Noma assisted multi-isac user terminal joint transmit-receive beamforming method

Abstract

The application discloses a NOMA-assisted multi-ISAC user terminal joint transmission-reception beam forming method, comprising the following steps: constructing a communication and perception fusion architecture supporting multi-ISAC user terminals; constructing a multi-signal model; determining an evaluation index of multi-user terminal grouping using the NOMA technology, and determining a multi-user terminal grouping algorithm process according to the evaluation index; constructing an optimization problem of user terminal and rate maximization to obtain a user terminal transmission beam forming matrix; constructing an optimization problem of user terminal and rate maximization to obtain a covariance matrix of a dedicated radar perception signal transmitted by the user terminal; constructing an optimization problem of user terminal radar signal and clutter, interference and noise ratio maximization to obtain a radar reception beam forming matrix of the user terminal; and constructing an optimization problem of user terminal cluster and rate maximization to obtain a base station reception beam forming matrix. The application can meet the requirements of communication and radar perception in future networks.

Description

TECHNICAL FIELD

[0001] The application belongs to the technical field of dual-function radar communication, and particularly relates to a NOMA-assisted multi-ISAC user terminal joint transmission-reception beamforming method. BACKGROUND

[0002] In future networks, wireless technology is considered as a key driving factor for a series of emerging applications such as unmanned aerial vehicles, autonomous driving, smart homes, virtual and augmented reality, and smart cities, leading to the trend of the fusion of communication, sensing, control, and other functions. Among them, people envisage that future wireless networks should be able to simultaneously perform sensing and communication. In view of this trend, integrated sensing and communication (ISAC) is proposed and widely concerned by academia and industry. The goal of ISAC is to integrate radar sensing and wireless communication together, share the same spectrum and infrastructure, improve spectrum and energy efficiency, reduce cost, and achieve mutual auxiliary functions such as communication-assisted sensing and sensing-assisted communication.

[0003] Spectrum sharing of radar and communication schemes is mainly based on the existence of partial overlap between the spectrum of wireless communication and radar sensing, and the commonly used spectrum sharing method is interference suppression technology to ensure that the mutual interference between radar and communication does not affect their normal work. However, these radar and communication coexistence methods require information collection between the two systems and a centralized controller, which is often difficult to implement in practice. Compared with existing solutions, the concept of ISAC is to use shared hardware and spectrum to simultaneously perform wireless communication and radar sensing, i.e., a single device can realize communication and sensing functions, and can reduce the size, weight, and cost of the device. Therefore, ISAC-enabled user terminals (UTs) can be suitable for various scenarios such as unmanned aerial vehicles, robots, cars, etc.

[0004] In recent years, ISAC technology has been a focus of attention. However, most of the existing solutions do not consider the influence of spatially correlated channels and system overload states on the performance of ISAC systems. In traditional multi-antenna technology, when the channel correlation is high or the system is overloaded, the communication users will be severely interfered. Therefore, this will also affect the communication requirements in the ISAC system, and thus affect the integration of sensing functions into the communication system. As an effective method, non-orthogonal multiple access (NOMA) technology can multiplex communication users in the power domain, and reduce inter-user interference through successive interference cancellation (SIC). Compared with traditional multiple access technologies, NOMA can serve more users, achieve higher spectrum efficiency, and provide additional spatial degrees of freedom, which prompts us to study an ISAC sensing interference cancellation scheme based on NOMA.

[0005] To explore better antenna implementation schemes, researchers have discussed separate radar and communication antenna deployment schemes and shared antenna deployment. The results show that the shared antenna deployment scheme is superior to the separate deployment scheme because it can achieve better beam pattern quality and link SINR trade-off. At the same time, the waveform design of the ISAC-enabled MIMO transmitter considers separate precoding design and optimizes communication performance under the constraint of radar transmit covariance. In addition, both MIMO radar and multi-user MIMO communication consider joint transmitter beamforming design and make radar-centric or communication-centric optimization to achieve the boundary of the performance region. Although ISAC technology has been widely discussed, existing research usually only considers single ISAC-enabled device scenarios such as base stations (BS), while more general multi-antenna user terminal communication and radar sensing scenarios have not been fully studied. Therefore, we study a NOMA-assisted multi-ISAC user terminal communication and sensing system, in which multi-antenna UTs communicate with the BS and perform radar sensing on the shared spectrum simultaneously, and for the NOMA technology, the receiver uses SIC to mitigate part or all of the co-channel interference. This will help better apply ISAC technology and improve the performance and efficiency of communication and radar sensing.

[0006] In view of this, it is necessary to provide a NOMA-assisted multi-ISAC user terminal joint transmit-receive beamforming method to solve the above problems. SUMMARY

[0007] The purpose of the present application is to provide a NOMA-assisted multi-ISAC user terminal joint transmit-receive beamforming method. This method uses NOMA technology and large-scale multiple-input multiple-output arrays and dual-function radar communication technology, and uses successive interference cancellation technology to reduce interference between user terminals, simultaneously performs radar sensing and communication functions on the same spectrum, and meets the needs of communication and radar sensing in future networks.

[0008] A NOMA-assisted multi-ISAC user terminal joint transmit-receive beamforming method, comprising the following steps:

[0009] A NOMA communication and sensing fusion architecture supporting multi-ISAC user terminals is constructed, wherein the fusion architecture includes multi-user terminals, a base station and a detection target, wherein each user terminal in the multi-user terminals has radar sensing function and communication function, and the radar sensing function and the communication function share the spectrum and share the hardware device; the base station acquires the transmit signal sent by the user terminal, wherein the transmit signal is a communication signal and a dedicated radar sensing signal, both of which are used for radar sensing;

[0010] A user terminal transmission signal model is constructed, a wireless transmission and reception signal model between a user terminal and a base station based on NOMA technology is constructed, a user terminal radar perception reception beamforming model is constructed, and a user terminal target echo signal interference model by other user terminals is constructed;

[0011] An evaluation index of a multi-user terminal grouping using NOMA technology is determined, and a multi-user terminal grouping algorithm process is determined according to the evaluation index;

[0012] An optimization problem of maximizing a user terminal rate is constructed, and a user terminal transmission beamforming matrix is obtained by solving the optimization problem;

[0013] An optimization problem of maximizing a user terminal rate is constructed, and a user terminal dedicated radar perception signal covariance matrix is obtained by solving the optimization problem;

[0014] An optimization problem of maximizing a ratio of a user terminal radar signal to clutter, interference and noise is constructed, and a user terminal radar reception beamforming matrix is obtained by solving the optimization problem;

[0015] An optimization problem of maximizing a base station rate is constructed, and a base station reception beamforming matrix is obtained by solving the optimization problem;

[0016] It is determined whether the obtained beamforming matrix satisfies a convergence condition, and if not, the optimization problem is iteratively solved until convergence.

[0017] Further, the user terminals (UTs) can be divided into K clusters, and can be represented as a set The base station has M antennas, and each UT has N antennas. The i-th user terminal in the k-th cluster can be represented as UT(k, i). The UTs in the k-th cluster can be represented as a set

[0018] The user terminal transmission signal model is specifically represented by the following formula:

[0019] X k,i =W k,i s k,i +D k,i (2)

[0020] wherein, is a precoding matrix of a communication symbol of the i-th user terminal in the k-th cluster, is d parallel communication symbols to be sent by the i-th user terminal in the k-th cluster to the base station, wherein s k,i [n] satisfies is a dedicated radar perception signal sent by the i-th user terminal in the k-th cluster, and is subject to a distribution wherein R k,i is a dedicated radar perception signal Ck,i a semi-positive definite covariance matrix of the radar sensing signal C

[0021] Further, the wireless transmission and reception signal model between the user terminal and the base station is given by

[0022]

[0023] wherein,

[0024] denotes the base station receive beamforming matrix of the kth cluster, denotes the channel matrix of the ith user terminal to the base station of the kth cluster, denotes the precoding matrix of the ith user terminal communication symbol of the kth cluster, denotes the d parallel communication symbols of the ith user terminal of the kth cluster to be transmitted to the base station, wherein s k,i [n] satisfies denotes the dedicated radar sensing signal transmitted by the ith user terminal of the kth cluster, which is subject to a distribution wherein R k,i is a semi-positive definite covariance matrix of the dedicated radar sensing signal C k,i

[0025] The ith user terminal of the kth cluster can be denoted as UT(k,i), and the data rate expression between UT(k,i) and the base station is given by

[0026]

[0027] The user terminal radar sensing reception signal model is given by

[0028]

[0029] wherein, denotes the reflection coefficient between UT(k,i) and its radar target, denotes the radar receive beamforming matrix of UT(k,i), and are the transmit and receive array steering vectors of UT(k,i), respectively, n k denotes the sum of the propagation delays to and from the target of UT(k,i), denotes the interference channel from UT(k,i) to UT(j,c), denotes the clutter signal experienced by UT(k,i), whose covariance matrix is R c,(k,i) , z k,i [n] denotes an AWGN vector, which is subject to​

[0030] The user terminal is interfered by other user terminal target echo signal model, the specific formula is:

[0031]

[0032] Wherein, β (j,c),(k,i) Reflectance and path loss from UT(j, c) to its radar Target(j, c), and UT(k, i), And UT(j, c) to its radar Target(j, c) and the receiving array steering vector from radar Target(j, c) to UT(k, i), Target(j, c) represents the radar detection target of the jth UT of the cth cluster.

[0033] Further, the evaluation index of the multi-user terminal group using NOMA technology is determined, including the following steps:

[0034] The evaluation index of the user terminal group based on NOMA technology is determined, including channel correlation and channel gain difference;

[0035] Wherein, the specific formula of the channel correlation is:

[0036]

[0037] Wherein, The communication channel from the mth user terminal to the base station;

[0038] The specific formula of the channel gain difference is:

[0039]

[0040] The evaluation index of the channel correlation and the channel gain difference is comprehensively considered, and the specific calculation formula is:

[0041] c(m, n) = {Corr(m, n) + d(m, n) | Corr(m, n) >= p, d(m, n) >= zeta} (16)

[0042] Wherein, c(m, n) represents the utility expression of the evaluation index of the channel correlation and the channel gain difference.

[0043] Further, the optimization problem of maximizing the user terminal and rate is specifically:

[0044]

[0045] Wherein, the set is defined as Constraint C1 represents the minimum SCINR requirement for UT(k,i), and constraint C2 represents the transmit power of UT(k,i) not exceeding P. max Constraint C3 represents the modulo-1 constraint on the UT(k,i) radar receiving beamforming matrix, and constraint C4 represents the modulo-1 constraint on the base station receiving beamforming matrix. In constraint C1, the ratio of the user terminal radar signal to clutter, interference, and noise is calculated using the following formula:

[0046]

[0047] in, This represents the ratio function of the user terminal radar signal to clutter, interference, and noise.

[0048] Furthermore, solving the optimization problem to obtain the user terminal transmit beamforming matrix specifically includes the following steps:

[0049] The Lagrange dual transformation method is used to transform the rate function R. k,i and rate It can be represented as:

[0050]

[0051] in, Represents the set of auxiliary variables. This indicates that all channels of the user terminal are subject to interference and noise.

[0052] Given the precoding matrix and the base station receive beamforming matrix, the derivation is... Optimal γ k,i The calculation formula is:

[0053]

[0054] Use fractional transformation to transform the sum-rate function, and then transform the sum-rate function. Recalculated as follows:

[0055]

[0056] in, Represents a set of auxiliary variables;

[0057] Given the precoding matrix and the auxiliary variable γ, the derivation is... Optimal y k,i The calculation formula is:

[0058]

[0059] N k,i Substitute and rate function The calculation formula is:

[0060]

[0061] Among them, ||·|| 2 The function is convex, in order to make the sum and rate function For a concave function, the first term is approximated using the differential convex approximation method. definition So g k,i (W k,i Around the feasible solution point in the nth iteration The first-order Taylor expansion can be expressed as:

[0062]

[0063] in, It's about W k,i Affine;

[0064] Will Substitute and rate function The calculation formula is

[0065]

[0066] Function Convert to transmission precoding matrix The concave function, constraint C1, can be expressed as:

[0067]

[0068] in, Represents the covariance matrix of all transmitted signals. R represents the covariance matrix of the transmitted communication signal. k,i This is represented as the covariance matrix of the transmitted signal sensed by the dedicated radar. This represents the covariance matrix of the signal-correlated clutter in UT(k,i). The covariance matrix of UT(k,i) is represented by the interference from radar echo signals from other users.

[0069] The constraint C1 is solved using the differential convex approximation method, defined as follows: So Around the feasible solution point in the nth iteration The first-order Taylor expansion can be expressed as:

[0070]

[0071] in, It's about W k,i The affine curve; constraint C1 is further expressed as:

[0072]

[0073] The optimization problem of maximizing sum rate is converted into a convex optimization problem, and the calculation formula is:

[0074]

[0075] An iterative optimization method is used to solve the optimization problem to obtain the user terminal transmit beamforming matrix.

[0076] Further, the optimization problem is solved to obtain the covariance matrix of the user terminal transmitting dedicated radar sensing signals, specifically comprising the following steps:

[0077] The Lagrange dual transformation method and fractional transformation are used to transform the sum rate function, and the sum rate formula is recalculated as:

[0078]

[0079] Wherein, ||·|| F 2 The function, the Tr(·) function is a convex function, and the sum rate function Also a concave function about ;

[0080] The function is converted into a concave function about the transmit precoding matrix , and the constraint C1 can be represented as:

[0081]

[0082] Wherein,

[0083] R represents the covariance matrix of all transmit signals, R represents the covariance matrix of the transmit communication signal, R k,i R represents the covariance matrix of the dedicated radar sensing transmit signal, R represents the covariance matrix of the signal related clutter of UT(k, i), R represents the covariance matrix of the UT(k, i) interfered by other user radar echoes;

[0084] The differential convex approximation method is used to solve the constraint C1, and the definition Then The first-order Taylor expansion around the feasible solution point at the n-th iteration can be expressed as:

[0085]

[0086] Wherein, is about R k,i The constraint C1 is further expressed as:

[0087]

[0088] The optimization problem of maximizing the sum rate of the user terminals is converted into a convex optimization problem, and the calculation formula is:

[0089]

[0090] An iterative optimization method is used to solve the optimization problem to obtain the covariance matrix of the radar-specific signal transmitted by the user terminal.

[0091] Further, an optimization problem of maximizing the ratio of the radar signal of the user terminal to the clutter, interference and noise is constructed, and the optimization problem is solved to obtain the radar receive beamforming matrix of the user terminal, specifically including the following steps:

[0092] The optimization problem of maximizing the ratio of the radar signal of the user terminal to the clutter, interference and noise is constructed, and the optimization problem is decomposed into a sub-optimization problem, and the specific formula is:

[0093]

[0094] Wherein, J k,i represents the radar signal clutter and interference and noise of UT(k, i), and the specific formula is:

[0095]

[0096] A generalized Rayleigh entropy method is used to obtain a closed-form solution of the radar receive beamforming matrix of the user terminal, and the specific formula is:

[0097]

[0098] Wherein, eig(·) represents the generalized eigenvalue corresponding to the maximum generalized eigenvalue;

[0099] The closed-form solution of the radar receive beamforming matrix of the user terminal is expressed as a normalized closed-form solution, and the specific formula is:

[0100]

[0101] Further, an optimization problem of maximizing the sum rate of the user terminal cluster is constructed, and the optimization problem is solved to obtain the base station receive beamforming matrix, specifically including the following steps:

[0102] The optimization problem of maximizing the sum rate of the user terminal cluster is constructed, and the specific formula of the sum rate of each user terminal cluster is:

[0103] ​

[0104] The sum-rate of the user terminal cluster is converted using the Lagrangian dual transformation and fractional transformation method, and the specific formula is:

[0105]

[0106] Let The objective function is equivalently represented as:

[0107]

[0108] Wherein, the Tr(·) function is a convex function, in order to make the sum-rate function A concave function, the first item is approximated using the differential convex approximation method Then h(P k ) is the first-order Taylor expansion around the feasible solution point At the n-th iteration, which can be expressed as:

[0109]

[0110] Wherein, is an affine about P k ;

[0111] Substitute into the sum-rate function The calculation formula is

[0112]

[0113] For γ, Each set of is concave, when the precoding matrix and auxiliary variable are given, the problem is converted into:

[0114]

[0115] The sequential rank-one constraint relaxation method is used to handle the rank-one constraint, and the rank-one constraint is converted into:

[0116]

[0117] Wherein, represents the solution obtained at the n-th iteration, represents the eigenvector corresponding to the maximum eigenvalue , and ε (n) ∈[0,1] represents the relaxation coefficient limiting the value of Tr(P k ), in the iteration process, gradually increase the value of ε (n) , until ε (n)= 1, and the specific formula of the relaxation coefficient at the n+1th iteration is:

[0118]

[0119] wherein, denotes the maximum eigenvalue of the matrix , and (n+1) denotes the update step of the relaxation coefficient, and in the n+1th iteration, the problem is further converted into:

[0120]

[0121] The optimization problem is solved using an iterative optimization method to obtain the base station receiving beamforming matrix.

[0122] Compared with the prior art, the beneficial effects of the present application are as follows:

[0123] 1. The present application proposes a NOMA-assisted multi-ISAC user terminal communication and sensing system scheme, and multiple user terminals can be grouped into clusters, which has the beneficial effect of simultaneously performing radar sensing and communication on the same spectrum, which can effectively alleviate the intra-cluster user interference.

[0124] 2. The user terminal and rate, the ratio of the user terminal signal to clutter, interference and noise, and the user cluster and rate maximization problem are constructed respectively, which has the effective effect of effectively solving the user terminal transmit beamforming matrix, the covariance matrix of the dedicated radar sensing signal, the user terminal receive beamforming vector and the base station end beamforming vector, and the transmit-receive beamforming matrix is solved to meet the requirements of radar sensing and communication transmission.

[0125] 3. The user terminal is interfered by other user terminal target echo signal interference model, which has the beneficial effect of distinguishing from the existing user terminal radar sensing receive beamforming model, considering the interference of other user terminal target echo signal on the current user terminal receive radar signal, and the model construction is more comprehensive and specific. BRIEF DESCRIPTION OF DRAWINGS

[0126] Other features, objects and advantages of the present application will become more apparent from the following detailed description of non-limiting embodiments made with reference to the accompanying drawings:

[0127] Figure 1 The flowchart of the NOMA-assisted multi-ISAC user terminal transmit-receive beamforming method in the embodiment is shown in the figure;

[0128] Figure 2 The schematic diagram of the multi-ISAC user terminal communication and sensing system architecture in the embodiment is shown in the figure;

[0129] Figure 3This is a schematic diagram of the interference model of a user terminal being affected by the echo signal of another user terminal, as proposed in the embodiment. Detailed Implementation

[0130] To make the objectives, technical solutions, and advantages of this invention clearer, the invention will be described in detail below with reference to the accompanying drawings and specific embodiments.

[0131] The embodiments of the present invention will be further described in detail below with reference to the accompanying drawings:

[0132] like Figure 1 As shown, this embodiment provides a NOMA-assisted multi-ISAC user terminal transmit-receive beamforming method, specifically including:

[0133] like Figure 2 As shown, a user terminal communication and sensing fusion architecture supporting multiple ISACs is constructed. Multi-antenna UTs are clustered using NOMA technology, communicate with multi-antenna BSs using shared spectrum, and perform radar sensing using transmitted signals (communication signals) and dedicated radar sensing signals. Then, the achievable data rate and the radar signal-to-clutter, interference, and noise ratio (SCINR) are used as performance indicators for UT-BS communication and UT radar sensing, respectively.

[0134] The following models are constructed: user terminal transmission signal model, user terminal and base station wireless transmission and reception beamforming model based on NOMA technology, user terminal radar sensing transmission-reception beamforming model, and user terminal target echo interference model.

[0135] Specifically, assume the base station BS has M antennas, and each UT is equipped with N antennas. The signal transmitted by each UT can be represented as:

[0136] X k,i =W k,i s k,i +D k,i (1)

[0137] in, This represents the precoding matrix for the communication symbol of the i-th user terminal in the k-th cluster.

[0138] This represents the d parallel communication symbols that the i-th user terminal in the k-th cluster needs to send to the base station, where s k,i [n] satisfies This represents the dedicated radar sensing signal transmitted by the i-th user terminal in the k-th cluster, which follows a distribution. Where R k,i It is a dedicated radar sensing signal D k,i The positive semidefinite covariance matrix;

[0139] At time slot n, the BS receive beamforming for all UTs from the kth cluster can be represented as:

[0140]

[0141] where, Hkdenotes the BS receive beamforming matrix for the kth cluster, Hk,i denotes the channel matrix from the ith user terminal to the BS for the kth cluster, Vk,i denotes the precoding matrix for the ith user terminal communication symbol for the kth cluster, sk,i denotes the d parallel communication symbols to be transmitted by the ith user terminal to the BS for the kth cluster, where, k,i [n] satisfies

[0142] Ck,i,j denotes the dedicated radar sensing signal transmitted by the ith user terminal for the jth cluster, which is subject to a distribution where Rk,i,j j,i is the semi-positive definite covariance matrix of the dedicated radar sensing signal Ck,i,j j,i , z c [n] denotes a Gaussian additive white noise, which is subject to a distribution

[0143] Based on the aforementioned received signal model, NOMA mitigates inter-user interference by exploiting SIC, so that a UT (k, i) within the same cluster will remove all interference from strong channels (l < i) and decode its own signal, then the achievable data rate between the UT (k, i) and the BS is given by:

[0144]

[0145] To facilitate analysis and obtain the performance upper bound, we assume that the BS has perfect channel state information of all UTs. In addition, the transmit covariance matrix of the UT (k, i) is given by:

[0146]

[0147] where, Rk,i is the covariance matrix of the transmitted communication signal, Rk,i,j k,i is the covariance matrix of the transmitted dedicated radar sensing signal.

[0148] Then, the transmit power constraint for each UT is represented as:

[0149]

[0150] where Pmax max is the maximum transmit power limited by the system for each UT.

[0151] When multiple ISAC-enabled UTs perform sensing and communication, each UT receives not only the echoes from its targets, but also interference from other UT communication signals and other target echo signals. If a single point-like target is located in the far field of UT(k, i) in direction θ k,i The received radar echo signal of UT(k, i) is represented as:

[0152]

[0153] where, denotes the reflection coefficient between UT(k, i) and its radar target, denotes the radar receive beamforming matrix of UT(k, i), and are the transmit and receive array steering vectors of UT(k, i), respectively, n k denotes the sum of the propagation delays to and from the target of UT(k, i), denotes the interference channel from UT(k, i) to UT(j, c), denotes the clutter signal experienced by UT(k, i), whose covariance matrix is R c,(k,i) , z k,i [n] denotes the AWGN vector, which is subject to

[0154] Since ISAC-enabled UTs share antenna arrays, we have a R (θ k,i ) = a T (θ k,i ) = a(θ k,i ), a(θ k,i ) is represented as:

[0155]

[0156] where d and λ denote the antenna spacing and signal wavelength of UT(k, i), respectively. Without loss of generality, let d = λ2.

[0157] The clutter related to the signal is modeled as:

[0158]

[0159] where C k,i is the number of clutters, is the direction angle of the lth clutter, with a path loss factor

[0160] Assume that each radar target and clutter reflectivity coefficient is an independent complex Gaussian variable, Therefore, the covariance of the signal-dependent clutter of UT(k, i) is expressed as:

[0161]

[0162] As Figure 3 shown, in the multi-UT radar sensing scenario, a UT not only receives echoes from its targets, but also suffers from interference from other UT communication signals. In addition to this, radar echo signals from a UT's corresponding targets can reach another UT radar receiver and cause interference. Therefore, consider establishing a user terminal interference model from other UT target echo signals. Assume that the target echo signals of UT-1 reach UT-2 and also act as interference signals to the radar receiver of UT-2. Therefore, inter-UT radar echo signal interference can be modeled as a bistatic radar system. Consider a bistatic radar system with a radar receiver (Rx) and a radar transmitter (Tx), the signal transmitted from Tx to Rx is reflected by the target in the reflection link. Therefore, UT-1 can be regarded as the radar Tx and UT-2 as the Rx.

[0163] Based on this, the jth detected target of the cth cluster, denoted as Target(j, c), the user terminal interference model from other UT target echo signals is:

[0164]

[0165] where β j,c represents the reflection coefficient and path fading from UT(j, c) to its Target(j, c) and to UT(k, i), and are the transmit and receive array steering vectors of Target(j, c), respectively, and the transmit-receive steering matrix is denoted as Therefore, the covariance of the signal-dependent clutter of UT(k, i) is expressed as:

[0166]

[0167] For radar sensing, the commonly used performance indicator is the signal-to-clutter-plus-noise ratio. It is worth noting that there is inter-UT signal interference in the system. Therefore, we use the signal-to-clutter, interference, and noise ratio (SCINR) to evaluate the performance of radar sensing, and the SCINR of UT(k, i) can be expressed as:

[0168]

[0169] Step S3, construct an optimization problem with user terminal and rate maximization, considering the minimum radar communication rate and SCINR as constraints of user terminal transmit power, which is specifically expressed as:

[0170]

[0171] Wherein, define the set Constraint C1 represents the minimum SCINR requirement of UT(k, i), constraint C2 represents that the transmit power of UT(k, i) cannot exceed P max , constraint C3 represents the modulus one limit of UT(k, i) radar receiving beamforming matrix and constraint C4 represents the modulus one limit of base station end receiving beamforming matrix, due to the coupling of beamforming matrix in the objective function and constraints, the problem is a non-convex optimization problem.

[0172] Step S4, determine the evaluation index of grouping multiple user terminals using NOMA technology; then, according to the determined evaluation index, propose a specific algorithm flow.

[0173] Specifically, first determine the evaluation index of user terminal grouping based on NOMA technology, which are channel correlation and channel gain difference respectively, the channel correlation between user terminals is expressed as:

[0174]

[0175] In the formula, is the communication channel from the mth UT to the base station.

[0176] Select channel gain difference as another evaluation index, the channel gain difference between user terminals is expressed as:

[0177]

[0178] Considering the two evaluation indexes of channel correlation and channel gain difference, define the utility expression:

[0179] c(m, n) = {Corr(m, n) + d(m, n) Corr(m, n) ≥ ρ, d(m, n) ≥ ζ} (16)

[0180] In the formula, the utility ensures that the channel correlation and channel gain difference between the same cluster UTs can meet the threshold.

[0181] Then, taking the two evaluation indexes of channel correlation and channel gain difference as the basis of UT grouping, the specific UT grouping algorithm pseudocode is shown in Table 1:

[0182] Table 1 User terminal grouping algorithm based on NOMA technology

[0183]

[0184] Step S5, using Lagrangian dual transformation and fractional transformation method to transform the achievable rate function into a concave function, and considering the transmit beamforming matrix; then, using a first-order Taylor expansion scheme to solve the minimum requirement of the ratio of the user terminal radar signal to clutter, interference and noise; finally, using an iterative optimization method to solve the optimization problem to obtain the UT end radar transmit beamforming matrix.

[0185] Specifically, first, the Lagrangian dual transformation method is used to transform the rate function R k,i , and the rate can be expressed as:

[0186]

[0187] wherein, and is a set of auxiliary variables, denotes the total signal interference plus noise of the user terminal.

[0188] When the precoding matrix and the base station end receive beamforming matrix are given, the optimal γ of k,i can be expressed as:

[0189]

[0190] The sum rate function in the formula is transformed using fractional transformation, and the sum rate function can be re-expressed as:

[0191]

[0192] wherein, is a set of auxiliary variables.

[0193] When the precoding matrix and the auxiliary variable γ are given, the optimal y of k,i can be expressed as:

[0194]

[0195] Substituting N k,i into the formula, it can be further transformed into:

[0196]

[0197] wherein, ||·|| 2 The function is a convex function, in order to make the sum rate function a concave function, the first item is approximated using differential convex approximation method. definition Then g k,i (W k,i ) the first-order Taylor expansion around the feasible solution point at the n-th iteration can be expressed as:

[0198]

[0199] where, is affine with respect to W k,i

[0200] Substitute into the rate function The formula is

[0201]

[0202] Then, the radar SCINR function is converted into a concave function with respect to the transmit precoding matrix The constraint C1 is expressed as:

[0203]

[0204] where, Since ||·||2 2 function is convex, the above formula is the differential of two convex functions. Then, the differential convex approximation method is used to solve it. For ease of analysis, define Then The first-order Taylor expansion around the feasible solution point at the n-th iteration can be expressed as:

[0205]

[0206] where, is expressed as:

[0207]

[0208] Obviously, is affine with respect to W k,i , which is further expressed as:

[0209]

[0210] According to the result, the problem is converted into the following convex optimization problem:

[0211]

[0212] The iterative optimization method is used to solve the optimization problem to obtain the user terminal transmit beamforming matrix. The specific solving algorithm is shown in Table 2:

[0213] ​Table 2 Algorithm to solve user terminal transmit beamforming

[0214]

[0215]

[0216] Step S6, using Lagrangian dual transformation and fractional transformation method to transform the achievable rate function into a concave function, and considering the covariance matrix of transmitting dedicated radar sensing signal; then, using first order Taylor expansion scheme to solve the minimum requirement of the ratio of user terminal radar signal to clutter, interference and noise; finally, using iterative optimization method to solve the optimization problem to obtain the covariance matrix of UT end transmitting dedicated radar sensing signal.

[0217] Specifically, first, the Lagrangian dual transformation method is used to transform the rate function R k,i , and the rate can be expressed as:

[0218]

[0219] Next, using the Lagrangian dual transformation and fractional transformation method to transform the achievable rate function into a concave function, the rate function can be further transformed into:

[0220]

[0221] The function is transformed into a concave function about the covariance matrix of transmitting dedicated radar signal , and the constraint C1 can be expressed as:

[0222]

[0223] wherein, denotes the covariance matrix of all transmitting signals, denotes the covariance matrix of transmitting communication signals, R k,i denotes the covariance matrix of transmitting dedicated radar sensing signals, denotes the covariance matrix of signal-related clutter of UT(k, i), denotes the covariance matrix of UT(k, i) interfered by other user radar echoes;

[0224] Using differential convex approximation method to solve the constraint C1, define then The first order Taylor expansion around the feasible solution point at the n-th iteration can be expressed as:

[0225]

[0226] wherein, is an affine function of R k,i The constraint C1 is further expressed as:

[0227]

[0228] The optimization problem of maximizing the user terminal and rate is converted into a convex optimization problem, and the calculation formula is:

[0229]

[0230] An iterative optimization method is used to solve the optimization problem to obtain the user terminal transmitting dedicated radar sensing signal covariance matrix, and the specific solving algorithm is shown in Table 3:

[0231] Table 3 Algorithm for solving the covariance matrix of the user terminal radar dedicated signal

[0232]

[0233] Step S8, an optimization problem of maximizing the ratio of user terminal radar signal to clutter, interference and noise is constructed, and a generalized Rayleigh entropy method is used to obtain the user terminal radar receiving beamforming matrix.

[0234] Specifically, an optimization problem of maximizing the ratio of user terminal radar signal to clutter, interference and noise is constructed, and the optimization problem is decomposed into L sub-optimization problems:

[0235]

[0236] wherein, J k,i is the radar signal clutter and interference plus noise of UT(k,i), X k,i is expressed as:

[0237]

[0238] A generalized Rayleigh entropy method is used to obtain a closed-form solution of the UT(k,i) radar receiving beamforming matrix:

[0239]

[0240] wherein, eig(·) is the generalized eigen vector corresponding to the maximum generalized eigen value, therefore, it is further expressed as a normalized closed-form solution:

[0241]

[0242] Step S9, using Lagrangian dual transformation and fractional transformation method to transform the sum and rate function within the cluster into a concave function, and considering the base station end receiving beamforming matrix; then, using sequential rank-one constraint relaxation method to solve the rank-one requirement; finally, using iterative optimization method to solve the optimization problem to obtain the base station end receiving beamforming matrix.

[0243] Specifically, first, an optimization problem of maximizing the sum rate of each user terminal cluster is constructed, and the sum rate of each user terminal cluster is is expressed as:

[0244]

[0245] Then, using Lagrangian dual transformation and fractional transformation method to transform the achievable rate function into a concave function, the rate function can be further transformed into:

[0246]

[0247] Let The objective function is equivalently expressed as:

[0248]

[0249] Wherein, the Tr(·) function is a convex function, in order to make the sum rate function is a concave function, using differential convex approximation method to approximate the first item is defined as: Then h(P k ) is the first-order Taylor expansion around the feasible solution point at the n th iteration, which can be expressed as:

[0250]

[0251] Wherein, is affine with respect to P k ;

[0252] Substituting into the sum rate function , the calculation formula is

[0253]

[0254] For γ, and , each set is concave, and when the precoding matrix and auxiliary variable are given, the problem can be transformed into:

[0255]

[0256] Wherein, due to the existence of rank-one constraint, the problem is still a non-convex optimization problem.

[0257] Then, the rank-one constraint is processed using the sequential rank-one constraint relaxation method, and thus the rank-one constraint is transformed into:

[0258]

[0259] wherein, is the solution obtained in the nth iteration, represents the maximum eigenvalue corresponding eigenvector, and ε (n) ∈[0,1] is a relaxation coefficient for limiting the value of Tr(P k ), and in the iteration process, the value of ε (n) is gradually increased until ε (n) =1 to obtain a feasible solution meeting the rank-one requirement, and then the relaxation coefficient in the (n+1)th iteration is represented as:

[0260]

[0261] wherein, is the maximum eigenvalue of the matrix , and δ (n+1) represents the update step of the relaxation coefficient. Thus, in the (n+1)th iteration, the problem (23) can be further transformed into:

[0262]

[0263] The iterative optimization method is used to solve the optimization problem to obtain the base station receive beamforming vector, and a specific algorithm for solving the base station beamforming vector is shown in Table 4:

[0264] Table 4 Algorithm for solving the base station beamforming vector

[0265]

[0266]

[0267] In summary, the present application proposes a NOMA-assisted multi- ISAC user terminal communication and sensing system scheme, multiple user terminals can be grouped into clusters, and radar sensing and communication can be performed at the same time in the same frequency spectrum, and interference between user terminals can be effectively reduced, and by solving the transmit-receive beamforming matrix to meet the requirements of radar sensing and communication transmission.

[0268] The above embodiments are only used to illustrate the technical solutions of the present application rather than limiting the present application, and although the present application has been described in detail with reference to the preferred embodiments, it should be understood by those skilled in the art that the technical solutions of the present application can be modified or replaced equivalently without departing from the spirit and scope of the technical solutions of the present application.

Claims

1. A NOMA-assisted joint transmit-receive beamforming method for multiple ISAC user terminals, characterized in that, Includes the following steps: A NOMA communication and sensing fusion architecture supporting multiple ISAC user terminals is constructed. The fusion architecture includes multiple user terminals, a base station, and a detection target. Each user terminal in the multiple user terminals has radar sensing and communication functions, which share spectrum and hardware devices. The base station acquires the transmitted signals sent by the user terminals, which are communication signals and dedicated radar sensing signals, both of which are used for radar sensing. Construct a user terminal transmission signal model, a wireless transmission and reception signal model between the user terminal and the base station based on NOMA technology, a user terminal radar sensing reception beamforming model, and a user terminal interference model caused by echo signals from other user terminal targets. Determine the evaluation metrics for multi-user terminal grouping using NOMA technology, and determine the multi-user terminal grouping algorithm flow based on the evaluation metrics; Construct an optimization problem to maximize the user terminal and the rate, and solve the optimization problem to obtain the user terminal transmit beamforming matrix; Construct an optimization problem that maximizes the user terminal and the rate, and solve the optimization problem to obtain the covariance matrix of the user terminal's dedicated radar sensing signal; An optimization problem is constructed to maximize the ratio of the user terminal radar signal to clutter, interference and noise. The radar receiving beamforming matrix of the user terminal is obtained by solving the optimization problem. Construct an optimization problem that maximizes the sum and rate within the user terminal cluster, and solve the optimization problem to obtain the base station receiving beamforming matrix; Check whether the calculated beamforming matrix satisfies the convergence condition. If not, iterate through the optimization problem until convergence.

2. The method according to claim 1, characterized in that, User terminal, or UT, is divided into... There are clusters, and they are represented as sets. Base stations have Each UT has one antenna. The root antenna, the i-th user terminal of the k-th cluster is represented as UT The UT in the k-th cluster is represented as a set. , The specific formula for the transmitted signal model of the user terminal is as follows: (1) in, This represents the precoding matrix for the communication symbol of the i-th user terminal in the k-th cluster. This represents the d parallel communication symbols that the i-th user terminal in the k-th cluster needs to send to the base station, where... satisfy , This represents the dedicated radar sensing signal transmitted by the i-th user terminal in the k-th cluster, which follows a distribution. ,in It is a dedicated radar sensing signal The positive semidefinite covariance matrix.

3. The method according to claim 2, characterized in that, The wireless transmission and reception signal model between the user terminal and the base station, specifically calculated using the following formula: (2) in, This represents the base station receive beamforming matrix for the k-th cluster. This represents the channel matrix from the i-th user terminal in the k-th cluster to the base station; The i-th user terminal in the k-th cluster is denoted as UT(k,i), and the data rate expression between UT(k,i) and the base station is as follows: (3) The specific calculation formula for the user terminal radar sensing and receiving signal model is as follows: (6) in, This represents the reflection coefficient between UT(k,i) and its radar target. Let UT(k,i) represent the radar receiver beamforming matrix. , and These are the transmit and receive array steering vectors of UT(k,i), respectively. This represents the sum of propagation delays to and from the target UT(k,i). This represents the interference channel from UT(k,i) to UT(j,c). The clutter signal experienced by UT(k,i) has the following covariance matrix: , Represents an AWGN vector, which follows the... ; The interference model of the user terminal being affected by the echo signal of other user terminals is specifically formulated as follows: (10) in, This represents the reflection coefficient and path loss from UT(j,c) to its radar target(j,c), and then to UT(k,i). and These are the transmission vector from UT (j,c) to its radar Target (j,c) and the reception vector from radar Target (j,c) to UT (k,i), respectively. Target (j,c) represents the radar detection target of the j-th UT in the c-th cluster.

4. The method according to claim 3, characterized in that, Determine the evaluation metrics for multi-user terminal groups using NOMA technology, including the following steps: Determine the evaluation metrics for user terminal groups based on NOMA technology, including channel correlation and channel gain difference; The specific formula for the channel correlation is as follows: (14) in, This represents the communication channel from the m-th user terminal to the base station; The specific formula for the channel gain difference is: (15) Taking into account both channel correlation and channel gain difference evaluation indicators, the specific calculation formula is as follows: (16) in, This represents a utility expression that comprehensively considers both channel correlation and channel gain difference evaluation indicators.

5. The method according to claim 4, characterized in that, The optimization problem of maximizing user terminals and speed is specifically formulated as follows: (13) Among them, the set is defined. , , , ,constraint Represents the minimum SCINR requirement for UT(k,i), and the constraint. This means that the transmit power of UT(k,i) cannot exceed [a certain value]. ,constraint This represents the modulus-1 constraint on the UT(k,i) radar receiver beamforming matrix, constraining... This represents the modulo-1 constraint on the beamforming matrix received by the base station, wherein the constraint In the context of radar signals from user terminals, the ratio of clutter, interference, and noise is calculated using the following formula: （12） in, This represents the ratio function of the user terminal radar signal to clutter, interference, and noise.

6. The method according to claim 5, characterized in that, Solving the optimization problem to obtain the user terminal transmit beamforming matrix includes the following steps: The rate function is transformed using the Lagrange dual transformation method. and rate Represented as: (17) in, , Represents the set of auxiliary variables. This indicates that all channels of the user terminal are subject to interference and noise. Given the precoding matrix and the base station receive beamforming matrix, the derivation is... optimal The calculation formula is: (18) Use fractional transformation to transform the sum-rate function, and then transform the sum-rate function. Recalculated as follows: (19) in, Represents a set of auxiliary variables; When the precoding matrix and auxiliary variables Given the time, derive optimal The calculation formula is: (20) Will Substitute and rate function The calculation formula is: (21) in, The function is convex, in order to make the sum and rate function For a concave function, the first term is approximated using the differential convex approximation method. ,definition ,So Around the feasible solution point in the nth iteration The first-order Taylor expansion can be expressed as: （22） in, , It is about Affine; Will Substitute and rate function The calculation formula is: （23） Function Convert to transmission precoding matrix concave function, constraint Represented as: (24) in, , , Represents the covariance matrix of all transmitted signals. The covariance matrix represents the transmitted communication signal. This is represented as the covariance matrix of the transmitted signal sensed by the dedicated radar. This represents the covariance matrix of the signal-correlated clutter of UT(k,i). Let represent the covariance matrix of UT(k,i) affected by interference from radar echo signals from other users; The constraints are solved using the differential convex approximation method. ,definition ,So Around the feasible solution point in the nth iteration The first-order Taylor expansion can be expressed as: (25) in, , It is about Affine; constraint Further expressed as: (27) The optimization problem of maximizing user terminals and speed is transformed into a convex optimization problem, and the calculation formula is as follows: (28) The user terminal transmit beamforming matrix is ​​obtained by solving the optimization problem using an iterative optimization method.

7. The method according to claim 6, characterized in that, Solving the optimization problem to obtain the covariance matrix of the user terminal's transmitted radar sensing signal involves the following steps: The sum-rate function is transformed using the Lagrange dual transformation and fractional transformation, and the sum-rate formula is recalculated as follows: (30) in, function, The function is a convex function, and the rate function is... Also about The concave function; Function Convert to transmission precoding matrix concave function, constraint Represented as: (31) in, , , Represents the covariance matrix of all transmitted signals. Represented as the covariance matrix of the transmitted communication signal, This is represented as the covariance matrix of the transmitted signal sensed by the dedicated radar. This represents the covariance matrix of the signal-correlated clutter of UT(k,i). Let represent the covariance matrix of UT(k,i) affected by radar echo interference from other users; The constraints are solved using the differential convex approximation method. ,definition ,So Around the feasible solution point in the nth iteration The first-order Taylor expansion can be expressed as: (32) in, , It is about Affine; constraint Further expressed as: (33) The optimization problem of maximizing user terminals and speed is transformed into a convex optimization problem, and the calculation formula is as follows: (34) The covariance matrix of the radar-specific signal transmitted by the user terminal is obtained by solving the optimization problem using an iterative optimization method.

8. The method according to claim 7, characterized in that, An optimization problem is constructed to maximize the ratio of the user terminal's radar signal to clutter, interference, and noise. Solving the optimization problem yields the radar receiving beamforming matrix of the user terminal. The specific steps include: An optimization problem is constructed to maximize the ratio of the user terminal radar signal to clutter, interference, and noise. This optimization problem is decomposed into sub-optimization problems, with the specific formula as follows: (35) in, The radar signal-clutter and interference-plus-noise ratio of UT(k,i) is represented by the following formula: (36) The closed-form solution of the radar receiving beamforming matrix of the user terminal is obtained using the generalized Rayleigh entropy method. The specific formula is as follows: (37) in, This represents the generalized eigenvector corresponding to the largest generalized eigenvalue; The closed-form solution of the radar receiving beamforming matrix of the user terminal is expressed as a normalized closed-form solution, and the specific formula is as follows: (38)。 9. The method according to claim 8, characterized in that, An optimization problem is constructed to maximize the sum and rate within the user terminal cluster. Solving the optimization problem yields the base station receiving beamforming matrix, specifically including the following steps: Construct an optimization problem to maximize the sum rate within each user terminal cluster, where the sum rate of each user terminal cluster is... The specific formula is: (39) The sum rate of the user terminal cluster is transformed using Lagrange dual transformation and fractional transformation methods. The specific formula is as follows: (40) set up , ,Will Equivalently represented as: (41) in, The function is convex, in order to make the sum and rate function For a concave function, the first term is approximated using the differential convex approximation method. ,definition ,So Around the feasible solution point in the nth iteration The first-order Taylor expansion can be expressed as: (42) in, , It is about Affine; Will Substitute and rate function The calculation formula is: (43) for , and Each set is concave, and given the precoding matrix and auxiliary variables, the problem is transformed into: (44) Using the sequential rank-one constraint relaxation method to handle rank-one constraints, the rank-one constraint is transformed into: (45) in, This represents the solution obtained in the nth iteration. Represents the largest eigenvalue The corresponding feature vector, Indicates restriction The relaxation coefficient of the value gradually increases during the iteration process. Value, until The specific formula for the relaxation coefficient in the (n+1)th iteration is: (46) in, Representation matrix The largest eigenvalue, The update step size for the relaxation coefficients is represented. In the (n+1)th iteration, the problem is further transformed into: (47) The base station receive beamforming matrix is ​​obtained by solving the optimization problem using an iterative optimization method.

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