embodiments, the array comprises a plurality of different planar columns having radiating elements.

[0089] The joint beamforming includes calculation of the theoretical radiation pattern of the array of multiple radiating elements, wherein the array includes at least one column with multiple radiating elements, and the theoretical radiation pattern of the array consists of the radiation pattern of a single radiating element and a linear phase shift vector along the axis of the radiating element array. The joint beamforming also includes the coupling matrix influence of multiple radiating elements, wherein the electromagnetic radiation between the radiating elements will couple with each other, thereby changing the theoretical spatial radiation pattern of the radiating antenna array. The joint beamforming theory also includes spherical wave expansion of the radiation patterns of multiple radiating elements, wherein the radiation patterns of the multiple radiating elements can be fully simulated with and without coupling, and the obtained electric fields can be spherically expanded. The joint beamforming theory also includes calculation of the coupling matrix of multiple radiating elements, wherein the electromagnetic coupling coefficients between the radiating elements can be determined based on the spherical wave expansion coefficients of the radiation patterns of the multiple radiating elements.

[0090] In the communication environment of the embodiment of the present invention, the random scattering channel generation includes that there are L scatterers and K users in the communication environment containing random scatterers, and the link channel coefficients from the 3D stereoscopic super-directional antenna to the user via these scatterers can be represented by an L×K matrix. The array theoretical radiation matrix calculation of multiple radiating units includes that the array theoretical radiation pattern of the multiple radiating units is a function of the spatial azimuth angle, and the array theoretical radiation matrix of the multiple radiating units is obtained by sampling and recording the spatial radiation coefficients for the L scatterer azimuths. The array actual radiation matrix calculation of multiple radiating units includes that the array theoretical radiation matrix is ​​an actual radiation matrix in space after being subjected to simulated excitation beamforming modulation and coupling matrix. The comprehensive channel model integrating antenna pattern and electromagnetic coupling effect includes that the array actual radiation matrix acts on the random scattering channel to generate a comprehensive channel model integrating actual antenna radiation. The signal transmission model integrating antenna pattern includes that the transmitted signal is modulated by the digital beamforming algorithm and then passes through the comprehensive channel model to obtain a received signal integrating actual antenna radiation. The joint beamforming theory also includes an iterative optimization algorithm for analog digital beamforming in a single-user communication scenario, wherein the best analog beamforming vector under fixed digital beamforming conditions and the best digital beamforming vector under fixed analog beamforming conditions can be directly obtained by derivation in a single-user communication scenario, and the calculation process of the two can be iteratively optimized. The joint beamforming theory also includes an iterative optimization algorithm for analog digital beamforming in a multi-user communication scenario, wherein, due to the existence of inter-user interference in a multi-user communication scenario, the sum rate maximization problem is converted into an SDP problem by variable conversion when the digital beamforming is fixed, and the convex optimization toolkit is used to solve the optimal antenna array analog excitation current vector under the fixed digital beamforming condition as the optimal analog beamforming; the sum rate maximization problem is converted into an SDP problem by variable conversion when the digital beamforming is fixed, and the convex optimization toolkit is used to solve the optimal digital beamforming matrix under the fixed analog beamforming condition, and the calculation process of the two can be iteratively optimized.

[0091] In any of the above aspects / embodiments, the radiating unit may have any radiation pattern;

[0092] In any of the above aspects / embodiments, the spherical wave expansion is a spatially complete orthogonal basis function that can fully describe any electric field distribution;

[0093] In any of the above aspects / embodiments, the radiating element array may have any antenna spacing; the antenna spacing within half a wavelength is effective;

[0094] In any of the above aspects / embodiments, the joint beamforming algorithm may be applicable to communication scenarios with only spatial scattering paths.

[0095] In any of the above aspects / embodiments, the joint beamforming algorithm can be applicable to communication scenarios where direct paths and scattered paths exist simultaneously in space.

[0096] In any of the above aspects / embodiments, the joint beamforming algorithm may be applicable to a scenario where there are users randomly distributed at a single position in space.

[0097] In any of the above aspects / embodiments, the joint beamforming algorithm may be applicable to a scenario where there are multiple users randomly distributed in space.

[0098] In an embodiment of the present invention, the base station includes a 3D stereo super-directional antenna for sending and receiving in wireless communications. The base station also includes an array of multiple radiating elements, wherein the array includes at least one column with multiple radiating elements, and the array is used to generate a radiation field. The 3D stereo super-directional antenna also includes an excitation circuit for providing excitation to the radiating element array, wherein the excitation circuit provides the required excitation to the radiating element, so that the 3D stereo super-directional antenna generates a super-directional beam. The base station also includes a transmitter coupled to the 3D stereo super-directional antenna for providing a transmission signal. The base station also includes a receiver coupled to the 3D stereo super-directional antenna for receiving a reception signal. The excitation provided by the excitation circuit in the 3D stereo super-directional antenna is determined according to the analog-digital joint beamforming theory, and the amplitude and phase can be adjusted arbitrarily.

[0099] In any of the above aspects / embodiments, in the excitation circuit of the 3D stereo super-directional antenna, the excitation provided by the excitation circuit is determined according to the analog-digital joint beamforming theory, and the joint beamforming theory is based on the coupling effect, the spatial position and spatial radiation pattern of the radiating unit, and the random scattering characteristics of the spatial channel.

[0100] Specifically, the specific implementation steps of the analog-digital joint beamforming solution of the present invention in the 3D stereoscopic super-directional antenna transmission and single-user reception communication scenario are as follows:

[0101] S1, 3D stereoscopic super-directional antenna transmission, single-user reception communication scenario modeling: Figure 1 As shown, the present invention studies a communication system downlink in which the transmitting end is equipped with the 3D stereoscopic super-directional antenna transmitting array and the receiving end is a single-user receiving end. The base station (BS) deploys a 3D stereoscopic super-directional antenna to generate a super-directional beam for the user to improve the transmission quality. The 3D stereoscopic super-directional antenna is composed of N tThe 3D super-directional antenna and the target user are in a random scattering environment. There may be a direct link between the BS and the user, as well as a reflection link through a reflector. Since the position of the base station is fixed, for simplicity, we assume that the elevation angle and horizontal angle of the scatterer in the communication environment relative to the base station can be obtained by the base station through environmental perception or channel estimation. Assuming there are L scatterers, the channel coefficients between these L scatterers and the target user can be represented by an L×1 channel vector.

[0102] S2. Super-directional beamforming: The existing beamforming algorithm does not consider the electromagnetic coupling effect between the transmitting antennas. When applied to 3D stereo super-directional antennas, the spatial beam formed will be affected by coupling distortion and cannot be aimed at the user. The new analog-digital joint beamforming theory and method proposed in this paper is divided into iterative optimization of analog and digital beamforming. The analog excitation design adjusts the antenna radiation pattern in real time based on the electromagnetic coupling effect, thereby generating a super-directional beam, adapting to the communication environment, and improving the performance gain of the communication system; the digital beamforming matrix designs the optimal digital beamforming according to the antenna pattern and the characteristics of the wireless link, and combines analog beamforming to iteratively improve system performance.

[0103] S2.1, 3D stereo super-directional antenna modeling: First, the dipole array element is modeled in commercial electromagnetic simulation software and a substrate of appropriate size is placed underneath it to meet the actual processing requirements. There are already perfect analytical expressions for the electromagnetic radiation of the dipole antenna in electromagnetics. The directional pattern of a single dipole antenna is simulated by software and compared with the analytical expression in the existing electromagnetic theory to confirm the correctness of the modeling. The radiation electric field intensity generated by the dipole antenna along the Z axis obtained by modeling follows the sin(θ) distribution law, which is consistent with the result of the analytical expression. Then, the modeled dipole array is evenly spaced in a plane (the interval is less than half a wavelength) to form a linear 3D stereo super-directional antenna. Each antenna array element theoretically has the same radiation pattern, but because of the coupling effect, the actual radiation pattern of each antenna array element needs to be simulated.

[0104] S2.2, Spherical wave expansion of radiation pattern: After the 3D super-directional antenna with dense antennas is modeled, it is necessary to calculate the electromagnetic coupling between its array elements. First, it is necessary to record the radiation patterns generated by all arrays when there is no coupling. Due to the different spatial coordinates of different antenna elements, even if their radiation patterns are the same when there is no coupling, the electromagnetic radiation intensity and phase received by different transmitting antennas at the same receiving point will be different when observed in the near field. Therefore, it is necessary to record its uncoupled radiation pattern according to the actual spatial position of the antenna array element after the 3D super-directional antenna is modeled. This is achieved by setting the array factor for a single dipole element. In the array factor setting, by specifying the coordinate difference between different array elements and the excitation coefficient of the antenna element, the linear superposition of the radiation field of different elements after being excited separately can be generated in space. The electric field generated by different elements in this way is only related to their spatial position and excitation coefficient, and naturally does not include the coupling effect of other radiating elements. The space is discretized into P directions (the elevation angle and horizontal angle of the spherical coordinates are evenly divided), and the electric field strength in the theta direction and the phi direction of each direction is recorded as the radiation field of the current solution array element.

[0105] Secondly, it is necessary to calculate the radiation patterns of different antenna elements when coupling exists. The simulation method is to model all the antenna elements of the 3D stereoscopic super-directional antenna in the simulation software, and then only excite the antenna elements that need to be solved to generate electromagnetic radiation when setting the excitation of the array. The other antenna elements are connected to the matching impedance network as loads, and the space is also discretized into P directions, and the electric field strength in the theta direction and the phi direction of each direction is recorded. Further, this process is repeated for all modeled antenna elements, and the radiation field generated when all elements are only excited is recorded.

[0106] Finally, after obtaining the radiation fields with and without coupling, the radiation fields can be expanded by the spherical wave coefficients:

[0107]

[0108] in is the wave number, where λ is the wavelength of the electromagnetic wave at the operating frequency, Z is the impedance of free space, (r,θ,φ) are the coordinate parameters of the spherical coordinate system, and the three parameters (s,n,m) represent the mode of the electromagnetic wave (TE / TM wave), the expansion dimension of the electromagnetic wave, and the expansion order of the electromagnetic wave, respectively. Q s,m,n is the spherical wave expansion coefficient, F s,m,n (r,θ,φ) is a spherical wave function, which can be used to describe any spatial radiation field as a set of complete basis functions in space. The specific expression is as follows

[0109]

[0110]

[0111]

[0112] where z n (κr) is the nth-order spherical Hankel function of the first kind, is the normalized correlation Legendre function, is the unit vector pointing to the user in the spherical coordinate system, e θ and e φ are the unit vectors in the θ and φ directions respectively.

[0113] S2.3, coupling matrix calculation:

[0114] After obtaining the radiation patterns of the 3D super-directional antenna in the uncoupled and coupled cases, we can express the coupled radiation electric field of a single element as a linear combination of the uncoupled radiation electric fields of multiple elements. If the total number of transmitting antennas is M, the uncoupled radiation field is The coupled radiation field is denoted by The linear representation is:

[0115]

[0116] The electric field coefficient e can be entered using either the actual recorded radiation electric field parameters or the spherical wave expansion coefficient. The latter is more flexible and can adjust the number of expansion items according to the required accuracy. Linear combination coefficient c nm The physical meaning of is the influence of the radiation field of the nth antenna element on the radiation field of the mth antenna when there is coupling. From the above definition, it can be seen that through the coupling matrix, we have established the connection between the coupled electromagnetic field and the uncoupled electromagnetic field, and expressed the coupled field as a linear combination of multiple uncoupled fields. Since the above multiple formulas can be abbreviated in matrix form as:

[0117]

[0118] in is the recorded coupled electric field, is the recorded uncoupled electric field, C is given by the above coupling coefficient c nm The coupling matrix composed of and In the case of a matrix, the calculation formula of the C matrix is:

[0119]

[0120] The coupling matrix can be derived from the simulation results according to the above process.

[0121] S3. Communication model of fusion antenna array radiation pattern

[0122] The radiation pattern of the uncoupled antenna array can be expressed as:

[0123]

[0124] in is the radiation pattern of a single antenna element without coupling, k is the wave number, is a unit vector pointing in the direction of the user, r m is the spatial position of the mth antenna. In addition, since the number of scatterers in space is limited, it is only necessary to sample and record the antenna radiation pattern to obtain the radiation intensity of the array at different angles in space. Matrix. Each column represents the radiation pattern of different antennas for a single scattering direction, and each row represents the radiation intensity of the same antenna for different directions. It is a matrix expression of the above formula. When a single antenna element is excited by current, its radiation pattern becomes Where i is a complex excitation containing amplitude and phase. Therefore, the uncoupled array radiation after excitation is IR, where I = diag(i) represents the simulated excitation vector of the antenna array. Finally, the actual array radiation pattern after coupling is CIR. After multiplying it by the previously modeled channel matrix S of dimension L×K, the received signal vector can be written as y = (CIRS) T W BB x+n. Where x is the signal vector, W BB is the digital beamforming matrix, y is the receive vector, and n is the receive vector.

[0125] S3.1, 3D stereoscopic super-directional antenna single-user beamforming

[0126] According to the above communication model, the SNR of a single user can be expressed as

[0127]

[0128] Since both analog excitation and digital beamforming have energy constraints in actual transmission, the corresponding received signal-to-noise ratio under the condition of maximizing fixed transmission energy is:

[0129]

[0130] S3.2, 3D stereoscopic super-directional antenna single-user analog beamforming

[0131] By taking the derivative of the antenna array excitation vector i through the objective formula (*) and setting the result equal to 0, we can get the optimal analog beamforming expression:

[0132]

[0133] Among them A * and A H They represent the conjugate matrix and conjugate transposed matrix of matrix A respectively. BB is the digital beamforming vector, s is the multipath channel scattering coefficient, C, R, i have the same meaning as above, representing the coupling matrix, array radiation matrix and array excitation vector respectively, i t-1 represents the simulated stimulus obtained in the previous iteration, i t Represents the simulated excitation vector obtained in the current t-th cycle.

[0134] S3.3, 3D stereoscopic super-directional antenna single-user digital beamforming

[0135] Similarly, the antenna array excitation vector w is given by the target formula (*) BB Taking the derivative and setting the result equal to 0, we can get the optimal digital beamforming expression as

[0136]

[0137] where w BB,t-1 represents the digital excitation vector obtained in the previous iteration, w BB,t Represents the digital excitation vector obtained in the current t-th cycle.

[0138] S4. Super-directional array structure optimization

[0139] Although theoretical analysis shows that as the spacing between antenna elements decreases, the directivity that the array can achieve increases, for a linear antenna array with N antenna elements, the maximum directivity that can be achieved when the element spacing d→0 is N 2. However, through simulation experiments, it is found that as the element spacing d decreases, the coupling effect increases, the radiation efficiency of the antenna decreases, and there is a radiation efficiency jump zone in the range of d = 0.35λ→0.2λ (the antenna radiation efficiency drops sharply). The reduction in antenna radiation efficiency means that the increase in directivity does not necessarily translate into an increase in actual energy efficiency. This is because the actual antenna energy gain Realized Gain = efficiency*Direcitivity. When the antenna spacing is too large, the radiation efficiency is high but the achievable directivity is low; when the antenna spacing is too small, the directivity is high but the radiation efficiency is too low. Both will lead to too small an achievable energy gain. Therefore, the design of the array geometry must be optimized. The analog and digital beamforming expressions derived above can be used to simulate and find the optimal antenna element spacing for a 3D stereo super-directional antenna. The judgment criterion is to achieve the maximum achievable gain, that is, to achieve the best trade-off between radiation efficiency and directivity.

[0140] The specific implementation steps of the beamforming scheme of the present invention in the 3D stereoscopic super-directional antenna multi-user reception communication scenario are:

[0141] S1, 3D stereoscopic super-directional antenna transmission, single-user reception communication scenario modeling: Figure 1 As shown in FIG. 1 , the present invention studies a downlink communication system in which the transmitting end is equipped with a 3D stereoscopic super-directional transmitting antenna and the receiving end is a single-user receiving system. A 3D stereoscopic super-directional antenna is deployed at the base station (BS) end to generate a super-directional beam through joint beamforming while adapting to the channel randomness to improve the transmission quality. The 3D stereoscopic super-directional antenna is composed of N t The 3D super-directional antenna and the target user are composed of densely distributed antenna elements. We assume that the 3D stereoscopic super-directional antenna and the target user are in a random scattering environment. There may be a direct link between the BS and the user, as well as a reflection link through a reflector. Since the position of the base station is fixed, for the sake of simplicity, we assume that the elevation angle and horizontal angle of the scatterer in the communication environment relative to the base station can be obtained by the base station through methods such as environmental perception or channel estimation. Assuming there are L scatterers and K users, the channel coefficients between these L scatterers and the target user can be represented by an L×K channel matrix.

[0142] S2. Super-directional beamforming: The existing beamforming algorithm does not consider the electromagnetic coupling effect between the transmitting antennas. When applied to 3D stereo super-directional antennas, the spatial beam formed will be affected by coupling distortion and cannot be aimed at the user. The new analog-digital joint beamforming theory and method proposed in this paper is divided into iterative optimization of analog and digital beamforming. The analog excitation design adjusts the antenna radiation pattern in real time based on the electromagnetic coupling effect, thereby generating a super-directional beam, adapting to the communication environment, and improving the performance gain of the communication system; the digital beamforming matrix designs the optimal digital beamforming according to the antenna pattern and the characteristics of the wireless link, and combines analog beamforming to iteratively improve system performance.

[0143] S2.1, 3D stereo super-directional antenna modeling: First, the dipole array element is modeled in commercial electromagnetic simulation software and a substrate of appropriate size is placed underneath it to meet the actual processing requirements. There are already perfect analytical expressions for the electromagnetic radiation of the dipole antenna in electromagnetics. The directional pattern of a single dipole antenna is simulated by software and compared with the analytical expression in the existing electromagnetic theory to confirm the correctness of the modeling. The radiation electric field intensity generated by the dipole antenna along the Z axis obtained by modeling follows the sin(θ) distribution law, which is consistent with the result of the analytical expression. Then, the modeled dipole array is evenly spaced in a plane (the interval is less than half a wavelength) to form a linear 3D stereo super-directional antenna. Each antenna array element theoretically has the same radiation pattern, but because of the coupling effect, the actual radiation pattern of each antenna array element needs to be simulated.

[0144] S2.2, Spherical wave expansion of radiation pattern: After the 3D super-directional antenna with dense antennas is modeled, it is necessary to calculate the electromagnetic coupling between its array elements. First, it is necessary to record the radiation patterns generated by all arrays when there is no coupling. Due to the different spatial coordinates of different antenna elements, even if their radiation patterns are the same when there is no coupling, the electromagnetic radiation intensity and phase received by different transmitting antennas at the same receiving point will be different when observed in the near field. Therefore, it is necessary to record its uncoupled radiation pattern according to the actual spatial position of the antenna array element after the 3D super-directional antenna is modeled. This is achieved by setting the array factor for a single dipole element. In the array factor setting, by specifying the coordinate difference between different array elements and the excitation coefficient of the antenna element, the linear superposition of the radiation field of different elements after being excited separately can be generated in space. The electric field generated by different elements in this way is only related to their spatial position and excitation coefficient, and naturally does not include the coupling effect of other radiating elements. The space is discretized into P directions (the elevation angle and horizontal angle of the spherical coordinates are evenly divided), and the electric field strength in the theta direction and the phi direction of each direction is recorded as the radiation field of the current solution array element.

[0145] Secondly, it is necessary to calculate the radiation patterns of different antenna elements when coupling exists. The simulation method is to model all the antenna elements of the 3D stereoscopic super-directional antenna in the simulation software, and then only excite the antenna elements that need to be solved to generate electromagnetic radiation when setting the excitation of the array. The other antenna elements are connected to the matching impedance network as loads, and the space is also discretized into P directions, and the electric field strength in the theta direction and the phi direction of each direction is recorded. Further, this process is repeated for all modeled antenna elements, and the radiation field generated when all elements are only excited is recorded.

[0146] Finally, after obtaining the radiation fields with and without coupling, the radiation fields can be expanded using the spherical wave coefficients:

[0147]

[0148] in is the wave number, where λ is the wavelength of the electromagnetic wave at the operating frequency, Z is the impedance of free space, (r,θ,φ) are the coordinate parameters of the spherical coordinate system, and the three parameters (s,n,m) represent the mode of the electromagnetic wave (TE / TM wave), the expansion dimension of the electromagnetic wave, and the expansion order of the electromagnetic wave, respectively. Q s,m,n is the spherical wave expansion coefficient, F s,m,n (r,θ,φ) is a spherical wave function. As a set of complete basis functions in space, it can be used to describe any spatial radiation field. Its specific expression is as follows:

[0149]

[0150]

[0151]

[0152] where z n (κr) is the nth-order spherical Hankel function of the first kind, is the normalized correlation Legendre function, is the unit vector pointing to the user in the spherical coordinate system, e θ and e φ are the unit vectors in the θ and φ directions respectively.

[0153] S2.3, coupling matrix calculation:

[0154] After obtaining the radiation patterns of the 3D super-directional antenna in the uncoupled and coupled cases, we can express the coupled radiation electric field of a single element as a linear combination of the uncoupled radiation electric fields of multiple elements. If the total number of transmitting antennas is M, the uncoupled radiation field is The coupled radiation field is denoted by The linear representation is:

[0155]

[0156] The electric field coefficient e can be entered using either the actual recorded radiation electric field parameters or the spherical wave expansion coefficient. The latter is more flexible and can adjust the number of expansion items according to the required accuracy. Linear combination coefficient c nm The physical meaning of is the influence of the radiation field of the nth antenna element on the radiation field of the mth antenna when there is coupling. From the above definition, it can be seen that through the coupling matrix, we have established the connection between the coupled electromagnetic field and the uncoupled electromagnetic field, and expressed the coupled field as a linear combination of multiple uncoupled fields. Since the above multiple formulas can be abbreviated in matrix form as:

[0157]

[0158] in is the recorded coupled electric field, is the recorded uncoupled electric field, C is given by the above coupling coefficient c nm The coupling matrix composed of and In the case of a matrix, the calculation formula of the C matrix is:

[0159]

[0160] The coupling matrix can be derived from the simulation results according to the above process.

[0161] S2.4 Communication model of fusion antenna array radiation pattern

[0162] The radiation pattern of the uncoupled antenna array can be expressed as:

[0163]

[0164] in is the radiation pattern of a single antenna element without coupling, κ is the wave number, is a unit vector pointing in the direction of the user, r m is the spatial position of the mth antenna. In addition, since the number of scatterers in space is limited, it is only necessary to sample and record the antenna radiation pattern to obtain the radiation intensity of the array at different angles in space. Matrix. Each column represents the radiation pattern of different antennas for a single scattering direction, and each row represents the radiation intensity of the same antenna for different directions. It is a matrix expression of the above formula. When a single antenna element is excited by current, its radiation pattern becomes Where i is a complex excitation containing amplitude and phase. Therefore, the uncoupled array radiation after excitation is IR, where I = diag(i) represents the simulated excitation vector of the antenna array. Finally, the actual array radiation pattern after coupling is CIR. After multiplying it by the previously modeled channel matrix S of dimension L×K, the received signal vector can be written as y = (CIRS) T W BB x+n. Where x is the signal vector, W BB is the digital beamforming matrix, y is the receive vector, and n is the noise vector.

[0165] S3, 3D stereoscopic super-directional antenna multi-user beamforming

[0166] According to the above communication model, the SINR considering interference during multi-user reception can be expressed as

[0167]

[0168] The corresponding optimization problem is

[0169]

[0170] &s.tP T,analog +P T,digital ≤P T

[0171] where e rad is the antenna array radiation efficiency, X = RS obtained by multiplying two matrices, W BB,k is the digital beamforming matrix corresponding to the kth user, and σ is the standard deviation of the channel additive Gaussian noise. T,analog , P T,digital and P T They represent the analog beamforming energy limit, digital beamforming energy limit and the total energy limit of the transmitter respectively.

[0172] S3.1. Multi-user analog beamforming

[0173] By variable substitution, it is transformed into the following optimization problem

[0174]

[0175]

[0176]

[0177] stTr(G)≤P T，analog

[0178] strank(G), G ≥ 0

[0179]

[0180] Where G = ii H represents the rank 1 matrix composed of the simulated excitation vector multiplied by its own conjugate transpose, Q i represents the rank 1 matrix composed of the interference vector of the i-th user to the k-th user multiplied by its own conjugate transpose; t k represents the lower limit of the signal-to-noise ratio of the kth user, u k represents the upper limit of the interference plus noise term of the kth user.

[0181] After removing the rank 1 constraint, the problem becomes the SDP problem. The optimal analog beamforming matrix can be solved by convex optimization, and the Lagrange multiplier method can be used to prove that the convex optimization solution must satisfy the rank = 1 condition. Finally, the optimal analog beamforming vector can be obtained by eigenvalue decomposition (SVD).

[0182] S3.2 Multi-user digital beamforming

[0183] By variable substitution, it is transformed into the following optimization problem

[0184]

[0185]

[0186]

[0187]

[0188] strank(F k )=1,F k ≥0

[0189]

[0190] in H represents the rank 1 matrix composed of the digital beamforming vector corresponding to the kth user multiplied by its own conjugate transpose. k represents the rank 1 matrix consisting of the channel vector corresponding to the kth user multiplied by its own conjugate transpose; t k represents the lower limit of the signal-to-noise ratio of the kth user, u k represents the upper limit of the interference plus noise term of the kth user.

[0191] After removing the rank 1 constraint, the problem becomes the SDP problem. The optimal digital beamforming matrix can be solved by convex optimization, and the Lagrange multiplier method can be used to prove that the convex optimization solution must satisfy the rank = 1 condition. Finally, one column of the optimal digital beamforming matrix can be obtained by eigenvalue decomposition (SVD). Repeating the above process can obtain the complete optimal beamforming matrix.

[0192] The 3D stereoscopic super-directional antenna array obtained by the above modeling and the corresponding multi-directional super-directional beams are shown in Figure 2 shown.

[0193] S4. Super-directional array structure optimization

[0194] Although theoretical analysis shows that as the spacing between antenna elements decreases, the directivity that the array can achieve increases, for a linear antenna array with N antenna elements, the maximum directivity that can be achieved when the element spacing d→0 is N 2 . However, through simulation experiments, it is found that as the element spacing d decreases, the coupling effect increases, the radiation efficiency of the antenna decreases, and there is a radiation efficiency jump zone in the range of d = 0.35λ→0.2λ (the antenna radiation efficiency drops sharply). The reduction in antenna radiation efficiency means that the increase in directivity does not necessarily translate into an increase in actual energy efficiency. This is because the actual antenna energy gain Realized Gain = efficiency*Directivity. When the antenna spacing is too large, the radiation efficiency is high but the achievable directivity is low; when the antenna spacing is too small, the directivity is high but the radiation efficiency is too low. Both will lead to too small an achievable energy gain. Therefore, the design of the array geometry must be optimized. The analog and digital beamforming expressions derived above can be used to simulate and find the optimal antenna element spacing for a 3D stereo super-directional antenna. The judgment criterion is to achieve the maximum achievable gain, that is, to achieve the best trade-off between radiation efficiency and directivity.

[0195] The functions and effects of the present invention are further illustrated by the following simulation experiments:

[0196] (1) Single-layer 3D stereoscopic super-directional antenna single user scenario

[0197] (1.1) Simulation conditions

[0198] Assume that the number of users is K=1, the number of scatterers is L=3, the number of 3D super-directional antenna layers is B=1, the antenna array operating frequency is 1.6GHz, and the antenna array is composed of microstrip dipole antennas. For simplicity, for the 3D super-directional antenna array, the embodiment of the present invention considers a group of antenna arrays deployed in the xy plane, where the antenna elements are arranged along the x-axis, and the multi-layer antennas are arranged along the y-axis. In the simulation, the embodiment of the present invention considers two cases of 3D super-directional antenna arrays: the array aperture area remains unchanged, and the number of antennas is inversely proportional to the antenna spacing; the total number of antennas remains unchanged, and the array aperture is directly proportional to the antenna spacing. In addition, the simulation assumes that the user is in the vertical plane of the 3D super-directional antenna, so the elevation angle from the 3D super-directional antenna to each user is The horizontal azimuth is θa ∈[0,2π]. The excitation energy of the antenna array is set to 1W in the simulation.

[0199] During simulation, the embodiment of the present invention compares the heterogeneous antenna hybrid beamforming method of the present invention with the ZF method in the existing MIMO array that does not consider coupling in terms of the communication rate index obtained by the array.

[0200] (1.2) Simulation results

[0201] Figure 3 The effect of the antenna element spacing on the communication rate of a single-user 3D stereo super-directional antenna when the antenna array aperture area is fixed is plotted. Under the same simulation scenario setting, it can be seen from the simulation results that as the antenna element spacing changes, the method proposed in the embodiment of the present invention is always better than the ZF algorithm without considering coupling. This is because the super-directional analog beamforming method proposed in the present invention is based on the coupling effect between the radiating units of the 3D stereo super-directional antenna array. When the element spacing decreases, the array coupling effect will also be enhanced accordingly, and the corresponding super-directivity is improved. However, the coupling effect will cause the radiation efficiency of the antenna array to decrease, thereby reducing the proportion of the directional gain converted into the actual energy gain of the antenna transmission. Therefore, there is a trade-off between directivity and radiation efficiency. The result of the trade-off between these two factors is that the communication rate curve shows a trend of first increasing and then decreasing: in the small interval part, due to the low radiation efficiency, the gain that can be achieved is not high; in the large interval part, due to the weak coupling effect of the antenna element, the super-directivity is not obvious, and in the area with high radiation efficiency and strong coupling effect, the application of this heterogeneous antenna structure and the proposed joint beamforming method achieves a higher antenna energy gain, which can effectively reduce communication energy loss or increase communication rate.

[0202] (2) Multi-layer 3D stereoscopic super-directional antenna single user scenario

[0203] (2.1) Simulation conditions

[0204] Assume that the number of users is K=1, the number of scatterers is L=3, the number of 3D super-directional antenna layers is B=4, the antenna array operating frequency is 1.6GHz, and the antenna array is composed of microstrip dipole antennas. For simplicity, for the 3D super-directional antenna, the embodiment of the present invention considers a group of antenna arrays deployed in the xy plane, where the antenna elements are arranged along the x-axis, and the multi-layer antennas are arranged along the y-axis. In the simulation, the embodiment of the present invention considers two cases of 3D super-directional antennas: the array aperture area remains unchanged, and the number of antennas is inversely proportional to the antenna spacing; the total number of antennas remains unchanged, and the array aperture is directly proportional to the antenna spacing. In addition, the simulation assumes that the user is in the vertical plane of the 3D super-directional antenna, so the elevation angle from the 3D super-directional antenna to each user is The horizontal azimuth is θa ∈[0,2π]. The excitation energy of the antenna array is set to 1W in the simulation.

[0205] During simulation, the embodiment of the present invention compares the communication rate index obtained by the array with the novel analog-digital hybrid beamforming theory of the present invention and the ZF method without considering coupling in the existing MIMO array.

[0206] (2.2) Simulation results

[0207] Figure 6 The effect of the antenna element spacing on the communication rate of a single-user 3D stereo super-directional antenna system when the antenna array aperture area is fixed is plotted. Under the same simulation scenario setting, it can be seen from the simulation results that as the antenna element spacing changes, the method proposed in the embodiment of the present invention is always better than the ZF algorithm without considering coupling. This is because the super-directional analog beamforming method proposed in the present invention is based on the coupling effect between the 3D stereo super-directional antenna radiation units. When the element spacing decreases, the array coupling effect will also be enhanced accordingly, and the corresponding super-directivity is improved. However, the coupling effect will cause the radiation efficiency of the antenna array to decrease, thereby reducing the proportion of the directional gain converted into the actual energy gain of the antenna transmission. Therefore, there is a trade-off between directivity and radiation efficiency. The result of the trade-off between these two factors is that the communication rate curve shows a trend of first increasing and then decreasing: in the small interval part, due to the low radiation efficiency, the gain that can be achieved is not high; in the large interval part, due to the weak coupling effect of the antenna element, the super-directivity is not obvious, and in the area with high radiation efficiency and strong coupling effect, the application of this heterogeneous antenna structure and the proposed joint beamforming method achieves a higher antenna energy gain, which can effectively reduce communication energy loss or increase communication rate.

[0208] (3) Single-layer 3D stereoscopic super-directional antenna multi-user scenario

[0209] (3.1) Simulation conditions

[0210] Set the number of users to K=2, the number of scatterers to L=3, the number of 3D super-directional antenna layers to B=1, the antenna array operating frequency to 1.6GHz, and the antenna array to consist of microstrip dipole antennas. For simplicity, for the 3D super-directional antenna, the embodiment of the present invention considers a group of antenna arrays deployed in the xy plane, where the antenna elements are arranged along the x-axis, and the multi-layer antennas are arranged along the y-axis. In the simulation, the embodiment of the present invention considers two 3D super-directional antenna situations: the array aperture area remains unchanged, and the number of antennas is inversely proportional to the antenna spacing; the total number of antennas remains unchanged, and the array aperture is directly proportional to the antenna spacing. In addition, the simulation assumes that the user is on the vertical plane of the 3D super-directional antenna, so the elevation angle from the 3D super-directional antenna to each user is The horizontal azimuth is θa ∈[0,2π]. The excitation energy of the antenna array is set to 1W in the simulation.

[0211] During simulation, the embodiment of the present invention compares the communication rate index obtained by the array by using the analog-digital hybrid beamforming theory and the ZF method that does not consider coupling in the existing MIMO array:

[0212] (3.2) Simulation results

[0213] Figure 4 The effect of the antenna element spacing on the communication rate of a single-user 3D stereo super-directional antenna when the antenna array aperture area is fixed is plotted. Under the same simulation scenario setting, it can be seen from the simulation results that as the antenna element spacing changes, the method proposed in the embodiment of the present invention is always better than the ZF algorithm without considering coupling. This is because the super-directional analog beamforming method proposed in the present invention is based on the coupling effect between the 3D stereo super-directional antenna radiation units. When the element spacing decreases, the array coupling effect will also be enhanced accordingly, and the corresponding super-directivity is improved. However, the coupling effect will cause the radiation efficiency of the antenna array to decrease, thereby reducing the proportion of the directional gain converted into the actual energy gain of the antenna transmission. Therefore, there is a trade-off between directivity and radiation efficiency. The result of the trade-off between these two factors is that the communication rate curve shows a trend of first increasing and then decreasing: in the small interval part, due to the low radiation efficiency, the gain that can be achieved is not high; in the large interval part, due to the weak coupling effect of the antenna element, the super-directivity is not obvious, and in the area with high radiation efficiency and strong coupling effect, the application of this heterogeneous antenna structure and the proposed joint beamforming method achieves a higher antenna energy gain, which can effectively reduce communication energy loss or increase communication rate.

[0214] (4) Multi-layer 3D stereoscopic super-directional antenna multi-user scenario

[0215] (4.1) Simulation conditions

[0216] Set the number of users to K=2, the number of scatterers to L=3, the number of 3D super-directional antenna layers to B=4, the antenna array operating frequency to 1.6GHz, and the antenna array to consist of microstrip dipole antennas. For simplicity, for the 3D super-directional antenna, the embodiment of the present invention considers a group of antenna arrays deployed in the xy plane, where the antenna elements are arranged along the x-axis, and the multi-layer antennas are arranged along the y-axis. In the simulation, the embodiment of the present invention considers two cases of 3D super-directional antennas: the array aperture area remains unchanged, and the number of antennas is inversely proportional to the antenna spacing; the total number of antennas remains unchanged, and the array aperture is directly proportional to the antenna spacing. In addition, the simulation assumes that the user is on the vertical plane of the 3D super-directional antenna, so the elevation angle from the 3D super-directional antenna to each user is The horizontal azimuth is θ a∈[0,2π]. The excitation energy of the antenna array is set to 1W in the simulation.

[0217] During simulation, the embodiment of the present invention compares the communication rate index obtained by the array with the novel analog-digital hybrid beamforming theory of the present invention and the ZF method without considering coupling in the existing MIMO array.

[0218] (4.2) Simulation results

[0219] Figure 7 The effect of the antenna element spacing on the communication rate of the multi-user multi-layer 3D stereo super-directional antenna system when the antenna array aperture area is fixed is plotted. Under the same simulation scene setting, it can be seen from the simulation results that as the antenna element spacing changes, the method proposed in the embodiment of the present invention is always better than the ZF algorithm without considering coupling. This is because the super-directional analog beamforming method proposed in the present invention is based on the coupling effect between the 3D stereo super-directional antenna radiation units. When the element spacing decreases, the array coupling effect will also be enhanced accordingly, and the corresponding super-directivity is improved. However, the coupling effect will cause the radiation efficiency of the antenna array to decrease, thereby reducing the proportion of the directional gain converted into the actual energy gain of the antenna transmission. Therefore, there is a trade-off between directivity and radiation efficiency. The result of the trade-off between these two factors is that the communication rate curve shows a trend of first increasing and then decreasing: in the small interval part, due to the low radiation efficiency, the gain that can be achieved is not high; in the large interval part, due to the weak coupling effect of the antenna element, the super-directivity is not obvious, and in the area with high radiation efficiency and strong coupling effect, the application of this heterogeneous antenna structure and the proposed joint beamforming method achieves a higher antenna energy gain, which can effectively reduce communication energy loss or increase communication rate.

[0220] (5) Multi-user SNR variation scenario with multi-layer 3D stereoscopic super-directional antenna

[0221] (5.1) Simulation conditions

[0222] Assume that the number of users is K=2, the number of scatterers is L=3, the number of 3D super-directional antenna layers is B=4, the antenna array operating frequency is 1.6 GHz, and the antenna array is composed of microstrip dipole antennas. For simplicity, for heterogeneous HMIMO arrays, the embodiment of the present invention considers a group of antenna arrays deployed in the xy plane, where antenna elements are arranged along the x-axis, and multiple layers of antennas are arranged along the y-axis. In the simulation, the embodiment of the present invention considers two cases of 3D super-directional antennas: the array aperture area remains unchanged, and the number of antennas is inversely proportional to the antenna spacing; the total number of antennas remains unchanged, and the array aperture is directly proportional to the antenna spacing. In addition, the simulation assumes that the user is on the vertical plane of the 3D super-directional antenna, so the elevation angle from the 3D super-directional antenna to each user is The horizontal azimuth is θa ∈[0,2π]. The excitation energy of the antenna array is set to 1W in the simulation.

[0223] During simulation, the embodiment of the present invention compares the communication rate index obtained by the array using the novel analog-digital hybrid beamforming theory and method of the present invention and the ZF method that does not consider coupling in the existing MIMO array.

[0224] (5.2) Simulation results

[0225] Figure 5 and Figure 8 The influence of the received SNR on the communication rate of the multi-user 3D stereo super-directional antenna when the antenna array aperture area is fixed is plotted. Under the same simulation scenario setting, it can be seen from the simulation results that as the SNR changes, the method proposed in the embodiment of the present invention is always better than the ZF algorithm without considering coupling. This is because the super-directional analog beamforming method proposed in the present invention is based on the coupling effect between the radiating units of the 3D stereo super-directional antenna and has good performance in all SNR regions.

[0226] It can be seen from the above results that the present invention not only has the characteristic of simulating super-directional beam-enhanced antenna array directivity, but also has the ability to match random channels through digital beamforming.

[0227] In some examples, the present invention describes a new analog-digital hybrid beamforming theory and method, which is also applicable to large-scale MIMO communications in 5G networks. In various examples, the disclosed 3D super-directional antenna can use multiple dual-polarized or single-polarized radiating units arranged in a single-column or multi-column array, and the corresponding analog and digital beamforming are designed by utilizing the proposed new analog-digital hybrid beamforming theory. The analog excitation design adjusts the antenna radiation pattern in real time based on the electromagnetic coupling effect, thereby generating a super-directional beam, adapting to the communication environment, and improving the performance gain of the communication system; the digital beamforming matrix designs the optimal digital beamforming according to the antenna pattern and the characteristics of the wireless link, and combines the analog beamforming to iteratively improve the system performance.

[0228] The disclosed novel analog-digital hybrid beamforming theory and method can utilize the mutual coupling effect between radiating elements and realize a practical super-directional beam at the same time.

[0229] Various examples of the disclosed novel analog-digital hybrid beamforming theory and method can be applied to any random scattering environment and 3D antenna array structure, and the super-directional beam direction can be adjusted in real time in practical applications.

[0230] On the other hand, an embodiment of an analog-digital joint beamforming device of the present invention can be applied to any device with data processing capabilities, and the device with data processing capabilities can be a device or apparatus such as a computer. The device embodiment can be implemented through software, or through hardware or a combination of software and hardware. Taking software implementation as an example, as a device in a logical sense, it is formed by the processor of any device with data processing capabilities in which it is located reading the corresponding computer program instructions in the non-volatile memory into the memory and running them. From the hardware level, if Fig. 9 As shown, it is a hardware structure diagram of any device with data processing capability where an analog digital joint beamforming device is located under the air-ground network architecture of the present invention, except Fig. 9 In addition to the processor, memory, network interface, and non-volatile memory shown, any device with data processing capabilities in which the apparatus in the embodiments is located may also include other hardware, generally based on the actual functions of the device with data processing capabilities, which will not be described in detail.

[0231] The implementation process of the functions and effects of each unit in the above-mentioned device is specifically described in the implementation process of the corresponding steps in the above-mentioned method, and will not be repeated here.

[0232] For the device embodiment, since it basically corresponds to the method embodiment, the relevant parts can refer to the partial description of the method embodiment. The device embodiment described above is only schematic, wherein the units described as separate components may or may not be physically separated, and the components displayed as units may or may not be physical units, that is, they may be located in one place, or they may be distributed on multiple network units. Some or all of the modules may be selected according to actual needs to achieve the purpose of the scheme of the present invention. Ordinary technicians in this field can understand and implement it without paying creative work.

[0233] The present disclosure may be embodied in other specific forms without departing from the subject matter of the claims. The described exemplary embodiments are merely illustrative and not restrictive in all respects. Selected features from one or more of the above embodiments may be combined to create alternative embodiments not explicitly described, and features suitable for such combinations are understood to fall within the scope of the present invention. For example, although the calculation order of the disclosed novel analog-digital hybrid beamforming theory and method is shown, other representation methods and solution orders may be used.

[0234] All values ​​and sub-ranges within the disclosed ranges are also disclosed. In addition, although the systems, algorithms, and processes disclosed and illustrated herein may include a specific number of elements / components and solution methods, these systems, devices, and components may be modified to include more or fewer such elements / components and solution methods with the same key steps. For example, although any disclosed hybrid beamforming algorithm may be the result of calculations under specific conditions, the embodiments disclosed herein may be modified to include more or fewer such conditions and the result of calculations with replacement steps. The subject matter described herein is intended to cover and encompass all appropriate technical changes.

Claims

1. An analog-digital joint beamforming method, characterized in that: The method includes: S1. Acquire communication scenario information and establish a 3D super-directional antenna array through a dense array of radiation units and an analog excitation circuit; S2, record the radiation field generated when there is no coupling in the array and the radiation field of the uniquely excited different antenna elements when there is coupling; S3, performing spherical wave coefficient expansion on the radiation fields before and after coupling, establishing the connection between the coupled electromagnetic field and the uncoupled electromagnetic field, and obtaining a coupling matrix; S4. The coupling matrix is ​​integrated with the communication model to calculate the optimal analog beamforming and the optimal digital beamforming, wherein the communication model is divided into a single-user reception model and a multi-user reception model. Specifically: Under the single-user receiving model, an optimal analog beamforming vector under a fixed digital beamforming condition and an optimal digital beamforming vector under a fixed analog beamforming condition are obtained by derivation and iterative optimization; Under the multi-user receiving model, when analog beamforming is fixed, the sum rate maximization problem is converted into an SDP problem through variable conversion, and the optimal antenna array analog excitation current vector under the fixed digital beamforming condition is solved by using a convex optimization toolkit as the optimal analog beamforming; when digital beamforming is fixed, the sum rate maximization problem is converted into an SDP problem through variable conversion, and the optimal digital beamforming matrix under the fixed analog beamforming condition is solved by using a convex optimization toolkit; and iterative optimization is performed during the solution; S5. Geometry adjustment: Find the optimal antenna element spacing that best balances the radiation efficiency and directivity of the 3D super-directional antenna through simulation.

2. The analog-digital joint beamforming method according to claim 1, characterized in that: The communication scenario information includes: an elevation angle and a horizontal angle of a scatterer in a communication environment relative to a base station.

3. The analog-digital joint beamforming method according to claim 1, characterized in that: To establish a 3D super-directional antenna array, the array is N t The densely distributed antenna array elements are evenly spaced in a plane, where the interval between the elements is less than half a wavelength.

4. The analog-digital joint beamforming method according to claim 1, characterized in that: In the S2, the actual spatial position is used to record the radiation field generated when there is no coupling, the elevation angle and the horizontal angle of the spherical coordinates are evenly divided, the space is discretized into P directions, and the electric field strength in the theta direction and the phi direction of each direction is recorded as the radiation field of the current array element being solved; when coupling is present, the radiation field of different antenna elements that are uniquely excited is recorded as follows: when setting the excitation of the array, only the antenna element unit that needs to be solved is excited to generate electromagnetic radiation, and the other antenna elements are connected to the matching impedance network as a load, and the space is also discretized into P directions, and the electric field strength in the theta direction and the phi direction of each direction is recorded.

5. The analog-digital joint beamforming method according to claim 1, characterized in that: The connection between the coupled electromagnetic field and the uncoupled electromagnetic field is specifically established as follows: the coupled radiation electric field of a single antenna element is expressed as a linear combination of the uncoupled radiation electric fields of multiple elements. If the total number of transmitting antennas is M, the uncoupled radiation field is The coupled radiation field is denoted by The linear representation is: The electric field coefficient e is introduced by using the actual recorded radiation electric field parameters or the spherical wave expansion coefficient, and the number of expansion items is adjusted according to the required accuracy; the linear combination coefficient c nm The physical meaning of is the influence of the radiation field of the nth antenna element on the radiation field of the mth antenna when there is coupling; The coupled field is represented by a linear combination of several uncoupled fields, and the above formula is simplified in matrix form as follows: in is the recorded coupled electric field, is the recorded uncoupled electric field, C is the linear combination coefficient c nm The coupling matrix composed of and In the case of a matrix, the calculation formula of the C matrix is:

6. The analog-digital joint beamforming method according to claim 1, characterized in that: The coupling matrix and communication model are integrated as follows: The radiation pattern of the uncoupled antenna array is expressed as: in is the radiation pattern of a single antenna element without coupling, k is the wave number, is a unit vector pointing in the direction of the user, r m is the spatial position of the mth antenna; The antenna radiation pattern is sampled and recorded to obtain the radiation intensity of the array at different angles in space. matrix, L is the number of scatterers, N is t is the number of antenna elements; each column represents the radiation pattern of different antennas for a single scattering direction, and each row represents the radiation intensity of the same antenna for different directions; when a single antenna element is excited by current, its radiation pattern becomes where i is a complex excitation containing amplitude and phase; therefore, the uncoupled array radiation after excitation is IR, where I = diag(i) represents the simulated excitation vector of the antenna array; finally, the actual array radiation pattern after coupling is CIR, which is multiplied by the channel matrix S of dimension L × K, and the received signal vector is written as y = (CIRS) T W BB x+n; where x is the signal vector, K is the number of users, W BB is the digital beamforming matrix, y is the receive vector, and n is the noise vector.

7. The analog-digital joint beamforming method according to claim 6, characterized in that: The optimal analog beamforming and the optimal digital beamforming are calculated under the single-user model as follows: The SNR for single-user reception is expressed as where e rad is the radiation efficiency of the antenna array; σ is the standard deviation of the channel additive Gaussian noise; Since both analog excitation and digital beamforming have energy constraints in actual transmission, it is actually necessary to maximize the corresponding received signal-to-noise ratio under fixed transmission energy conditions, specifically: The optimal analog beamforming vector under fixed digital beamforming conditions: By taking the derivative of the antenna array excitation vector i through the objective formula (*) and setting the result equal to 0, the optimal analog beamforming expression is obtained: Among them A * and A H denote the conjugate matrix and conjugate transposed matrix of matrix A respectively, w BB is the digital beamforming vector, s is the multipath channel scattering coefficient, C, R, i represent the coupling matrix, array radiation matrix and array excitation vector respectively, i t-l represents the simulated stimulus obtained in the previous iteration, i t Represents the simulated excitation vector obtained in the current t-th cycle; The optimal digital beamforming vector under fixed analog beamforming conditions: The antenna array excitation vector w is determined by the objective formula (*) BB Taking the derivative and setting the result equal to 0, the optimal digital beamforming expression is obtained: where w BB,t-1 represents the digital excitation vector obtained in the previous iteration, w BB，t Represents the digital excitation vector obtained in the current t-th cycle.

8. The analog-digital joint beamforming method according to claim 6, characterized in that: The optimal analog beamforming and the optimal digital beamforming are calculated under the multi-user model as follows: Among them, the actual array radiation pattern after coupling is CIR, and the corresponding optimization problem is: &s.t.P T，analog +P T，digital ≤P T where e rad is the antenna array radiation efficiency, X = RS obtained by multiplying two matrices, W BB，k is the digital beamforming matrix corresponding to the kth user, σ is the standard deviation of the channel additive Gaussian noise; P T，analog , P T，digital and P T They represent the analog beamforming energy limit, the digital beamforming energy limit and the total energy limit of the transmitter respectively; Solve the optimal antenna array analog excitation current vector under fixed digital beamforming conditions as the optimal analog beamforming: By variable substitution, it is transformed into the following optimization problem stTr(G)≤P T，analog s.t. After removing the rank 1 constraint, the problem becomes the SDP problem. The optimal analog beamforming matrix is ​​solved by convex optimization. The Lagrange multiplier method is used to prove that the convex optimization solution satisfies the rank = 1 condition. Finally, the optimal analog beamforming vector is obtained by eigenvalue decomposition. Solve the optimal digital beamforming matrix under the fixed analog beamforming condition and transform it into the following optimization problem through variable substitution: s.t. where F k The digital beamforming vector corresponding to the kth user multiplied by its own conjugate transpose is a rank 1 matrix, G = ii H represents the rank 1 matrix composed of the simulated excitation vector multiplied by its own conjugate transpose, Q i represents the rank 1 matrix composed of the interference vector of the i-th user to the k-th user multiplied by its own conjugate transpose; t k represents the lower limit of the signal-to-noise ratio of the kth user, u k represents the upper limit of the interference plus noise term of the kth user; After removing the rank-1 constraint, the problem becomes the SDP problem. The optimal digital beamforming matrix is ​​solved by convex optimization. The Lagrange multiplier method is used to prove that the convex optimization solution satisfies the rank-1 condition. Finally, one column of the optimal digital beamforming matrix is ​​obtained by eigenvalue decomposition. The above process is repeated to obtain the complete optimal beamforming matrix.

9. The analog-digital joint beamforming method according to claim 1, characterized in that: The goal of the geometric structure adjustment is to achieve the maximum achievable gain Realized Gain; wherein Realized Gain = efficiency * directivity. As the spacing between antenna elements decreases, the directivity that the array can achieve increases, but as the element spacing d decreases, the coupling effect increases and the radiation efficiency of the antenna decreases. The maximum achievable gain Realized Gain is obtained through simulation.

10. An analog-digital joint beamforming device, comprising a memory and one or more processors, wherein the memory stores executable code, characterized in that: When the one or more processors execute the executable code, they are used to implement the steps of the analog-digital joint beamforming method according to any one of claims 1 to 9.

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