CN117375683A - Communication-centric RIS-assisted non-cellular ISAC network joint beam forming method - Google Patents

Abstract

The invention relates to a communication-centric RIS-assisted non-cellular ISAC network joint beam forming method, belonging to the technical field of sensing and communication. The method solves the problems that no related work is established to establish a system model of the RIS auxiliary non-cellular ISAC network at present and a communication-centered design is proposed under the constraint of perceived performance. Includes building a system model in a RIS-assisted non-cellular ISAC network system; obtaining signal expressions of a communication system and a radar system; establishing an optimization problem of communication performance maximization in the RIS-assisted non-cellular ISAC network; the problem is converted into a base station beam forming problem and an RIS phase shift design problem; optimizing by using an alternating optimization method, wherein the sub-problem optimizing process adopts an alternating direction multiplication method; judging whether the convergence is carried out, and if the convergence is not carried out, carrying out the step five again, and completing the optimization by the convergence. The method establishes a model of the RIS auxiliary non-cellular ISAC network for the first time, and provides a communication-centric design, so that the scene requirement of high communication requirement in the design of the communication-sense integrated system is met.

Description

Communication-centric RIS-assisted non-cellular ISAC network joint beam forming method

Technical Field

The invention relates to a RIS-assisted non-cellular ISAC network combined beam forming method, belonging to the technical field of sensing and communication.

Background

Integrated sensing and communication (ISAC) has been increasingly recognized in recent years as a technology with great potential. This technical direction benefits from the similarity of hardware platforms and signal processing algorithms, and the common need for high frequency broadband multi-antenna systems by communication and radar sensing systems. By implementing communication and radar functions on the same platform, ISACs not only enable the two systems to share spectrum resources, but also make significant progress in improving spectrum, energy and hardware efficiency. Most of the current work on ISACs employs a single base station or cellular system architecture, leading to the following problems:

(1) In terms of communication, there is interference between cells, while users need to switch between different cells;

(2) In terms of perception, the perception capability of a single base station is limited, and a plurality of base stations are required to be combined so as to greatly improve the perception performance.

The architecture of the non-cellular (Cell-Free) network is a promising scheme, as the non-cellular network serves as a brand new architecture, can effectively solve the problems of inter-Cell interference and base station switching, and simultaneously brings possibility to joint perception of multiple base stations. Although Cell-Free ISAC greatly improves communication and radar sensing capabilities, performance degradation is still unavoidable in complex electromagnetic environments. The main reasons are: the Cell-Free ISAC network has a complex electromagnetic environment and generates serious interference, and the interference exists among users, interference of radar signals to communication users and radar signal interference among different base stations.

RIS technology is considered another key contributor to future wireless networks due to its ability to efficiently and intelligently model the propagation environment. RIS is typically a two-dimensional element surface, consisting of a number of passive reflective elements, which can be independently tuned. By controlling specific parameters of the electronic circuit associated with each element, the electromagnetic properties of the incident signal, such as amplitude, phase shift, etc., can be adjusted. By cooperatively and intelligently adjusting these reflective elements, passive beamforming gain may be achieved. The passive beam forming gain can be used for improving communication spectrum efficiency and energy efficiency and can also be used for improving radar perception performance.

Defects and deficiencies of the prior art:

(1) At present, no related work is done to build a system model of an RIS-assisted non-cellular ISAC network, and a communication-centric design under the constraint of perceived performance is proposed;

(2) In the design of the sense of continuity integration, most of research work is concentrated on single-base station scene design, the problem of inter-cell interference cannot be solved, and in addition, the design requirement of joint perception of multiple base stations cannot be met;

(3) RIS has great potential, but its application in a cellular-free ISAC network has not been proposed yet.

Therefore, there is a need to propose a communication-centric RIS-assisted non-cellular ISAC network joint beamforming method to solve the above technical problems.

Disclosure of Invention

The purpose of the present invention is to address the problems of no related work currently establishing a system model of an RIS-assisted cellular-less ISAC network and to propose a communication-centric design under perceptual performance constraints, a brief overview of the present invention is presented below in order to provide a basic understanding of some aspects of the present invention. It should be understood that this summary is not an exhaustive overview of the invention. It is not intended to identify key or critical elements of the invention or to delineate the scope of the invention.

The technical scheme of the invention is as follows:

a communication-centric RIS-assisted non-cellular ISAC network joint beamforming method comprising the steps of:

step one: establishing a system model in a RIS-assisted non-cellular ISAC network system;

step two: obtaining signal expressions of a communication system and a radar system based on a system model;

step three: based on the expression, establishing an optimization problem of communication performance maximization in the RIS-assisted non-cellular ISAC network;

step four: based on the optimization problem, converting and decomposing the problem into a base station beam forming problem and an RIS phase shift design problem;

step five: optimizing the beam and RIS phase shift of the base station by using an alternating optimization method, wherein the sub-problem optimization process adopts an alternating direction multiplication method;

Step six: judging whether the optimization parameters in the step five are converged or not, if not, carrying out the step five again, and if so, completing the optimization.

Preferably: in the first step, the system model includes a base station, an RIS, a user device and a perception target, the base station and the RIS are electrically connected with the central processing unit, the base station and the RIS are electrically connected with the user device, all the RIS serve all the user devices through joint beam forming design and are used for implementing communication functions, the base station is electrically connected with the user device and is used for implementing the perception function, the BSs is required to generate beams pointing to potential perception targets while generating beams pointing to the user device, the BSs also serve as a sensing receiver, and whether the perception targets exist or not is determined through echo.

Preferably: in the first step, the base station is provided with a transmitting antenna and a receiving antenna, the transmitting antenna and the receiving antenna are electrically connected to form downlink transmission, in the downlink transmission process, two subsets formed by all the base stations are included, the first subset comprises P subsets responsible for transmitting communication and sensing signals at the same time, the second subset comprises Q subsets, reflected or scattered signals generated by a sensing target are received, and the first subset and the second subset are assumed to be completely overlapped;

Preferably: in the second step, P sending BSs are set to transmit K communication flows and M sensing flows together, the sets of the communication flows and the sensing flows are defined as K and M respectively, the whole flow set is defined as i=kjcm, and it is assumed that(wherein->Complex vector representing Nt dimension) represents that the p-th transmitting BS is at the thThe transmission signal of l time slots can be obtained:

wherein f _p,k And f _p,m Respectively the communication symbols x _k [l]And radar waveform x _m [l]Is a beam forming vector of f _p,i Is x _i [l]Is used for the beam forming vector of (a),the first symbol of the ith stream, assuming the transmission symbol has normalized power, i.e., E [ |x _i | ² ]=1, wherein E represents a numerically expected operation; furthermore, the information of the 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′ Is the transposed conjugate of x _i′ Is different from x _i The formula shows that the same signal is multiplied by its own conjugate transpose to find the desired identity matrix, and the different signal is 0, such a radar signal can be generated by pseudo-random encoding;

the system model of step one, the channel between each transmitting BS and each user equipment comprises 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, and the equivalent channel from the p-th BS to the kth user is assumed to be unchanged during the transmission of continuous L symbols Can be expressed as:

wherein,representing the direct link between the p-th transmitting base station and the kth user, G _p,r And->Representing the channel between the p-th transmitting base station and the kth user and the r-th RIS, respectively, Θ _r Is the phase adjustment matrix of the r-th RIS, < >>Is theta _r Is defined as:

wherein θ _r,n Representing the Reflection Coefficient (RC) of RIS, note that the present invention contemplates the case of an ideal RIS, i.e., θ _r,n The amplitude and the phase of the pulse can be independently and continuously controlled; the signal received by user k can then be expressed as:

wherein n is _k A reception noise representing a kth UE; assuming that the channel remains unchanged over the transmission of L symbols, the radar waveform is x _m [l]The introduced symbol j represents other users x than k _j [l]The first symbol, f, representing the j-th stream _p,j Is x _j [l]Is a beamforming vector of (1); then, the signal-to-interference-and-noise ratio (SINR) of the kth UE may be expressed as:

wherein,representative of the Gaussian noise variance of the received signal for user k, typical communication and rate metrics are used to evaluate the performance of multi-user communication, the sum rate (WSR) R of all UEs _sum Can be expressed as:

assuming that there is a direct line of sight (LOS) connection between the perceived target location and each base station BS, in the present system model, the receive antennas are assumed to be spaced sufficiently widely in the radar structure that the spatial correlation between the receive antennas can be ignored.

The reflected path channel through the target between p of the transmitting BS and q of the receiving BS can be expressed as:

wherein,satisfying a complex Gaussian distribution is a combination of sensor channel gain, including through target and target Radar Cross Section (RCS), of +.>Is the conjugate transpose of the array antenna response vector formed by the transmit angles,is the array antenna response vector composed of the arrival angles, < ->Is at a corresponding angle; the invention considers that the sensing channel accords with Swerl inThe g-I target fluctuation model shows that the fluctuation of RCS of a perception target is slow, and a sensing symbol is not changed in a unit time slot;

in the presence of a target, the first time slot signal received by the qth receiving BS through a horizontal Uniform Linear Array (ULA) base station antenna may be expressed as:

wherein,is the reception noise of base station q in time slot l, x _p [l]Signals transmitted in time slot l for the previously defined transmitting BS;

the L symbols are integrated together, as defined below:

note here that the ordering and transformation of the matrix, ^T representing the transpose of the matrix []The inner part represents the arrangement and arrangement condition of corresponding matrix elements;

the signal of the L symbols received for the qth receiving BS can be expressed as:

wherein,satisfying complex Gaussian distribution is the integrated noise vector matrix F _p 、X、N _q The p-th BS finished by the arrangement of the formula (9) transmits a beam forming vector, a symbol matrix and a noise matrix;

the sensing signals of the plurality of receiving BSs are jointly processed, so as to obtain a joint sensing SNR, and a formula of the sensing SNR can be expressed as:

wherein the method comprises the steps ofFor v between transmitting BS p to receiving BS q _p,q Variance of complex Gaussian distribution, ">Is the variance of the received noise.

Preferably: in step three, definition is performed based on the expressions (6) and (11) established in step two

Wherein, ^T for transpose operations, diag is the diagonalization of the matrix, and the formula Θ is the value Θ ₁ To theta _R Diagonal matrix, G _p 、U _k 、F _k And F is a new matrix generated after rearranging the matrix, the optimization problem can be expressed as:

wherein the abbreviation s.t. is subject to stands for constraint of the optimization problem, P is the set of transmitting BSs, P _max For maximum power of the transmitting base station, ρ is the perceived SNR ^(s) And θ _r,n An nth reflection unit which is an nth RIS, N represents a set of reflection units, R represents a set of RIS,representing any E in mathematics as belonging meaning;

constraints C1, C2, and C3 are base station power constraints, perceived SNR constraints, and RIS phase constraints, respectively.

Preferably: in the fourth step, an auxiliary variable α= [ α ] is first introduced ₁ ,...,α _K ]The objective function of equation (13) can equivalently be restated as:

this transformation does not affect the result of the optimization, alpha _k The update process of (2) can be realized by using the derivative as zero, and the update formula can be obtained as follows:

then, when the introduced auxiliary variable α is fixed, the variable to be optimized is concentrated on the last term of the formula (14), and this term is extracted separately to become a new optimization problem, which can be expressed as:

the problem is decomposed into two sub-problems for decoupling, the first being to fix Θ to optimize F and the other being to fix F to solve Θ.

Preferably: in step four, the first sub-problem: beamforming design for BS

Wherein,a gaussian noise variance representing the received signal of user k;

a second sub-problem: phase shift design of RIS

Preferably: step five, a first sub-problem solving and a second sub-problem solving are included;

the first sub-problem solution: firstly, carrying out beam forming design of a BS; f is solved by fixing Θ and α, in which case the optimization equation (16) can be equivalent to

Representational of this sub-problem using a quadratic transformation, introducing the auxiliary variable β= [ β ] ₁ ,…,β _K ]The objective function can then equivalently be restated as:

wherein,representing the real part operation of complex numbers,/>Representative pair auxiliary variable beta _k Conjugation of the auxiliary variable beta _k The update mode of (2) is updated by solving a first order derivative as 0, and an update formula in the alternate optimization process can be expressed as follows:

in order to obtain a more obvious and easily solved qqp form, the present invention organizes equation (20) and defines the following:

wherein,the Cronecker product operation of the representative matrix, C is the matrix, v, which is formulated for the expression of the quadratic term in equation (24) _p,k 、V _k V is a matrix which is formulated for the expression of the coefficients of the first order term in equation (24), D is a constant term, and I (k) is a tuning variable defined in the present invention, which can be expressed as

The invention thus far deals with the form of the partial formula in the objective function of equation (19) and is put into a quadratic form that is easy to solve:

F ^H V ^H the constraint condition C2 caused by the radar system still belongs to a partial form, and for arrangement into a format easy to solve, the following expression form is defined:

wherein,cronecker product operation of representative matrix, 1 _(K+M)PNt A unit vector representing (K+M) PN dimension, e _p The vector representing the dimension P is 0, A, and +.>E _p New matrix symbols defined for the sake of sorting the expression form of the constraint +.>For the arrangement of the constant terms derived, +.>For v between transmitting BS p to receiving BS q _p,q Variance of complex Gaussian distribution, ">Is the variance of the received noise, I _Nt 、I _K+M After the transformation and arrangement, the sub-problem equation (17) is completely arranged into the equivalent problem form of qqp and is expressed as:

the present invention solves such problems using the Alternate Direction Multiplier Method (ADMM); in order to convert the problem into a form suitable for alternating direction multiplication (ADMM), the invention first rewrites the original problem (24) as:

then a Lagrangian function is defined:

wherein, ^H represents the conjugate transpose, L () represents the Lagrangian function form, V ^H A ^H Represents the conjugate transpose of the corresponding matrix, with lambda, zeta and mu being mu ₂ Penalty terms introduced for the optimization mode of ADMM; setting the upper standard b as an iteration index, wherein b+1 is the next iterationThe proposed step of solving for F based on ADMM is expressed as:

step 5.11: updating F: other variables are fixed first and the optimization problem is solved for F:

F ^b+1 ＝argmin _F L(F,Y ^b ,λ ^b ,ζ ^b ). (29)

By taking the first derivative and setting it to zero, one can get:

F ^b+1 ＝(C+C ^H +μI) ^-1 (2V+μY ^b ). (30)

wherein C is ^H Represents the conjugate transpose of C;

step 5.12: updating Y: with other variables fixed, solve the optimization problem for Y:

Y ^b+1 ＝argmin _Y L(F ^b+1 ,Y,λ ^b ,ζ ^b ). (31)

by taking the derivative to be zero, the following solution can be obtained:

Y ^b+1 ＝(2E _p λ+μI) ^-1 (μF ^b+1 +Aζ). (32)

wherein, ^-1 representing inversion operation;

step 5.13: updating Lagrangian multipliers lambda and ζ:

step 5.14: iterating to convergence: repeating from the step 5.1 until convergence or the maximum iteration number requirement is reached;

the second sub-problem solution: to simplify the expression of the problem of equation (18), the reflection beam forming design of RIS is obtained by making definitions in advance to sort equation (2) and equation (12):

the formula Θ is the value Θ ₁ To theta _R Diagonal matrix, G _p 、U _k Is a new matrix generated after rearranging the matrixΘ ^H 、/>Is a conjugate transposed form of the matrix;

fixing F and alpha to solve Θ, the optimization problem equation (18) can be equivalent to

Wherein,obtaining a reflection design sub-problem form to be solved; note that this problem is also satisfied in a fractional form, introducing the auxiliary variable of the quadratic transformation, γ= [ γ ] ₁ ,…,γ _K ]Can obtain

Wherein 3a represents the transformation of equation (35) to the next form Representing complex number gamma _k Conjugation of (2);

similarly, for gamma _k The updating mode is as follows:

considering the complexity of the RIS channel, the variables are combined and defined and expressed as:

wherein 1 is _RN As a unit vector of RN dimension, then, by omitting constant terms that have no influence on the optimization result, the equation (36) is converted into:

of them, θ ^H For the conjugate transpose of θ, W is a constant term that has no effect on optimization and can be omitted, and the specific form of the finished matrix/vector is:

then, the process is carried out,H _p,k for the conjugate form of the corresponding matrix, Φ and O are the quadratic coefficient matrix and the first order coefficient matrix, respectively, which are the symbols defined for the sorting into quadratic form, and the sorted formula (40) and constraint C3 are combined together into a new equivalent qqp optimization problem, with the result that:

representing any E in mathematics as belonging meaning; adopting an ADMM-based optimization mode to solve the equivalent QCSP optimization problem (41), and expressing the equivalent ADMM form as:

where z is an auxiliary variable introduced by the ADMM method, and subsequently the lagrangian function is expressed as:

η and μ ₂ Penalty term η introduced for optimization of ADMM ^H Is eta conjugate transpose; θ can be solved by the ADMM step:

Step 5.21: updating z: by fixing other variables, the optimization problem that needs to be solved is:

z ^b+1 ＝argmin _z L(z,θ ^b ,η ^b ). (44)

the analytical formula of the obtained optimization process is as follows:

wherein, ^-1 representing inversion operation, θ ^b 、η ^b Is the value of the last iteration;

step 5.22: updating theta: with other variables fixed, solve the optimization problem for θ:

θ ^b+1 ＝argmin _θ L(z ^b+1 ,θ,η ^b ). (46)

the derived iterative formula is:

θ ^b+1 ＝(2Φ+μ ₂ I _N ) ^-1 (2O+η ^b +μ ₂ z ^b+1 ), (47)

wherein I is _N Is a unit vector;

step 5.23: updating Lagrangian multiplier η: the update formula is:

η ^b+1 ＝2Φ θ ^b+1 -2O. (48)

step 5.24: iterating to convergence: this process is repeated starting from step 5.21 until convergence or the maximum number of iterations is reached.

Preferably: in the sixth step, the termination condition of the algorithm is that the growth rate of the optimization target WSR is smaller than the set threshold value, and the growth rate can be obtained by the following formula:

the invention has the following beneficial effects:

(1) The invention establishes a model of the RIS auxiliary non-cellular ISAC network for the first time, and provides a communication-centric design, thereby meeting the scene requirement of higher requirements on communication requirements in the design of a communication-sense integrated system;

(2) The invention solves the interference problem between cells, the interference problem between users and the interference problem of a radar system to a communication system, and simultaneously, the users need to switch between different cells, thereby greatly improving the communication performance under the constraint of satisfying the perception performance;

(3) The invention provides an iterative solving process based on a split planning and alternating optimization algorithm, which can effectively solve the problems of base station beam forming and RIS phase design in an RIS auxiliary non-cellular ISAC network.

Drawings

FIG. 1 is a flow chart of a communication-centric RIS assisted cellular-less ISAC network joint beamforming method;

FIG. 2 is a schematic diagram of a system model;

FIG. 3 is a schematic diagram of a system simulation;

FIG. 4 is a schematic diagram of the trade-off between communication and radar performance;

FIG. 5 is a schematic diagram of an algorithm convergence simulation;

FIG. 6 is a schematic diagram of the effect of user location on system performance;

FIG. 7 is a schematic diagram of the effect of RIS unit number;

fig. 8 is a schematic diagram of the effect of base station transmit power.

In the figure, the BS-base station, the UE-user equipment, the Target-perception Target, the CPU-central processing unit.

Detailed Description

For the purpose of making the objects, technical solutions and advantages of the present invention more apparent, the present invention is described below by means of specific embodiments shown in the accompanying drawings. It should be understood that the description is only illustrative and is not intended to limit the scope of the invention. In addition, in the following description, descriptions of well-known structures and techniques are omitted so as not to unnecessarily obscure the present invention.

The first embodiment is as follows: the communication-centric RIS-assisted non-cellular ISAC network joint beamforming method of the present embodiment is described with reference to fig. 1-8, comprising the steps of:

step one: establishing a system model in a RIS-assisted non-cellular ISAC network system;

step two: based on the system model established in the first step, respectively obtaining the expressions of signals of a communication system and a radar system and related system indexes;

step three: establishing an optimization problem of communication performance maximization in the RIS-assisted non-cellular ISAC network based on the expression established in the step two;

step four: based on the optimization problem of the step three, carrying out problem transformation, and decomposing the transformed problem into a base station beam forming problem and an RIS phase shift design problem;

step five: respectively optimizing the base station beam and the RIS phase shift by adopting an alternative optimization method, and obtaining optimization parameters of the base station beam and the RIS phase shift by adopting an alternative direction multiplier method in a sub-problem optimization process;

step six: judging whether the optimization parameters in the step five are converged or not, if not, carrying out the step five again, and if so, completing the optimization; the invention establishes the RIS-assisted non-cellular ISAC network model for the first time, and provides a communication-centric design, thereby meeting the scene requirement of high communication requirement in the communication-demand integrated system design.

The second embodiment is as follows: 1-8, in a step I, the present invention deploys RIS in a Cell-Free ISAC MIMO system to enhance the performance of the communication system; as shown in fig. 2, the system model includes B base stations BS, R RIS, K user equipments UE and a perception Target, where the base stations BS and RIS are electrically connected to a central processing unit CPU, the base stations BS and RIS are electrically connected to the antennas of the user equipments UE, the antennas of the user equipments UE are 1, all RIS serve all the user equipments through joint beamforming design, for implementing a communication function, the base stations BS are electrically connected to the antennas of the user equipments UE, for implementing a perception function, the perception function is implemented in two stages, where in the first stage, all BSs (transmitting antennas) are required to generate beams of potential perception targets pointing to the user equipments UE while generating beams of potential perception targets pointing to the user equipments UE, and in the other stage, all BSs are also used as sensing receivers (receiving antennas), BSs are a plurality of BSs, whether there is a perception Target is determined by echo (receiving beams of potential perception targets pointing to the known locations) through the receiving antennas, the number of antennas of the user equipments is 1, the K user equipments UE share one antenna, and each RIS is equipped with N independent adjustable units; the invention assumes that all B base stations BS and R RI S are connected with a central processing unit CPU through a control return link to realize unified management and coordination, all base stations are configured to be completely synchronous, have the capability of digital beam forming and realize simplified model.

And a third specific embodiment: referring to fig. 1-8, a method for joint beamforming of a RIS-assisted non-cellular ISAC network with communication as a center in the present embodiment is described, in which, in the first step, each base station BS is equipped with a base station antenna, where the base station antenna includes Nt transmitting antennas and Nr receiving antennas to meet the dual-function requirements of communication and perception, the transmitting antennas and the receiving antennas are electrically connected to form a downlink transmission, in the downlink transmission process, two subsets composed of all base stations are mainly focused, the first subset includes P transmitting base stations responsible for transmitting communication and sensing signals simultaneously, the second subset includes Q receiving base stations, and then focuses on receiving reflected or scattered signals generated by the perception target, where the two subsets may not overlap, or may have different degrees of overlapping, P, Q, B, R, K, nt, N, L, nr, M is a natural number, and the uppercase letters represent the maximum number, where the elements are represented by lowercase letters; the invention aims at discussing the optimization of communication performance, and considers that the first subset and the second subset are supposed to be completely overlapped, namely all base stations have full duplex capability; and the phase adjustment of the RIS only serves the communication function, which requires that the RIS and the user equipment UE are located as close as possible to obtain the best effect, where the RIS is a plurality of RIS;

The specific embodiment IV is as follows: 1-8, in the RIS assisted non-cellular ISAC network combined beam forming method with communication as center, in the second step, the transmitting signal is set as the weighted sum of the communication symbol and the radar waveform, so as to realize the dual functions of communication and sensing; specifically, the P sending BSs are set to jointly transmit K communication flows (implemented by using a communication function) and M sensing flows (implemented by using a sensing function), wherein the sets of the communication flows and the sensing flows are respectively defined as K and M, and the present invention can define the whole flow set as i=ku M, provided that(wherein->Complex vector representing Nt dimension) represents the transmission signal of the p-th transmitting BS (the transmitting antenna of the p-th base station) in the first slot, it is possible to obtain:

wherein f _p,k And f _p,m Respectively the communication symbols x _k [l]And radar waveform x _m [l]Is a beam forming vector of f _p,i Is x _i [l]Is used for the beam forming vector of (a),the present invention assumes that the transmission symbol has normalized power, i.e., E [ |x _i | ² ]=1, wherein E represents a valueA desired operation; furthermore, the information of the 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′ Is the transposed conjugate of x _i′ Is different from x _i The formula shows that the same signal is multiplied by its own conjugate transpose to find the desired identity matrix, and the different signal is then 0, noting that such radar signals can be generated by pseudo-random encoding;

the invention sets that all base stations BS have digital beam forming capability, and all base stations BS are completely synchronous, and each unit on RIS can be independently regulated; all base stations BS and RIS are connected to the same CPU through a control return link, and can be considered to be uniformly scheduled and controlled, so that simple and convenient processing is realized; in the RIS-assisted non-cellular ISAC system proposed in the present invention, i.e., the system model of 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, under this framework, each BS-RIS-user link can be further decomposed into a BS-RIS link and a RIS-user link, the present invention assumes that the channel remains unchanged during the transmission of consecutive L symbols, and the equivalent channel from the p-th BS to the k-th user is considered in view of these channel componentsCan be expressed as:

wherein,representing the direct link between the p-th transmitting base station and the kth user, G _p,r And->Representing the channel between the p-th transmitting base station and the kth user and the r-th RIS, respectively, Θ _r Is the phase adjustment matrix of the r-th RIS, < >>Is theta _r Is defined as:

wherein θ _r,n Representing the Reflection Coefficient (RC) of RIS, note that the present invention contemplates the case of an ideal RIS, i.e., θ _r,n The amplitude and the phase of the pulse can be independently and continuously controlled; the signal received by user k can then be expressed as:

wherein n is ^k A reception noise representing a kth UE; assuming that the channel remains unchanged over the transmission of L symbols, the radar waveform is x _m [l]The introduced symbol j represents other users x than k _j [l]The first symbol, f, representing the j-th stream _p,j Is x _j [l]Is a beamforming vector of (1); then, the signal-to-interference-and-noise ratio (SINR) of the kth UE may be expressed as:

wherein,gaussian noise representing received signal of user kVariance, then, the present invention evaluates typical communication and rate metrics to evaluate the performance of multi-user communication, the aggregate rate (WSR) R of all UEs (multiple users) _sum Can be expressed as:

for the sensing model, the invention adopts a multi-base sensing model; for simplicity of implementation, the invention assumes that there is a direct-ray (LOS) connection between the perceived target location and each base station BS, ignoring non-direct-ray (NLOS) connections, in the present system model, it is assumed that the receive antennas are spaced sufficiently widely in the radar structure that spatial correlation between the receive antennas can be ignored;

The reflected path channel through the target between p of the transmitting BS and q of the receiving BS can be expressed as:

wherein,satisfying a complex Gaussian distribution is a combination of sensor channel gain, including through target and target Radar Cross Section (RCS), of +.>Is the conjugate transpose of the array antenna response vector formed by the transmit angles,is the array antenna response vector composed of the arrival angles, < ->Is at a corresponding angle; the invention considers that the sensing channel accords with the Swerl ing-I target fluctuation model, which shows that the fluctuation of RCS of a sensing target is slower, the sensing symbol is not changed in a unit time slot, and capital letters representMaximum number, wherein the elements are represented by lowercase letters;

assuming that the CPU knows the transmitted signalThen echo signals which are not reflected by the perception target can be eliminated in the received signals in a signal processing mode; therefore, in the presence of a target, the first slot signal received by the qth receiving BS through a horizontal Uniform Linear Array (ULA) base station antenna may be expressed as:

wherein,is the reception noise of base station q in time slot l, x _p [l]Signals transmitted in time slot l for the previously defined transmitting BS;

the L symbols are integrated together, as defined below:

Note that here, the arrangement and transformation of the matrix, has no practical meaning, ^T representing the transpose of the matrix []The inner part represents the arrangement and arrangement condition of corresponding matrix elements;

the signal of the L symbols received for the qth receiving BS can be expressed as:

wherein,satisfying complex Gaussian distribution is the integrated noise vector matrix F _p 、X、N _q Respectively finishing formula (9)The formed p-th BS transmits a beam forming vector, a symbol matrix and a noise matrix;

for the description of the perception performance, the invention adopts the typical perception SNR to measure the performance of the radar system, and the perception SNR as a basic index of the radar system can influence the performance of various sensing tasks (such as target detection and parameter estimation); the invention is directed to a Cell-Free ISAC architecture, which considers that the sensing signals of a plurality of receiving BSs are processed in a combined way, so that a combined sensing SNR is obtained, and a formula of the sensing SNR can be expressed as follows:

wherein the method comprises the steps ofFor v between transmitting BS p to receiving BS q _p,q Variance of complex Gaussian distribution, ">Is the variance of the received noise;

thanks to the centralized signal processing of the CPU end, the invention can find that the perception performance is influenced by the communication beam and the radar beam together through the expression of the perception SNR; the invention solves the interference problem between cells, the interference problem between users and the interference problem of a radar system to a communication system, and simultaneously, the users need to switch between different cells, thereby greatly improving the communication performance under the constraint of satisfying the perception performance.

Fifth embodiment: 1-8, in the third step, based on the expressions (6) and (11) established in the second step, based on the above description of the system model, the present invention realizes the beam forming and reflection design of communication priority in the system; the optimization problem of the present invention is to maximize WSR by jointly optimizing the sensing beamforming of the BS, the communication beamforming and the phase shift of the RIS under the constraint of radar perceived SNR; by definition

Wherein, ^T for transpose operations, diag is the diagonalization of the matrix, and the formula Θ is the value Θ ₁ To theta _R Diagonal matrix, G _p 、U _k 、F _k And F is a new matrix generated after rearranging the matrix, the optimization problem can be expressed as:

wherein the abbreviation s.t. is subject to stands for constraint of the optimization problem, P is the set of transmitting BSs, P _max For maximum power of the transmitting base station, ρ is the perceived SNR ^(s) And θ _r,n An nth reflection unit which is an nth RIS, N represents a set of reflection units, R represents a set of RIS,representing any E in mathematics as belonging meaning;

constraints C1, C2 and C3 are respectively a base station power constraint, a perceived SNR constraint and an RIS phase constraint, and it is obvious that the form of the objective function formula (13) is a complex multivariable coupling function in the form of a hybrid partial formula, and meanwhile, the constraint conditions also include partial formulas.

Specific embodiment six: 1-8, in step four, in order to solve the complex form existing in the objective function, the present invention considers processing by using the quadratic transformation of the split-plan (FP); first, auxiliary change is introducedQuantity alpha= [ alpha ] ₁ ,...,α _K ]The objective function of equation (13) can equivalently be restated as:

this transformation does not affect the result of the optimization, alpha _k The update process of (2) can be realized by using the derivative as zero, and the update formula can be obtained as follows:

then, when the introduced auxiliary variable α is fixed, the variable to be optimized is concentrated in the last term of the formula (14), and the invention extracts this term alone to become a new optimization problem, which can be expressed as:

note that the problem still has coupling, the invention advocates that the problem is split into two sub-problems for decoupling and updated in an alternate optimization way; the first sub-problem is to fix Θ optimization F, and the other sub-problem is to fix F to solve Θ; the invention provides an iterative solving process based on a split planning and alternating optimization algorithm, which can effectively solve the problems of base station beam forming and RIS phase design in an RIS auxiliary non-cellular ISAC network.

Seventh embodiment: referring to fig. 1-8, a communication-centric RIS-assisted non-cellular ISAC network joint beamforming method according to the present embodiment will be described, in which, in step four, the first sub-problem: beamforming design for BS

Wherein,a gaussian noise variance representing the received signal of user k;

a second sub-problem: phase shift design of RIS

Eighth embodiment: 1-8, the communication-centric RIS-assisted non-cellular ISAC network joint beamforming method of the present embodiment includes a first sub-problem solving and a second sub-problem solving in a fifth step;

the first sub-problem solution: firstly, carrying out beam forming design of a BS; the solution to F is achieved by fixing Θ and α, in which case the optimization problem equation (16) can be equivalent to

The sub-problem is restated by using quadratic transformation, and auxiliary variable beta= [ beta ] is introduced ₁ ,…,β _K ]The sub-problem equation (19) objective function can be equivalently restated as:

wherein,representing the real part operation of complex numbers,/>Representative pair auxiliary variable beta _k Conjugation of the auxiliary variable beta _k Is updated by solving the first order of 0, and is optimized alternatelyThe update formula in the chemical process can be expressed as:

in order to obtain a more obvious and easily solved qqp form, the present invention organizes equation (20) and defines the following:

wherein,the Cronecker product operation of the representative matrix, C is the matrix, v, which is formulated for the expression of the quadratic term in equation (24) _p,k 、V _k V is a matrix which is formulated for the expression of the coefficients of the first order term in equation (24), D is a constant term, and I (k) is a tuning variable defined in the present invention, which can be expressed as

The invention thus far deals with the form of the partial formula in the objective function of equation (19) and is put into a quadratic form that is easy to solve:

F ^H V ^H the conjugate transposes of the corresponding matrices, respectively, however, the constraint C2 caused by the radar system still belongs to the form of division, and for the sake of arrangement into a format that is easy to solve, the following expression form is defined:

wherein,cronecker product operation of representative matrix, 1 _(K+M)PNt A unit vector representing (K+M) PN dimension, e _p The vector representing the dimension P is 1 at the P-th element and 0 at the other elements, and this step is to define the symbol in the finishing symbol, A,/-, etc>E _p New matrix symbols defined for the sake of sorting the expression form of the constraint +. >For the arrangement of the constant terms derived, +.>For v between transmitting BS p to receiving BS q _p,q Variance of complex Gaussian distribution, ">Is the variance of the received noise,/>I _K+M After the transformation and arrangement, the invention completely arranges the sub-problem formula (17) into the equivalent problem form of qqp and is expressed as:

the present invention solves such problems using the Alternate Direction Multiplier Method (ADMM); in order to convert the problem into a form suitable for alternating direction multiplication (ADMM), the invention first rewrites the original problem (24) as:

the present invention then defines a Lagrangian function:

wherein, ^H represents the conjugate transpose, L () represents the Lagrangian function form, V ^H A ^H Represents the conjugate transpose of the corresponding matrix, with lambda, zeta and mu being mu ₂ Penalty terms introduced for the optimization mode of ADMM; the invention sets the superscript b as an iteration index, b+1 is the value of the next iteration, and the step of solving F based on ADMM provided by the invention is expressed as follows:

step 5.11: updating F: other variables are fixed first and the optimization problem is solved for F:

F ^b+1 ＝argmin _F L(F,Y ^b ,λ ^b ,ζ ^b ). (29)

by taking the first derivative and setting it to zero, one can get:

F ^b+1 ＝(C+C ^H +μI) ^-1 (2V+μY ^b ). (30)

wherein C is ^H Represents the conjugate transpose of C;

Step 5.12: updating Y: with other variables fixed, further comprising solving an optimization problem with respect to Y:

Y ^b+1 ＝argmin _Y L(F ^b+1 ,Y,λ ^b ,ζ ^b ). (31)

similarly, by taking the derivative to be zero, the following solution can be obtained:

Y ^b+1 ＝(2E _p λ+μI) ^-1 (μF ^b+1 +Aζ). (32)

wherein, ^-1 representing inversion operation;

step 5.13: updating Lagrangian multipliers lambda and ζ:

step 5.14: iterating to convergence: repeating from the step 5.1 until convergence or the maximum iteration number requirement is reached;

the second sub-problem solution: in order to simplify the expression form of the problem of the formula (18), the invention makes some definitions in advance to arrange the formula (2) and the formula (12) to obtain the following formula:

the formula Θ is the value Θ ₁ To theta _R Diagonal matrix, G _p 、U _k Is a new matrix generated after rearranging the matrixΘ ^H 、/>Is a conjugate transposed form of the matrix;

fixing F and alpha to solve Θ, the optimization problem equation (18) can be equivalent to

Wherein,then, the invention obtains the reflection design sub-problem form to be solved; note that this problem is equally satisfied in the form of a partial, similarly, the invention also introduces an auxiliary variable of the quadratic transformation, γ= [ γ ] ₁ ,…,γ _K ]Can obtain

Wherein 3a represents the transformation of equation (35) to the next form Representing complex number gamma _k Conjugation of (2);

similarly, for gamma _k The updating mode is as follows:

considering the complexity of the RIS channel, the variables are combined and defined, sorted and expressed as:

wherein 1 is _RN As a unit vector of RN dimension, then, by omitting constant terms that have no influence on the optimization result, the equation (36) is converted into:

of them, θ ^H For the conjugate transpose of θ, W is a constant term that has no effect on optimization and can be omitted, and the specific form of the finished matrix/vector is:

then, the process is carried out,H _p,k in the conjugated form of the corresponding matrix, phi and O are respectively quadratic coefficient matrix andthe present invention combines the sorted formula (40) and constraint C3 together into a new equivalent qqp optimization problem, resulting in:

representing any E in mathematics as belonging meaning; similarly, the invention takes an ADMM-based optimization approach to solve the equivalent qqp optimization problem (41) and expresses the equivalent ADMM form as:

where z is an auxiliary variable introduced by the ADMM method, and subsequently the lagrangian function is expressed as:

η and μ ₂ Penalty term η introduced for optimization of ADMM ^H Is eta conjugate transpose; similarly, the present invention can solve for θ by the following ADMM steps:

step 5.21: updating z: by fixing other variables, the optimization problem that needs to be solved is:

z ^b+1 ＝argmin _z L(z,θ ^b ,η ^b ). (44)

the analytical formula of the optimization process can be obtained by the invention:

wherein, ^-1 representative calculationInverse operation, θ ^b 、η ^b Is the value of the last iteration;

step 5.22: updating theta: with other variables fixed, further comprising solving an optimization problem with θ:

θ ^b+1 ＝argmin _θ L(z ^b+1 ,θ,η ^b ). (46)

similarly, the iterative formula derived by the present invention is:

θ ^b+1 ＝(2Φ+μ ₂ I _N ) ^-1 (2O+ η ^b +μ ₂ z ^b+1 ), (47)

wherein I is _N Is a unit vector;

step 5.23: updating Lagrangian multiplier η: the update formula is:

η ^b+1 ＝2Φ θ ^b+1 -2O. (48)

step 5.24: iterating to convergence: this process is repeated starting from step 5.21 until convergence or maximum iteration number requirements are reached;

based on the deduction, the invention provides a combined active and passive beam forming design algorithm for a RIS-assisted Cell-FreeSAC system, and an alternate updating method is used; the termination condition of the algorithm is that the growth rate of the optimization target is smaller than a set threshold value; notably, the algorithm of the present invention guarantees a monotonic non-decreasing equivalent objective function after each iteration, and therefore, while involving transformations and iterations, the algorithm converges to at least one locally optimal solution; the present invention can verify its effectiveness by comparison with a baseline scheme.

Detailed description nine: referring to fig. 1-8, a method for joint beamforming of a communication-centric RIS-assisted non-cellular ISAC network according to the present embodiment will be described, in the sixth step, the termination condition of the algorithm is that the growth rate of the optimization target WSR is smaller than a set threshold, where the growth rate can be obtained by the following formula:

notably, the algorithm of the present invention guarantees a monotonic non-decreasing equivalent objective function after each iteration, and therefore, while involving transformations and iterations, the algorithm converges to at least one locally optimal solution; the present invention can verify its effectiveness by comparison with a baseline scheme.

Example 1:

as shown in fig. 3, the simulation scene is set to a 2D plane, wherein coordinates of three Base Stations (BS) are set to (20 m,50 m), (50 m ) and (80 m,50 m), respectively, two RIS are set to sum (20 m,5 m) and (80 m,5 m), respectively, and the perception target position is set to (50 m,0 m); 4 (K=4) single-antenna users are randomly distributed in a circle with the radius of 1m, and the center coordinates can move along the x axis;

for communication channels, the present invention employs a distance-based path LOSs model in which BS-RIS links are modeled as line-of-sight (LOS) connections for rice fading channels, and BS-user links and RIS-user links are modeled as non-line-of-sight (NLOS) connections for rayleigh fading channels; meanwhile, path loss indexes of 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; setting parameters of radar channels as And->Further, other parameter settings are expressed as: p (P) _max ＝0.3W，L＝10，/>Base station antenna number nt=nr=9 and radar signal-to-noise ratio constraint ρ=0.09;

the comparison algorithm is specifically as follows:

(1) No RIS assistance: this scheme (labeled "NO-RIS") only optimizes the beamforming of Cell-FreeBS, not involving phase shift optimization of RIS;

(2) Random phase shift: this scheme (labeled "random") randomly sets the phase shift of the RIS and employs the same active beamforming design as case 1;

(3) Ideal RIS: this scheme (labeled "RIS") sets the phase and amplitude of the RIS to be continuously adjustable and simultaneously optimizes the active beamforming of the base station and the reflection coefficient of the RIS using algorithm 1;

(4) Non-ideal RIS: this scheme (labeled "2 bit-RIS") considers the possible 2bit phase RIS in the actual deployment, i.e., the RIS phase has only four possible values;

(5) Single base station ISAC: this scheme (labeled "SingleBS ISAC") sets RIS as ideal, leaving only one base station at (50 m ), with transmit and receive antennas set to 9;

(6) Cellular network ISAC: in the scheme (marked as 'Cell ISAC'), RIS is set as an ideal condition, a base station in the figure is divided into three cells, interference among the cells is regarded as Gaussian noise, meanwhile, transmitting and receiving antennas of each cellular base station are set to 27 (total number of antennas corresponding to Cell-Free situations), the invention omits the base station switching process to set that the whole simulation process is that communication users only access an intermediate base station, and the radar sensing aspect can be cooperatively realized among a plurality of base stations;

As shown in fig. 5, the present invention first shows the convergence behavior of the proposed algorithm. By setting the user center as (20 m,0 m) and the radar constraint as 1 to carry out numerical simulation, the invention observes that the user communication rate of all schemes monotonically increases with the increase of the iteration times; in addition, all schemes finally reach a stable state, which verifies that the algorithm provided by the invention has good convergence;

as shown in FIG. 6, the present invention compares different schemes by changing the user center position as a result of the simulation of the effect of the user position on the system performance; here, the invention allows the x-coordinate of the user center to be changed from 0m to 100m while setting the radar constraint to 1; the results show that RIS can form significant gain at deployment site, even "2bit-RIS" can bring significant performance improvement; in order to evaluate the superiority of the Cell-Free architecture proposed by the present invention, the present invention takes SingleBS ISAC and cellular network as a comparison; the result shows that the performance of the Cell-Free architecture is obviously better than that of a single-base station architecture, mainly because the Cell-Free architecture not only has more antennas and has wider service areas, but also can eliminate interference among base stations and greatly improve the performance of the system compared with the CellISAC; in addition, the performance improvement can be brought when the user is coincident with the perception target position; this may result from the high spatial concentration of the beams, which is both easy to satisfy perceptual constraints and allows communications to benefit from the gain of all beams;

As shown in fig. 4, the trade-off simulation result between communication and radar performance is always an important problem in ISAC system design, and the present invention fixes users near RIS, and varies radar perceived SNR constraints; the results show that the communication rate decreases with increasing SNR constraints; this is because stronger radar constraints result in more beam resources for target detection, thereby reducing the communication beam; however, application of RIS can mitigate communication performance degradation, confirming the great potential of RIS; it can be found that the performance of Single BS ISACs is greatly reduced because Cell-Free has more antennas, it is easier to meet the radar system constraint threshold, and at the same time, it is able to provide higher communication gain; in addition, even if the Cell ISAC scheme and the Cell-Free have the same antenna quantity, the communication performance of users is greatly influenced due to interference among base stations, so that the rationality and the advantage of selecting the Cell-Free architecture are verified;

finally, the invention researches the influence of system parameters on performance to obtain the insight of system design; in the next experiments, the present invention fixes the user center coordinates near RIS (20 m,0 m); in one aspect, as shown in FIG. 7, the relationship of WSR to the number (N) of RIS reflective elements is illustrated; as expected, as N increases, the WSR increases as more reflective elements can provide greater passive beamforming gain; this provides a system design concept for the present invention, namely adding low cost RIS units to optimize system performance; on the other hand, the present invention also researches the relation between WSR and base station power budget in fig. 8; the results show that as the power budget increases, the WSR of all schemes improves, since the base station has more power resources available for communication and perception; notably, the performance improvement provided by RIS is more significant; thus, system design can exploit the RIS potential to a greater extent by increasing power.

In the above embodiments, as long as the technical solutions that are not contradictory can be arranged and combined, a person skilled in the art can exhaust all the possibilities according to the mathematical knowledge of the arrangement and combination, so the present invention does not describe the technical solutions after the arrangement and combination one by one, but should understand that the technical solutions after the arrangement and combination have been disclosed by the present invention.

The above description is only of the preferred embodiments of the present invention and is not intended to limit the present invention, but various modifications and variations can be made to the present invention by those skilled in the art. Any modification, equivalent replacement, improvement, etc. made within the spirit and principle of the present invention should be included in the protection scope of the present invention.

Claims (9)

1. A communication-centric RIS-assisted non-cellular ISAC network joint beamforming method, characterized by: the method comprises the following steps:

step one: establishing a system model in a RIS-assisted non-cellular ISAC network system;

step two: obtaining signal expressions of a communication system and a radar system based on a system model;

step three: based on the expression, establishing an optimization problem of communication performance maximization in the RIS-assisted non-cellular ISAC network;

step four: based on the optimization problem, converting and decomposing the problem into a base station beam forming problem and an RIS phase shift design problem;

Step five: optimizing the beam and RIS phase shift of the base station by using an alternating optimization method, wherein the sub-problem optimization process adopts an alternating direction multiplication method;

step six: judging whether the optimization parameters in the step five are converged or not, if not, carrying out the step five again, and if so, completing the optimization.

2. The communication-centric RIS-assisted non-cellular ISAC network joint beamforming method of claim 1, wherein: in the first step, the system model includes a Base Station (BS), an RIS, a User Equipment (UE) and a perception target, where the Base Station (BS) and the RIS are electrically connected with a Central Processing Unit (CPU), the Base Station (BS) and the RIS are electrically connected with the User Equipment (UE), and all the RIS serve all the user equipment through joint beam forming design and are used for implementing a communication function, the Base Station (BS) is electrically connected with the User Equipment (UE) and is used for implementing the perception function, and the realization of the perception function requires BSs to generate a beam pointing to the potential perception target while generating a beam pointing to the User Equipment (UE), and the BSs also serves as a sensing receiver and determines whether the perception target exists through echo.

3. The communication-centric RIS-assisted non-cellular ISAC network joint beamforming method of claim 2, wherein: in step one, a Base Station (BS) is equipped with a transmitting antenna and a receiving antenna, where the transmitting antenna and the receiving antenna are electrically connected to form a downlink transmission, and in the downlink transmission process, all the base stations form two subsets, the first subset includes P reflected or scattered signals responsible for transmitting communication and sensing signals simultaneously, and the second subset includes Q reflected or scattered signals generated by a sensing target, where it is assumed that the first subset and the second subset completely overlap.

4. A communication-centric RIS-assisted non-cellular ISAC network joint beamforming method according to claim 3, wherein: in the second step, P sending BSs are set to transmit K communication flows and M sensing flows together, the sets of the communication flows and the sensing flows are defined as K and M respectively, the whole flow set is defined as i=kjcm, and it is assumed that(wherein->Complex vector representing Nt dimension) represents the transmission signal of the p-th transmitting BS in the l-th slot, it is possible to obtain:

wherein f _p,k And f _p,m Respectively the communication symbols x _k [l]And radar waveform x _m [l]Is a beam forming vector of f _p,i Is x _i [l]Is used for the beam forming vector of (a),the first symbol of the ith stream, assuming the transmission symbol has normalized power, i.e., E [ |x _i | ² ]=1, wherein E represents a numerically expected operation; furthermore, the information of the radar and communication signals is statistically independent, i.eAnd->For I, I '∈I and i+.i', where I is the identity matrix, +.>Represents x _i′ Is the transposed conjugate of x _i′ Is different from x _i The formula shows that the same signal is multiplied by its own conjugate transpose to find the desired identity matrix, and the different signal is 0, such a radar signal can be generated by pseudo-random encoding;

the system model of step one, the channel between each transmitting BS and each user equipment comprises 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, and the equivalent channel from the p-th BS to the kth user is assumed to be unchanged during the transmission of continuous L symbols Can be expressed as:

wherein,representing the direct link between the p-th transmitting base station and the kth user, G _p,r And->Representing the channel between the p-th transmitting base station and the kth user and the r-th RIS, respectively, Θ _r Is the phase adjustment matrix of the r-th RIS, < >>Is theta _r Is defined as:

wherein θ _r,n Representing the Reflection Coefficient (RC) of RIS, note that the present invention contemplates the case of an ideal RIS, i.e., θ _r,n The amplitude and the phase of the pulse can be independently and continuously controlled; the signal received by user k can then be expressed as:

wherein n is _k A reception noise representing a kth UE; assuming that the channel remains unchanged over the transmission of L symbols, the radar waveform is x _m [l]The introduced symbol j represents other users x than k _j [l]The first symbol, f, representing the j-th stream _p,j Is x _j [l]Is a beamforming vector of (1); then, the signal-to-interference-and-noise ratio (SINR) of the kth UE may be expressed as:

wherein,representative of the Gaussian noise variance of the received signal for user k, typical communication and rate metrics are used to evaluate the performance of multi-user communication, the sum rate (WSR) R of all UEs _sum Can be expressed as:

assuming that there is a direct-ray (LOS) connection between the perceived target location and each Base Station (BS), in the present system model, the receive antennas in the radar structure are assumed to be spaced sufficiently wide that the spatial correlation between the receive antennas can be ignored.

The reflected path channel through the target between p of the transmitting BS and q of the receiving BS can be expressed as:

wherein,satisfying a complex Gaussian distribution is a combination of sensor channel gain, including through target and target radar cross section (RC S), of +.>Is the conjugate transpose of the array antenna response vector formed by the transmission angles, ">Is the array antenna response vector composed of the arrival angles, < ->Is at a corresponding angle; the invention considers that the sensing channel accords with the switching-I target fluctuation model, which shows that the fluctuation of RCS of a sensing target is slower, and the sensing symbol is in unit timeThe gap is not changed;

in the presence of a target, the first time slot signal received by the qth receiving BS through a horizontal Uniform Linear Array (ULA) base station antenna may be expressed as:

wherein,is the reception noise of base station q in time slot l, x _p [l]Signals transmitted in time slot l for the previously defined transmitting BS;

the L symbols are integrated together, as defined below:

note that here, the matrix arrangement and transformation are performed, T represents the transpose of the matrix, and [ (within ] represents the arrangement condition of the corresponding matrix elements);

the signal of the L symbols received for the qth receiving BS can be expressed as:

wherein,satisfying complex Gaussian distribution is the integrated noise vector matrix F _p 、X、N _q The p-th BS finished by the arrangement of the formula (9) transmits a beam forming vector, a symbol matrix and a noise matrix;

the sensing signals of the plurality of receiving BSs are jointly processed, so as to obtain a joint sensing SNR, and a formula of the sensing SNR can be expressed as:

wherein the method comprises the steps ofFor v between transmitting BS p to receiving BS q _p,q Variance of complex Gaussian distribution, ">Is the variance of the received noise;

the invention can find that the perception performance is influenced by the communication beam and the radar beam together through the expression of the perception SNR thanks to the centralized signal processing of the CPU end.

5. The communication-centric RIS-assisted non-cellular ISAC network joint beamforming method of claim 4, wherein: in step three, definition is performed based on the expressions (6) and (11) established in step two

Wherein, ^T for transpose operations, diag is the diagonalization of the matrix, and the formula Θ is the value Θ ₁ To theta _R Diagonal matrix, G _p 、U _k 、F _k And F is a new matrix generated after rearranging the matrix, the optimization problem can be expressed as:

wherein the abbreviation s.t. is subject to stands for constraint of the optimization problem, P is the set of transmitting BSs, P _max For maximum power of the transmitting base station, ρ is the perceived SNR ^(s) And θ _r,n An nth reflection unit which is an nth RIS, N represents a set of reflection units, R represents a set of RIS,representing any E in mathematics as belonging meaning;

constraints C1, C2, and C3 are base station power constraints, perceived SNR constraints, and RIS phase constraints, respectively.

6. The communication-centric RIS-assisted non-cellular ISAC network joint beamforming method of claim 5, wherein: in the fourth step, an auxiliary variable α= [ α ] is first introduced ₁ ,...,α _K ]The objective function of equation (13) can equivalently be restated as:

this transformation does not affect the result of the optimization, alpha _k The update process of (2) can be realized by using the derivative as zero, and the update formula can be obtained as follows:

then, when the introduced auxiliary variable α is fixed, the variable to be optimized is concentrated on the last term of the formula (14), and this term is extracted separately to become a new optimization problem, which can be expressed as:

the problem is decomposed into two sub-problems for decoupling, the first being to fix Θ to optimize F and the other being to fix F to solve Θ.

7. The communication-centric RIS-assisted non-cellular ISAC network joint beamforming method of claim 6, wherein: in step four, the first sub-problem: beamforming design for BS

Wherein,a gaussian noise variance representing the received signal of user k;

a second sub-problem: phase shift design of RIS

8. The communication-centric RIS-assisted non-cellular ISAC network joint beamforming method of claim 7, wherein: step five, a first sub-problem solving and a second sub-problem solving are included;

the first sub-problem solution: firstly, carrying out beam forming design of a BS; f is solved by fixing Θ and α, in which case the optimization equation (16) can be equivalent to

Representational of this sub-problem using a quadratic transformation, introducing the auxiliary variable β= [ β ] ₁ ,...,β _K ]The objective function can then equivalently be restated as:

wherein,representing the real part operation of complex numbers,/>Representative pair auxiliary variable beta _k Conjugation of the auxiliary variable beta _k The update mode of (2) is updated by solving a first order derivative as 0, and an update formula in the alternate optimization process can be expressed as follows:

in order to obtain a more obvious and easily solved qqp form, the present invention organizes equation (20) and defines the following:

wherein,the Cronecker product operation of the representative matrix, C is the matrix, v, which is formulated for the expression of the quadratic term in equation (24) _p,k 、V _k V is a matrix which is formulated for the expression of the coefficients of the first order term in equation (24), D is a constant term, and I (k) is a tuning variable defined in the present invention, which can be expressed as

The invention thus far deals with the form of the partial formula in the objective function of equation (19) and is put into a quadratic form that is easy to solve:

F ^H V ^H the constraint condition C2 caused by the radar system still belongs to a partial form, and for arrangement into a format easy to solve, the following expression form is defined:

wherein,cronecker product operation of representative matrix, 1 _(K+M)PNt A unit vector representing (K+M) PN dimension, e _p The vector representing the dimension P is 0, A, and +.>E _p New matrix symbols defined for the sake of sorting the expression form of the constraint +.>For the arrangement of the constant terms derived, +.>For v between transmitting BS p to receiving BS q _p,q Variance of complex Gaussian distribution, ">Is the variance of the received noise, I _Nt 、I _K+M After the transformation and arrangement, the sub-problem equation (17) is completely arranged into the equivalent problem form of qqp and is expressed as:

the present invention solves such problems using the Alternate Direction Multiplier Method (ADMM); in order to convert the problem into a form suitable for alternating direction multiplication (ADMM), the invention first rewrites the original problem (24) as:

then a Lagrangian function is defined:

Wherein, ^H represents the conjugate transpose, L () represents the Lagrangian function form, V ^H A ^H Represents the conjugate transpose of the corresponding matrix, with lambda, zeta and mu being mu ₂ Penalty terms introduced for the optimization mode of ADMM; setting the superscript b as an iteration index, b+1 being the value of the next iteration, the proposed step of solving F based on ADMM is expressed as:

step 5.11: updating F: other variables are fixed first and the optimization problem is solved for F:

F ^b+1 ＝arg min _F L(F,Y ^b ,λ ^b ,ζ ^b ). (29)

by taking the first derivative and setting it to zero, one can get:

F ^b+1 ＝(C+C ^H +μI) ^-1 (2V+μY ^b ). (30)

wherein C is ^H Represents the conjugate transpose of C;

step 5.12: updating Y: with other variables fixed, solve the optimization problem for Y:

Y ^b+1 ＝arg min _Y L(F ^b+1 ,Y,λ ^b ,ζ ^b ). (31)

by taking the derivative to be zero, the following solution can be obtained:

Y ^b+1 ＝(2E _p λ+μI) ^-1 (μF ^b+1 +Aζ). (32)

wherein, ^-1 representing inversion operation;

step 5.13: updating Lagrangian multipliers lambda and ζ:

step 5.14: iterating to convergence: repeating from the step 5.1 until convergence or the maximum iteration number requirement is reached;

the second sub-problem solution: to simplify the expression of the problem of equation (18), the reflection beam forming design of RIS is obtained by making definitions in advance to sort equation (2) and equation (12):

the formula Θ is the value Θ ₁ To theta _R Diagonal matrix, G _p 、U _k Is a new matrix generated after rearranging the matrixΘ ^H 、/>Is a conjugate transposed form of the matrix;

fixing F and alpha to solve Θ, the optimization problem equation (18) can be equivalent to

Wherein,obtaining a reflection design sub-problem form to be solved; note that this problem is also satisfied in a fractional form, introducing the auxiliary variable of the quadratic transformation, γ= [ γ ] ₁ ,...,γ _K ]Can obtain

Wherein 3a represents the transformation of equation (35) to the nextPersonal formRepresenting complex number gamma _k Conjugation of (2);

similarly, for gamma _k The updating mode is as follows:

considering the complexity of the RIS channel, the variables are combined and defined and expressed as:

wherein 1 is _RN As a unit vector of RN dimension, then, by omitting constant terms that have no influence on the optimization result, the equation (36) is converted into:

of them, θ ^H For the conjugate transpose of θ, W is a constant term that has no effect on optimization and can be omitted, and the specific form of the finished matrix/vector is:

then, the process is carried out,H _p,k for the conjugate form of the corresponding matrix, Φ and O are the quadratic coefficient matrix and the first order coefficient matrix, respectively, which are the symbols defined for the sorting into quadratic form, and the sorted formula (40) and constraint C3 are combined together into a new equivalent qqp optimization problem, with the result that:

Representing any E in mathematics as belonging meaning; adopting an ADMM-based optimization mode to solve the equivalent QCSP optimization problem (41), and expressing the equivalent ADMM form as:

where z is an auxiliary variable introduced by the ADMM method, and subsequently the lagrangian function is expressed as:

η and μ ₂ Penalty term η introduced for optimization of ADMM ^H Is eta conjugate transpose; θ can be solved by the ADMM step:

step 5.21: updating z: by fixing other variables, the optimization problem that needs to be solved is:

z ^b+1 ＝arg min _z L(z,θ ^b ,η ^b ). (44)

the analytical formula of the obtained optimization process is as follows:

wherein, ^-1 representing inversion operation, θ ^b 、η ^b Is the value of the last iteration;

step 5.22: updating theta: with other variables fixed, solve the optimization problem for θ:

θ ^b+1 ＝arg min _θ L(z ^b+1 ,θ,η ^b ). (46)

the derived iterative formula is:

θ ^b+1 ＝(2Φ+μ ₂ I _N ) ^-1 (2O+η ^b +μ ₂ z ^b+1 ), (47)

wherein I is _N Is a unit vector;

step 5.23: updating Lagrangian multiplier η: the update formula is:

η ^b+1 ＝2Φ θ ^b+1 -2O. (48)

step 5.24: iterating to convergence: this process is repeated starting from step 5.21 until convergence or the maximum number of iterations is reached.

9. The communication-centric RIS-assisted non-cellular ISAC network joint beamforming method of claim 8, wherein: in the sixth step, the termination condition of the algorithm is that the growth rate of the optimization target WSR is smaller than the set threshold value, and the growth rate can be obtained by the following formula:

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