Communication-centric ris-aided cell-free isac network joint beamforming method

Abstract

The present application relates to a communication-centered RIS-assisted joint beamforming method for ISAC network without cells, and belongs to the technical field of sensing and communication. The present application solves the problem that there is no related work to establish a system model for RIS-assisted ISAC network without cells, and proposes a communication-centered design under the constraint of sensing performance. The present application includes establishing a system model in the RIS-assisted ISAC network without cells; obtaining the signal expression of the communication system and the radar system; establishing an optimization problem for maximizing the communication performance in the RIS-assisted ISAC network without cells; converting the problem into a base station beamforming problem and an RIS phase shift design problem; using the alternating optimization method for optimization, and using the alternating direction multiplier method for sub-problem optimization; judging whether to converge, and if not, repeating step five, and if converging, completing the optimization. The present application first establishes a model for RIS-assisted ISAC network without cells, and proposes a communication-centered design, which meets the scene demand of high communication requirement in the integrated sensing and communication system design.

Description

Technical Field

[0001] This invention relates to a method for joint beamforming in RIS-assisted non-cellular ISAC networks, belonging to the field of sensing and communication technology. Background Technology

[0002] Integrated Sensing and Communication (ISAC) has been increasingly recognized as a technology with great potential in recent years. This technology benefits from the similarity of hardware platforms and signal processing algorithms, as well as the shared need for high-frequency, wideband, multi-antenna systems in both communication and radar sensing systems. By implementing communication and radar functions on the same platform, ISAC not only enables these two systems to share spectrum resources but also achieves significant progress in improving spectrum, energy, and hardware efficiency. Currently, most research on ISAC employs a single-base station or cellular system architecture, leading to the following problems:

[0003] (1) In terms of communication, there is interference between cellular cells, and users need to switch between different cells;

[0004] (2) In terms of perception, the perception capability of a single base station is limited, and multiple base stations need to work together to achieve a significant improvement in perception performance.

[0005] Cellular-free networks, as a novel architecture, can effectively solve inter-cell interference and base station handover problems, while also enabling joint sensing by multiple base stations. Therefore, the architecture of cell-free networks is a promising solution. Although Cell-Free ISAC greatly improves communication and radar sensing capabilities, performance degradation is still inevitable when propagating in complex electromagnetic environments. The main reason is that the complex electromagnetic environment in Cell-Free ISAC networks generates severe interference, including interference between users, radar signal interference to communication users, and radar signal interference between different base stations.

[0006] RIS (Reflective Beamforming) technology, due to its ability to efficiently and intelligently shape the propagation environment, is considered another key driving force for future wireless networks. A RIS is typically a two-dimensional elemental surface composed of numerous passive reflective elements that can be independently adjusted. By controlling specific parameters of the electronic circuitry associated with each element, the electromagnetic characteristics of the incident signal, such as amplitude and phase shift, can be adjusted. Through the coordinated and intelligent adjustment of these reflective elements, passive beamforming gain can be achieved. Passive beamforming gain can not only be used to improve communication spectral efficiency and energy efficiency but also to enhance radar sensing performance.

[0007] Defects and shortcomings of existing technology:

[0008] (1) There is currently no relevant work to establish a system model of RIS-assisted non-cellular ISAC network and propose a communication-centric design under the constraint of perception performance;

[0009] (2) In the design of integrated sensing, most research work focuses on single base station scenario design, which cannot solve the problem of inter-cell interference, and cannot meet the design requirements of joint sensing of multiple base stations.

[0010] (3) RIS has great potential, but no one has proposed its application in non-cellular ISAC networks.

[0011] Therefore, there is an urgent need to propose a communication-centric RIS-assisted non-cellular ISAC network joint beamforming method to solve the above-mentioned technical problems. Summary of the Invention

[0012] The purpose of this invention is to address the lack of existing system models for RIS-assisted non-cellular ISAC networks and to propose a communication-centric design under sensing performance constraints. A brief overview of the invention is provided below to offer a basic understanding of certain aspects thereof. It should be understood that this overview is not an exhaustive summary of the invention. It is not intended to identify key or essential parts of the invention, nor is it intended to limit the scope of the invention.

[0013] The technical solution of the present invention:

[0014] A communication-centric RIS-assisted joint beamforming method for non-cellular ISAC networks includes the following steps:

[0015] Step 1: Establish a system model in a RIS-assisted non-cellular ISAC network system;

[0016] Step 2: Based on the system model, obtain the signal expressions for the communication system and the radar system;

[0017] Step 3: Based on the expression, establish an optimization problem to maximize communication performance in a RIS-assisted non-cellular ISAC network;

[0018] Step 4: Based on the optimization problem, the problem is transformed and decomposed into a base station beamforming problem and a RIS phase shift design problem;

[0019] Step 5: Optimize the base station beam and RIS phase shift using an alternating optimization method, with the sub-problem optimization process employing the alternating direction multiplier method;

[0020] Step Six: Determine whether the optimization parameters from Step Five have converged. If they have not converged, repeat Step Five. If they have converged, the optimization is complete.

[0021] Preferred configuration: In step one, the system model includes a base station, a RIS (Radio Router System), user equipment (User Equipment), and a sensing target. The base station and RIS are electrically connected to the central processing unit (CPU) and the user equipment. All RIS serve all user equipment through a joint beamforming design to implement communication functions. The base station is electrically connected to the user equipment to implement sensing functions. The implementation of sensing functions requires the BS (Base Station Service) to generate beams pointing towards the user equipment and beams pointing towards potential sensing targets. The BS also acts as a sensor receiver, using echoes to determine whether a sensing target exists.

[0022] Preferred: In step one, the base station is equipped with a transmitting antenna and a receiving antenna. The transmitting antenna and the receiving antenna are electrically connected to form a downlink transmission. During the downlink transmission, all base stations form two subsets. The first subset contains P base stations responsible for simultaneously transmitting communication and sensing signals, and the second subset contains Q base stations responsible for receiving reflected or scattered signals generated by the sensing target. It is assumed that the first subset and the second subset completely overlap.

[0023] Preferred method: In step two, assume there are P sending BSs that need to jointly transmit K communication streams and M sensor streams. The sets of communication streams and sensor streams are defined as K and M, respectively. The entire stream set is defined as I = K∪M. Assume... (in Let Nt be a complex vector representing the p-th transmitting BS in the l-th time slot. We can obtain:

[0024]

[0025] Among them, f p,k and f p,m These are the communication symbols x k [l] and radar waveform x m The beamforming vector of [l], f p,i It is x i The beamforming vector of [l] Let represent the l-th symbol of the i-th stream, assuming the transmitted symbol has normalized power, i.e., E[|x] i | 2 ] = 1, where E represents the numerical expectation operation; furthermore, the information from radar and communication signals is statistically independent, i.e. and For i, i′∈I and i≠i′, where I is the identity matrix. Represents x i′ The transpose and conjugate of x i′ It is different from x iAnother element of the formula is that the expected value of the same signal multiplied by its conjugate transpose is an identity matrix, while it is 0 for different signals. Such radar signals can be generated through pseudo-random coding.

[0026] In the system model of step one, the channel between each transmitting BS and each user equipment includes a BS-user link and R BS-RIS-user links. Each BS-RIS-user link can be decomposed into a BS-RIS link and a RIS-user link. Assuming the channel remains unchanged during the transmission of L consecutive symbols, the equivalent channel from the p-th BS to the k-th user is... It can be represented as:

[0027]

[0028] in, G represents the direct link between the p-th transmitting base station and the k-th user. p,r and Let Θ represent the channels between the p-th transmitting base station and the k-th user and the r-th RIS, respectively. r It is the phase adjustment matrix of the r-th RIS. For Θ r The transpose and conjugate of are defined as:

[0029]

[0030] Where, θ r,n This represents the reflection coefficient (RC) of the RIS. Note that this invention considers the case of an ideal RIS, i.e., θ. r,n The amplitude and phase can be independently and continuously controlled; then, the signal received by user k can be expressed as:

[0031]

[0032] Where, n k Let x represent the received noise of the k-th UE; assuming the channel remains constant over L symbols, the radar waveform is x. m [l], the introduced symbol j represents other users x besides k. j [l] represents the l-th symbol of the j-th stream, f p,j It is x j The beamforming vector of [l]; then, the signal-to-interference-plus-noise ratio (SINR) of the k-th UE can be expressed as:

[0033]

[0034] in, The Gaussian noise variance of the received signal for user k is used to evaluate the performance of multi-user communication using typical communication and rate metrics, with the sum-of-the-parts rate (WSR) of all UEs being the sum-of-the-parts rate (WSR). sum It can be represented as:

[0035]

[0036] Assuming there is a line-of-sight (LOS) connection between the perceived target location and each base station (BS), in this system model, it is assumed that the spacing between the receiving antennas in the radar structure is wide enough to ignore the spatial correlation between the receiving antennas.

[0037] The reflection path channel through the target between the transmitting BS p and the receiving BS q can be represented as:

[0038]

[0039] in, Satisfying a complex Gaussian distribution, it is a combined sensing channel gain that includes the target and the target's radar cross section (RCS). It is the conjugate transpose of the array antenna response vector formed by the transmission angle. It is the array antenna response vector composed of the angle of arrival. For the corresponding angle; this invention considers that the sensing channel conforms to the Swerling-I target fluctuation model, which indicates that the RCS of the sensed target fluctuates slowly and the sensing symbol does not change in a unit time slot;

[0040] Given the presence of the target, the l-th time slot signal received by the q-th receiving BS through the horizontal uniform linear array (ULA) base station antenna can be expressed as:

[0041]

[0042] in, It is the received noise of base station q in time slot l, x p [l] represents the signal transmitted by the previously defined transmitting BS in time slot l;

[0043] The L symbols are combined and defined as follows:

[0044]

[0045] Note that this section involves matrix simplification and transformation. T Represents the transpose of the matrix, and the square brackets [] indicate the arrangement of the matrix elements.

[0046] The signal of the L symbols received by the q-th receiving BS can be represented as:

[0047]

[0048] in, The noise vector matrix F satisfies a complex Gaussian distribution and is the integrated noise vector matrix. p X, N q The p-th BS transmit beamforming vector, transmit symbol matrix, and noise matrix are respectively derived from formula (9);

[0049] By jointly processing the sensor signals from multiple receivers (BS), a joint sensing SNR can be obtained. The formula for the sensing SNR can be expressed as:

[0050]

[0051] in For the ν between transmitting BS p and receiving BS q p,q The variance of a complex Gaussian distribution It is the variance of the received noise.

[0052] Preferred: In step three, the expressions (6) and (11) established in step two are defined.

[0053]

[0054] in, T For transpose, `diag` is the matrix diagonalization operation. In this formula, Θ represents the transformation of Θ1 to Θ2. R A new matrix, G, arranged diagonally p U k F k Let F be the new matrix generated after rearranging the matrix. Then the optimization problem can be expressed as:

[0055]

[0056] Where st is an abbreviation for subjectto, representing the constraints of the optimization problem, and P is the set of emitters BS. max ρ is the maximum power of the transmitting base station, and ρ is the sensing SNR. (s) The minimum threshold, θ r,n It is the nth reflection unit of the r-th RIS, where N represents the set of reflection units and R represents the set of RIS. In mathematics, ∈ represents any and means "belongs to";

[0057] Constraints C1, C2, and C3 are the base station power constraint, the sensing SNR constraint, and the RIS phase constraint, respectively.

[0058] Preferred method: In step four, first introduce auxiliary variables α = [α1,...,α] KThe objective function of equation (13) can be equivalently restated as:

[0059]

[0060] This transformation will not affect the optimization result, α k The update process can be achieved by taking the derivative as zero, and the update formula can be obtained as follows:

[0061]

[0062] Then, with the introduced auxiliary variable α fixed, the variables that need to be optimized are concentrated in the last term of formula (14). Extracting this term separately and turning it into a new optimization problem can be expressed as:

[0063]

[0064] The problem is decomposed into two sub-problems for decoupling. The first sub-problem is to optimize F while keeping Θ constant, and the second sub-problem is to solve for Θ while keeping F constant.

[0065] Preferred: In step four, the first sub-problem: beamforming design of the BS.

[0066]

[0067] in, The Gaussian noise variance represents the signal received by user k.

[0068] The second sub-problem: Phase shift design of RIS

[0069]

[0070] Preferably, step five includes solving the first subproblem and solving the second subproblem;

[0071] Solving the first subproblem: First, perform beamforming design of BS; solve F by fixing Θ and α. At this time, the optimization formula (16) can be equivalent to

[0072]

[0073] This subproblem can be reformulated using a quadratic transformation, introducing auxiliary variables β = [β1, ..., β]. K After that, the objective function can be equivalently restated as:

[0074]

[0075] in, This represents the operation of finding the real part of a complex number. Represents the effect of auxiliary variable β kFind the conjugate for the auxiliary variable β. k The update method adopts the approach of finding the first derivative to be 0. The update formula in the alternating optimization process can be expressed as:

[0076]

[0077] To obtain a more obvious and easier-to-solve form of QCQP, this invention reorganizes formula (20) and defines it as follows:

[0078]

[0079] in, The matrix represents the Kronecker product operation, C is the matrix that is rearranged to express the quadratic term in formula (24), and v p,k V k V is a matrix derived from the expression of the coefficients of the first-order terms in formula (24), D is a constant term, and I(k) is an adjustment variable defined in this invention, which can be expressed as:

[0080]

[0081] Thus, this invention has eliminated the fractional form in the objective function of formula (19) and simplified it into a quadratic form that is easy to solve:

[0082]

[0083] F H V H The constraints C2 imposed by the radar system are still in fractional form, and are the conjugate transposes of the corresponding matrices, respectively. To simplify the expression, the following form is defined:

[0084]

[0085]

[0086] in, Represents the Kronecker product operation of matrices, 1 (K+M)PNt Represents a (K+M)PN-dimensional unit vector, e p A represents a P-dimensional vector where the p-th element is 1 and all other elements are 0. E p It is a new matrix notation defined to organize the expression of constraints. To organize the obtained constant terms, For the ν between transmitting BS p and receiving BS q p,q The variance of a complex Gaussian distribution It is the variance of the received noise, I Nt IK+M Let Nt and K+M represent the identity matrices, respectively. After the above transformation and simplification, the subproblem formula (17) is completely transformed into an equivalent QCQP problem form, and is expressed as:

[0087]

[0088] This invention utilizes the Alternating Direction Multiplier Method (ADMM) to solve such problems; in order to transform the problem into a form suitable for the Alternating Direction Multiplier Method (ADMM), by introducing an auxiliary quantity Y, this invention first rewrites the original problem (24) as follows:

[0089]

[0090] Then define the Lagrange function:

[0091]

[0092] in, H L() represents finding the conjugate transpose, and V() represents the Lagrange function form. H A H Let represent the conjugate transpose of the corresponding matrix, λ, ζ, and μ be the penalty terms introduced by the ADMM optimization method, and let b be the superscript index, b+1 be the value of the next iteration. The proposed steps for solving F based on ADMM are expressed as follows:

[0093] Step 5.11: Update F: First, fix other variables and solve the optimization problem for F:

[0094] F b+1 =argmin F L(F,Y b ,λ b ,ζ b (29)

[0095] By taking the first derivative and setting it to zero, we can obtain:

[0096] F b+1 = (C+C) H +μI) -1 (2V+μY b (30)

[0097] Among them, C H Represents the conjugate transpose of C;

[0098] Step 5.12: Update Y: With other variables fixed, solve the optimization problem regarding Y:

[0099] Y b+1 =argmin Y L(Fb+1 ,Y,λ b ,ζ b (31)

[0100] By taking the derivative as zero, we can obtain the following solution:

[0101] Y b+1 =(2E p λ+μI) -1 (μF b+1 +Aζ). (32)

[0102] in, -1 This represents the inverse operation;

[0103] Step 5.13: Update the Lagrange multipliers λ and ζ:

[0104]

[0105] Step 5.14: Iterate to convergence: Repeat step 5.1 until convergence or the maximum number of iterations is reached;

[0106] The second sub-problem is to design the reflected beamforming of the RIS. To simplify the expression of equation (18), some definitions are made in advance. By rearranging equations (2) and (12), we can obtain:

[0107]

[0108] This formula Θ represents Θ1 to Θ... R A new matrix, G, arranged diagonally p U k It is a new matrix generated after rearranging the matrix. Θ H , This is the conjugate transpose of the matrix;

[0109] By fixing F and α to solve Θ, the optimization problem formula (18) can be equivalent to:

[0110]

[0111] in, The form of the reflection design subproblem to be solved is obtained; noting that this problem also satisfies the fractional form, an auxiliary variable of quadratic transformation is introduced, γ=[γ1,…,γ K [Can be obtained]

[0112]

[0113] Where 3a represents transforming formula (35) into the next form. Represents the complex number γk The conjugate;

[0114] Similarly, for γ k The update method is:

[0115]

[0116] Considering the complexity of RIS channels, the variables are merged and defined, and represented as follows:

[0117]

[0118] Among them, 1 RN Let be an RN-dimensional unit vector. Then, by omitting constant terms that have no effect on the optimization result, formula (36) is transformed into:

[0119]

[0120] Among them, θ H The term is the conjugate transpose of θ. W is a constant term that has no effect on optimization and can be omitted. The final matrix / vector form is:

[0121]

[0122] Then, H p,k Let Φ and O be the conjugate form of the corresponding matrix, respectively, and let O be the coefficient matrix of the quadratic term and the coefficient matrix of the linear term. These are symbols defined to simplify the matrix into a quadratic form. The simplified formula (40) and constraint C3 are combined to form a new equivalent QCQP optimization problem, and the result is:

[0123]

[0124] In mathematics, ∈ represents any and means belonging; an ADMM-based optimization approach is adopted to solve the equivalent QCQP optimization problem (41), and the equivalent ADMM form is expressed as:

[0125]

[0126] Where z is an auxiliary variable introduced by the ADMM method, the Lagrange function is then expressed as:

[0127]

[0128] η and μ2 are the penalty terms introduced by the ADMM optimization method. H Given the conjugate transpose of η, θ can be solved using the following ADMM steps:

[0129] Step 5.21: Update z: By fixing other variables, the optimization problem to be solved is:

[0130] z b+1 =argmin z L(z,θ b ,η b (44)

[0131] The analytical expression for the optimization process is:

[0132]

[0133] in, -1 Represents the inverse operation, θ b η b The value from the previous iteration;

[0134] Step 5.22: Update θ: With other variables fixed, solve the optimization problem with respect to θ:

[0135] θ b+1 =argmin θ L(z b+1 ,θ,η b (46)

[0136] The derived iterative formula is:

[0137] θ b+1 =(2Φ+μ2I) N ) -1 (2O+η b +μ2z b+1 ), (47)

[0138] Among them, I N It is a unit vector;

[0139] Step 5.23: Update the Lagrange multiplier η: The updated formula is:

[0140] η b+1 =2Φ θ b+1 -2O. (48)

[0141] Step 5.24: Iterate to convergence: This process is repeated from step 5.21 until convergence or the maximum number of iterations is reached.

[0142] Preferred method: In step six, the algorithm terminates when the growth rate of the target WSR is less than a set threshold. The growth rate can be derived from the following formula:

[0143]

[0144] The present invention has the following beneficial effects:

[0145] (1) This invention establishes a model of RIS-assisted non-cellular ISAC network for the first time and proposes a communication-centric design to meet the needs of scenarios with high communication requirements in the design of integrated sensing systems.

[0146] (2) This invention solves the problems of interference between cellular cells, mutual interference between users, and interference between radar systems and communication systems. At the same time, users need to switch between different cells. Under the constraint of sensing performance, it greatly improves communication performance.

[0147] (3) This invention proposes an iterative solution process based on fractional programming and alternating optimization algorithms, which can effectively solve the problems of base station beamforming and RIS phase design in RIS-assisted non-cellular ISAC networks. Attached Figure Description

[0148] Figure 1 This is a flowchart of a communication-centric RIS-assisted non-cellular ISAC network joint beamforming method;

[0149] Figure 2 This is a schematic diagram of the system model;

[0150] Figure 3 This is a schematic diagram of the system simulation;

[0151] Figure 4 This is a diagram illustrating the trade-off between communication and radar performance;

[0152] Figure 5 This is a simulation diagram illustrating the algorithm's convergence.

[0153] Figure 6 This is a diagram illustrating the impact of user location on system performance;

[0154] Figure 7 This is a schematic diagram illustrating the impact of the number of RIS units;

[0155] Figure 8 This is a schematic diagram illustrating the impact of base station transmit power.

[0156] In the diagram, BS is the base station, UE is the user equipment, Target is the sensing target, and CPU is the central processing unit. Detailed Implementation

[0157] To make the objectives, technical solutions, and advantages of this invention clearer, the invention is described below with reference to specific embodiments shown in the accompanying drawings. However, it should be understood that these descriptions are merely exemplary and not intended to limit the scope of the invention. Furthermore, descriptions of well-known structures and technologies are omitted in the following description to avoid unnecessarily obscuring the concept of the invention.

[0158] Specific implementation method one: Combining Figure 1-8 This embodiment describes a communication-centric RIS-assisted non-cellular ISAC network joint beamforming method, which includes the following steps:

[0159] Step 1: Establish a system model in a RIS-assisted non-cellular ISAC network system;

[0160] Step 2: Based on the system model established in Step 1, obtain the signal expressions and relevant system indicators for the communication system and radar system, respectively;

[0161] Step 3: Based on the expression established in Step 2, establish an optimization problem to maximize communication performance in a RIS-assisted non-cellular ISAC network;

[0162] Step 4: Based on the optimization problem in Step 3, transform the problem and decompose it into a base station beamforming problem and a RIS phase shift design problem;

[0163] Step 5: Optimize the base station beam and RIS phase shift separately using an alternating optimization method. The sub-problem optimization process uses the alternating direction multiplier method to obtain the optimized parameters of the base station beam and RIS phase shift.

[0164] Step Six: Determine whether the optimization parameters in Step Five have converged. If they have not converged, repeat Step Five. If they have converged, the optimization is complete. This invention establishes a model of a RIS-assisted non-cellular ISAC network for the first time and proposes a communication-centric design, which meets the needs of scenarios with high communication requirements in the design of integrated sensing systems.

[0165] Specific Implementation Method Two: Combining Figure 1-8 This embodiment describes a communication-centric RIS-assisted beamforming method for non-cellular ISAC networks. In step one, the invention deploys a RIS in a Cell-Free ISAC MIMO system to enhance the performance of the communication system; as follows... Figure 2As shown, the system model includes B base stations (BS), R RIS, K user equipment (UE), and a sensing target. The base stations (BS) and RIS are electrically connected to the central processing unit (CPU). The transmitting antennas of the base stations (BS) and the RIS are electrically connected to the antennas of the user equipment (UE). Each UE has one antenna. All RIS are designed using joint beamforming to serve all user equipment and implement communication functions. The transmitting antennas of the base stations (BS) are electrically connected to the antennas of the user equipment (UE) to implement sensing functions. The implementation of sensing functions is divided into two stages. In the first stage, all BSs (transmitting antennas) need to generate beams pointing towards the user equipment (UE) and simultaneously generate beams pointing towards potential sensing targets at known locations. In the second stage, all BSs also act as sensor receivers (receiving antennas). Multiple BSs determine the presence of a sensing target by receiving the echo (the receiving antennas receive the beams pointing towards potential sensing targets at known locations). Each user equipment (UE) has one antenna, with K UEs sharing one antenna. Each RIS is equipped with N independently adjustable units. This invention assumes that all B base stations (BS) and R RIS... All base stations are connected to a central processing unit (CPU) via a control backhaul link, enabling unified management and coordination. All base stations are configured to be fully synchronized and have digital beamforming capabilities, thus achieving a simplified model.

[0166] Specific implementation method three: Combining Figure 1-8 This embodiment describes a communication-centric RIS-assisted non-cellular ISAC network joint beamforming method. In step one, each base station (BS) is equipped with a base station antenna, which includes Nt transmit antennas and Nr receive antennas to meet the dual functional requirements of communication and sensing. The transmit and receive antennas are electrically connected to form downlink transmission. During downlink transmission, the focus is on two subsets consisting of all base stations. The first subset contains P transmit base stations responsible for simultaneously transmitting communication and sensing signals, and the second subset contains Q receive base stations that focus on receiving reflected or scattered signals generated by the sensing target. These two subsets may not overlap or may overlap to varying degrees. P, Q, B, R, K, Nt, N, L, Nr, and M are all natural numbers, with uppercase letters representing the maximum number and lowercase letters representing the elements. The objective of this invention is to explore the optimization of communication performance. This invention considers the assumption that the first and second subsets completely overlap, i.e., all base stations have full-duplex capability. Furthermore, the phase adjustment of the RIS only serves the communication function. This requires the RIS and the user equipment (UE) to be positioned as close as possible to obtain the best effect. RISs consists of multiple RISs.

[0167] Specific implementation method four: Combination Figure 1-8This embodiment describes a RIS-assisted non-cellular ISAC network joint beamforming method centered on communication. In step two, the transmitted signal is defined as a weighted sum of communication symbols and radar waveforms to achieve dual functions of communication and sensing. Specifically, P transmitting base stations (BSs) are assumed to jointly transmit K communication streams (implemented using communication functions) and M sensing streams (implemented using sensing functions). The sets of communication streams and sensing streams are defined as K and M, respectively. This invention defines the entire stream set as I = K∪M. Assuming... (in Let Nt be a complex vector representing the p-th transmitting BS (the transmit antenna of the p-th base station) in the l-th time slot. We can obtain:

[0168]

[0169] Among them, f p,k and f p,m These are the communication symbols x k [l] and radar waveform x m The beamforming vector of [l], f p,i It is x i The beamforming vector of [l] Let represent the l-th symbol of the i-th stream. This invention assumes that the transmitted symbol has a normalized power, i.e., E[|x] i | 2 ] = 1, where E represents the numerical expectation operation; furthermore, the information from radar and communication signals is statistically independent, i.e. and For i, i′∈I and i≠i′, where I is the identity matrix. Represents x i′ The transpose and conjugate of x i′ It is different from x i Another element of the formula is that the expected value of the product of the same signal and its conjugate transpose is the identity matrix, while it is 0 for different signals. Note that such radar signals can be generated by pseudo-random coding.

[0170] This invention assumes that all base stations (BSs) possess digital beamforming capabilities and are fully synchronized, with each unit on the RIS capable of independent adjustment. All BSs and RISs are connected to the same central processing unit (CPU) via control backhaul links, and are considered to be subject to unified scheduling and control for simplified processing. In the RIS-assisted non-cellular ISAC system proposed in this invention (i.e., the system model in step one), each base station has Nt antennas. The channel between each transmitting BS and each user equipment includes a BS-user link and R BS-RIS-user links. Within this framework, each BS-RIS-user link can be further decomposed into a BS-RIS link and a RIS-user link. This invention assumes that the channel remains unchanged during the transmission of L consecutive symbols. Considering these channel components, the equivalent channel from the p-th BS to the k-th user... It can be represented as:

[0171]

[0172] in, G represents the direct link between the p-th transmitting base station and the k-th user. p,r and Let Θ represent the channels between the p-th transmitting base station and the k-th user and the r-th RIS, respectively. r It is the phase adjustment matrix of the r-th RIS. For Θ r The transpose and conjugate of are defined as:

[0173]

[0174] Where, θ r,n This represents the reflection coefficient (RC) of the RIS. Note that this invention considers the case of an ideal RIS, i.e., θ. r,n The amplitude and phase can be independently and continuously controlled; then, the signal received by user k can be expressed as:

[0175]

[0176] Where, n k Let x represent the received noise of the k-th UE; assuming the channel remains constant over L symbols, the radar waveform is x. m [l], the introduced symbol j represents other users x besides k. j [l] represents the l-th symbol of the j-th stream, f p,j It is x j The beamforming vector of [l]; then, the signal-to-interference-plus-noise ratio (SINR) of the k-th UE can be expressed as:

[0177]

[0178] in, Let the Gaussian noise variance of the received signal for user k be represented. Then, this invention uses typical communication and rate metrics to evaluate the performance of multi-user communication, specifically the sum-rate (WSR) R of all UEs (multiple users). sum It can be represented as:

[0179]

[0180] For the sensing model, this invention adopts a multi-base sensing model; for simplicity, this invention assumes that there is a straight ray (LOS) connection between the sensing target location and each base station (BS), and ignores non-straight ray (NLOS) connections. In this system model, it is assumed that the spacing between the receiving antennas in the radar structure is wide enough to ignore the spatial correlation between the receiving antennas.

[0181] The reflection path channel through the target between the transmitting BS p and the receiving BS q can be represented as:

[0182]

[0183] in, Satisfying a complex Gaussian distribution, it is a combined sensing channel gain that includes the target and the target's radar cross section (RCS). It is the conjugate transpose of the array antenna response vector formed by the transmission angle. It is the array antenna response vector composed of the angle of arrival. For the corresponding angle; this invention considers that the sensing channel conforms to the Swerling-I target fluctuation model, which indicates that the RCS of the sensed target fluctuates slowly, the sensing symbol does not change in a unit time slot, uppercase letters represent the maximum number, and the elements are represented by lowercase letters.

[0184] Assuming the CPU knows the transmitted signal Then, echo signals that were not reflected by the target can be eliminated from the received signal through signal processing; therefore, in the presence of the target, the l-th time slot signal received by the q-th receiving BS through the horizontal uniform linear array (ULA) base station antenna can be expressed as:

[0185]

[0186] in, It is the received noise of base station q in time slot l, x p [l] represents the signal transmitted by the previously defined transmitting BS in time slot l;

[0187] The L symbols are combined and defined as follows:

[0188]

[0189] Note that this section describes matrix simplification and transformation, and has no practical meaning. T Represents the transpose of the matrix, and the square brackets [] indicate the arrangement of the matrix elements.

[0190] The signal of the L symbols received by the q-th receiving BS can be represented as:

[0191]

[0192] in, The noise vector matrix F satisfies a complex Gaussian distribution and is the integrated noise vector matrix. p X, N q The p-th BS transmit beamforming vector, transmit symbol matrix, and noise matrix are respectively derived from formula (9);

[0193] For describing sensing performance, this invention uses typical sensing SNR to measure radar system performance. Sensing SNR, as a fundamental indicator of radar systems, can affect the performance of various sensing tasks (such as target detection and parameter estimation). For Cell-Free ISAC architecture, this invention considers jointly processing the sensing signals from multiple receiving base stations (BSs) to obtain a joint sensing SNR. The formula for sensing SNR can be expressed as:

[0194]

[0195] in For the ν between transmitting BS p and receiving BS q p,q The variance of a complex Gaussian distribution It is the variance of the received noise;

[0196] Thanks to centralized signal processing on the CPU, this invention can discover that sensing performance is affected by both communication beams and radar beams through the expression of sensing SNR. This invention also solves the problems of inter-cell interference, mutual interference between users, and interference between radar systems and communication systems. At the same time, users need to switch between different cells. Under the constraint of sensing performance, this invention greatly improves communication performance.

[0197] Specific Implementation Method Five: Combining Figure 1-8This embodiment describes a communication-centric RIS-assisted non-cellular ISAC network joint beamforming method. In step three, based on expressions (6) and (11) established in step two, and based on the above system model description, this invention achieves communication-priority beamforming and reflection design in the system. The optimization problem of this invention is to maximize WSR under the constraint of radar sensing SNR by jointly optimizing the sensing beamforming, communication beamforming, and phase shift of RIS. By defining...

[0198]

[0199] in, T For transpose, `diag` is the matrix diagonalization operation. In this formula, Θ represents the transformation of Θ1 to Θ2. R A new matrix, G, arranged diagonally p U k F k Let F be the new matrix generated after rearranging the matrix. Then the optimization problem can be expressed as:

[0200]

[0201] Where st is an abbreviation for subjectto, representing the constraints of the optimization problem, and P is the set of emitters BS. max ρ is the maximum power of the transmitting base station, and ρ is the sensing SNR. (s) The minimum threshold, θ r,n It is the nth reflection unit of the r-th RIS, where N represents the set of reflection units and R represents the set of RIS. In mathematics, ∈ represents any and means "belongs to";

[0202] Constraints C1, C2 and C3 are respectively base station power constraint, sensing SNR constraint and RIS phase constraint. Obviously, the objective function (13) is a complex multivariate coupled function in the form of mixed fractions. At the same time, the constraints also contain fractions. This invention proposes a transformation strategy based on fractional programming (FP) in step four, and then transforms and decomposes the problem into a series of easier-to-solve sub-problems, and solves them in an alternating manner to perform change processing and simplify the form.

[0203] Specific Implementation Method Six: Combination Figure 1-8 This embodiment describes a communication-centric RIS-assisted non-cellular ISAC network joint beamforming method. In step four, to address the complex form of the objective function, this invention considers using a quadratic transformation of fractional programming (FP). First, auxiliary variables α = [α1,...,α] are introduced. K The objective function of equation (13) can be equivalently restated as:

[0204]

[0205] This transformation will not affect the optimization result, α k The update process can be achieved by taking the derivative as zero, and the update formula can be obtained as follows:

[0206]

[0207] Then, with the introduced auxiliary variable α fixed, the variables that need to be optimized are concentrated in the last term of formula (14). This invention extracts this term separately and turns it into a new optimization problem, which can be expressed as:

[0208]

[0209] Noting that the problem still has coupling, this invention advocates decomposing the problem into two sub-problems for decoupling and using an alternating optimization approach for updating; the first sub-problem is to optimize F with a fixed Θ, and the other sub-problem is to solve Θ with a fixed F; this invention proposes an iterative solution process based on fractional programming and alternating optimization algorithms, which can effectively solve the problems of base station beamforming and RIS phase design in RIS-assisted non-cellular ISAC networks.

[0210] Specific implementation method seven: Combining Figure 1-8 This embodiment describes a communication-centric RIS-assisted non-cellular ISAC network joint beamforming method. In step four, the first sub-problem is the beamforming design of the BS (Browser Base).

[0211]

[0212] in, The Gaussian noise variance represents the signal received by user k.

[0213] The second sub-problem: Phase shift design of RIS

[0214]

[0215] Specific implementation method eight: Combination Figure 1-8 This embodiment describes a communication-centric RIS-assisted non-cellular ISAC network joint beamforming method. Step five includes solving the first sub-problem and the second sub-problem.

[0216] Solving the first subproblem: This invention first performs beamforming design of BS; by fixing Θ and α, F is solved. At this time, the optimization problem formula (16) can be equivalent to

[0217]

[0218] The fractional summation form of the objective function in subproblem formula (19) causes nonconvexity. This invention uses a quadratic transformation to reformulate this subproblem and introduces auxiliary variables β = [β1, ..., β2]. K After that, the objective function of the subproblem formula (19) can be equivalently restated as:

[0219]

[0220] in, This represents the operation of finding the real part of a complex number. Represents the effect of auxiliary variable β k Find the conjugate for the auxiliary variable β. k The update method adopts the approach of finding the first derivative to be 0. The update formula in the alternating optimization process can be expressed as:

[0221]

[0222] To obtain a more obvious and easier-to-solve form of QCQP, this invention reorganizes formula (20) and defines it as follows:

[0223]

[0224] in, The matrix represents the Kronecker product operation, C is the matrix that is rearranged to express the quadratic term in formula (24), and v p,k V k V is a matrix derived from the expression of the coefficients of the first-order terms in formula (24), D is a constant term, and I(k) is an adjustment variable defined in this invention, which can be expressed as:

[0225]

[0226] Thus, this invention has eliminated the fractional form in the objective function of formula (19) and simplified it into a quadratic form that is easy to solve:

[0227]

[0228] F H V H These are the conjugate transposes of the corresponding matrices, but the constraint C2 imposed by the radar system is still in fractional form. To simplify it into a more easily solvable form, the following expression is defined:

[0229]

[0230]

[0231] in, Represents the Kronecker product operation of matrices, 1 (K+M)PNt Represents a (K+M)PN-dimensional unit vector, e p This represents a P-dimensional vector where the p-th element is 1 and all other elements are 0. This step involves organizing the symbols and defining the symbols. A, E p It is a new matrix notation defined to organize the expression of constraints. To organize the obtained constant terms, For the ν between transmitting BSP and receiving BSP q p,q The variance of a complex Gaussian distribution It is the variance of the received noise. I K+M Let Nt and K+M represent the identity matrices, respectively. After the above transformation and rearrangement, the present invention completely transforms the subproblem formula (17) into an equivalent QCQP problem form, which is expressed as:

[0232]

[0233] This invention utilizes the Alternating Direction Multiplier Method (ADMM) to solve such problems; in order to transform the problem into a form suitable for the Alternating Direction Multiplier Method (ADMM), by introducing an auxiliary quantity Y, this invention first rewrites the original problem (24) as follows:

[0234]

[0235] Then, this invention defines the Lagrange function:

[0236]

[0237] in, H L() represents finding the conjugate transpose, and V() represents the Lagrange function form. H A H Let represent the conjugate transpose of the corresponding matrix, and λ, ζ, and μ be the penalty terms introduced by the ADMM optimization method. In this invention, the superscript b is used as the iteration index, and b+1 is the value for the next iteration. The steps for solving F based on ADMM proposed in this invention are expressed as follows:

[0238] Step 5.11: Update F: First, fix other variables and solve the optimization problem for F:

[0239] F b+1 =argmin F L(F,Y b ,λ b ,ζ b (29)

[0240] By taking the first derivative and setting it to zero, we can obtain:

[0241] F b+1 = (C+C) H +μI) -1 (2V+μY b (30)

[0242] Among them, C H Represents the conjugate transpose of C;

[0243] Step 5.12: Update Y: With other variables fixed, this further includes solving an optimization problem with respect to Y:

[0244] Y b+1 =argmin Y L(F b+1 ,Y,λ b ,ζ b (31)

[0245] Similarly, by taking the derivative as zero, we can obtain the following solution:

[0246] Y b+1 =(2E p λ+μI) -1 (μF b+1 +Aζ). (32)

[0247] in, -1 This represents the inverse operation;

[0248] Step 5.13: Update the Lagrange multipliers λ and ζ:

[0249]

[0250] Step 5.14: Iterate to convergence: Repeat step 5.1 until convergence or the maximum number of iterations is reached;

[0251] The second sub-problem is to perform the reflection beamforming design of RIS. In order to simplify the expression of the problem in formula (18), this invention makes some definitions in advance. By rearranging formulas (2) and (12), we can obtain:

[0252]

[0253] This formula Θ represents Θ1 to Θ... R A new matrix, G, arranged diagonally p U k It is a new matrix generated after rearranging the matrix. Θ H , This is the conjugate transpose of the matrix;

[0254] By fixing F and α to solve Θ, the optimization problem formula (18) can be equivalent to:

[0255]

[0256] in, Next, the present invention yields the form of the reflection design subproblem to be solved; noting that this problem also satisfies a fractional form, similarly, the present invention also introduces auxiliary variables of a quadratic transformation, γ=[γ1,…,γ K [Can be obtained]

[0257]

[0258] Where 3a represents transforming formula (35) into the next form. Represents the complex number γ k The conjugate;

[0259] Similarly, for γ k The update method is:

[0260]

[0261] Considering the complexity of RIS channels, the variables are merged and defined, the variables are organized, and they are represented as follows:

[0262]

[0263] Among them, 1 RN Let be an RN-dimensional unit vector. Then, by omitting constant terms that have no effect on the optimization result, formula (36) is transformed into:

[0264]

[0265] Among them, θ H The term is the conjugate transpose of θ. W is a constant term that has no effect on optimization and can be omitted. The final matrix / vector form is:

[0266]

[0267] Then, H p,k Let Φ and O be the conjugate form of the corresponding matrix, respectively, and let O be the coefficient matrix of the quadratic term and the coefficient matrix of the linear term. These are symbols defined to simplify the matrix into a quadratic form. In this invention, the simplified formula (40) and constraint C3 are combined to form a new equivalent QCQP optimization problem, and the result is:

[0268]

[0269] In mathematics, ∈ represents any and signifies belonging; similarly, this invention adopts an ADMM-based optimization approach to solve the equivalent QCQP optimization problem (41), and expresses the equivalent ADMM form as:

[0270]

[0271] Where z is an auxiliary variable introduced by the ADMM method, the Lagrange function is then expressed as:

[0272]

[0273] η and μ2 are the penalty terms introduced by the ADMM optimization method. H For η, the conjugate transpose; similarly, the present invention can solve for θ using the following ADMM steps:

[0274] Step 5.21: Update z: By fixing other variables, the optimization problem to be solved is:

[0275] z b+1 =argmin z L(z,θ b ,η b (44)

[0276] The present invention yields the analytical expression for the optimization process as follows:

[0277]

[0278] in, -1 Represents the inverse operation, θ b η b The value from the previous iteration;

[0279] Step 5.22: Update θ: With other variables fixed, this further includes solving an optimization problem with respect to θ:

[0280] θ b+1 =argmin θ L(z b+1 ,θ,η b (46)

[0281] Similarly, the iterative formula derived in this invention is:

[0282] θ b+1 =(2Φ+μ2I) N ) -1 (2O+ η b +μ2z b+1 ), (47)

[0283] Among them, IN It is a unit vector;

[0284] Step 5.23: Update the Lagrange multiplier η: The updated formula is:

[0285] η b+1 =2Φ θ b+1 -2O. (48)

[0286] Step 5.24: Iterate to convergence: This process is repeated from step 5.21 until convergence or the maximum number of iterations is reached;

[0287] Based on the above derivation, this invention proposes a joint active and passive beamforming design algorithm for RIS-assisted Cell-FreeISAC systems, using an alternating update method. The algorithm terminates when the growth rate of the optimization objective is less than a set threshold. Notably, the algorithm of this invention guarantees that the equivalent objective function remains monotonically non-decreasing after each iteration. Therefore, despite the involvement of transformations and iterations, this algorithm will at least converge to a local optimum. The effectiveness of this invention can be verified by comparing it with benchmark schemes.

[0288] Specific Implementation Method Nine: Combining Figure 1-8 This embodiment describes a communication-centric RIS-assisted non-cellular ISAC network joint beamforming method. In step six, the algorithm terminates when the growth rate of the target WSR is less than a set threshold. The growth rate can be derived from the following formula:

[0289]

[0290] It is worth noting that the algorithm of this invention guarantees that the equivalent objective function is monotonically non-decreasing after each iteration. Therefore, despite the involvement of transformations and iterations, this algorithm will at least converge to a local optimum. The effectiveness of this invention can be verified by comparing it with the benchmark scheme.

[0291] Example 1:

[0292] like Figure 3 As shown, the simulation scenario is set as a 2D plane, where the coordinates of the three base stations (BS) are set to (20m, 50m), (50m, 50m) and (80m, 50m) respectively, the two RIS are set at (20m, 5m) and (80m, 5m) respectively, and the location of the sensing target is set at (50m, 0m); there are 4 (K=4) single-antenna users randomly distributed in a circle with a radius of 1m, and the center coordinates of the circle can move along the x-axis;

[0293] For the communication channel, this invention employs a distance-based path loss model, where the BS-RIS link simulates a line-of-sight (LOS) connection in a Ricean fading channel, and the BS-user and RIS-user links simulate non-line-of-sight (NLOS) connections in a Rayleigh fading channel. Simultaneously, the path loss exponents for the BS-RIS, RIS-target, RIS-user, BS-target, and BS-user links are set to 2.2, 2.3, 2.4, and 3.5, respectively. The parameters of the radar channel are set as follows: and In addition, other parameter settings are represented as: P max =0.3W, L=10, The number of base station antennas Nt = Nr = 9 and the radar signal-to-noise ratio constraint ρ = 0.09;

[0294] The comparison algorithm is as follows:

[0295] (1) No RIS assistance: This scheme (marked as "NO-RIS") only optimizes the beamforming of Cell-FreeBS and does not involve phase shift optimization of RIS;

[0296] (2) Random phase shift: This scheme (labeled "Randomphase") randomly sets the phase shift of RIS and adopts the same active beamforming design as Case 1;

[0297] (3) Ideal RIS: This scheme (labeled "RIS") sets the phase and amplitude of RIS to be continuously adjustable and uses Algorithm 1 to simultaneously optimize the active beamforming of the base station and the reflection coefficient of RIS.

[0298] (4) Non-ideal RIS: This scheme (labeled "2-bit-RIS") takes into account the possible 2-bit phase RIS in actual deployment, that is, the phase of the RIS has only four possible values;

[0299] (5) Single base station ISAC: This scheme (marked as "SingleBS ISAC") sets the RIS to the ideal situation, retains only one base station at (50m, 50m), and sets the transmit and receive antennas to 9;

[0300] (6) Cellular ISAC: This scheme (labeled "Cell ISAC") sets RIS to the ideal case, divides the base station in the figure into three cells, treats the interference between cells as Gaussian noise, and sets the transmit and receive antennas of each cellular base station to 27 (corresponding to the total number of antennas in the Cell-Free case). For simplicity, this invention ignores the base station handover process and sets the communication user to only access the intermediate base station in the entire simulation process, while radar sensing can be achieved through the collaboration of multiple base stations.

[0301] like Figure 5 As shown in the simulation results, this invention first demonstrates the convergence behavior of the proposed algorithm. By setting the user center to (20m, 0m) and the radar constraint to 1 for numerical simulation, this invention observes that the user communication rate of all schemes increases monotonically with the number of iterations; furthermore, all schemes eventually reach a stable state, which verifies that the algorithm proposed in this invention has good convergence.

[0302] like Figure 6 As shown, the simulation results illustrate the impact of user location on system performance. This invention compares different schemes by changing the user center location. Here, this invention changes the x-coordinate of the user center from 0m to 100m, while setting the radar constraint to 1. The results show that RIS can generate significant gain at the deployment location, and even "2-bit-RIS" can bring significant performance improvement. To evaluate the superiority of the proposed Cell-Free architecture, this invention uses SingleBS ISAC and cellular networks as controls. The results show that the Cell-Free architecture significantly outperforms the single-base station architecture. This is mainly because the Cell-Free architecture not only has more antennas but also a wider service area. Compared with CellISAC, this invention finds that Cell-Free can eliminate interference between base stations, greatly improving system performance. In addition, performance improvement is also brought when the user's location coincides with the perceived target's location. This may be due to the high spatial concentration of beams, which easily satisfies the sensing constraint and allows communication to benefit from the gain of all beams.

[0303] like Figure 4 As shown in the simulation results, the trade-off between communication and radar performance is a crucial issue in ISAC system design. This invention fixes the user's location near the RIS (Radio Recognition System) while varying the radar sensing SNR constraint. The results show that the communication rate decreases as the SNR constraint increases. This is because stronger radar constraints lead to more beam resources being used for target detection, thus reducing the communication beam. However, the application of RIS can mitigate the communication performance degradation, demonstrating the significant potential of RIS. It can be observed that the performance of Single BS ISAC drops significantly because Cell-Free has more antennas, making it easier to meet radar system constraint thresholds while providing higher communication gain. Furthermore, even if the Cell ISAC scheme and Cell-Free have the same number of antennas, interference between base stations greatly affects the user's communication performance, validating the rationality and advantages of choosing the Cell-Free architecture in this invention.

[0304] Finally, this invention investigated the impact of system parameters on performance to gain insights into system design; in the subsequent experiments, this invention fixed the user center coordinates at (20m, 0m) near the RIS; on the one hand, as Figure 7 The diagram illustrates the relationship between WSR and the number of RIS reflective elements (N). As expected, WSR increases with increasing N because more reflective elements provide greater passive beamforming gain. This provides a system design approach for this invention: increasing low-cost RIS units to optimize system performance. Furthermore, this invention... Figure 8 The relationship between WSR and base station power budget was also studied. The results showed that the WSR of all schemes improved with the increase of power budget, because the base station has more power resources available for communication and sensing. It is worth noting that the performance improvement provided by RIS is more significant. Therefore, system design can maximize the potential of RIS by increasing power.

[0305] In the above embodiments, as long as the technical solutions are not contradictory, they can be arranged and combined. Those skilled in the art can exhaust all possibilities based on the mathematical knowledge of permutation and combination. Therefore, the present invention will not describe the technical solutions after permutation and combination one by one, but it should be understood that the technical solutions after permutation and combination have been disclosed by the present invention.

[0306] The above description is merely a preferred embodiment of the present invention and is not intended to limit the invention. Various modifications and variations can be made to the present invention by those skilled in the art. Any modifications, equivalent substitutions, improvements, etc., made within the spirit and principles of the present invention should be included within the scope of protection of the present invention.

Claims

1. A communication-centric RIS-assisted non-cellular ISAC network joint beamforming method, characterized in that: Includes the following steps: Step 1: Establish a system model in a RIS-assisted non-cellular ISAC network system; Step 2: Based on the system model, obtain the signal expressions for the communication system and the radar system; Total Rate of All UEs (WSR) Represented as: （1） Assuming there is a line-of-sight (LOS) connection between the perceived target location and each base station (BS), in this system model, it is assumed that the spacing between the receiving antennas in the radar structure is wide enough to ignore the spatial correlation between the receiving antennas; The reflection path channel through the target between the transmitting BS p and the receiving BS q is represented as: （2） in, Satisfying a complex Gaussian distribution, it is a combined sensing channel gain that includes the target and the target's radar cross section (RCS). It is the conjugate transpose of the array antenna response vector formed by the transmission angle. It is the array antenna response vector composed of the angle of arrival. For the corresponding angle; considering that the sensing channel conforms to the Swerling-I target fluctuation model, this indicates that the RCS of the sensed target fluctuates slowly and the sensing symbol does not change in a unit time slot; Given the presence of the target, the q-th receiving BS receives the th [unclear text - possibly a specific data point or parameter] through the horizontal uniform linear array (ULA) base station antenna. l The time-slot signal is represented as: （3） in, It is the base station q in the time slot l Received noise, For the previously defined transmit BS in the time slot l The transmitted signal; The L symbols are combined and defined as follows: （4） Note that this section involves matrix simplification and transformation. T Represents the transpose of the matrix, and the square brackets [] indicate the arrangement of the matrix elements. The signal of the L symbols received by the q-th receiving BS is represented as: （5） in, It satisfies a complex Gaussian distribution and is the integrated noise vector matrix. , , The p-th BS transmit beamforming vector, transmit symbol matrix, and noise matrix are respectively derived from formula (4); The sensor signals from multiple receivers (BS) are jointly processed to obtain the joint sensing SNR. The formula for the sensing SNR is expressed as: （6） in For the transmission BS p to the receiving BS q The variance of a complex Gaussian distribution is the variance of the received noise, and Q represents the number of receiving base stations in the second subset; Thanks to centralized signal processing on the CPU, the expression for SNR reveals that sensing performance is affected by both communication beams and radar beams. Step 3: Based on the expression, establish an optimization problem to maximize communication performance in a RIS-assisted non-cellular ISAC network; In step three, based on the expressions (1) and (6) established in step two, the definitions are... （7） in, For transpose, `diag` is the matrix diagonalization operation. This formula... To be to A new matrix arranged diagonally. , , and If the matrix is ​​rearranged to produce a new matrix, then the optimization problem can be expressed as: （8） in, "Subject to" is an abbreviation representing the constraints of the optimization problem. The set consisting of the transmitting BS, This is the maximum power of the transmitting base station. For perception The minimum threshold, It is the nth reflection unit of the r-th RIS. Represents a collection of reflective units. Represents the set of RIS. In mathematics, it represents any "belonging to" means "belonging to". This represents the signal-to-interference-to-noise ratio (SNR) of the k-th UE. yes Beamforming vector; Constraints C1, C2, and C3 are respectively the base station power constraint, the sensed SNR constraint, and the RIS phase constraint; Step 4: Based on the optimization problem, the problem is transformed and decomposed into a base station beamforming problem and a RIS phase shift design problem; Step 5: Optimize the base station beam and RIS phase shift using an alternating optimization method, with the sub-problem optimization process employing the alternating direction multiplier method; Step Six: Determine whether the optimization parameters from Step Five have converged. If they have not converged, repeat Step Five. If they have converged, the optimization is complete.

2. The communication-centric RIS-assisted non-cellular ISAC network joint beamforming method according to claim 1, characterized in that: In step one, the system model includes base stations (BS), reference frames (RIS), user equipment (UE), and sensing targets. Both the base stations (BS) and RIS are electrically connected to the central processing unit (CPU) and the user equipment (UE). All RIS serve all user equipment through a joint beamforming design to implement communication functions. The base stations (BS) are electrically connected to the user equipment (UE) to implement sensing functions. The implementation of sensing functions requires the BSs to generate beams pointing to the user equipment (UE) and beams pointing to potential sensing targets at the same time. The BSs also act as sensor receivers, using echoes to determine whether a sensing target exists.

3. The communication-centric RIS-assisted non-cellular ISAC network joint beamforming method according to claim 2, characterized in that: In step one, the base station (BS) is equipped with a transmit antenna and a receive antenna. The transmit antenna and the receive antenna are electrically connected to form the downlink transmission. During the downlink transmission, all base stations form two subsets. The first subset contains P base stations responsible for simultaneously transmitting communication and sensing signals, and the second subset contains Q base stations receiving reflected or scattered signals generated by the sensing target. It is assumed that the first subset and the second subset completely overlap.

4. The communication-centric RIS-assisted non-cellular ISAC network joint beamforming method according to claim 3, characterized in that: In step two, it is assumed that there are P transmitting BSs that need to jointly transmit K communication streams and M sensor streams. The sets of communication streams and sensor streams are defined as K and M, respectively. The entire stream set is defined as... Assuming This represents the transmission signal of the p-th transmitting BS in the l-th time slot, where Representing an Nt-dimensional complex vector, we get: （9） in, and These are communication symbols and radar waveform Beamforming vector, yes beamforming vector, Let represent the l-th symbol of the i-th stream, assuming the transmitted symbol has normalized power, i.e. ,in This represents the calculation of numerical expectation; furthermore, the information from radar and communication signals is statistically independent, i.e. and for and in, It is the identity matrix. represent The transpose and conjugate of , It is different Another element of the formula is that the expectation of multiplying the same signal by its conjugate transpose is an identity matrix, while it is 0 for different signals. This radar signal is generated through pseudo-random coding. In the system model of step one, the channel between each transmitting BS and each user equipment includes a BS-user link and R BS-RIS-user links. Each BS-RIS-user link is decomposed into a BS-RIS link and a RIS-user link. Assuming the channel remains unchanged during the transmission of L consecutive symbols, the equivalent channel from the p-th BS to the k-th user is... Represented as: （10） in, This represents the direct link between the p-th transmitting base station and the k-th user. and These represent the channels between the p-th transmitting base station and the k-th user and the r-th RIS, respectively. It is the phase adjustment matrix of the r-th RIS. for The transpose and conjugate of are defined as: （11） in, This represents the reflection coefficient (RC) of the RIS. Note that this method considers the case of an ideal RIS, i.e. Both the amplitude and phase are independently and continuously controlled. Let N represent an N×N dimensional complex vector; then, the signal received by user k is represented as: （12） in, Let represent the received noise of the k-th UE; assuming the channel remains unchanged over L symbols, the radar waveform is... The introduced symbol j represents users other than k. This represents the l-th symbol of the j-th stream. yes The beamforming vector; then, the signal-to-interference-plus-noise ratio (SINR) of the k-th UE is expressed as: （13） in, The Gaussian noise variance representing the received signal for user k is used to evaluate the performance of multi-user communication using typical communication and rate metrics.

5. The communication-centric RIS-assisted non-cellular ISAC network joint beamforming method according to claim 4, characterized in that: In step four, we first introduce auxiliary variables. The objective function of equation (8) is equivalently restated as: （14） This transformation will not affect the optimization results. The update process is achieved by taking the derivative as zero, resulting in the update formula: （15） Then, in the introduced auxiliary variables When fixed, the variables that need to be optimized are concentrated in the last term of formula (14). Extracting this term separately and turning it into a new optimization problem is expressed as: （16） This problem is decoupled into two sub-problems. The first sub-problem is fixed. optimization Another sub-problem is fixed Solve .

6. The communication-centric RIS-assisted non-cellular ISAC network joint beamforming method according to claim 5, characterized in that: In step four, the first sub-problem is: Beamforming design for the BS. （17） in, The Gaussian noise variance represents the signal received by user k. The second sub-problem: Phase shift design of RIS （18）。 7. The communication-centric RIS-assisted non-cellular ISAC network joint beamforming method according to claim 6, characterized in that: Step five includes solving the first subproblem and the second subproblem; Solving the first sub-problem: First, perform beamforming design for the BS; by fixing and Solve At this point, the optimized formula (16) is equivalent to （19） This subproblem can be reformulated using a quadratic transformation, introducing auxiliary variables. Then, the objective function is equivalently restated as: （20） in, This represents the operation of finding the real part of a complex number. Represents the auxiliary variable Find the conjugate for the auxiliary variable. The update method adopts the approach of finding the first derivative to be 0. The update formula in the alternating optimization process is expressed as: （21） To obtain a more obvious and easier-to-solve form of QCQP, formula (20) is rearranged and defined as follows: （22） in, Represents the Kronecker product operation of matrices. This is a matrix that is rearranged to express the quadratic terms in formula (24). , , This is a matrix derived from the simplified expression of the coefficients of the linear terms in formula (24). For the constant term, I(k) is a defined adjustment variable, expressed as: （23） Thus, the fractional form in the objective function of formula (19) has been eliminated, and the function has been rearranged into a quadratic form that is easier to solve: （24） The constraints C2 imposed by the radar system are still in fractional form, and are the conjugate transposes of the corresponding matrices, respectively. To simplify the expression, the following form is defined: （25） in, Represents the Kronecker product operation of matrices. represent A unit vector of dimension 1 Let p represent a P-dimensional vector, where the p-th element is 1 and all other elements are 0. , , It is a new matrix notation defined to organize the expression of constraints. To organize the obtained constant terms, For the transmission BS p to the receiving BS q The variance of a complex Gaussian distribution It is the variance of the received noise. , Let Nt and K+M represent the identity matrices, respectively. After the above transformation and simplification, the subproblem formula (17) is completely transformed into an equivalent QCQP problem form, and is expressed as: （26） This type of problem is solved using the Alternating Direction Multiplier Method (ADMM). To transform the problem into a form suitable for the Alternating Direction Multiplier Method (ADMM), the original problem (24) is first rewritten as follows by introducing an auxiliary quantity Y: （27） Then define the Lagrange function: （28） in, This represents finding the conjugate transpose. ( ) represents the form of the Lagrange function. This represents the conjugate transpose of the corresponding matrix. , and for A penalty term is introduced for the ADMM optimization method; the superscript b is set as the iteration index, and b+1 is the value of the next iteration. A solution based on ADMM is proposed. The steps are represented as follows: Step 5.11: Update First, fix the other variables, and then target... Solve the optimization problem: （29） By taking the first derivative and setting it to zero, we get: （30） in, represent The conjugate transpose of; Step 5.12: Update Solve an optimization problem for Y with other variables fixed: （31） By taking the derivative as zero, the following solution is obtained: （32） in, This represents the inverse operation; Step 5.13: Update the Lagrange multipliers and : （33） Step 5.14: Iterate to convergence: Repeat step 5.1 until convergence or the maximum number of iterations is reached; The second sub-problem is to design the reflected beamforming of the RIS. To simplify the expression of equation (18), some definitions are made in advance to reorganize equations (2) and (12) to obtain: （34） This formula To be to A new matrix arranged diagonally. , It is a new matrix generated after rearranging the matrix. , , This is the conjugate transpose of the matrix; fixed and Solve The optimization problem formula (18) is equivalent to （35） in, The form of the reflection design subproblem to be solved is obtained; noting that this problem also satisfies the fractional form, an auxiliary variable for a quadratic transformation is introduced. get （36） Where 3a represents transforming formula (35) into the next form. Represents complex numbers The conjugate; Similarly, for The update method is: （37） Considering the complexity of RIS channels, the variables are merged and defined, and represented as follows: （38） in, for The unit vector of dimension is then transformed into equation (36) by omitting constant terms that have no effect on the optimization result: （39） Among them, for The conjugate transpose of . The constant terms, which have no effect on optimization, are omitted. The final matrix / vector form is as follows: （40） Then, This is the conjugate form of the corresponding matrix. and These are the quadratic and linear coefficient matrices, respectively, which are symbols defined to transform the problem into a quadratic form. Combining the transformed formula (40) with constraint C3 results in a new equivalent QCQP optimization problem: （41） In mathematics, it represents any The meaning of "belonging to" is adopted; the ADMM-based optimization method is used to solve the equivalent QCQP optimization problem (41), and the equivalent ADMM form is expressed as: （42） in, The auxiliary variables introduced for the ADMM method are then expressed by the Lagrange function as follows: （43） and Penalty terms introduced for ADMM optimization methods for Conjugate transpose; solved using the following ADMM steps. : Step 5.21: Update By fixing other variables, the optimization problem to be solved is: （44） The analytical expression for the optimization process is: （45） in, This represents the inverse operation. , The value from the previous iteration; Step 5.22: Update With other variables fixed, solve for... Optimization issues: （46） The derived iterative formula is: （47） in, It is a unit vector; Step 5.23: Update the Lagrange multipliers The updated formula is: （48） Step 5.24: Iterate to convergence: This process is repeated from step 5.21 until convergence or the maximum number of iterations is reached.

8. The communication-centric RIS-assisted non-cellular ISAC network joint beamforming method according to claim 7, characterized in that: In step six, the algorithm terminates when the growth rate of the target WSR is less than a set threshold, which is calculated using the following formula: （49）。

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