A near-far field robust security communication fusion method based on non-orthogonal multiple access technology

Abstract

The application discloses a near-far field robust security communication fusion method based on a non-orthogonal multiple access technology, and comprises the following steps: setting a channel model of a near field ISAC system, and acquiring a reachable rate of a user decoded by an eavesdropper; taking an error matched by a weighted beam pattern as an optimization target, setting an optimization problem P1 for the error matched by the weighted beam pattern; and adopting an S-Procedure technology and an alternating optimization technology to split the optimization problem P1 into sub-problems 1-3, and solving the optimization problem P1. The application sets a security rate of a user under eavesdropper interference, establishes a robust near field user model under the condition that an eavesdropping channel has a channel error, and under the influence of the error, guarantees that the near field user has a basic successful decoding rate and a minimum security rate requirement, and jointly optimizes a user service quality and a potential target sensing performance.

Description

TECHNICAL FIELD

[0001] The present application relates to the field of wireless communication and sensing technology, in particular to a near-far field robust safety sensing fusion method based on non-orthogonal multiple access technology. BACKGROUND

[0002] The sixth generation (6G) wireless network is expected to achieve huge throughput, ultra-large scale communication and ultra-high spectral efficiency; among them, the near-field wireless propagation mode in the 6G network is attracting much attention, and the near-field communication is gradually dominating the current communication scene, leading to a new paradigm of near-field communication; in the far-field communication mode of the previous generation of wireless networks, the electromagnetic wave front is approximately regarded as a plane, and the signal transmission and positioning have great limitations, while in near-field communication, a unique spherical wave front is used to produce a focused beam, i.e., beam focusing, thereby providing new degrees of freedom in the angular and distance domains to achieve precise signal enhancement and single / multi-user co-channel interference suppression.

[0003] The wireless communication and sensing fusion technology involved in the present application refers to an integrated system that can simultaneously realize information transmission and environmental sensing in a wireless communication system, i.e., ISAC technology; in the traditional method of frequency division sensing and communication, separate frequency bands and infrastructure are needed to realize these two functions, while the significant feature of ISAC is that it can use the same time, frequency, power and hardware resources for communication and sensing; therefore, ISAC technology has higher spectral efficiency, lower energy consumption and lower hardware requirements than traditional frequency division sensing and communication.

[0004] Multiple access technologies can be roughly divided into two different methods: orthogonal multiple access (OMA) and non-orthogonal multiple access (NOMA); compared with orthogonal multiple access (OMA), non-orthogonal multiple access (NOMA) allows multiple users to be allocated the same frequency band within the same cell at the same time, and has many advantages, including improved spectral efficiency, higher cell edge throughput, relaxed channel feedback and lower transmission latency.

[0005] To meet the growing demand for communication and sensing performance, future sensing-integrated systems will develop towards ultra-large antenna element arrays and high-frequency terahertz bands, which are crucial for improving communication capacity and sensing resolution, and when a large number of service users are in the near-field range, the trend from plane wave propagation to spherical wave propagation will significantly change the electromagnetic properties of the wireless environment, leading to inevitable near-field effects; therefore, there may be a mismatch between the existing sensing-integrated design based on the traditional far-field assumption and the actual wireless environment. SUMMARY

[0006] In view of the above-mentioned disadvantages of the prior art, the present application provides a near-far field robust security sensing fusion method based on non-orthogonal multiple access technology. Non-orthogonal multiple access (NOMA) is used to provide services for multiple users while sensing a plurality of potential targets.

[0007] To achieve the above-mentioned effects, the technical solutions of the present application are as follows:

[0008] The present application provides a near-far field robust security sensing fusion method based on non-orthogonal multiple access technology, comprising the following steps:

[0009] Step 1: setting the channel model of the near-field ISAC system, i.e.:

[0010] A base station equipped with N antenna elements is set, assuming that the antenna at the base station adopts a uniform linear array, wherein the base station transmits communication signals for K single-antenna element legitimate users in the near field, and there are L eavesdroppers near the legitimate users, and the base station also sends radar sensing signals for M potential sensing targets in the far field;

[0011] Without loss of generality, the origin of the coordinate system is placed at the center of the uniform linear array at the base station; the coordinates of the nth antenna element of the uniform linear array are wherein is the coordinate system coefficient of each antenna element in the Cartesian coordinate system, and d represents the distance between two adjacent antenna elements;

[0012] Step 2: obtaining the eavesdropper E l The achievable rate of the decoding user k;

[0013] Step 3: based on the eavesdropper E l The problem of inaccurate channel information, a robust channel model is established to obtain the near-field channel error parameters;

[0014] Step 4: taking the error matched by the minimum weighted beam pattern as the optimization target, setting the optimization problem P1 for the error matched by the weighted beam pattern; based on the S-Procedure technology and the alternating optimization technology, the optimization problem P1 is decomposed into sub-problems 1, 2 and 3, and the optimization problem P1 is solved;

[0015] The optimization problem P1 in step 4 is:

[0016]

[0017] s.t C1:R k ≥R min，k , R k→j ≥R j

[0018]

[0019] C3:||Ah l ||≤δ

[0020]

[0021] where the objective function f0is the error function matched by the weighted beam pattern between the transmit beam patterns; is the digital beamforming vector, R s is the covariance matrix of the sensing signal s0, and a is the scaling factor; constraint C1represents the minimum communication rate requirement R min,k and the decoding success rate requirement, which requires the user to decode its own communication rate to the minimum rate limit R j , otherwise it is decoding interruption; constraint C2represents the minimum security rate limit for user k in the eavesdropping state to reduce the user information theft by the eavesdropper; constraint C3represents the two-norm constraint of the channel error term, and d is the channel estimation error value; constraint C4represents the base station transmit power constraint P0; constraint C5represents the R s is semi-positive definite.

[0022] Further, step 1 further comprises: defining the user k set K represents the strongest user of the channel, and the eavesdropper E l set E l represents the lth eavesdropper; use to represent the set of M sensing targets; the distance of user k from the center of the uniform linear array is r k and the angle is q k , the coordinates of user k are r k = [r k cos q k , r k sin q k ] T ; the distance from the nth antenna element to user k is calculated as follows:

[0023]

[0024] User k is in the Fresnel region of the near field, that is, D represents the aperture size of the uniform linear array at the base station, D = (N-1)d; assuming that the channel gain of each link between the antenna element and user k is the same, the channel gain of the near-field link is calculated as the free space path loss of the central link, which is given by , where represents the path loss at a reference distance of 1m, and l represents the carrier wavelength; therefore, the near-field channel between the nth antenna element and user k is:

[0025]

[0026] Where, θ k Indicates the angle of arrival of user k. Represents the complex channel gain; denoted by r n,k Indicates r n,k (r k ,θ k ); Set up a near-field channel between the free-space line-of-sight propagation base station and user k. and near-field array response They are respectively:

[0027]

[0028] in, Represents an N×1 dimensional matrix (column vector);

[0029] Base stations and eavesdroppers E l The near-field channel between them is defined as

[0030] Base station design integrates downlink communication and sensor signal x[t]:

[0031]

[0032] in, This is a digital beamforming vector used to beam information symbols c. k [t] is passed to user k; s0 is a dedicated sensing signal; assuming the information symbol c k [t] is independent and identically distributed and has unit power, that is, if k = i, otherwise make The covariance matrix of the dedicated sensing signal s0 is used to obtain the covariance matrix R of the joint communication signal x[t]. x :

[0033]

[0034] Furthermore, the near-field and far-field ISAC system employs non-orthogonal multiple access technology to provide data services to multiple users simultaneously; that is, the base station will... By superimposing the signals of multiple users together using superposition coding technology, we obtain... Use h k and h l They represent h respectively B,k (r,θ) and h B,l (r,θ); in user k and eavesdropper E l The signals received at the location are as follows:

[0035]

[0036] in, and This represents additive white Gaussian noise; w k w i Both represent digital beamforming vectors; c i [t] represents the information symbol transmitted by the base station to user i.

[0037] Furthermore, step 2 includes:

[0038] Assume that the user's index is in ascending order with respect to their channel gain, i.e., |h1|≤|h2|≤…≤|h K Therefore, user 1 is the user with the weakest channel, while user K is the user with the strongest channel. In non-orthogonal multiple access, user 1 is detected and deleted first. For user K, serial interference cancellation technology is used to decode the information of all users j with weaker channels. At the same time, the information of user i with a stronger channel is used as interference noise, where The achievable communication rate for user k decoding itself is:

[0039]

[0040] For user j, first decode the weaker signal of user k and remove it, then decode its own signal, where The achievable communication rate for user j to decode weaker user k is:

[0041]

[0042] To ensure that user j can successfully decode user k's signal, R must be satisfied. k→j ≥R j ;

[0043] At user K, serial interference eliminates interference from the remaining users; the achievable communication rate for user K is then:

[0044]

[0045] Therefore, the total communication throughput of K users is determined by Give;

[0046] For the eavesdropper E l In the security analysis at the physical layer, the worst-case assumption is used, i.e., the eavesdropper E... l Knowing the user's decoding order and the corresponding digital beamforming vector, the eavesdropper E l The achievable communication rate for decoding user k is:

[0047]

[0048] At this time, the worst-case security rate of the user signal when L eavesdroppers are set to eavesdrop is defined as:

[0049] R S，k = [R k -max 1≤l≤L {R l，k}] + (13).

[0050] Further, step 3 is specifically:

[0051] The transmit beam pattern is used as a key performance indicator for setting radar target detection in the base station; the transmit beam pattern represents the power distribution of the transmitted signal relative to the sensing angle θ m , ranging from Radar and communication signals act on the sensing target; the transmit beam pattern gain generated by the radar and communication signals acting on the sensing target is:

[0052]

[0053] wherein, represents the far-field steering vector at angle θ m ;

[0054] Based on the problem that the channel information of the eavesdropper E l is not accurate, a robust channel model is established, and the near-field channel error parameter is defined as:

[0055]

[0056] wherein, and are the estimation terms of the angle of arrival and the distance, θ l and r l are the true terms of the angle of arrival and the distance, Δθ l and Δr l are the error terms of the angle of arrival and the distance;

[0057] The error terms Δθ l and Δr l are constrained in the known set, i.e. and Δr l ∈ [-ξ, ξ] for Therefore, the channel error model of the eavesdropper E l is modeled as follows:

[0058] ​

[0059] Φ l = {||Δh l ||≤δ} (17)

[0060] where, for channel error terms have a two-norm constraint δ > 0, the eavesdropper E l 's channel error model is denoted by

[0061] Let denote the required beam pattern for a given design, specifying the transmit power distribution at M angles in space ; for a target sensing task, a uniform distribution, while for target tracking, a non-zero constant at the angles of potential targets of interest, the required weighted beam pattern matched between the transmit beam pattern is defined as:

[0062]

[0063] where a(θ m ) denotes the steering vector at direction θ m ; α is a scaling factor to adjust the scaling level of .

[0064] Further, the optimization problem P1 in step 4 is:

[0065]

[0066] s.t C1:R k ≥R min,k , R k→j ≥R j

[0067]

[0068] C3:||Δh l ||≤δ

[0069]

[0070] where the objective function f0 is the error function matched between the weighted beam pattern and the transmit beam pattern; is the digital beamforming vector, R s is the covariance matrix of the sensing signal s0, and α is the scaling factor; the constraint C1 represents the minimum communication rate requirement R min,k and the decoding success rate requirement for user k, requiring the user to decode its own communication rate to reach the minimum rate limit R​j , otherwise, decoding is interrupted; constraint C2 represents the minimum secure rate limit for user k in the eavesdropping state to reduce the eavesdropping of user information; constraint C3 represents a two-norm constraint of the channel error term, and δ is the channel estimation error value; constraint C4 represents the base station transmission power constraint P0; constraint C5 represents R s is semi-positive definite.

[0071] Further, based on the S-Procedure technology and the alternating optimization technology, the optimization problem P1 is decomposed into subproblem 1, subproblem 2, and subproblem 3.

[0072] To solve the semi-infinite constraint in constraint C2, a slack variable and the S-Procedure technology are used to transform the non-convex constraint, and the S-Procedure technology is represented as:

[0073]

[0074] wherein, is a Hermitian matrix, wherein, represents an MxM matrix;

[0075] represents an Mx1 matrix (column vector), represents a real number;

[0076] If x satisfying f1(x)≤0 all have f2(x)≤0, f1(x) is said to dominate f2(x) through the S-Procedure technology; the conversion condition is that there is a non-negative variable ω such that the following inequality holds:

[0077]

[0078] wherein f1(x)≤0 is said to contain f2(x)≤0.

[0079] Further, the subproblem 1 is represented as:

[0080] Due to the existence of the error term Δh l in constraint C2, ||Δh l ||≤δ is a bounded two-norm constraint, and for the error term Δh l The above constraint is coupled and has a semi-infinite constraint, that is, non-convex; to convert constraint C2 into a convex constraint, R k in the secure rate is replaced by its lower bound , a slack variable is introduced, and is substituted into the eavesdropping rate to convert it into:

[0081]

[0082] where, The semi-infinite constraint problem is converted into a linear matrix inequality (LMI) form by applying the S-Procedure technique:

[0083]

[0084] where, is the introduced slack variable;

[0085] The optimization problem P1 is rewritten as optimization problem P1.1:

[0086]

[0087] s.t C1:R k ≥R min,k , R k→j ≥R j

[0088]

[0089] C3:||Δh l ||≤δ

[0090]

[0091] Further, the subproblem 2 is expressed as:

[0092] The scaling factor a is a quadratic function of the objective function, and the optimal solution a of the objective function can be obtained by using the typical first-order optimality criterion * , the optimization problem P1.1 is still non-convex after the semi-infinite constraint is converted into an LMI problem. The semi-definite relaxation (SDR) strategy is used to relax part of the constraints, and the rank-one constraint Rank(W k )≤1 in the constraint C5 is removed to obtain the optimization problem P2.1:

[0093]

[0094] s.t C1:R k ≥R min,k , R k→j ≥R j

[0095]

[0096] C3:||Δh l ||≤δ

[0097]

[0098] Using the alternating optimization method, the relaxation variable μ is fixed l and Optimize R s and w k , the optimization problem P2.1 is effectively solved, and let represent the optimal solution of the optimization problem P2.1, if The relaxation process is tight, that is, the optimal solution of the optimization problem P2.1 is the optimal solution of the optimization problem P1, and the optimal solution of the optimization problem P1 is obtained by using the eigenvalue decomposition method Where v k represents the corresponding eigenvector corresponding to the eigenvalue λ k .

[0099] Further, the subproblem 3 is represented as:

[0100] Fix R s and w k , optimize the relaxation variable μ l and Initialization Let the iteration index i=0, for given R s and w k , the equivalent optimal solution is reconstructed based on the optimization problem P2.1 Substitute into the objective function, update The iteration process is stopped until the objective value between two iterations is less than a tolerance level ε or the maximum iteration number is reached; the digital beamforming vector, the covariance matrix, the scaling factor and all relaxation variables obtained in the last iteration are output.

[0101] Compared with the prior art, the beneficial effects of the technical scheme of the present application are:

[0102] The present application applies non-orthogonal multiple access technology, which not only allows multiple users to share the same frequency spectrum to achieve high spectral efficiency, but also has better coverage and larger system capacity, and has communication and sensing capabilities; at the same time, the channel estimation of the base station to the non-perfect channel state information of the eavesdropper is set, so that the method has certain robustness.

[0103] The application is based on near-far field area robust security sensing fusion under non-orthogonal multiple access (NOMA), and jointly optimizes the communication rate of users under eavesdropper interference, the security rate and the error function matching the potential target sensing beam pattern gain. The near-far field robust security sensing fusion method based on non-orthogonal multiple access (NOMA) proposed in the application can meet the communication service quality QoS of users in the near field while improving the accuracy of far field target sensing in the required direction under a certain robustness. BRIEF DESCRIPTION OF DRAWINGS

[0104] Figure 1 is a near field ISAC system schematic diagram based on non-orthogonal multiple access of the application;

[0105] Figure 2 is a user power allocation schematic diagram based on non-orthogonal multiple access (NOMA) of the application. DETAILED DESCRIPTION

[0106] The embodiments of the application will be described below with reference to the accompanying drawings and preferred embodiments, and other advantages and effects of the application can be easily understood by those skilled in the art from the disclosure in the specification. The application can also be implemented or applied by different specific embodiments, and various modifications or changes can be made to the details in the specification based on different views and applications without departing from the spirit of the application. It should be understood that the preferred embodiments are only used to illustrate the application, and are not intended to limit the protection scope of the application.

[0107] It should be noted that the diagrams provided in the following embodiments only illustrate the basic concept of the application in a schematic manner, and only the components related to the application are shown in the diagrams, not the number, shape and size of the components when actually implemented. The actual implementation of each component may be a random change in type, number and proportion, and the component layout pattern may also be more complex.

[0108] Glossary:

[0109] Successive interference cancellation (SIC)

[0110] Semi-infinite constraints (SICs)

[0111] Channel state information (CSI)

[0112] EMBODIMENT

[0113] The embodiment proposes a near-far field robust security sensing fusion method based on non-orthogonal multiple access technology. Please refer toFigure 1 comprising the following steps:

[0114] Step 1: setting the channel model of the near-far field ISAC system, i.e.

[0115] Setting a base station (BS) equipped with N antenna elements, assuming that the antenna at the base station adopts a uniform linear array (ULA), wherein the base station transmits communication signals for K single-antenna element legitimate users in the near field, and there are L eavesdroppers near the legitimate users, and the base station also sends radar sensing signals for M potential sensing targets in the far field;

[0116] Without loss of generality, the origin of the coordinate system is placed at the center of the uniform linear array at the base station; the coordinates of the nth antenna element of the uniform linear array are wherein is the coordinate system coefficient of each antenna element in the Cartesian coordinate system, and d represents the spacing between two adjacent antenna elements;

[0117] Step 2: obtaining the eavesdropper E l decoding the achievable rate of the user k;

[0118] Step 3: based on the eavesdropper E l channel information inaccuracy problem, establishing a robust channel model to obtain the near-field channel error parameter;

[0119] Step 4: taking the error matched by the minimum weighted beam pattern as the optimization objective, setting the optimization problem P1 for the error matched by the weighted beam pattern; based on the S-Procedure technology and the alternating optimization (AO) technology, decomposing the optimization problem P1 into subproblem 1, subproblem 2 and subproblem 3 to solve the optimization problem P1;

[0120] The optimization problem P1 in Step 4 is:

[0121]

[0122] s.t C1:R k ≥R min ,R k→j ≥R j

[0123]

[0124] C3:||Δh l ||≤δ

[0125]

[0126] Wherein, the objective function f0 is the error function for matching the weighted beam pattern between the transmitted beam patterns; R is the digital beamforming vector. s Let be the covariance matrix of the sensing signal s0, and α be the scaling factor; constraint C1 represents the minimum communication rate requirement R for user k. min,k And decoding success rate requirements, requiring users to decode their own communication rate to reach a minimum rate limit R. j Otherwise, decoding is interrupted; constraint C2 represents the minimum secure rate limit for user k in eavesdropping mode. Reduce the risk of eavesdroppers stealing user information; constraint C3 represents the L2 constraint of the channel error term, where δ is the channel estimation error value; constraint C4 represents the base station transmit power constraint P0; constraint C5 represents R s It is positive semidefinite.

[0127] As a preferred technical solution, in this embodiment, step 1 further includes: defining a user set k. K represents the user with the strongest channel, and E represents the eavesdropper. l gather E l Indicates the l-th eavesdropper; using Let r represent the set of M sensing targets; the distance r between user k and the center of the uniform linear array. k And the angle is θ k User k's coordinates are r k =[r k cosθ k ,r k sinθ k ] T The distance from the nth antenna element to user k is calculated as follows:

[0128]

[0129] User k is in the Fresnel region of the near field, i.e. D represents the aperture size of the uniform linear array at the base station, D = (N-1)d; assuming that the channel gain of each link between the antenna element and user k is approximately the same, the channel gain for the near-field link is calculated as the free-space path loss of the center link, from... Given, among which Let λ represent the path loss at a reference distance of 1m, and λ represent the carrier wavelength; therefore, the near-field channel between the nth antenna element and user k is:

[0130]

[0131] Where, θ k This represents the angle of arrival (AOD) of user k. Represents the complex channel gain; denoted by r n,k Indicates r n,k (r k ,θ k ); Set up a near-field channel between the free-space line-of-sight propagation base station and user k. and near-field array response They are respectively:

[0132]

[0133] in, Represents an N×1 dimensional matrix (column vector);

[0134] Base stations and eavesdroppers E l The near-field channel between them is defined as

[0135] Base station design integrates downlink communication and sensor signal x[t]:

[0136]

[0137] in, This is a digital beamforming vector used to beam information symbols c. k [t] is passed to user k; s0 is a dedicated sensing signal; assuming the information symbol c k [t] is independent and identically distributed and has unit power, that is, if k = i, otherwise make The covariance matrix of the dedicated sensing signal s0 is used to obtain the covariance matrix R of the joint communication signal x[t]. x :

[0138]

[0139] In this invention, user k is a legitimate user k. The base station is a dual-function base station.

[0140] As a preferred technical solution, in this embodiment, (i) communication mode

[0141] The near-field and far-field ISAC system employs non-orthogonal multiple access (NOMA) technology to provide data services to multiple users simultaneously; that is, the base station will... By superimposing the signals of multiple users together using superposition coding technology, we obtain... like Figure 2 As shown, h k and h l They represent h respectively B,k (r,θ) and h B,l (r,θ); in user k and eavesdropper E l The signals received at the location are as follows:

[0142]

[0143] in, and This represents additive white Gaussian noise; w k w i Both represent digital beamforming vectors; c i [t] represents the information symbol transmitted by the base station to user i.

[0144] As a preferred technical solution, in this embodiment, step 2 includes:

[0145] Without loss of generality, assume that the user's index is in ascending order with respect to their channel gain, i.e., |h1|≤|h2|≤…≤|h K Therefore, user 1 is the user with the weakest channel, while user K is the user with the strongest channel. In non-orthogonal multiple access, user 1 is detected and deleted first. For user K, serial interference cancellation technology is used to decode the information of all users j with weaker channels. At the same time, the information of user i with a stronger channel is used as interference noise, where The achievable communication rate for user k decoding itself is:

[0146]

[0147] For user j, first decode the weaker signal of user k and remove it, then decode its own signal, where The achievable communication rate for user j to decode weaker user k is:

[0148]

[0149] To ensure that user j can successfully decode user k's signal, R must be satisfied. k→j ≥R j ;

[0150] At user K, serial interference is eliminated by interference from the remaining users; the communication rate achievable by user K at this time is:

[0151]

[0152] Therefore, the total communication throughput of K users is determined by Give;

[0153] For the eavesdropper E l In the security analysis at the physical layer, the worst-case assumption is used, i.e., the eavesdropper E... l Knowing the user's decoding order and the corresponding digital beamforming vector, the eavesdropper El The achievable communication rate of user k is decoded as:

[0154]

[0155] At this time, the worst-case security rate of the user signal when L eavesdroppers are set to eavesdrop is defined as:

[0156] R S，k = [R k -max 1≤l≤L {R l，k}] + (13).

[0157] As a preferred technical solution, in the embodiment, step 3 is specifically: (ii) sensing mode

[0158] The transmit beam pattern is used as the key performance indicator of radar target detection in the base station; the transmit beam pattern represents the power distribution of the transmitted signal relative to the sensing angle θ m , ranging from In the present application, the radar and communication signals jointly act on the sensing target; the radar and communication signals acting on the sensing target produce a transmit beam pattern gain :

[0159]

[0160] Wherein, represents the far-field steering vector at angle θ m ;

[0161] In practice, the transmit beam pattern is designed according to the radar target sensing requirements; for example, if it is necessary to perform a detection task without knowing the direction of the potential target, a uniformly distributed beam pattern is required; in contrast, if the direction of the target is roughly known, for example, for target tracking, only the beam pattern gain of these potential directions of interest needs to be maximized.

[0162] Problem description and solution:

[0163] With the development of technology, the channel CSI acquisition technology under near-field conditions is also mature, without loss of generality, it is assumed that the base station has perfect CSI of the user channel; however, for the eavesdropper, it is difficult to obtain perfect CSI, because the eavesdropper E l remains silent to steal the user's information, and does not actively send signals, which increases the complexity of channel estimation, therefore, in the actual system design, perfect channel state information {(r l , θ l )} cannot be obtained; based on the eavesdropper E lTo address the issue of inaccurate channel information, a robust channel model is established, with the near-field channel error parameters defined as:

[0164]

[0165] where, and are the estimated terms of the angle of arrival and distance, respectively, l and r l are the true terms of the angle of arrival and distance, respectively, l and Δr l are the error terms of the angle of arrival and distance, respectively.

[0166] The error terms Δθ l and Δr l are constrained in the known set, i.e., and Δr l ∈ [-ξ, ξ] for Thus, the channel error model of the eavesdropper E l is modeled as follows:

[0167]

[0168] Φ l = {||Δh l ||≤ δ} (17)

[0169] where, for all channel error terms have a deterministic two-norm constraint δ > 0, and the channel error model of the eavesdropper E l is denoted by

[0170] Let denote the required beam pattern for a given design, specifying the required transmit power distribution at M angles in the space; for target sensing tasks, a uniform distribution, while for target tracking, a non-zero constant at the angles of potential targets of interest, and zero elsewhere; in this case, the required error function matched by the weighted beam pattern between and the transmit beam pattern is defined as:

[0171]

[0172] where a(θ m ) denotes the steering vector at direction θ m ; α serves as a scaling factor to adjust ​the scaling level of the transmit beam pattern to better match the scaling of the desired beam pattern.

[0173] As a preferred technical solution, in the embodiment, the optimization problem P1 in step 4 is:

[0174]

[0175] s.t C1:R k ≥R nin,k , R k→j ≥R j

[0176]

[0177] C3:||Δh l ||≤δ

[0178]

[0179] wherein, constraint C1 represents the minimum rate requirement and the decoding success rate requirement of the user k, requiring the user to decode the own rate to reach the minimum rate limit, otherwise it is decoding interruption; constraint C2 represents the minimum security rate limit of the user k in the eavesdropping state, reducing the information stealing of the eavesdropper to the user; constraint C3 represents the two norm constraint of the channel error term; constraint C4 represents the base station transmission power constraint.

[0180] As a preferred technical solution, in the embodiment, for the problem of minimizing the weighted beam pattern gain matching error, due to the existence of the channel state information CSI error term, this optimization problem is a semi-infinite non-convex constraint, which is difficult to solve directly, so the present application decomposes the optimization problem P1 into sub-problem 1, sub-problem 2 and sub-problem 3 based on S-Procedure technology and alternating optimization (AO) technology;

[0181] To solve the semi-infinite constraint in constraint C2, the non-convex constraint is transformed by using a slack variable and S-Procedure technology, and the S-Procedure technology involves two quadratic functions, which are represented as:

[0182]

[0183] wherein, is a Hermitian matrix, wherein, represents an MxM matrix;

[0184] represents an Mx1 matrix (column vector), represents a real number;

[0185] If x satisfying f1(x)≤0 all have f2(x)≤0, then f1(x) is said to dominate f2(x) by S-Procedure technique; the conversion condition is: there exists non-negative variable ω such that the following inequality holds:

[0186]

[0187] Wherein f1(x)≤0 is said to contain f2(x)≤0.

[0188] As a preferred technical solution, in the embodiment, the sub-problem 1 is expressed as:

[0189] Due to the existence of error term Δh l in the constraint C2, ||Δh l ||≤δ is a bounded two-norm constraint, and for error term Δh l The above constraint is coupled, and there is a semi-infinite constraint, i.e. non-convex; to convert the constraint C2 into a convex constraint, first replace R k in the safety rate with its lower bound , and introduce a slack variable , and substitute into the eavesdropping rate to convert it into:

[0190]

[0191] Wherein, After applying S-Procedure technique, the above semi-infinite constraint problem is converted into a linear matrix inequality (LMI) form:

[0192]

[0193] Wherein, is the introduced slack variable;

[0194] The optimization problem P1 is rewritten as optimization problem P1.1:

[0195]

[0196] s.t C1:R k ≥R min，k , R k→j ≥R j

[0197]

[0198] C3:||Δh l ||≤δ

[0199]

[0200] As a preferred technical solution, in the embodiment, the sub-problem 2 is represented as:

[0201] The scaling factor a is a quadratic function of the objective function, and the optimal solution a of the objective function can be obtained by using a typical first-order optimization criterion * , substitute into the optimization problem P1, after the optimization problem P1.1 converts the semi-infinite constraint into an LMI problem, the optimization problem P1.1 is still non-convex, and the semi-definite relaxation SDR strategy is used to relax part of the constraints. The rank-one constraint Rank(W k )≤1 in the constraint C5 is removed, and the optimization problem P2.1 is obtained:

[0202]

[0203] s.t C1:R k ≥R min，k , R k→j ≥R j

[0204]

[0205] C3:||Δh l ||≤δ

[0206]

[0207] Using the alternating optimization (AO) method, fix the relaxation variable μ l and optimize R s and w k , since the optimization problem P2.1 is a semi-definite programming, use an effective solver (such as the CVX tool) to effectively solve the optimization problem P2.1, let represent the optimal solution of the optimization problem P2.1, if then the relaxation process is tight, that is, the optimal solution of the optimization problem P2.1 is the optimal solution of the optimization problem P1, and the optimal solution of the optimization problem P1 is obtained by using the eigenvalue decomposition method where v k represents the eigenvector corresponding to the eigenvalue λ k ; if , the optimization problem P1 needs to be reconstructed to obtain the optimal solution.

[0208] As a preferred technical solution, in the embodiment, the sub-problem 3 is represented as:

[0209] Fix R s and w k , optimize the relaxation variable μ l and Initialize Let iteration index i = 0, for a given R s and w k , reconstruct the equivalent optimal solution based on optimization problem P2.1 Substitute into the objective function, update The iteration process is stopped until the objective value between two iterations is less than a tolerance level ε or the maximum number of iterations is reached; the digital beamforming vector, covariance matrix, scaling factor and all relaxation variables obtained in the last iteration are output.

[0210] The embodiments of the present application have the following beneficial effects:

[0211] The present application sets up near-field multi-user communication services and far-field potential target awareness under non-orthogonal multiple access, proposes an error function f0 (formula 18, referred to as error function f0) between the required beam pattern and the transmit beam pattern under the condition of meeting the basic rate requirement of each user and the total base station transmission power limit. For target awareness, the required beam pattern is a non-zero constant at the angle of interest of the potential target, and is zero elsewhere, and the error function f0 is minimized to maximize the radar performance of target tracking or detection.

[0212] In addition, there are several potential eavesdroppers in the near-field communication area, and since the eavesdroppers steal the user's information in a silent manner, it is difficult for the base station to obtain perfect channel state information (CSI) of the eavesdropping channel, the present application sets up the security rate of the user under the eavesdropper interference, and under the condition that the eavesdropping channel has channel error, a robust near-field user model and far-field target awareness model are established, under the influence of this error, the near-field user meets the rate requirement of successful decoding and the minimum security rate requirement, and the user communication service quality and potential target awareness performance are jointly optimized.

[0213] Obviously, the above embodiments of the present application are only examples for clearly illustrating the present application, and are not intended to limit the embodiments of the present application. For those skilled in the art, other different forms of changes or variations can be made on the basis of the above description. Here, all the embodiments are not required to be exhausted. Any modification, equivalent replacement and improvement made within the spirit and principle of the present application shall be included in the protection scope of the claims of the present application.

Claims

1. A near-far field robust secure communication fusion method based on non-orthogonal multiple access technology, characterized in that, The method comprises the following steps: Step 1: setting a channel model of a near-field ISAC system, namely: A base station equipped with N antenna elements is set, assuming that the antenna at the base station adopts a uniform linear array, wherein the base station transmits communication signals for K single-antenna legitimate users in a near field, and there are L eavesdroppers near the legitimate users, and the base station also sends radar sensing signals for M potential sensing targets in a far field; Without loss of generality, the origin of the coordinate system is placed at the center of the uniform linear array at the base station; the coordinates of the nth antenna element of the uniform linear array are wherein are the coordinate system coefficients of each antenna element in the Cartesian coordinate system, and d represents the spacing between two adjacent antenna elements; Step 2: Acquire eavesdropper E l Decode the achievable rate of user k; Step 3: Based on the eavesdropper E l To solve the problem of inaccurate channel information, a robust channel model is established to obtain near-field channel error parameters; Step 4: taking the error matched by the weighted beam pattern as an optimization target, setting an optimization problem P1 for the error matched by the weighted beam pattern; based on S-Procedure technology and alternating optimization technology, the optimization problem P1 is decomposed into subproblem 1, subproblem 2 and subproblem 3, and the optimization problem P1 is solved; The optimization problem P1 in step 4 is: s.t C1:R k ≥R min，k , R k→j ≥R j C3: ||Δh l ||≤δ where the objective function f0is the error function of the weighted beam pattern matched between the transmit beam patterns; is the digital beamforming vector, R s is the covariance matrix of the sensing signal s0, and a is the scaling factor; constraint C1represents the minimum communication rate requirement R min,k and the decoding success rate requirement, which requires the user to decode its own communication rate to reach the minimum rate limit R j , otherwise the decoding is interrupted; constraint C2represents the minimum security rate limit for the user k in the eavesdropping state to reduce the user information theft by the eavesdropper; constraint C3represents the two-norm constraint of the channel error term, and d is the channel estimation error value; constraint C4represents the base station transmit power constraint P0; constraint C5represents R s is semi-positive definite.

2. The method of claim 1, wherein, Step 1 also includes defining the set of users k K represents the user with the strongest channel, the eavesdropper E l Set E l represents the lth eavesdropper; use represents the set of M sensing targets; the distance of user k from the center of the uniform linear array is r k and the angle is θ k The coordinates of user k are r k = [r k cos θ k , r k sin θ k ] T The distance from the nth antenna element to user k is calculated as follows: User k is in the Fresnel region of the near field, i.e. D represents the aperture size of the uniform linear array at the base station, D = (N - 1)d; assuming that the channel gain of each link between the antenna element and user k is the same, the channel gain for the near field link is calculated as the free space path loss of the central link, which is given by where denotes the path loss at the reference distance of 1m, and λ represents the carrier wavelength; thus, the near field channel between the nthantenna element and user k is: where θ k denotes the angle of arrival of user k, denotes the complex channel gain; with r n,k denotes r n,k (r k ,θ k ); the near-field channel between the line-of-sight propagation base station and user k is set and the near-field array response are respectively: wherein denotes an N x 1 -dimensional matrix (column vector); The near field channel between the base station and the eavesdropper E is defined as l Hnearfield= Hbase station - Heavesdropper The base station end designs a joint downlink communication and sensing signal x[t]: wherein is a digital beamforming vector for mapping information symbols c k [t] is delivered to user k; s0is a dedicated sensing signal; Assume information symbols c k [t] are independent and identically distributed with unit power, i.e. if Otherwise Let denote the covariance matrix of the dedicated sensing signal s0, the covariance matrix R x of the joint communication signal x[t] is obtained 3. The method of claim 1, wherein, The near-far ISAC system employs non-orthogonal multiple access technology to provide data services for multiple users simultaneously; that is, the base station will Superimpose the signals of multiple users together by superposition coding technology to obtain Let h k and h l denote h B,k (r,θ) and h B,l (r,θ), respectively; the signals received at user k and eavesdropper E l , respectively, are: wherein and denotes additive white Gaussian noise; w k , w i each denote a digital beamforming vector; c i [t] denotes an information symbol transmitted by the base station to user i, 4. The method of claim 1, wherein, Step 2 comprises: Assume that the users' indices are in increasing order with respect to their channel gains, i.e., |hi| < |h2| <... < |hk| ; user 1 is the weakest user and user K is the strongest user; in non-orthogonal multiple access, user 1 is detected and removed first, and a serial interference cancellation technique is employed to decode the information of all the weaker users j for user k, where K |; user 1 is the weakest user and user K is the strongest user; in non-orthogonal multiple access, user 1 is detected and removed first, and a serial interference cancellation technique is employed to decode the information of all the weaker users j for user k, where |; user 1 is the weakest user and user K is the strongest user; in non-orthogonal multiple access, user 1 is detected and removed first, and a serial interference cancellation technique is employed to decode the information of all the weaker users j for user k, where |; user 1 is the weakest user and user K is the strongest user; in non-orthogonal multiple access, user 1 is detected and removed first, and a serial interference cancellation technique is employed to decode the information of all the weaker users j for user k, where For user j, the signal of the weaker user k is first decoded and removed, and then the signal of itself is decoded, where The achievable communication rate of user j decoding the weaker user k is then To ensure that user j can successfully decode user k's signal, the following must be satisfied: R k→j ≥ R j ; At the user K, interference cancellation is performed on interference from the remaining other users; at this time, the achievable communication rate of the user K is: So the total communication throughput of K users is given by is given; For the eavesdropper E l In the security analysis on the physical layer, the worst-case assumption is adopted, i.e. the eavesdropper E l knows the decoding order of the users and the corresponding digital beamforming vectors, the eavesdropper E l The achievable communication rate for user k is: At this time, the worst-case security rate when L eavesdroppers eavesdrop on the user signal is defined as: R S，k = [R k -max 1≤l≤L {R l，k}] + (13).

5. The method of claim 1, wherein, Step 3 specifically comprises: The transmit beam pattern is used as a key performance indicator for radar target detection in the base station; the transmit beam pattern represents the power distribution of the transmitted signal with respect to the look angle θ m ranging from The radar and communication signals act on the sensing target; the transmit beam pattern gain produced by the radar and communication signals acting on the sensing target is : wherein represents the far field steering vector at angle θ m at angle θ Based on the eavesdropper E l To solve the problem of inaccurate channel information, a robust near-field channel model is established, and the near-field channel error parameter is defined as wherein, and are the estimated terms of angle of arrival and distance, respectively, l and r l are the true terms of angle of arrival and distance, respectively, l and Δr l are the error terms of angle of arrival and distance, respectively; Set the error term Δθ l and Δr l are constrained in the known set, i.e. and Δr l ∈ [-ξ, ξ] for the eavesdropper E l The channel error model for the eavesdropper E is modeled as follows: Φ l = { || Δh l || ≤ δ} (17) wherein, For The channel error terms all have a two-norm constraint δ > 0, and the eavesdropper E l The channel error model for E is denoted by ​ Let denote the required beam pattern for a given design, specifying the transmit power distribution at M angles in space ; for a target sensing task, a uniform distribution, while for target tracking, a non-zero constant at angles of potential interest, the required error function matched to a weighted beam pattern between the transmit beam pattern is defined as: where a(θ m ) denotes the steering vector at direction θ m ; and α is a scaling factor to adjust the scaling level of .

6. The method of claim 1, wherein, The S-Procedure technology and the alternating optimization technology decompose the optimization problem P1 into subproblem 1, subproblem 2 and subproblem 3, which comprise: In order to solve the semi-infinite constraint in constraint C2, a slack variable and S-Procedure technology are used to convert the non-convex constraint, and the S-Procedure technology is represented as: wherein is a Hermitian matrix, where denotes a M x M dimensional matrix; denotes an M x 1 dimensional matrix (column vector), denotes a real number; If x satisfying f1(x)≤0 all have f2(x)≤0, it is said that f1(x) dominates f2(x) through the S-Procedure technology; the conversion condition is that there are non-negative variables ω that make the following inequality hold: wherein then f1(x) < 0 is said to contain f2(x) < 0.

7. The method of claim 6, wherein, The subproblem 1 is represented as: Due to the presence of the error term Δh l in constraint C2, ||Δh l ||≤δ is a bounded two-norm constraint, for the error term Δh l The above constraint is coupled, with the presence of semi-infinite constraints, i.e. non-convex; to convert constraint C2 into a convex constraint, first replace R k in the safe rate with its lower bound Introduce a slack variable Replace in the eavesdropping rate with the following conversion: where After applying the S-Procedure technique, the semi-infinite problem is converted into a linear matrix inequality (LMI) form: wherein is an introduced slack variable; The optimization problem P1 is rewritten as an optimization problem P1.1: s.t C1:R k ≥R min,k , R k→j ≥R j C3: ||Δh l ||≤δ 8. The method of claim 7, wherein, The subproblem 2 is represented as: The scaling factor a is a quadratic function of the objective function, and the optimal solution a of the objective function can be obtained by using a typical first-order optimization criterion * , and substituting it into the optimization problem P1, the optimization problem P1.1 is still non-convex after converting the semi-infinite constraint into an LMI problem. The semi-definite relaxation (SDR) strategy is used to relax part of the constraints, and the rank-one constraint Rank(W k )≤1 in the constraint C5 is removed, and the optimization problem P2.1 is obtained: s.t C1:R k ≥R min，k , R k→j ≥R j C3: ||Δh l ||≤δ The relaxation variable μ is fixed by using the alternate optimization method l and Optimization R s and w k , the optimization problem P2.1 is solved effectively, and let represent the optimal solution of the optimization problem P2.1, if the relaxation process is tight, that is, the optimal solution of the optimization problem P2.1 is the optimal solution of the optimization problem P1, and the optimal solution of the optimization problem P1 is obtained by using the eigenvalue decomposition method where v k represents the corresponding eigenvector of the eigenvalue λ k .

9. The method of claim 8, wherein, The subproblem 3 is represented as: Fix R s and w k , optimize the relaxation variable μ l and Initialization Let iteration index i = 0, for a given R s and w k , reconstruct the equivalent optimal solution based on the optimization problem P2.1 Substitute into the objective function, update The iteration process stops until the objective value between two iterations is less than a tolerance level ε or the maximum number of iterations is reached; output the digital beamforming vector, covariance matrix, scaling factor and all relaxation variables obtained in the last iteration.

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