Satellite massive MIMO communication positioning integrated transmission method

Abstract

The application discloses a satellite large-scale MIMO communication positioning integrated transmission method, which is characterized in that a large-scale MIMO antenna array is equipped at a satellite end, and multiple users are simultaneously served; communication and positioning use the same spectrum resource and the same hardware platform, communication positioning integration is implemented by transmitting pilot and data signals; rough position information of the satellite and the user is obtained at the satellite end in the form of initial access or tracking, and the pre-coded pilot and data signals are transmitted to each user based on the rough position information; the user end estimates channel parameters from the received pilot signals, and obtains more accurate position information, which is fed back to the satellite end. The application fully utilizes spectrum resources, simultaneously realizes wireless communication and positioning functions based on a low-orbit satellite, greatly improves communication performance and positioning accuracy, and realizes global communication coverage and seamless positioning.

Description

A satellite-based large-scale MIMO communication and positioning integrated transmission method Technical Field

[0001] This invention relates to a satellite massive MIMO communication and positioning integrated transmission method. It belongs to the technical field of satellite communication. Background Technology

[0002] 6G mobile communication systems, with their higher frequency bands, wider bandwidth, and larger antenna arrays, promise to achieve ubiquitous and seamless coverage, enhanced communication capabilities, and improved positioning accuracy, thus enabling integrated communication and positioning within a single system. This integration achieves spectrum sharing for communication and positioning by sharing the same hardware platform, while simultaneously performing integrated waveform and signal processing, improving resource utilization. Current efforts in integrated communication and positioning primarily focus on terrestrial networks; however, the performance of terrestrial networks is limited by the deployment of terrestrial infrastructure, and signals are susceptible to congestion. In these scenarios, satellite networks can serve as a supplement to terrestrial networks.

[0003] Current research on downlink precoding design for integrated terrestrial network communication and positioning systems exists, but the signal propagation characteristics of terrestrial and satellite systems differ significantly, thus these studies cannot be directly applied to satellite systems. Specifically, due to the long distance between the satellite and the user terminal, and the mobility of the transceiver, the system experiences long propagation delays and significant Doppler shifts. Therefore, it is difficult to estimate the time-varying instantaneous channel state information between the satellite and the user terminal, and the estimated results may be outdated. Consequently, using instantaneous channel state information for downlink precoding design in large-scale multiple-input multiple-output (MIMO) satellite communication and positioning systems is a challenging task. Summary of the Invention

[0004] Technical Problem: In view of the above-mentioned prior art, this invention proposes a satellite large-scale MIMO communication and positioning integrated transmission method based on slowly varying statistical channel state information, so as to balance communication capacity and positioning accuracy, and use spectral efficiency and lower bound of squared position error to evaluate the performance of communication and positioning respectively, thereby realizing the effective utilization of spectrum resources and significantly improving communication capacity and positioning accuracy.

[0005] Technical Solution: This invention is a satellite-based large-scale MIMO communication and positioning integration transmission method. The method involves equipping a satellite with a large-scale MIMO antenna array to simultaneously serve multiple users. Communication and positioning utilize the same spectrum resources and the same hardware platform, implementing communication and positioning integration through the transmission of pilot and data signals. Through initial access or tracking, the satellite obtains coarse position information for both the satellite and the users, and based on this, transmits pre-coded pilot and data signals to each user. The user terminal estimates channel parameters from the received pilot signals and obtains more precise position information, which is then fed back to the satellite. The communication and positioning integration precoding is a hybrid precoding scheme based on the principles of maximizing spectral effectiveness and minimizing the lower bound of the squared position error, along with multi-objective optimization. Each antenna element of the large-scale MIMO antenna array transmits signals independently, employing a fully digital, analog, or hybrid transmission method. During the dynamic movement of the satellite and each user terminal, the communication and positioning integration precoding is updated as the position information of the satellite and each user terminal changes.

[0006] The method integrates communication and positioning by transmitting pilot signals and data signals, and introduces a weighting coefficient ρ∈[0,1] to balance the performance of communication and positioning.

[0007] The design method of the integrated communication and positioning precoding is as follows:

[0008] To design a hybrid precoder for a satellite communication and positioning integrated system, including both digital and analog precoders, the following optimization problem is established to maximize the downlink spectral efficiency R. sum Simultaneously minimize the lower bound of the sum of squared errors Let the set of digital precoders W BB,n N represents the digital precoder on the nth subcarrier. sc Let the number of subcarriers be represented, and the objective function be defined as a vector. The superscript T indicates transpose, W RF Let represent the analog preencoder; therefore, the corresponding multi-objective optimization problem is expressed as:

[0009]

[0010] In the formula, Represent the Frobenius norm of a matrix. (Problem) It is a vector based on communication and positioning indicators. The maximization problem is defined as simultaneously maximizing communication and positioning metrics. In formula (1), P represents the transmission power budget, which is the set of constraints that the simulated pre-encoder needs to satisfy. in, and These represent the constraints that the analog precoder must satisfy under fully connected and partially connected structures, respectively. For the partially connected structure, the antenna element is divided into N... rf Groups, each group has N g =N t / N rf N antenna elements t Let represent the total number of antennas. Therefore, the corresponding analog precoder can be represented in the form of a block diagonal matrix, that is, w RF,i Indicates analog pre-encoder W RF The non-zero part of the i-th column, blkdiag{·}, represents a block diagonal matrix.

[0011] The integrated communication and positioning precoding design includes a digital precoder for the signal on each subcarrier and a common analog precoder for the signals on all subcarriers.

[0012] Step 1: For communication, let W be the product of the digital and analog pre-encoders on the nth subcarrier. n =W RF W BB,n Let u represent the linear receiver on the nth subcarrier of user k. k,n Let them gather K represents the total number of users, and an auxiliary weight variable is introduced. ω k,n Let represent the weight variables on the k-th user and the n-th subcarrier. Thus, maximizing the spectral effectiveness is equivalent to minimizing the weighted sum mean square error, i.e.,

[0013]

[0014] In the formula, ε k,n (W n ,u k,n ) represents the estimated signal and transmission signal s k,n The mean square error, log(·) represents the logarithm, and is given by the following formula.

[0015]

[0016] Among them, h k,n w represents the channel on the nth subcarrier of the kth user. k,n Let w represent the precoding vector of the k-th user. i,n This represents the precoding vector for the i-th user, where the superscript H denotes the conjugate transpose, N0 represents the noise variance, and |·| denotes the magnitude. Indicates taking the expected value;

[0017] Step 2: For positioning, the product of the digital and analog pre-encoders on the nth subcarrier is considered as a whole, that is, Design of pre-encoder To minimize the lower bound of the sum of squared positional errors, the following optimization problem is established.

[0018]

[0019] In the formula, E = [e1, e2, e3], where, This represents a vector whose i-th element is 1 and all other elements are 0. This represents the channel parameters between the k-th user and the satellite. The Fisher information matrix, where Tr{·} denotes the trace;

[0020] Therefore, minimizing the lower bound of the sum-squared position error is transformed into a product summation problem of the hybrid precoder. Minimize the Euclidean distance between precoders obtained in the process;

[0021] Step 3: Let the auxiliary matrix Then the problem Transformed into the following rank-constrained optimization problem

[0022]

[0023] In the formula, rank{·} denotes taking the rank, and A≥B denotes AB as positive semi-definite;

[0024] Step 4: Introduce auxiliary variables satisfy

[0025]

[0026] Note the Fisher information matrix Given the positive semidefiniteness of the property, using the property of Schur complement, formula (6) can be expressed as follows:

[0027]

[0028] Therefore, the problem Transform into

[0029]

[0030] Step 5: To improve computational efficiency, the relaxation problem is addressed. The optimal solution is expressed as

[0031]

[0032] In the formula, Z n Let L represent a 3K×3K positive semidefinite matrix, with auxiliary matrix L. n =[V n V n,x V n,y ], where the auxiliary matrix V n =[v 1,n ,...,v K,n ], v k,n Let d represent the array response of the k-th user, for d∈{x,y}, and the auxiliary matrix be y. Defined as array response v k,n Angle of arrival on the d-axis The derivative, For partial differential operators; using the decomposition of formula (9), the problem Transform into

[0033]

[0034] Step 6: Use the MM algorithm to solve the problem. This is transformed into a series of subproblems that can be solved iteratively more easily; let Z n,t Let represent the solution to the subproblem in the t-th iteration. Then, in the (t+1)-th iteration, Replace it with its second-order Taylor expansion The (i,j)th element is represented as

[0035]

[0036] In the formula, L represents the Lipschitz constant. Regarding variable Z n,t The first derivative is given by the following formula.

[0037]

[0038] In the formula, [·] i,j Let represent the (i,j)th element of the matrix, [·] m,n The matrix representing the m-th symbol on the n-th subcarrier, auxiliary matrix. The superscript * indicates the conjugate operation, [·] i The auxiliary matrix represents the i-th element of the vector. Among them, κ k Represents the Rice parameter, γ k Let represent the average energy of the channel; therefore, in the (t+1)th iteration, the subproblem can be expressed as...

[0039]

[0040] This problem can be solved using semidefinite programming (SDP).

[0041] Step 7: Solve We obtain the symmetric positive definite matrix Z n Afterwards, it can be known that The corresponding localization precoder can be obtained by the Cholisky decomposition and randomization process;

[0042] Step 8: Let the auxiliary matrix Auxiliary matrix Establish the following weighted sum problem

[0043]

[0044] In the formula, ρ∈[0,1] represents the weighting coefficient, used to weigh the performance between communication and positioning, and W RF W BB,n and The Euclidean distance d between them sum Defined as

[0045]

[0046] Step 9: Introduce auxiliary variables This indicates the i-th column of the auxiliary variable, which will be used to solve the problem. Transform into

[0047]

[0048] In the formula, the auxiliary function G represents k,n and The Euclidean distance between them, expanding formula (3) into G k,n The form of expression, that is

[0049]

[0050] Step 10: Inspired by the alternating direction multiplier method, the augmented Lagrangian function method is used to introduce dual variables. and the corresponding multiplier η k,n >0. Next, let the auxiliary set... Auxiliary set Then the problem The objective function can be transformed into

[0051]

[0052] In the formula, the auxiliary function

[0053]

[0054] Therefore, the problems related to this objective function Represented as

[0055]

[0056] question Iterative solution, in each iteration, for G k,n u k,n ω k,n W BB,n W RF Q k,n η k,n The elements are updated.

[0057] The G k,n renew,

[0058] G will be updated k,n The optimization problem is represented as

[0059]

[0060] Introducing the Lagrange multiplier μ, the corresponding Lagrange function can be expressed as:

[0061]

[0062] Using the KKT conditions, we know that G k,n according to The update is performed, in which the Hermitian matrix A k,n It can be broken down into Λ k,n and D k,n Let A represent the eigenvalue and eigenvector matrices, respectively. k,n and auxiliary matrix Ψ k,n The expression is given by the following formula.

[0063]

[0064] Express the left side of the constraint equation in formula (20) as a function of μ, that is,

[0065]

[0066] In the formula, the auxiliary matrix The Lagrange multiplier μ can be obtained from the complementary relaxation condition. Specifically, if δ(0)≤PK, then μ=0; otherwise, μ needs to satisfy δ(μ)=PK. The corresponding value is obtained through binary search.

[0067] The u k,n renew

[0068]

[0069] The ω k,n renew

[0070]

[0071] Step 14: Update W BB,n The optimization problem is represented as

[0072]

[0073] For fully connected and partially connected structures, let the function Regarding W BB,i The derivative is 0, which is used to update W. BB,i The expression, that is, In particular, for partial connection structures, there are N represents rf 3D identity matrix;

[0074] The W RF Update, will update W RF The optimization problem is represented as

[0075]

[0076] For a fully connected structure, W RF according to To be updated, among which, The imaginary unit is ∠, ∠ is the angle operator, exp{·} represents the exponential function e, e represents the base of the natural logarithm, and the auxiliary matrix is ​​∠. λ max (T) represents the auxiliary matrix The largest eigenvalue;

[0077] For partially connected structures, the objective function in equation (27) is expanded, and then... Transform the problem into

[0078]

[0079] In the formula, Indicates rounding up. This indicates taking the real part; therefore, W RF The (i,j)th element can be determined according to Update;

[0080] The Q k,n According to Q k,n =Q k,n +G k,n -W RF W BB,n Update.

[0081] The η k,n The update, at the end of each iteration, is applied to the multiplier η. k,n Make the following updates.

[0082]

[0083] In the formula, the parameters

[0084] Beneficial effects: The satellite massive MIMO communication and positioning integrated method of the present invention has the following advantages:

[0085] (1) In this invention, the upper bound of the ergodic spectrum effect of the large-scale MIMO satellite system and the lower bound of the channel parameter estimate are derived, and on this basis, the lower bound of the squared position error used to measure downlink positioning performance is derived.

[0086] (2) In this invention, a hybrid precoding multi-objective optimization problem based on spectral efficiency and lower bound index of squared position error is established, thereby making a trade-off between communication capacity and positioning accuracy;

[0087] (3) In this invention, an efficient hybrid precoding strategy based on statistical channel state information is proposed. By designing the signal waveforms of communication and positioning simultaneously, spectrum sharing between communication and positioning is achieved, and the performance of communication and positioning is guaranteed. Attached Figure Description

[0088] Figure 1 is a schematic diagram of a satellite massive MIMO communication and positioning integrated system;

[0089] Figure 2 is a schematic diagram of the time-frequency structure of the pilot and data signals of the system. Detailed Implementation

[0090] The invention will now be further explained with reference to the accompanying drawings.

[0091] This invention is a method for integrating satellite-based massive MIMO communication and positioning. The satellite is equipped with a massive MIMO antenna array, simultaneously serving multiple users, as shown in Figure 1. Communication and positioning utilize the same spectrum resources and the same hardware platform, implementing integrated communication and positioning by transmitting pilot and data signals. Through initial access or tracking, the satellite can obtain coarse location information for both the satellite and the users, and based on this, pre-coded pilot and data signals are transmitted to each user. The user terminal estimates channel parameters from the received pilot signals and obtains more accurate location information, which is then fed back to the satellite. The integrated communication and positioning precoding is a hybrid precoding scheme based on the principles of maximizing spectral effectiveness and minimizing the lower bound of the squared position error, along with multi-objective optimization. Each antenna element of the massive MIMO antenna array transmits signals independently, employing fully digital, analog, or hybrid transmission methods. During the simultaneous implementation of communication and positioning by transmitting pilot and data signals, weighting coefficients are introduced to balance the performance of communication and positioning. During the dynamic movement of the satellite and each user terminal, the integrated communication and positioning precoding is updated as the location information of the satellite and each user terminal changes.

[0092] Specifically, as shown in Figure 1, the system at carrier frequency f c The corresponding wavelength is λ. c =c / f c Given, where c represents the speed of light. The system consists of a star at position q = [q x ,q y ,q z ] T and azimuth All known satellites serve locations unknown. The speed at is K single-antenna users, k = 1, ..., K, where q x q y and q z These represent the satellite's position on the x, y, and z axes, respectively. and These represent the rotation angles about the positive y-axis and the negative x′ axis, respectively. and These represent the positions of the k-th user on the x, y, and z axes, respectively. and Let x, y, and z represent the velocities of the k-th user on the x, y, and z axes, respectively, and T denote the matrix transpose operator. The satellite is equipped with a massive MIMO antenna array containing hundreds of antenna elements, each of which can be a single-polarized or multi-polarized antenna. The array structure is a uniform area array, with the number of antennas in the x and y directions being respectively... and Total number of antennas is The antenna spacing is half a wavelength, and a hybrid analog / digital transmitter is used. The number of RF chains required for the transmitter is N. rf K≤N rf ≤N t .

[0093] As shown in Figure 2, to reduce inter-symbol interference, Orthogonal Frequency Division Multiplexing (OFDM) modulation technology is used to achieve downlink broadband transmission in the low-Earth orbit satellite communication and positioning integrated system. Let B w and T s These represent the system bandwidth and sampling period, respectively. For the time-frequency structure of the pilot and data signals, assume each frame consists of M... s It consists of 1 time slot, and each time slot contains M sp and M sd Each OFDM symbol is used for pilot and data transmission, respectively. Assume a total of N symbols are used. sc There are N subcarriers, and the cyclic prefix length is N. cp The subcarrier spacing is f s Then the frequency of the nth subcarrier can be expressed as

[0094]

[0095] Meanwhile, the OFDM symbol lengths including and excluding the cyclic prefix are respectively represented as T = N. sc T s +N cp T s and T sc =N sc T s The following will use subscripts and superscripts g∈{p,d} to represent pilot signals and data transmission, respectively.

[0096] 1. Channel Model

[0097] In a broadband massive MIMO satellite communication and positioning integrated system, the antenna array response depends not only on the launch angle but also on the frequency. Therefore, the array response v of the l-th propagation path of the k-th user at frequency f is... k,l (f) is represented as

[0098]

[0099] In the formula, Indicates the Kronecker product. Representing complex space, This represents the angle of arrival. Additionally, the array response vectors on the x and y axes are respectively... and Represented as

[0100]

[0101]

[0102] In the formula, auxiliary variables It represents the imaginary unit.

[0103] Generally, satellites are deployed at altitudes much higher than the scattering objects around the user. Therefore, the angle of arrival for each propagation path of the channel between the satellite and user k can be approximated as the same, that is, Similarly, we can obtain v k,l (f)=v k (f), make Assuming perfect time-frequency synchronization between the satellite and the user, then the m-th time of the k-th user... g The equivalent channel vector on the nth OFDM symbol and the nth subcarrier It can be represented as

[0104]

[0105] In the formula, and These are the direct (LoS) and non-direct (NLoS) path components of the channel, respectively, and can be further represented as...

[0106]

[0107]

[0108] Define gain Because there are multiple transmission paths, It can be approximated as the superposition of the LoS component and multiple independent and identically distributed multipath components. In this case, we can assume... Obtained by Rice parameter κ k The average energy is The Ricean distribution, where |·| represents the amplitude. The complex gain of the LoS path. Given by the following formula

[0109]

[0110] Where exp{·} denotes the exponential function e, e represents the base of the natural logarithm, and ν k and τ kThese represent the Doppler frequency shift and transmission delay of the LoS path for the k-th user, respectively. Furthermore, the coefficient α... k satisfy Where φ k ∈(0,2π] is a random phase. The complex gain of the NLoS path. Follow the distribution This represents a cyclically symmetric complex Gaussian distribution.

[0111] 2. Signal Model

[0112] The mth p The transmitted pilot signal on each OFDM symbol is represented as follows: For m p =1,...,M p ,have satisfy in, This indicates the number of subcarriers corresponding to the pilot. Indicates taking the expectation, I K Let represent a K-order identity matrix, and H denote the matrix conjugate transpose operator. The m-th... d The transmitted data signal on each OFDM symbol is represented as follows: in, m d =1,...,M d ,satisfy and Where δ(·) represents the δ function, This indicates the number of subcarriers corresponding to the data, and * indicates conjugate.

[0113] At the mth g On the OFDM symbol and the nth subcarrier, the transmitted signal First, it passes through a baseband (digital) pre-encoder. Then it goes through an analog (RF) pre-encoder Therefore, the final transmitted signal can be expressed as The equivalent hybrid precoding matrix is ​​represented by W. n =[w n,1 ,w n,2 ,...,w n,K ] indicates that w n,k This is the equivalent hybrid precoding vector for user k. The m-th... g The OFDM symbols and the received pilot or data signal on the nth subcarrier are represented as follows:

[0114]

[0115] In the formula, noise N0 represents the noise variance.

[0116] 3. Performance Indicators

[0117] (1) Communication spectrum effect

[0118] To better illustrate the statistical characteristics of the channel, OFDM symbol m is temporarily omitted. d And the subcarrier index n. During the data transmission phase, the traversal rate of the k-th user can be expressed as...

[0119]

[0120] Here, log(·) represents the logarithmic function to the base 2. It's worth noting that if the transmitting end can obtain perfect instantaneous channel state information, that is, h... k The traversal rate can then be estimated using the Monte Carlo method. However, the Monte Carlo method has high computational complexity, and due to the long transmission delay between the satellite and the user, it is difficult for the satellite transmitter to obtain accurate instantaneous channel state information. Therefore, statistical channel state information is considered in this invention. It is not difficult to deduce that R... k about Since it is concave, its upper bound can be given by the following formula.

[0121]

[0122] In the above formula, the expected expression Let represent the channel correlation matrix of the k-th user at the satellite end. It is not difficult to obtain... Therefore, the channel model based on statistical channel state information can be represented as:

[0123]

[0124] It is worth noting that the statistical channel state information includes the UPA response v k and channel gain γ k Assuming that these parameters remain constant over the observation time interval and can be dynamically updated according to changes in the channel, the upper bound of the ergodic rate based on statistical channel state information can be expressed as:

[0125]

[0126] In the formula The formula (41) is given. Here, we only focus on each time slot; for ease of expression, the OFDM symbol m is used. d Discard. In summary, SE can be represented as

[0127]

[0128] In the formula

[0129] (2) Positioning accuracy

[0130] a. Received signal model

[0131] For ease of representation, the superscript and subscript p are temporarily omitted. The received pilot signal for user k is given by the following formula.

[0132]

[0133] For ease of representation, let the equivalent noise be... Therefore, formula (44) can be transformed into

[0134]

[0135] In the formula, follow Distribution, and equivalent noise variance Given by the following formula

[0136]

[0137] b. Fisher Information Matrix

[0138] As mentioned earlier, channel parameters can be estimated from the received pilot signal. The channel parameters between the satellite and the k-th user can be represented as a 6×1 vector, i.e. in, and They represent α respectively k The real and imaginary parts of η. Next, the estimated value of the k-th user parameter vector is expressed as η. k Its mean square error has a lower bound, which is... Given that A≥B denotes AB as positive semi-definite, J ηk Represents the unknown vector η k The Fisher matrix, whose (i,j)th element can be calculated by the following formula.

[0139]

[0140] In the formula, This indicates the reception of the pilot signal without noise. This indicates taking the real part.

[0141] c. Conversion of position parameters

[0142] It is worth noting that, due to the channel parameter η k To position parameters The transformation is bijective. Therefore, the Fisher information matrix of the k-th user with respect to the transformed position parameters can be represented as: Transformation matrix Given by the following formula

[0143]

[0144] In the formula, blkdiag{·} represents a block diagonal matrix, Ξ k It can be represented as

[0145]

[0146] In the formula, Representing the real space, specific elements can be represented as

[0147]

[0148]

[0149] In the formula, ||·||2 represents the L2 norm of the vector. Let R(o) represent the rotation position vector associated with user k, where R(o) represents the rotation matrix, given by the following equation.

[0150]

[0151] In the formula, r1, r2 and r3 represent the 1st, 2nd and 3rd columns of R(o) respectively, and sin and cos represent the sine and cosine functions respectively.

[0152] d.SPEB

[0153] Positioning accuracy can be measured by the squared position error, which can be defined as the actual position p of user k. k and location estimate p k The mean square error, that is

[0154]

[0155] In the formula, according to Fisher's information inequality, the lower bound of the squared position error can be given by the following formula.

[0156]

[0157] In the formula, Tr{·} represents the trace, and thus, the lower bound of the sum-squared position error for all users is defined as

[0158]

[0159] In the formula, E = [e1, e2, e3], where, This represents a vector where the i-th element is 1 and all other elements are 0.

[0160] 4. Hybrid precoder design integrating communication and positioning

[0161] To design a hybrid precoder for an integrated satellite communication and positioning system, the following optimization problem is established to maximize downlink spectral efficiency while minimizing the lower bound of the sum-squared error. Let... And define the objective function as a vector Therefore, the corresponding multi-objective optimization problem can be expressed as:

[0162]

[0163] In the formula, Represent the Frobenius norm of a matrix. (Problem) It is a vector based on communication and positioning indicators. The maximization problem is defined as simultaneously maximizing communication and positioning metrics. In formula (56), P represents the transmission power budget. in, and These represent the constraints that the analog precoder must satisfy under fully connected and partially connected structures, respectively. For the partially connected structure, the antenna element is divided into N... rf Groups, each group has N g =N t / N rf There are one antenna element. Therefore, the corresponding analog precoder can be represented in the form of a block diagonal matrix, that is, ... The following section will design a digital precoder for the signal on each subcarrier, and at the same time, design a common analog precoder for the signal on all subcarriers.

[0164] Step 1: Let the product of the hybrid pre-encoders be W. n =W RF W BB,n Let u represent the linear receiver on the nth subcarrier of user k. k,n ,make And introduce auxiliary weight variables Thus, maximizing the spectral effectiveness is equivalent to minimizing the weighted sum mean square error, that is,

[0165]

[0166] In the formula, ε k,n (W n ,u k,n ) represents the estimated signal and transmission signal s k,n The mean square error is given by the following formula.

[0167]

[0168] Step 2: Treat the product of the digital and analog pre-encoders as a single unit, that is, Design of pre-encoder To minimize the lower bound of the sum of squared positional errors, the following optimization problem is established.

[0169]

[0170] Therefore, minimizing the lower bound of the sum-squared position error is transformed into a product summation problem of the hybrid precoder. Minimize the Euclidean distance between precoders obtained in the process.

[0171] Step 3: Let Then the problem Transformed into the following rank-constrained optimization problem

[0172]

[0173] In the formula, rank{·} represents taking the rank.

[0174] Step 4: Introduce auxiliary variables satisfy

[0175]

[0176] Note the Fisher information matrix Given the positive semidefiniteness of the property, using the property of Schul complement, formula (61) can be expressed as follows:

[0177]

[0178] Therefore, the problem It can be converted into

[0179]

[0180] Step 5: To improve computational efficiency, the relaxation problem can be addressed. The optimal solution is expressed as

[0181]

[0182] In the formula, Z n Let L represent a 3K×3K positive semi-definite matrix. n =[V n V n,x V n,y ], where V n =[v 1,n ,...,v K,n ], For d∈{x,y}, we have Using the decomposition of formula (64), the problem It can be converted into

[0183]

[0184] Step 6: Use the MM algorithm to solve the problem. This can be transformed into a series of subproblems that can be solved iteratively more easily. Let Z... n,t Let represent the solution to the subproblem in the t-th iteration. Then, in the (t+1)-th iteration, we can... Replace it with its second-order Taylor expansion The (i,j)th element can be represented as

[0185]

[0186] In the formula, Regarding variable Z n,t The first derivative is given by the following formula.

[0187]

[0188] In the formula, Therefore, in the (t+1)th iteration, the subproblem can be represented as

[0189]

[0190] This problem can be solved using semidefinite programming (SDP).

[0191] Step 7: Solve We obtain the symmetric positive definite matrix Z n Afterwards, it can be known that The corresponding positioning precoder can be obtained by the Jolisky decomposition and randomization process.

[0192] Step 8: Let Establish the following weighted sum problem

[0193]

[0194] In the formula, ρ∈[0,1] represents the weighting coefficient, used to weigh the performance between communication and positioning, and d sum Defined as

[0195]

[0196] Step 9: Introduce auxiliary variables The problem Transform into

[0197]

[0198] In the formula,

[0199] Step 10: Inspired by the Alternating Direction Multiplier Method (ADMM), the augmented Lagrangian function method is used to introduce dual variables. and the corresponding multiplier η k,n >0. Next, let... Then the problem The objective function can be transformed into

[0200]

[0201] In the formula,

[0202]

[0203] Therefore, the problems related to this objective function It can be represented as

[0204]

[0205] question The solution can be obtained iteratively. In each iteration, the update process for each element is as shown in steps 11-17.

[0206] Step 11: Update G k,n The optimization problem is represented as

[0207]

[0208] Introducing the Lagrange multiplier μ, the corresponding Lagrange function can be expressed as:

[0209]

[0210] Using the KKT conditions, we know that G k,n according to The update is performed, in which the Hermitian matrix A k,n It can be broken down into A k,n and Ψ k,n The expression is given by the following formula.

[0211]

[0212] Express the left side of the constraint equation in formula (75) as a function of μ, that is,

[0213]

[0214] In the formula, The Lagrange multiplier μ can be obtained based on the complementary relaxation condition. Specifically, if δ(0)≤PK, then μ=0; otherwise, μ needs to satisfy δ(μ)=PK. The corresponding value can be obtained through binary search.

[0215] Step 12: u k,n The update can be performed according to the following formula.

[0216]

[0217] Step 13: ω k,n Update according to the following formula

[0218]

[0219] Step 14: Update W BB,n The optimization problem is represented as

[0220]

[0221] For fully connected and partially connected structures, let the function Regarding W BB,i The derivative of is 0, which gives us the value used to update W. BB,i The expression, that is, In particular, for partial connection structures, there are

[0222] Step 15: Update W RF The optimization problem is represented as

[0223]

[0224] For a fully connected structure, W RF According to The update is performed, where ∠ is the angle operator, and the auxiliary matrix is... λ max (T) represents the auxiliary matrix The largest eigenvalue.

[0225] For partially connected structures, the objective function in formula (82) is expanded, and then... The problem can be transformed into

[0226]

[0227] In the formula, This indicates rounding up. Therefore, W RF The (i,j)th element can be determined according to Update.

[0228] Step 16: Q k,n According to Q k,n =Q k,n +G k,n -W RF W BB,n Update.

[0229] Step 17: At the end of each iteration, for the multiplier η k,n Make the following updates.

[0230]

[0231] In the formula,

[0232] During the dynamic movement of the satellite and each user terminal, as the statistical channel information of the satellite and each user terminal changes, the aforementioned integrated communication and positioning hybrid precoding process is dynamically implemented to form an updated integrated communication and positioning hybrid precoding method.

[0233] The above description is only a preferred embodiment of the present invention. It should be noted that for those skilled in the art, several improvements and modifications can be made without departing from the principle of the present invention, and these improvements and modifications should also be considered within the scope of protection of the present invention.

Claims

1. A satellite-based massive MIMO communication and positioning integrated transmission method, characterized in that, This method involves equipping a satellite with a large-scale MIMO antenna array to serve multiple users simultaneously; communication and positioning use the same spectrum resources and the same hardware platform, and communication and positioning are integrated by transmitting pilot and data signals; through initial access or tracking, the satellite obtains the approximate location information of the satellite and the users, and based on this, the pre-encoded pilot and data signals are sent to each user; The user terminal estimates the channel parameters from the received pilot signals and obtains more accurate location information, which is then fed back to the satellite. The integrated communication and positioning precoding is a hybrid precoding scheme based on the principles of maximizing spectral effectiveness and minimizing the lower bound of the squared position error, as well as multi-objective optimization. Each antenna element of a massive MIMO antenna array transmits signals independently and uses a fully digital, analog, or hybrid transmission method. During the dynamic movement of the satellite and each user terminal, the integrated communication and positioning precoding is updated as the position information of the satellite and each user terminal changes. The integrated communication and positioning precoding is designed as follows: To design a hybrid precoder for an integrated satellite communication and positioning system, including both digital and analog precoders, the following optimization problem is established to maximize downlink spectral efficiency. Simultaneously minimize the lower bound of the sum of squared errors ; Let the set of digital precoders ， Indicates the first Digital precoder on each subcarrier Let the number of subcarriers be represented, and the objective function be defined as a vector. superscript Indicates transpose. Let represent the analog preencoder; therefore, the corresponding multi-objective optimization problem is expressed as: (1), where, Representing the Frobenius norm of a matrix; problem It is a vector based on communication and positioning indicators. The maximization problem is defined as simultaneously maximizing communication and positioning metrics, as shown in formula (1). Represents the transmission power budget, which is the set of constraints that the simulated pre-encoder must satisfy. ,in, and These represent the constraints that the analog precoder must satisfy under fully connected and partially connected structures, respectively. For the partially connected structure, the antenna element is divided into... Groups, each group has One antenna element, Let represent the total number of antennas. Therefore, the corresponding analog precoder can be represented in the form of a block diagonal matrix, that is, ， Indicates analog pre-encoder The The non-zero part of the column, Represents a block diagonal matrix; the integrated communication positioning precoding, wherein a digital precoder is designed for the signal on each subcarrier, and a common analog precoder is designed for the signals on all subcarriers; Step 1: For communication, let the... The product of the digital and analog pre-encoders on each subcarrier is , will users The A linear receiver on each subcarrier is represented as follows: Let them gather ， This represents the total number of users, and introduces auxiliary weight variables. ， Indicates the first The user and the first The weighted variables on each subcarrier are such that maximizing the spectral effectiveness is equivalent to minimizing the weighted sum mean square error, that is, (2), where, Indicates the estimated signal and transmission signal The mean square error, The logarithmic function with base 2 is given by the following formula. (3), where, Indicates the first The user Channels on each subcarrier Indicates the first Precoded vectors for each user Indicates the first Precoded vectors for each user, superscript This indicates the conjugate transpose. Indicates the noise variance. Indicates the range, Indicate the expected value; Step 2: For the location, set the first... The product of the digital and analog precoders on each subcarrier is considered as a whole, that is, ， The aim is to design a pre-encoder To minimize the lower bound of the sum of squared positional errors, the following optimization problem is established. (4), where, ,in, Indicates the first A vector with one element being 1 and the rest being 0. Indicates the first One user about satellites and the first Channel parameters between users Fisher's information matrix, This represents trace taking; therefore, minimizing the lower bound of the sum-squared position error is transformed into a product sum problem of the hybrid precoder. Minimize the Euclidean distance between the precoders obtained in the process; Step 3: Let the auxiliary matrix Then the problem Transformed into the following rank-constrained optimization problem (5), where, Indicates taking the rank. express Semi-positive definite; Step 4: Introduce auxiliary variables ,satisfy (6), note the Fisher information matrix The positive semidefiniteness of the property can be expressed by using the property of Schul complement as follows: (7), therefore, the problem Transform into: (8), Step 5: To improve computational efficiency, the relaxation problem is... The optimal solution is expressed as (9), where, express positive semidefinite matrix, auxiliary matrix , where the auxiliary matrix ， Indicates the first The array response for each user, for auxiliary matrix ， Defined as array response right Angle of arrival on the axis The derivative of For partial differential operators; using the decomposition of formula (9), the problem Transform into: (10), Step 6: Use the MM algorithm to solve the problem. This is transformed into a series of subproblems that can be solved iteratively more easily; let Indicates the first The solution to the subproblem in the nth iteration, then, in the nth iteration In the next iteration, Replace it with its second-order Taylor expansion The first of them Each element is represented as: (11), where, Represents the Lipschitz constant. Regarding variables The first derivative is given by the following formula. (12), where, Represents the first of the matrix One element, Indicates the first The symbol of the first Matrix on each subcarrier, auxiliary matrix superscript This indicates the conjugate operation. The vector represents the first Elements, auxiliary matrix ,in, Represents Rice parameters, This represents the average energy of the channel; therefore, the first... In this iteration, the subproblem can be represented as: (13) This problem can be solved using semidefinite programming (SDP); Step 7: Solve Obtain the symmetric positive definite matrix Afterwards, it can be known that The corresponding localization precoder can be obtained by the Cholisky decomposition and randomization process; Step 8: Let the auxiliary matrix auxiliary matrix Establish the following weighted sum problem (14), where, These represent weighting coefficients used to weigh communication and positioning performance. and Euclidean distance between Defined as (15), Step 9: Introduce auxiliary variables ， This indicates the first auxiliary variable. List, the problem Transform into: (16), where the auxiliary function is... ， express and The Euclidean distance between them, expanding formula (3) into... The form of expression, that is Step 10: Inspired by the alternating direction multiplier method, the augmented Lagrange function method is used to introduce dual variables. and the corresponding multipliers Next, let the auxiliary set Auxiliary set Then the problem The objective function can be transformed into: (17), where the auxiliary function is... (18), and thus the problems related to this objective function. Represented as: (19), Problem Iterative solution, in each iteration, for 、 、 、 、 、 、 The elements are updated.

2. The satellite massive MIMO communication and positioning integrated transmission method according to claim 1, characterized in that, The method of integrating communication and positioning by transmitting pilot signals and data signals introduces a weighting coefficient. This is to balance the performance of communication and positioning.

3. The satellite massive MIMO communication and positioning integrated transmission method according to claim 1, characterized in that, The Update, will be updated The optimization problem is represented as (20) Introducing Lagrange multipliers The corresponding Lagrange function is expressed as (21), using the KKT conditions, we know that, according to Update the Hermitian matrix. It can be broken down into ， and These represent the eigenvalue and eigenvector matrices, respectively. and auxiliary matrix The expression is given by the following formula. (22), the left side of the constraint equation in formula (20) is expressed as The function, that is, (23), where the auxiliary matrix is... Lagrange multipliers This can be obtained from the complementary relaxation condition; specifically, if... Then there is ,otherwise Need to meet The corresponding value is obtained through binary search.

4. The satellite massive MIMO communication and positioning integrated transmission method according to claim 1, characterized in that, The renew (24)。 5. The satellite massive MIMO communication and positioning integrated transmission method according to claim 1, characterized in that, The renew (25), Step 14: Update The optimization problem is expressed as: (26), for fully connected and partially connected structures, let the function about The derivative is 0, which is used to update The expression, that is, In particular, for partially connected structures, there are ， express 3D identity matrix.

6. The satellite massive MIMO communication and positioning integrated transmission method according to claim 1, characterized in that, The Update, will be updated The optimization problem is expressed as: (27), for fully connected structures, according to To be updated, among which, The imaginary unit, To obtain the angle operator, express Exponential function Denotes the base of the natural logarithm, auxiliary matrix ， Representing the auxiliary matrix The maximum eigenvalue; for partially connected structures, expand the objective function in formula (27) and utilize Transform the problem into (28), where, ， Indicates rounding up. This indicates taking the real part; therefore, The Each element can be based on Update.

7. The satellite massive MIMO communication and positioning integrated transmission method according to claim 1, characterized in that, The according to Update.

8. The satellite massive MIMO communication and positioning integrated transmission method according to claim 1, characterized in that, The The update, at the end of each iteration, is applied to the multipliers. Make the following updates. (29), where the parameter is... ， ， 。

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