Multi-target CRB minimization method for near-field flux-sensing integration based on rate splitting

Abstract

The invention discloses a multi-target CRB minimization method based on near-field flux and inductance integration of rate splitting, and relates to the technical field of wireless communication and novel multiple access. The method comprises the following four steps: S1, establishing a near-field communication channel and a near-field sensing channel according to a spherical wave propagation model; s2, the base station encodes information required by a communication user into public and private information streams by using a rate splitting multiple access technology and sends the public and private information streams to the user side; s3, according to the array response vector of the near-field sensing channel, deriving CRBs for simultaneously estimating angles and distances of a plurality of sensing targets; and S4, establishing an optimization problem by satisfying the communication rate requirement and minimizing the CRB of multiple targets, and jointly optimizing the hybrid beam forming matrix and the common rate allocation variable by using a penalty dual decomposition and block coordinate descent method. The method can achieve the simultaneous estimation of the distances and angles of a plurality of sensing targets, and effectively reduces the estimation error.

Description

Technical Field

[0001] The present invention belongs to the field of wireless communication and novel multiple access technology, and in particular to a multi-objective CRB minimization method based on rate splitting and near-field synaesthesia integration. Background Art

[0002] Integrated Sensing and Communications (ISAC) organically combines communication and perception modules to expand the communication network to a dual-function network where communication and perception coexist, in order to support emerging applications such as autonomous driving, low-altitude economy and intelligent manufacturing. In order to enhance the perception resolution and data transmission rate, ISAC gradually evolves to adopt ultra-large-scale antenna arrays and ultra-high frequencies. The increasing antenna aperture and carrier frequency extend the Rayleigh distance to tens of meters or even hundreds of meters, causing the propagation characteristics of electromagnetic waves to change from far-field plane waves to near-field spherical waves. The far-field plane wave channel only contains the angle information of the target and can only estimate the angle of the target. Accurately estimating the distance of the target requires a lot of bandwidth resources. Compared with the far-field plane wave, the near-field spherical wave introduces the distance information of the target, so that the distance and angle of the target can be estimated simultaneously under limited bandwidth resources. In summary, the near-field spherical wave provides new opportunities for the development of ISAC, but the existing ISAC research is mainly based on the far-field plane wave channel model and cannot be directly applied to the near-field ISAC scenario. Therefore, it is urgent to study ISAC that adapts to the propagation characteristics of spherical waves to achieve simultaneous estimation of target distance and angle. However, this design faces two technical challenges, which are summarized as follows:

[0003] 1) The wireless environment is complex and changeable: The coexistence of communication and perception functions in ISAC leads to a complex and changeable wireless environment, making it difficult to accurately manage co-channel interference. Existing ISAC research mainly uses Space Division Multiple Access (SDMA) and Non-orthogonal Multiple Access (NOMA) technologies to manage co-channel interference. Specifically, SDMA treats all non-target information streams as additional noise signals and uses the spatial multiplexing gain generated by beamforming to weaken interference. When ISAC serves multiple users and perceives multiple targets at the same time, excessive interference will cause network performance saturation. NOMA uses serial interference elimination to decode all strong interference signals to enhance network connectivity and throughput. However, the performance gain of NOMA relies on complex receiver design and large channel gain differences, and is not suitable for ordinary user deployment scenarios. Therefore, it is urgent to design a flexible and accurate interference management solution to enhance network performance.

[0004] 2) High hardware deployment cost: When ISAC deploys ultra-large-scale antenna arrays, the hardware cost of equipping each antenna with a radio link is high or even impossible. Therefore, it is urgent to reduce the number of radio links in the base station in the near-field ISAC to reduce the deployment cost.

[0005] Rate Splitting Multiple Access technology and Hybrid Beamforming technology can solve the above two challenges respectively. Compared with SDMA and NOMA, Rate Splitting Multiple Access technology has two advantages: 1) This technology can achieve complete decoding interference, no decoding interference and decoding partial interference by controlling the proportion of public information flow, and has more flexible interference management capabilities; 2) The public information flow of Rate Splitting Multiple Access technology can accurately manage the interference between communication users, weaken the interference between communication and perception functions, and act as a perception beam to enhance target perception performance. Hybrid beamforming allows all transmission antennas to share each RF link without allocating a separate RF link to each antenna, which can significantly reduce the number of RF links required by the base station. In view of this, the present invention proposes a rate-splitting-assisted multi-target near-field ISAC, and uses penalty dual decomposition and block coordinate descent to jointly optimize the hybrid beamforming matrix and the public rate allocation variables.

[0006] Current research status at home and abroad

[0007] In 2024, Kexin Chen et al. published "Rate-Splitting Multiple Access for Simultaneous Multi-User Communication and Multi-Target Sensing" in IEEE Transactions on Vehicular Technology, using rate splitting multiple access technology to accurately manage co-channel interference to reduce CRB of multi-target angle estimation. However, this study used far-field plane wave channels and fully digital beamforming, which could not achieve simultaneous estimation of multi-target distances and angles, and the hardware deployment cost was relatively high.

[0008] In 2024, Diluka Galappaththige et al. published "Near-Field ISAC: Beamforming for Multi-Target Detection" in IEEE Wireless Communications Letters. They designed a fully digital precoding vector to maximize the signal-to-interference-to-noise ratio for multiple near-field sensing targets. However, using the signal-to-interference-to-noise ratio as the optimization target cannot directly obtain the target's perception performance, which may cause performance loss. In addition, the study used SDMA to manage interference, which would cause transmission performance saturation when there were too many targets.

[0009] In 2024, Kaiqian Qu et al. published "Near-Field Integrated Sensing and Communication: Performance Analysis and Beamforming Design" in IEEE Open Journal of the Communications Society, studying the design method of hybrid beamforming vectors to maximize the beam pattern matching value of a single target. However, this study still cannot directly obtain the perception performance of the target and only considers a single perception target.

[0010] In 2024, Haochen Li et al. published "Near-Field Integrated Sensing, Positioning, and Communication: A Downlink and Uplink Framework" in IEEE Journal on Selected Areas in Communications, studying the hybrid beamforming design method of near-field ISAC to reduce the CRB of target perception. However, this study only considered a single sensing target and used SDMA to manage co-channel interference, which could not ensure high-speed data transmission. Summary of the invention

[0011] The technical problem to be solved by the present invention is to provide a multi-objective CRB minimization method based on rate decomposition and near-field synaesthesia integration to address the shortcomings of the background technology; the present invention can achieve simultaneous estimation of the distances and angles of multiple perception targets and effectively reduce the estimation error.

[0012] The present invention adopts the following technical solutions to solve the above technical problems:

[0013] The multi-objective CRB minimization method based on rate splitting and near-field synaesthesia integration specifically includes the following steps;

[0014] Step S1, establishing near field communication and near field sensing channels according to a spherical wave propagation model;

[0015] Step S2: The base station encodes the information required by the communication user into public and private information streams using rate splitting multiple access technology and sends the information to the user end;

[0016] Step S3, deriving a CRB that simultaneously estimates angles and distances of multiple sensing targets based on an array response vector of a near-field sensing channel;

[0017] Step S4, establish an optimization problem for CRB that meets the communication rate requirement and minimizes multiple objectives, and jointly optimize the hybrid beamforming matrix and the common rate allocation variables using the penalty dual decomposition and block coordinate descent method.

[0018] As a further preferred solution of the multi-objective CRB minimization method based on rate splitting of the present invention, the near-field synaesthesia integration ISAC uses a N t Transmitting antennas and N r The base station with a receiving antenna simultaneously serves K single-antenna near-field users and senses M near-field targets; the near-field communication users and sensed target sets are respectively denoted as and In order to reduce the hardware deployment cost of base stations, a hybrid beamforming architecture is adopted, that is, the base station is only equipped with N f RF chains, where N f <N t ; Assume that the transmission and receiving antennas of the base station adopt uniform linear arrays and are placed along the positive and negative half axes of the y-axis respectively, then the coordinates of the nth transmission antenna are s n =(0, nd), where d is the spacing between adjacent antennas and The distance and angle of the kth user relative to the coordinate origin are denoted as r k and θ k , then the coordinates of the kth user are r k =(r k cosθ k , r k sinθ k ); The distance between the kth user and the nth transmission antenna is calculated as

[0019]

[0020] The Fresnel approximation formula shows that the path loss of all transmission antennas of the base station to the same user is equal, that is, the path loss of the kth user is Where f and c are the carrier frequency and the speed of light respectively; according to the spherical wave model, the channel between the kth user and the nth transmission antenna is expressed as where λ is the wavelength; according to the second-order Taylor expansion Available k，n ≈r k -δ k，n , where δ k，n =ndsinθ k -(n.d.) 2 cos 2 θ k / 2r k ; will d k，n Substitute the approximate value of into h k，n , can be obtained in Combining all transmission antennas, the near-field channel between the base station and the kth user is Expressed as

[0021]

[0022] where a(r, θ) is the near-field array response vector of the transmitting antenna;

[0023] In order to estimate the distance and angle of the target at the same time, the base station needs to collect the echo signal. Therefore, the two-way near-field channel needs to be considered for the sensing target base station. The distance, angle and path loss of the mth sensing target are recorded as and Similar to the modeling method of near-field communication channels, the perception channel matrix of the mth target can be obtained: for

[0024]

[0025] in and are the near-field array response vectors of the receiving and transmitting antennas of the mth sensing target, respectively.

[0026] As a further preferred solution of the multi-objective CRB minimization method based on rate splitting and near-field synaesthesia integration of the present invention, a transmission mechanism based on rate splitting multiple access technology is used to flexibly manage co-channel interference; specifically, the information of each user is split into a public part and a private part; then the K public parts are encoded into a public information stream s0, and the private parts are encoded into K private information streams {s1, ..., s K}; The public information flow is then superimposed on the top of the private information flow and sent to the user end; the discrete time index of a single coherent processing interval is recorded as L, then the information flow vector transmitted at the lth time index is expressed as in The information stream s(l) passes through the hybrid beamforming matrix Linear precoding is performed, where is the analog beamforming matrix, is the digital beamforming matrix; in W, and represent the digital beamforming vectors of the public information flow and the kth private information flow respectively; therefore, the signal transmitted by the base station at the kth time index is

[0027]

[0028] The data flow vector satisfies Indicates the independence between different elements, where I K+1is the identity matrix; the covariance matrix of the transmission is

[0029]

[0030] According to equation (4), the signal received by the kth user at the lth time index is

[0031]

[0032] in is additive Gaussian white noise; the power received by the kth user is

[0033]

[0034] To obtain the desired information, the kth user first treats all private information streams as additional noise and decodes the public information stream, and its signal-to-interference-to-noise ratio is Then the kth user uses serial interference cancellation technology to remove the public information stream and decode the private target information stream. The corresponding signal-to-interference-noise ratio is The rates at which the kth user decodes the public information stream and the private target information stream are R c，k =log(1+γ c，k ) and R p，k =log(1+γ p，k ); To ensure that all users can successfully decode the common information stream, the common rate needs to rely on the user with the worst channel state information, that is, the common rate cannot exceed At the same time, the public information stream is shared by all users. Among them C c，k represents the public information flow assigned to the kth user; the total transmission rate of the kth user is R k =C c，k +R p，k ;

[0035] The echo signal received by the base station at the lth time index is expressed as

[0036]

[0037] in is additive white Gaussian noise, is the self-interference channel; since the channel information from the base station transmitter to the receiver is easy to estimate accurately, assuming that the base station achieves perfect self-interference elimination, in the total time interval of L, equation (7) is equivalent to

[0038]

[0039] Where Y=[y(1),...,y(L)], N0=[n0(1),...,n0(L)], B = diag(β), and

[0040] 4. The multi-objective CRB minimization method based on rate splitting and near-field synaesthesia integration according to claim 3 is characterized in that: according to the observation value Y of M perception targets, and In order to achieve simultaneous estimation of target distance and angle, CRB is used as the performance indicator of target perception; the real and imaginary parts of the complex channel gain are recorded as and There are 4M real values ​​to be estimated, recorded as in and According to equation (9), the Fisher information matrix is

[0041]

[0042] in

[0043]

[0044] where x, y∈{θ, r}, and

[0045]

[0046] where i∈{r,t}; According to equation (10), the CRB for target distance and angle estimation is expressed as

[0047]

[0048] Under the condition of meeting the communication rate requirements, the CRB of multi-objective estimation is minimized by optimizing the hybrid beamforming matrix and the common rate allocation variable. Therefore, the modeled optimization problem is expressed as problem (14):

[0049]

[0050] Where c = [C c，1 , ..., C c，K ] T and P th is the maximum transmission power threshold; (14b) is the communication rate requirement limit; (14c) is the maximum transmission power limit; (14d) and (14e) are the rate allocation limits for public information flows; and (14f) is the unit modulus constraint for analog beamforming.

[0051] As a further preferred solution of the multi-objective CRB minimization method based on rate splitting and near-field synaesthesia integration of the present invention, a double-layer iterative optimization algorithm is designed by using penalty dual decomposition and block coordinate descent method to jointly optimize the hybrid beamforming matrix and the common rate allocation variable to solve the modeled non-convex optimization problem (14). The specific solution steps are as follows:

[0052] Step 1: Use the penalty dual decomposition method to restructure problem (14) into an equivalent but easy-to-solve form. The specific process is as follows: To eliminate the coupling between analog beamforming and digital beamforming, the auxiliary matrices P = FW and Q = PP are introduced. H ,in Substituting P = FW into equation (7), the power received by the kth user is expressed as

[0053]

[0054] Using Q=PP H , the Fisher matrix in equation (10) is updated to

[0055]

[0056] in

[0057]

[0058] In equation (17), x, y∈{θ, r}; according to the Schur complement condition, the equation restricts Q=PP H Equivalent split into

[0059]

[0060] Then, the auxiliary matrix is ​​introduced And meet

[0061]

[0062] According to the Schur complement condition, equation (19) can be decomposed into

[0063]

[0064] Since Tr(X -1 ) is a monotonically decreasing function of the semi-positive definite matrix X, minTr(CRB(r,θ)) is equivalent to minTr(U -1 ); Problem (14) is reconstructed as

[0065]

[0066] The restriction of equation (21b) makes the problem difficult to solve directly. The penalty dual decomposition is used to transfer the restriction (21b) to the objective function, and the problem is transformed into a two-layer loop iterative optimization problem, in which the outer layer is used to update the introduced dual matrix and penalty parameter, and the inner layer is used to solve the augmented Lagrangian problem. By introducing the penalty factor ρ and the dual matrix D, the augmented Lagrangian problem formed by problem (16) is expressed as problem (22):

[0067]

[0068] To solve the augmented Lagrangian problem (22), the following steps 2 to 4 will use the block coordinate descent method, that is, the optimization variables are divided into {P, Q, U, c}, {W} and {F}, and then each time the other variable block is optimized while fixing two variable blocks. The specific process is as follows:

[0069] Step 2: Under the condition of fixing {F, W}, the problem of optimizing {P, Q, U, c} is stated as

[0070]

[0071] To solve problem (23), the weighted minimum mean square error and first-order Taylor expansion are used to transform the fractional signal-to-noise ratio and the inequality constraint of restriction (18) into an easily solvable form; specifically, the kth user uses the equalizer ω c，k and ω p，k Estimate the public information flow s0 and private information flow s k , and their mean square errors are

[0072]

[0073] Then, solve and The optimal equalizer is

[0074]

[0075] Substituting the optimal equalizer into the mean square error, we can get the estimated error generated by the optimal equalizer:

[0076]

[0077] Using equation (26), the signal-to-interference-noise ratio of the kth user decoding the public information stream and the private information stream is converted to and Right now and Then we can get the weighted minimum mean square error function β c，k =η c，k δ c，k -log(η c，k ) and βp，k =η p，k δ p，k -log(η p，k ), where η c，k and η p，k is the weight parameter; by taking the equalizer and weight as optimization variables, the relationship between the transmission rate and the weighted minimum mean square error is modeled as

[0078]

[0079] Where τ=1 / ln2+log(ln2); by solving and Get the best equalizer and The optimal weight is expressed as

[0080]

[0081] By using the first-order Taylor expansion Tr(PP H ), inequality Tr(Q-PP H )≤0 is reconstructed as

[0082] 2Re(Tr(P (t) P H ))-Tr(P (t) (P (t) ) H )≥Tr(Q) (64)

[0083] The superscript (t) represents the optimal value of the output of the tth iteration; according to the relationship between the transmission rate and the weighted minimum mean square error and inequality (29), problem (23) is transformed into problem (30):

[0084]

[0085] in and The invention iteratively optimizes and For a given auxiliary variable Problem (30) will be transformed into a convex problem and then solved using CVX The variables in are solved by equations (25) and (28);

[0086] Step 3: When other variables are fixed, the problem of optimizing W is simplified to the following unconstrained optimization problem:

[0087]

[0088] The optimal solution is

[0089] W o =(F H F) -1 F H (P+ρD) (67)

[0090] Step 4: When other variables are fixed, the problem of optimizing F is modeled as

[0091]

[0092] Where Y = WW H and Z = (P + ρD)W H ; We use the element-by-element optimization method to solve problem (33), that is, to optimize F n，i The problem is equivalent to

[0093]

[0094] The optimal solution to problem (34) is

[0095]

[0096] in X=F (t) Y and F (t) is the optimal solution obtained in the tth iteration;

[0097] Step 5: According to the above steps 1 to 4, the specific process of solving the non-convex optimization problem (14) is as follows:

[0098] Two-layer loop optimization algorithm based on penalty dual decomposition

[0099] 1) Initialize F (0) , W (0) , D (0) , (0) and ψ (0) , set the outer iteration index n = 1;

[0100] 2) While non-convergent execution

[0101] 3) Set F (1) =F (n-1) and W (1) =W (n-1) and inner iteration index i=1;

[0102] 4) While non-convergent execution

[0103] 5) Update the auxiliary variables introduced by the weighted minimum mean square error according to equations (25) and (28);

[0104] 6) Solve problem (30) using CVX and obtain P (i) and c(i) ;

[0105] 7) Update the digital beamforming matrix W according to equation (32): (i+1) ;

[0106] 8) Update the analog beamforming matrix F according to equation (35): (i+1) ;

[0107] 9) Update iteration index i=i+1;

[0108] 10) end while

[0109] 11) Obtain the optimal P (n) 、F (n) and W (n) ;

[0110] 12)if||P (n) -F (n) w (n) || ∞ ≤ψ (n-1) implement

[0111] 13) Update

[0112] 14) else 15) Update ρ (n) =0.9ρ (n-1) , D (n) =D (n-1) ;

[0113] 16)end if17)Update ψ (n) =0.9||P (n) -F (n) W (n) || ∞ , n = n + 1;

[0114] 18) end while

[0115] 19) Output the optimal communication rate.

[0116] Compared with the prior art, the present invention adopts the above technical solution and has the following technical effects:

[0117] The present invention discloses a multi-objective CRB minimization method based on rate splitting and near-field synaesthesia integration, which relates to the field of wireless communication and new multiple access technology. It comprises four steps: S1, establishing near-field communication and near-field perception channels according to the spherical wave propagation model; S2, the base station uses rate splitting multiple access technology to encode the information required by the communication user into public and private information streams and send them to the user end; S3, deriving the CRB that simultaneously estimates the angles and distances of multiple perception targets based on the array response vector of the near-field perception channel; S4, establishing an optimization problem of the CRB that meets the communication rate requirements and minimizes multiple objectives, and jointly optimizing the hybrid beamforming matrix and the public rate allocation variables by using the penalty dual decomposition and block coordinate descent method; the present invention can realize the simultaneous estimation of the distances and angles of multiple perception targets, and effectively reduce the estimation error. BRIEF DESCRIPTION OF THE DRAWINGS

[0118] In order to more clearly illustrate the embodiments of the present application or the technical solutions in the prior art, the drawings required for use in the embodiments or the description of the prior art will be briefly introduced below. Obviously, the drawings described below are only some embodiments of the present application. For those skilled in the art, other drawings can be obtained based on these drawings without paying any creative work.

[0119] Figure 1 It is a schematic diagram of hybrid beamforming based on rate splitting and near-field synaesthesia integration of the present invention.

[0120] Figure 2 The relationship between the CRB and the transmission power of the angle estimation of the perceived target is simulated.

[0121] Figure 3 The relationship between CRB and transmission power of the distance estimation of the sensing target is simulated.

[0122] Figure 4 The relationship between the angle estimation of the perceived target and the number of RF links is simulated.

[0123] Figure 5 The relationship between the distance estimation of the perceived target and the number of RF links is simulated. DETAILED DESCRIPTION

[0124] The technical solution of the present invention is further described in detail below in conjunction with the accompanying drawings:

[0125] The technical solutions in the embodiments of the present invention will be clearly and completely described below in conjunction with the drawings in the embodiments of the present invention. Obviously, the described embodiments are only part of the embodiments of the present invention, rather than all of the embodiments. Based on the embodiments in the present invention, all other embodiments obtained by ordinary technicians in this field without creative work are within the scope of protection of the present invention. The present invention is described in detail below according to the drawings and preferred embodiments, and the purpose and effect of the present invention will become clearer. It should be understood that the specific embodiments described herein are only used to explain the present invention and are not used to limit the present invention.

[0126] Figure 1 The schematic diagram of the proposed hybrid beamforming based on rate splitting and near-field synaesthesia integration is shown. The designed near-field ISAC uses an N t Transmitting antennas and N r The base station with a receiving antenna simultaneously serves K single-antenna near-field users and senses M near-field targets. The near-field communication users and sensed target sets are denoted as and In order to reduce the hardware deployment cost of the base station, the present invention adopts a hybrid beamforming architecture, that is, the base station is only equipped with N f RF chains, where N f <N t Assuming that the transmission and receiving antennas of the base station adopt uniform linear arrays and are placed along the positive and negative half axes of the y-axis respectively, the coordinates of the nth transmission antenna are s n =(0, nd), where d is the spacing between adjacent antennas and The distance and angle of the kth user relative to the coordinate origin are denoted as r k and θ k , then the coordinates of the kth user are r k =(r k cosθ k , r k sinθ k ). Therefore, the distance between the kth user and the nth transmission antenna can be calculated as

[0127]

[0128] In addition, the Fresnel approximation formula shows that the path loss of all transmission antennas of the base station to the same user is equal, so the path loss of the kth user is Where f and c are the carrier frequency and the speed of light, respectively. According to the spherical wave model, the channel between the kth user and the nth transmission antenna can be expressed as Where λ is the wavelength. According to the second-order Taylor expansion Available k，n ≈r k -δk，n , where δ k，n =ndsinθ k -(n.d.) 2 cos 2 θk / 2r k . k，n Substitute the approximate value of into h k，n , can be obtained in Combining all transmission antennas, the near-field channel between the base station and the kth user is It can be expressed as

[0129]

[0130] where a(r,θ) is the near-field array response vector of the transmitting antenna.

[0131] In order to estimate the distance and angle of the target at the same time, the base station needs to collect the echo signal, so the two-way near-field channel needs to be considered for the sensing target base station. The distance, angle and path loss of the mth sensing target are respectively recorded as and Similar to the modeling method of near-field communication channels, the perception channel matrix of the mth target can be obtained: for

[0132]

[0133] in and are the near-field array response vectors of the receiving and transmitting antennas of the mth sensing target, respectively.

[0134] The present invention proposes a transmission mechanism based on rate splitting multiple access technology to flexibly manage co-channel interference. Specifically, the information of each user is split into a public part and a private part; then the K public parts are encoded into a public information stream s0, and the private part is encoded into K private information streams {s1,...,s K}; The public information flow is then superimposed on the private information flow and sent to the user end. Let the discrete time index of a single coherent processing interval be L, then the information flow vector transmitted at the lth time index can be expressed as in The information stream s(l) passes through the hybrid beamforming matrix Linear precoding is performed, where is the analog beamforming matrix, is the digital beamforming matrix. In W, and represent the digital beamforming vectors of the public information flow and the kth private information flow respectively. Therefore, the signal transmitted by the base station at the lth time index is

[0135]

[0136] The data flow vector satisfies This shows the independence of different elements. K+1 is the identity matrix. The covariance matrix of the transmission is

[0137]

[0138] According to equation (4), the signal received by the kth user at the lth time index is

[0139]

[0140] in is additive Gaussian white noise. Therefore, the power received by the kth user is

[0141]

[0142] To obtain the desired information, the kth user first treats all private information streams as additional noise and decodes the public information stream, and its signal-to-interference-to-noise ratio is Then the kth user uses serial interference cancellation technology to remove the public information stream and decode the private target information stream. The corresponding signal-to-interference-noise ratio is Therefore, the rates at which the kth user decodes the public information stream and the private target information stream are R c，k =log(1+γ c，k ) and R p，k =log(1+γ p，k ). However, to ensure that all users can successfully decode the common information stream, the common rate needs to depend on the user with the worst channel state information, that is, the common rate cannot exceed At the same time, public information streams are shared by all users, so Among them C c，k represents the public information flow assigned to the kth user. In summary, the total transmission rate of the kth user is R k =C c，k +R p，k .

[0143] The echo signal received by the base station at the lth time index can be expressed as

[0144]

[0145] in is additive white Gaussian noise, is the self-interference channel. Since the channel information from the base station transmitter to the receiver can be accurately estimated, the present invention assumes that the base station can achieve perfect self-interference elimination. Therefore, in the total time interval of L, equation (7) can be equivalent to

[0146]

[0147] Where Y=[y(1),...,y(L)], N0=[n0(1),...,n0(L)], B = diag(β), and The present invention focuses on the target tracking scenario, that is, the base station aims to estimate the M observation values ​​Y of the perceived targets. and In order to achieve simultaneous estimation of target distance and angle, the present invention adopts CRB as the performance indicator of target perception. The real part and imaginary part of the complex channel gain are respectively denoted as and There are 4M real values ​​to be estimated, recorded as in and According to equation (9), the Fisher information matrix is

[0148]

[0149] in

[0150]

[0151] where x, y∈{θ, r}, and

[0152]

[0153] where i∈{r,t}. According to equation (10), the CRB for target distance and angle estimation can be expressed as

[0154]

[0155] The present invention aims to minimize the CRB of multi-objective estimation by optimizing the hybrid beamforming matrix and the common rate allocation variable under the condition of meeting the communication rate requirement. Therefore, the modeling optimization problem can be expressed as

[0156]

[0157] Where c = [C c，1 , ..., C c，K ] T and P this the maximum transmission power threshold; (14b) is the communication rate requirement limit; (14c) is the maximum transmission power limit; (14d) and (14e) are the rate allocation limits for public information flows; and (14f) is the unit modulus constraint for analog beamforming.

[0158] Design of a two-layer iterative algorithm based on penalty dual decomposition:

[0159] In order to solve the modeled non-convex optimization problem (14), the present invention uses the penalty dual decomposition and block coordinate descent method to design a two-layer iterative optimization algorithm to jointly optimize the hybrid beamforming matrix and the common rate allocation variable. The specific solution steps are as follows:

[0160] Step 1: Use the penalty dual decomposition method to restructure problem (14) into an equivalent but easy-to-solve form. The specific process is as follows: To eliminate the coupling between analog beamforming and digital beamforming, the auxiliary matrices P = FW and Q = PP are introduced. H ,in Substituting P = FW into equation (7), the power received by the kth user can be expressed as

[0161]

[0162] Using Q=PP H , the Fisher matrix in equation (10) can be updated as

[0163]

[0164] in

[0165]

[0166] In equation (17), x, y∈{θ, r}. According to the Schur complement condition, the equation restricts Q=PP H Can be equivalently decomposed into

[0167]

[0168] Then, the auxiliary matrix is ​​introduced And meet

[0169]

[0170] According to the Schur complement condition, equation (19) can be decomposed into

[0171]

[0172] Since Tr(X -1 ) is a monotonically decreasing function with respect to the semi-positive definite matrix X. Therefore, minTr(CRB(r,θ)) is equivalent to minTr(U-1 ). Problem (14) can be reconstructed as

[0173]

[0174] The equation restriction (21b) makes the problem difficult to solve directly. To overcome this challenge, the present invention uses the penalty dual decomposition to transfer the restriction (21b) to the objective function, and transforms the problem into a two-layer loop iterative optimization problem, where the outer layer is used to update the introduced dual matrix and penalty parameter, and the inner layer is used to solve the augmented Lagrangian problem. By introducing the penalty factor ρ and the dual matrix D, the augmented Lagrangian problem formed by problem (16) can be expressed as

[0175]

[0176] To solve the augmented Lagrangian problem (22), the following steps 2 to 4 will use the block coordinate descent method, that is, the optimization variables are divided into {P, Q, U, c}, {W} and {F}, and then each time the other variable block is optimized while fixing two variable blocks. The specific process is as follows:

[0177] Step 2: Under the condition of fixed {F, W}, the problem of optimizing {P, Q, U, c} can be expressed as

[0178]

[0179] To solve problem (23), the present invention uses weighted minimum mean square error and first-order Taylor expansion to transform the fractional signal-to-noise ratio and the inequality constraint of restriction (18) into a form that is easy to solve. Specifically, the kth user uses the equalizer ω c，k and ω p，k Estimate the public information flow s0 and private information flow s k , and their mean square errors are

[0180]

[0181] Then, solve and The optimal equalizer is

[0182]

[0183] Substituting the optimal equalizer into the mean square error, we can get the estimated error generated by the optimal equalizer:

[0184]

[0185] Using equation (26), the signal-to-interference-noise ratio of the kth user decoding the public information stream and the private information stream can be converted to and Right now and Then we can get the weighted minimum mean square error function β c，k =η c，k δ c，k -log(η c，k ) and β p，k =η p，k δ p，k -log(η p，k ), where η c，k and η p，k is the weight parameter. By taking the equalizer and weight as optimization variables, the relationship between the transmission rate and the weighted minimum mean square error can be modeled as

[0186]

[0187] Where τ=1 / ln2+log(ln2). By solving and The optimal equalizer can be obtained and Similarly, the optimal weights can be expressed as

[0188]

[0189] By using the first-order Taylor expansion Tr(PP H ), inequality Tr(Q-PP H )≤0 is reconstructed as

[0190] 2Re(Tr(P (t) P H ))-Tr(P (t) (P (t) ) H )≥Tr(Q) (99)

[0191] The superscript (t) represents the optimal value of the output of the tth iteration. According to the relationship between the transmission rate and the weighted minimum mean square error and inequality (29), problem (23) can be transformed into

[0192]

[0193] in and For a given auxiliary variable Problem (30) will be transformed into a convex problem and can be solved by CVX Based on this, the present invention iteratively optimizes and in The variables in are solved by equations (25) and (28).

[0194] Step 3: When other variables are fixed, the problem of optimizing W can be simplified to the following unconstrained optimization problem:

[0195]

[0196] The optimal solution is

[0197] W o =(F H F) -1 F H (P+ρD) (102)

[0198] Step 4: When other variables are fixed, the problem of optimizing F can be modeled as

[0199]

[0200] Where Y = WW H and Z = (P + ρD)W H The present invention adopts an element-by-element optimization method to solve problem (33), that is, to optimize F n，i The problem is equivalent to

[0201]

[0202] The optimal solution to problem (34) is

[0203]

[0204] in X=F (t) Y and F (t) is the optimal solution obtained in the tth iteration.

[0205] Step 5: According to the above steps 1 to 4, the specific process of solving the non-convex optimization problem (14) is as follows:

[0206] Two-layer loop optimization algorithm based on penalty dual decomposition

[0207] 1) Initialize F (0) , W (0) , D (0) , (0) and ψ (0) , set the outer iteration index n = 1;

[0208] 2) While non-convergent execution

[0209] 3) Set F (1) =F (n-1) and W (1) =W (n-1) and inner iteration index i=1;

[0210] 4) While non-convergent execution

[0211] 5) Update the auxiliary variables introduced by the weighted minimum mean square error according to equations (25) and (28);

[0212] 6) Solve problem (30) using CVX and obtain P (i) and c (i) ;

[0213] 7) Update the digital beamforming matrix W according to equation (32): (i+1) ;

[0214] 8) Update the analog beamforming matrix F according to equation (35): (i+1) ;

[0215] 9) Update iteration index i=i+1;

[0216] 10) end while

[0217] 11) Obtain the optimal P (n) 、F (n) and W (n) ;

[0218] 12)if||P (n) -F (n) W (n) || ∞ ≤ψ (n-1) implement

[0219] 13) Update

[0220] 14) else 15) Update ρ (n) =0.9ρ (n-1) , D (n) =D (n-1) ;

[0221] 16)end if17)Update ψ (n) =0.9||P (n) -F (n) W (n) || ∞ , n = n + 1;

[0222] 18) end while

[0223] 19) Output the optimal communication rate.

[0224] Simulation results:

[0225] Simulation parameter setting: The base station with communication and perception functions is equipped with N t = 64 transmission antennas and N r= 32 receiving antennas, the aperture of the transmitting and receiving antennas is 0.5 meters, so the near-field area covered by the ISAC is 50 meters; the operating frequency of the base station and the number of RF links equipped are f c =30GHz and N f =8, K = 4 users and M = 2 are randomly and evenly distributed in the entire near field range. The minimum rate requirement of the near field communication user is R th =2bps / Hz; the transmission power threshold of the base station and the background noise of the network are set to P th =30dBm and σ 2 =-90dBm.

[0226] Figure 2 and Figure 3 The relationship between the CRB and transmission power of the angle and distance estimation of the perceived target was simulated respectively. The simulation results show that with the increase of the transmission power, the CRB of the angle and distance estimation errors of all transmission schemes will decrease. However, the scheme proposed in the present invention is always better than the near-field space division multiple access technology and the far-field rate split multiple access technology. The performance advantages of the scheme proposed in the present invention are mainly due to the following two reasons. First, compared with far-field beamforming, near-field beamforming can focus the beam energy on a specific spatial position, which helps to reduce interference between users; secondly, compared with space division multiple access technology, the public information flow of rate split multiple access technology can accurately manage interference between communication users, weaken interference between communication and perception functions, and act as a perception beam to enhance target perception performance.

[0227] Figure 4 and Figure 5 The relationship between the angle and distance estimation of the perceived target and the number of RF links is simulated respectively. The simulation results show that as the number of RF links increases, the CRB of the angle and distance estimation of all transmission schemes decreases. This is because increasing the number of RF links will expand the dimension of digital beamforming, and increasing the dimension of digital beamforming helps to weaken the interference between users. At the same time, compared with the two benchmark schemes, the scheme proposed in the present invention has always had obvious advantages.

[0228] Those skilled in the art can understand that the above are only preferred examples of the invention and are not intended to limit the invention. Although the invention is described in detail with reference to the above examples, those skilled in the art can still modify the technical solutions recorded in the above examples or replace some of the technical features with equivalents. Any modification, equivalent replacement, etc. made within the spirit and principle of the invention should be included in the protection scope of the invention. All technical features in this embodiment can be freely combined according to actual needs.

[0229] Finally, it should be noted that the above is only a preferred embodiment of the present invention and is not intended to limit the present invention. Although the present invention has been described in detail with reference to the aforementioned embodiments, it is still possible for those skilled in the art to modify the technical solutions described in the aforementioned embodiments or to make equivalent substitutions for some of the technical features therein. Any modifications, equivalent substitutions, improvements, etc. made within the spirit and principles of the present invention should be included in the protection scope of the present invention.

Claims

1. A multi-objective CRB minimization method based on rate splitting and near-field synaesthesia integration, characterized by: The specific steps include: Step S1, establishing near field communication and near field sensing channels according to a spherical wave propagation model; Step S2: The base station encodes the information required by the communication user into public and private information streams using rate splitting multiple access technology and sends the information to the user end; Step S3, deriving a CRB that simultaneously estimates angles and distances of multiple sensing targets based on an array response vector of a near-field sensing channel; Step S4, establish an optimization problem for CRB that meets the communication rate requirement and minimizes multiple objectives, and jointly optimize the hybrid beamforming matrix and the common rate allocation variables using the penalty dual decomposition and block coordinate descent method.

2. The multi-objective CRB minimization method based on rate splitting and near-field synaesthesia integration according to claim 1 is characterized by: The near-field synaesthesia integration ISAC utilizes an N t Transmitting antennas and N r The base station with a receiving antenna simultaneously serves K single-antenna near-field users and senses M near-field targets; the near-field communication users and sensed target sets are respectively denoted as and In order to reduce the hardware deployment cost of base stations, a hybrid beamforming architecture is adopted, that is, the base station is only equipped with N f RF chains, where N f <N t ; Assume that the transmission and receiving antennas of the base station adopt uniform linear arrays and are placed along the positive and negative half axes of the y-axis respectively, then the coordinates of the nth transmission antenna are s n =(0, nd), where d is the spacing between adjacent antennas and The distance and angle of the kth user relative to the coordinate origin are denoted as r k and θ k , then the coordinates of the kth user are r k =(r k cosθ k , r k sinθ k ); The distance between the kth user and the nth transmission antenna is The Fresnel approximation formula shows that the path loss of all transmission antennas of the base station to the same user is equal, that is, the path loss of the kth user is Where f and c are the carrier frequency and the speed of light respectively; according to the spherical wave model, the channel between the kth user and the nth transmission antenna is expressed as where λ is the wavelength; according to the second-order Taylor expansion Available k，n ≈r k -δ k，n , where δ k，n =nd sinθ k -(n.d.) 2 cos 2 θ k / 2r k ; will d k，n Substitute the approximate value of into h k，n , can be obtained in Combining all transmission antennas, the near-field channel between the base station and the kth user is Expressed as where a(r, θ) is the near-field array response vector of the transmitting antenna; In order to estimate the distance and angle of the target at the same time, the base station needs to collect the echo signal. Therefore, the two-way near-field channel needs to be considered for the sensing target base station. The distance, angle and path loss of the mth sensing target are recorded as and Similar to the modeling method of near-field communication channels, the perception channel matrix of the mth target can be obtained: for in and are the near-field array response vectors of the receiving and transmitting antennas of the mth sensing target, respectively.

3. The multi-objective CRB minimization method based on rate splitting and near-field synaesthesia integration according to claim 2 is characterized by: A transmission mechanism based on rate-splitting multiple access technology is proposed to flexibly manage co-channel interference; specifically, each user's information is split into a public part and a private part; then the K public parts are encoded into a public information stream s0, and the private parts are encoded into K private information streams {s1, ..., s K }; The public information flow is then superimposed on the top of the private information flow and sent to the user end; the discrete time index of a single coherent processing interval is recorded as L, then the information flow vector transmitted at the lth time index is expressed as in The information stream s(l) passes through the hybrid beamforming matrix Linear precoding is performed, where is the analog beamforming matrix, is the digital beamforming matrix; in W, and represent the digital beamforming vectors of the public information flow and the kth private information flow respectively; therefore, the signal transmitted by the base station at the lth time index is The data flow vector satisfies It shows the independence between different elements, where I K+1 is the identity matrix; The covariance matrix of the transmission is According to equation (4), the signal received by the kth user at the lth time index is in is additive Gaussian white noise; the power received by the kth user is To obtain the desired information, the kth user first treats all private information streams as additional noise and decodes the public information stream, and its signal-to-interference-to-noise ratio is Then the kth user uses serial interference cancellation technology to remove the public information stream and decode the private target information stream. The corresponding signal-to-interference-noise ratio is The rates at which the kth user decodes the public information stream and the private target information stream are R c，k =log(1+γ c，k ) and R p，k =log(1+γ p，k ); To ensure that all users can successfully decode the common information stream, the common rate needs to rely on the user with the worst channel state information, that is, the common rate cannot exceed At the same time, the public information stream is shared by all users. Among them C c，k represents the public information flow assigned to the kth user; the total transmission rate of the kth user is r k =C c，k +R p，k ; The echo signal received by the base station at the lth time index is expressed as in is additive white Gaussian noise, is the self-interference channel; since the channel information from the base station transmitter to the receiver is easy to estimate accurately, assuming that the base station achieves perfect self-interference elimination, in the total time interval of L, equation (7) is equivalent to Where Y=[y(1),...,y(L)], N0=[n0(1),...,n0(L)], B = diag(β), and 4. The multi-objective CRB minimization method based on rate splitting and near-field synaesthesia integration according to claim 3 is characterized by: Based on the observations Y of M perceived targets, and In order to achieve simultaneous estimation of target distance and angle, CRB is used as the performance indicator of target perception; the real and imaginary parts of the complex channel gain are recorded as and There are 4M real values ​​to be estimated, recorded as in and According to equation (9), the Fisher information matrix is in where x, y∈{θ, r}, and where i∈{{r, t}; According to equation (10), the CRB for target distance and angle estimation is expressed as Under the condition of meeting the communication rate requirements, the CRB of multi-objective estimation is minimized by optimizing the hybrid beamforming matrix and the common rate allocation variable. Therefore, the modeled optimization problem is expressed as problem (14): Where c = [C c，1 , ..., C c，K ] T and P th is the maximum transmission power threshold; (14b) is the communication rate requirement limit; (14c) is the maximum transmission power limit; (14d) and (14e) are the rate allocation limits for public information flows; and (14f) is the unit modulus constraint for analog beamforming.

5. The multi-objective CRB minimization method based on rate splitting and near-field synaesthesia integration according to claim 4 is characterized by: A two-layer iterative optimization algorithm is designed by using the penalty dual decomposition and block coordinate descent method to jointly optimize the hybrid beamforming matrix and the common rate allocation variable to solve the modeled non-convex optimization problem (14). The specific solution steps are as follows: Step 1: Use the penalty dual decomposition method to restructure problem (14) into an equivalent but easy-to-solve form. The specific process is as follows: To eliminate the coupling between analog beamforming and digital beamforming, the auxiliary matrices P = FW and Q = PP are introduced. H ,in Substituting P = FW into equation (7), the power received by the kth user is expressed as Using Q=PP H , the Fisher matrix in equation (10) is updated to in In equation (17), x, y∈{θ, r}; according to the Schur complement condition, the equation restricts Q=PP H Equivalent split into Then, the auxiliary matrix is ​​introduced And meet According to the Schur complement condition, equation (19) can be decomposed into Since Tr(X -1 ) is a monotonically decreasing function of the semi-positive definite matrix X, minTr(CRB(r,θ)) is equivalent to minTr(U -1 ); Problem (14) is reconstructed as The restriction of equation (21b) makes the problem difficult to solve directly. The penalty dual decomposition is used to transfer the restriction (21b) to the objective function, and the problem is transformed into a two-layer loop iterative optimization problem, in which the outer layer is used to update the introduced dual matrix and penalty parameter, and the inner layer is used to solve the augmented Lagrangian problem. By introducing the penalty factor ρ and the dual matrix D, the augmented Lagrangian problem formed by problem (16) is expressed as problem (22): To solve the augmented Lagrangian problem (22), the following steps 2 to 4 will use the block coordinate descent method, that is, the optimization variables are divided into {P, Q, U, c}, {W} and {F}, and then each time the other variable block is optimized while fixing two variable blocks. The specific process is as follows: Step 2: Under the condition of fixing {F, W}, the problem of optimizing {P, Q, U, c} is stated as To solve problem (23), the weighted minimum mean square error and first-order Taylor expansion are used to transform the fractional signal-to-noise ratio and the inequality constraint of restriction (18) into an easily solvable form; specifically, the kth user uses the equalizer ω c，k and ω p，k Estimate the public information flow s0 and private information flow s k , and their mean square errors are Then, solve and The optimal equalizer is Substituting the optimal equalizer into the mean square error, we can get the estimated error generated by the optimal equalizer: Using equation (26), the signal-to-interference-noise ratio of the kth user decoding the public information stream and the private information stream is converted to and Right now and Then we can get the weighted minimum mean square error function β c，k =η c，k δ c，k -log(η c，k ) and β p，k =η p，k δ p，k -log(η p，k ), where η c,k and η p，k is the weight parameter; by taking the equalizer and weight as optimization variables, the relationship between the transmission rate and the weighted minimum mean square error is modeled as Where τ=1 / ln2+log(1n2); by solving and Get the best equalizer and The optimal weight is expressed as By using the first-order Taylor expansion Tr(PP H ), inequality Tr(Q-PP H )≤0 is reconstructed as 2Re(Tr(P (t) p H ))-Tr(P (t) (P (t) ) H )≥Tr(Q) (29) The superscript (t) represents the optimal value of the output of the tth iteration; according to the relationship between the transmission rate and the weighted minimum mean square error and inequality (29), problem (23) is transformed into problem (30): in and The invention iteratively optimizes and For a given auxiliary variable Problem (30) will be transformed into a convex problem and then solved using CVX The variables in are solved by equations (25) and (28); Step 3: When other variables are fixed, the problem of optimizing W is simplified to the following unconstrained optimization problem: The optimal solution is W o =(F H F) -1 F H (P+ρD) (32) Step 4: When other variables are fixed, the problem of optimizing F is modeled as Where Y = WW H and Z = (P + ρD)W H ; We use the element-by-element optimization method to solve problem (33), that is, to optimize F n，i The problem is equivalent to The optimal solution to problem (34) is in X=F (t) Y and F (t) is the optimal solution obtained in the tth iteration; Step 5: According to the above steps 1 to 4, the specific process of solving the non-convex optimization problem (14) is as follows: Two-layer loop optimization algorithm based on penalty dual decomposition 1) Initialize F (0) , W (0) , D (0) , (0) and ψ (0) , set the outer iteration index n = 1; 2) While non-convergent execution 3) Set F (1) =F (n-1) and W (1) =W (n-1) and inner iteration index i=1; 4) While non-convergent execution 5) Update the auxiliary variables introduced by the weighted minimum mean square error according to equations (25) and (28); 6) Solve problem (30) using CVX and obtain P (i) and c (i) ; 7) Update the digital beamforming matrix W according to equation (32): (i+1) ; 8) Update the analog beamforming matrix F according to equation (35): (i+1) ; 9) Update iteration index i=i+1; 10) end while 11) Obtain the optimal P (n) 、F (n) and W (n) ; 12)if||P (n) -F (n) W (n) || ∞ ≤ψ (n-1) implement 13) Update ρ (n) =ρ (n-1) ; 14) else 15) Update ρ (n) =0.9ρ (n-1) , D (n) =D (n-1) ; 16)end if 17) Update ψ (n) =0.9||P (n) -F (n) W (n) || ∞ , n = n + 1; 18) end while 19) Output the optimal communication rate.

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