NOMA-assisted multi-ISAC user terminal joint transmitting-receiving beam forming method

Abstract

The invention discloses an NOMA-assisted multi-ISAC user terminal joint transmitting-receiving beam forming method. The method comprises the following steps: constructing a communication and perception fusion architecture supporting multiple 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 flow according to the evaluation index; constructing a user terminal and rate maximization optimization problem, and obtaining a user terminal emission beam forming matrix; constructing a user terminal and rate maximization optimization problem, and obtaining a covariance matrix of a special radar sensing signal emitted by the user terminal; constructing an optimization problem for maximizing the ratio of the radar signal of the user terminal to clutter, interference and noise, and obtaining a radar receiving beam forming matrix of the user terminal; and constructing an optimization problem of sum rate maximization in a user terminal cluster, and obtaining a base station receiving beam forming matrix. The method can meet the requirements of communication and radar perception in a future network.

Description

Technical Field

[0001] The present invention belongs to the technical field of dual-function radar communication, and in particular relates to a NOMA-assisted multi-ISAC user terminal joint transmit-receive beamforming method. Background Art

[0002] In future networks, wireless technology is seen as a key enabler for a range of emerging applications such as drones, autonomous driving, smart homes, virtual and augmented reality, and smart cities, leading the trend of integrating multiple functions such as communication, perception, and control. Among them, people envision that future wireless networks should be able to sense and communicate at the same time. In response to this trend, Integrated Sensing and Communication (ISAC) was proposed and has received widespread attention from academia and industry. The goal of ISAC is to integrate radar perception and wireless communication, share the same spectrum and infrastructure, improve spectrum and energy efficiency, reduce costs, and achieve mutual auxiliary functions such as communication-assisted perception and perception-assisted communication.

[0003] Spectrum sharing for radar and communication schemes is mainly based on the partial overlap of spectrum between wireless communication and radar sensing, and the commonly used spectrum sharing method is interference suppression technology to ensure that mutual interference between radar and communication does not affect their normal operation. However, these radar and communication coexistence methods require information collection between the two systems and a centralized controller, which is often difficult to achieve in practice. Compared with existing schemes, the concept of ISAC is to use shared hardware and spectrum for wireless communication and radar sensing at the same time, that is, a single device can realize communication and sensing functions, and can reduce the size, weight and cost of the device. Therefore, the user terminal (UT) supporting ISAC can be applied to various scenarios, such as drones, robots, cars, etc.

[0004] In recent years, the research on ISAC technology has attracted much attention. However, most of the existing schemes do not consider the impact of spatially correlated channels and system overload conditions 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 then affect the integration of perception 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 interference between users through successive interference suppression (SIC). Compared with traditional multiple access technology, NOMA can provide services to more users, achieve higher spectrum efficiency, and provide additional spatial degrees of freedom, which motivates us to study a NOMA-based ISAC perception interference cancellation scheme.

[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-offs. Meanwhile, the waveform design of the ISAC-enabled MIMO transmitter considers separate precoding design and optimizes the communication performance under the constraint of radar transmit covariance. In addition, both MIMO radar and multi-user MIMO communication consider joint transceiver beamforming design, and formulate radar-centric or communication-centric optimization to achieve the boundary of the performance area. Although ISAC technology has been widely discussed, existing studies usually only consider the scenario of a single ISAC-enabled device, such as a base station (BS), while the more general scenario of multi-ISAC-enabled multi-antenna user terminal communication and radar sensing has not been fully studied. Therefore, we study a NOMA-assisted multi-ISAC user terminal communication and sensing system, in which ISAC-enabled multi-antenna UTs communicate with the BS simultaneously and perform radar sensing on the shared spectrum. For the NOMA technology, the receiver adopts SIC to mitigate some or all co-channel interference. This will help better apply ISAC technology and improve the performance and efficiency of communications and radar sensing.

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

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

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

[0009] Construct a NOMA communication and perception fusion architecture supporting multiple ISAC user terminals, wherein the fusion architecture includes multiple user terminals, a base station, and a detection target, wherein each of the multiple user terminals has a radar perception function and a communication function, wherein the radar perception function and the communication function share a spectrum and a common hardware device; the base station obtains a transmission signal sent by the user terminal, wherein the transmission signal is a communication signal and a dedicated radar perception signal, both of which are used for radar sensing;

[0010] Construct the user terminal transmission signal model, the wireless transmission reception signal model between the user terminal and the base station based on NOMA technology, the user terminal radar perception reception beamforming model and the user terminal interference model of the target echo signal of other user terminals;

[0011] Determine the evaluation index of multi-user terminal grouping using NOMA technology, and determine the multi-user terminal grouping algorithm process according to the evaluation index;

[0012] Construct an optimization problem of maximizing the user terminal and rate, and solve the optimization problem to obtain the user terminal transmit beamforming matrix;

[0013] Construct an optimization problem for maximizing the user terminal and rate, and solve the optimization problem to obtain the covariance matrix of the user terminal dedicated radar perception signal;

[0014] Construct an optimization problem to maximize the ratio of the user terminal radar signal to clutter, interference and noise, and solve the optimization problem to obtain the radar receiving beamforming matrix of the user terminal;

[0015] Construct an optimization problem for maximizing the sum rate within the user terminal cluster, and solve the optimization problem to obtain the base station receive beamforming matrix;

[0016] The calculated beamforming matrix satisfies the convergence condition. If not, the optimization problem is solved iteratively until convergence.

[0017] Furthermore, the user terminals (UT) 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 the set

[0018] The transmission signal model of the user terminal is specifically expressed as follows:

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

[0020] in, represents the precoding matrix of the communication symbol of the i-th user terminal of the k-th cluster, represents the d parallel communication symbols to be sent by the i-th user terminal of the k-th cluster to the base station, where s k,i [n] Satisfaction represents the dedicated radar sensing signal sent by the i-th user terminal of the k-th cluster, which follows the distribution Where R k,i It is a special radar sensing signal Ck,i The semi-positive definite covariance matrix of ;

[0021] Furthermore, the wireless transmission receiving signal model between the user terminal and the base station is specifically calculated as follows:

[0022]

[0023] in,

[0024] represents the base station receive beamforming matrix of the kth cluster, represents the channel matrix from the ith user terminal of the kth cluster to the base station, represents the precoding matrix of the communication symbol of the i-th user terminal of the k-th cluster, represents the d parallel communication symbols to be sent by the i-th user terminal of the k-th cluster to the base station, where s k,i [n] Satisfaction represents the dedicated radar sensing signal sent by the i-th user terminal of the k-th cluster, which follows the distribution Where R k,i It is a special radar sensing signal C k,i The semi-positive definite covariance matrix of ;

[0025] The i-th user terminal of the k-th cluster can be represented as UT(k,i). The data rate expression between UT(k,i) and the base station is specifically:

[0026]

[0027] The user terminal radar perception receiving signal model, the specific calculation formula is:

[0028]

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

[0030] The user terminal is interfered by the target echo signal of other user terminals. The specific formula is:

[0031]

[0032] Among them, β (j,c),(k,i) represents the reflection coefficient and path loss from UT(j,c) to its radar Target(j,c) and then to UT(k,i), and are the sending and receiving array steering vectors from UT(j,c) to its radar Target(j,c) and from radar Target(j,c) to UT(k,i), respectively. Target(j,c) represents the radar detection target of the jth UT of the cth cluster.

[0033] Further, determining the evaluation index of multi-user terminal grouping using NOMA technology includes the following steps:

[0034] Determine the evaluation indicators for user terminal grouping based on NOMA technology, including channel correlation and channel gain difference;

[0035] The specific formula of the channel correlation is:

[0036]

[0037] in, represents the communication channel from the mth user terminal to the base station;

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

[0039]

[0040] Taking into account the channel correlation and channel gain difference evaluation indicators, the specific calculation formula is:

[0041] c(m,n)={Corr(m,n)+d(m,n)|Corr(m,n)≥ρ,d(m,n)≥ζ} (16)

[0042] Among them, c(m,n) represents the utility expression that comprehensively considers the channel correlation and channel gain difference evaluation indicators.

[0043] Furthermore, the optimization problem of maximizing the user terminal and rate is specifically formulated as follows:

[0044]

[0045] Among them, the definition set Constraint C1 represents the minimum SCINR requirement of UT(k,i), and constraint C2 represents that the transmit power of UT(k,i) cannot exceed P max , constraint C3 represents the modulus-1 restriction of the UT(k,i) radar receiving beamforming matrix, constraint C4 represents the modulus-1 restriction of the base station receiving beamforming matrix, wherein in constraint C1, the ratio of the user terminal radar signal to clutter, interference and noise is calculated as:

[0046]

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

[0048] Further, solving the optimization problem to obtain a 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 expressed as:

[0050]

[0051] in, represents a collection of auxiliary variables, Indicates the total channel interference plus noise of the user terminal;

[0052] When the precoding matrix and the base station receive beamforming matrix are given, we can derive Optimal γ k,i , the calculation formula is:

[0053]

[0054] Use fractional transformation to transform the sum rate function. Recalculate to:

[0055]

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

[0057] When the precoding matrix and auxiliary variable γ are given, we can derive The optimal y k,i , the calculation formula is:

[0058]

[0059] N k,i Substituting in the sum rate function The calculation formula is:

[0060]

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

[0062]

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

[0064] Will Substituting in the sum rate function The calculation formula is

[0065]

[0066] Function Transformed into the transmit precoding matrix The concave function of , constraint C1 can be expressed as:

[0067]

[0068] in, represents the covariance matrix of all transmitted signals, represents the covariance matrix of the transmitted communication signal, R k,i Expressed as the covariance matrix of the transmitted signal perceived by the dedicated radar, represents the covariance matrix of the signal-correlated clutter of UT(k,i), Represents the covariance matrix of UT(k,i) interfered by other users’ radar echo signals;

[0069] Use differential convex approximation to solve constraint C1, define So Around the feasible solution point at the nth iteration The first-order Taylor expansion of can be expressed as:

[0070]

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

[0072]

[0073] The optimization problem of maximizing user terminals and rates is transformed 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, solving the optimization problem to obtain the covariance matrix of the dedicated radar sensing signal transmitted by the user terminal specifically includes the following steps:

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

[0078]

[0079] Among them, ||·|| 2 function, Tr(·) function is a convex function, and rate function Also about Concave function of ;

[0080] Function Transformed into the transmit precoding matrix The concave function of , constraint C1 can be expressed as:

[0081]

[0082] in,

[0083] represents the covariance matrix of all transmitted signals, Represented as the covariance matrix of the transmitted communication signal, R k,i Expressed as the covariance matrix of the transmitted signal perceived by the dedicated radar, represents the covariance matrix of the signal-correlated clutter of UT(k,i), Represents the covariance matrix of UT(k,i) interfered by other users’ radar echoes;

[0084] Use differential convex approximation to solve constraint C1, define So Around the feasible solution point at the nth iteration The first-order Taylor expansion of can be expressed as:

[0085]

[0086] in, About R k,i The constraint C1 is further expressed as:

[0087]

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

[0089]

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

[0091] Furthermore, an optimization problem of maximizing the ratio of the user terminal radar signal to clutter, interference and noise is constructed, and solving the optimization problem to obtain the radar receiving beamforming matrix of the user terminal specifically includes the following steps:

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

[0093]

[0094] Among them, J k,i It represents the radar signal clutter and interference plus noise of UT(k,i). The specific formula is:

[0095]

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

[0097]

[0098] Where, eig(·) represents the generalized eigenvector 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] Furthermore, an optimization problem of maximizing the sum rate within the user terminal cluster is constructed, and solving the optimization problem to obtain the base station receive beamforming matrix specifically includes the following steps:

[0102] Construct an optimization problem to maximize the sum rate within a user terminal cluster. The sum rate of each user terminal cluster The specific formula is:

[0103]

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

[0105]

[0106] set up The objective function is equivalently expressed as:

[0107]

[0108] Among them, Tr(·) function is a convex function, in order to make the sum rate function For a concave function, the first term is approximated using differential convex approximation definition Then h(P k ) around the feasible solution point at the nth iteration The first-order Taylor expansion of can be expressed as:

[0109]

[0110] in, It's about P k Affine of ;

[0111] Will Substituting in the sum rate function The calculation formula is

[0112]

[0113] For γ, and Every set of is concave. When the precoding matrix and auxiliary variables are given, the problem is transformed into:

[0114]

[0115] The rank-one constraint is processed using the sequential rank-one constraint relaxation method. The rank-one constraint is transformed into:

[0116]

[0117] in, represents the solution obtained at the nth iteration, Represents the maximum eigenvalue The corresponding eigenvector, ε (n) ∈[0,1] represents the restriction Tr(P k ) value, gradually increasing ε during the iteration process (n) value, until ε (n)=1, the specific formula of the relaxation coefficient at the n+1th iteration is:

[0118]

[0119] in, Representation Matrix The maximum eigenvalue of (n+1) represents the update step of the relaxation coefficient. In the n+1th iteration, the problem is further transformed into:

[0120]

[0121] An iterative optimization method is used to solve the optimization problem to obtain the base station receive beamforming matrix.

[0122] Compared with the prior art, the present invention has the following beneficial effects:

[0123] 1. The present invention proposes a NOMA-assisted multi-ISAC user terminal communication and perception system solution. Multiple user terminals can be grouped into clusters. The beneficial effect is: radar perception and communication are performed simultaneously in the same spectrum, which can effectively alleviate the interference of users within the cluster.

[0124] 2. Construct 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 respectively. The effective effect is: it can effectively solve the user terminal transmit beamforming matrix, the covariance matrix of the dedicated radar perception signal, the user terminal receive beamforming vector and the base station beamforming vector, and solve the transmit-receive beamforming matrix to meet the requirements of radar perception and communication transmission.

[0125] 3. Construct a model of user terminal interference from target echo signals of other user terminals. The beneficial effect is: different from the existing user terminal radar perception receiving beamforming model, the model construction is more comprehensive and specific by considering the interference of target echo signals of other user terminals on the radar signal received by the current user terminal. BRIEF DESCRIPTION OF THE DRAWINGS

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

[0127] Figure 1 It is a flowchart of a NOMA-assisted multi-ISAC user terminal transmit-receive beamforming method in an embodiment;

[0128] Figure 2 A schematic diagram of a system architecture with multiple ISAC user terminals communicating and sensing in an embodiment;

[0129] Figure 3It is a schematic diagram of a model in which a user terminal is interfered by target echo signals of other user terminals proposed in the embodiment. DETAILED DESCRIPTION

[0130] In order to make the purpose, technical solutions and advantages of the present invention more clear, the present invention is described in detail below with reference to the accompanying drawings and specific embodiments.

[0131] The following is a further detailed description of the embodiments of the present invention in conjunction with the accompanying drawings:

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

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

[0134] Construct the transmission signal model of the user terminal, the wireless transmission reception beamforming model between the user terminal and the base station based on NOMA technology, the user terminal radar perception transmission-reception beamforming model, and the target echo interference model between user terminals.

[0135] Specifically, assuming that the base station BS has M antennas and each UT is equipped with N antennas, the signal transmitted by each UT can be expressed as:

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

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

[0138] represents the d parallel communication symbols to be sent by the i-th user terminal of the k-th cluster to the base station, where s k,i [n] Satisfaction represents the dedicated radar sensing signal sent by the i-th user terminal of the k-th cluster, which follows the distribution Where R k,i It is a special radar sensing signal D k,i The semi-positive definite covariance matrix of ;

[0139] At time slot n, the receive beamforming of the signals from all UTs in the k-th cluster by the BS can be expressed as:

[0140]

[0141] where, represents the base station receive beamforming matrix for the k-th cluster, represents the channel matrix from the i-th user terminal in the k-th cluster to the base station, represents the precoding matrix of the communication symbol of the i-th user terminal in the k-th cluster, represents d parallel communication symbols that the i-th user terminal in the k-th cluster wants to send to the base station, where s k,i [n] satisfies

[0142] represents the dedicated radar sensing signal sent by the i-th user terminal in the j-th cluster, which follows the distribution where R j,i is the positive semi-definite covariance matrix of the dedicated radar sensing signal C j,i , and z c [n] represents the additive white Gaussian noise, which follows the distribution

[0143] Based on the aforementioned received signal model, NOMA mitigates the interference between users by using SIC. Therefore, the UT(k,i) within the same cluster will remove all the interference from the 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] For the convenience of analysis and obtaining the performance upper bound, we assume that the BS has the perfect channel state information of all UTs. In addition, the transmit covariance matrix of the UT(k,i) is given by:

[0146]

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

[0148] Then, the transmit power constraint of each UT is expressed as:

[0149]

[0150] where, P 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 not only receives the echo from its target, but also is interfered by the communication signals of other UTs and the echo signals of other targets. k,i In the far field, the received radar echo signal of UT(k,i) is expressed as:

[0152]

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

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

[0155]

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

[0157] The clutter associated with the signal is modeled as:

[0158]

[0159] Among them, C k,i is the amount of clutter, is the azimuth angle of the lth clutter, with a path loss factor

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

[0161]

[0162] like Figure 3 As shown in the figure, in a multi-UT radar perception scenario, the UT not only receives the echo from its target, but also is interfered by the communication signals of other UTs. In addition, the radar echo signal from the target corresponding to the UT may reach another UT radar receiver and cause interference. Therefore, consider establishing a model in which the user terminal is interfered by the target echo signal of other UTs. Assume that after the target echo signal of UT-1 reaches UT-2, it will also reach the radar receiver of UT-2 as an interference signal. Therefore, the radar echo signal interference between UTs 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 radar Tx and UT-2 as Rx.

[0163] Based on this, the jth detection target of the cth cluster is expressed as Target(j,c), and the user terminal is modeled as follows:

[0164]

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

[0166]

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

[0168]

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

[0170]

[0171] Among them, the definition set Constraint C1 represents the minimum SCINR requirement of UT(k,i), and constraint C2 represents that the transmit power of UT(k,i) cannot exceed P max , constraint C3 represents the modulus-one restriction of the UT(k,i) radar receive beamforming matrix and constraint C4 represents the modulus-one restriction of the base station receive beamforming matrix. Due to the coupled beamforming matrix and constraints in the objective function, the problem is a non-convex optimization problem.

[0172] Step S4: determine the evaluation index for grouping multi-user terminals using the NOMA technology; then, propose a specific algorithm flow based on the determined evaluation index.

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

[0177]

[0178] Considering the two evaluation indicators of channel correlation and channel gain difference, the utility expression is defined as:

[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 UTs in the same cluster can meet the threshold.

[0181] Next, the two evaluation indicators of channel correlation and channel gain difference are used as the basis for UT grouping, and the specific UT grouping algorithm pseudo code is proposed as shown in Table 1:

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

[0183]

[0184] Step S5, using Lagrange dual transformation and fractional transformation method to convert the achievable rate function into a concave function, and consider the transmit beamforming matrix; then, use the 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, use the iterative optimization method to solve the optimization problem to obtain the UT end radar transmit beamforming matrix.

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

[0186]

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

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

[0189]

[0190] Use fractional transformation to transform the sum rate function. The sum rate function in the formula can be restated as:

[0191]

[0192] in, is a collection of auxiliary variables.

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

[0194]

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

[0196]

[0197] Among them, ||·|| 2 The function is a convex function, in order to make the sum rate function For a concave function, the first term is approximated using differential convex approximation definition Then g k,i (W k,i ) around the feasible solution point at the nth iteration The first-order Taylor expansion of can be expressed as:

[0198]

[0199] in, It's about W k,i Affine of ;

[0200] Will Substituting in the sum rate function The calculation formula is

[0201]

[0202] Next, set the radar SCINR function Transformed into the transmit precoding matrix The concave function of , constraint C1 is expressed as:

[0203]

[0204] in, Because ||·|| 2 The function is convex, and the above formula is the differential of two convex functions. Then, we use the differential convex approximation method to solve it. For the convenience of analysis, we define So Around the feasible solution point at the nth iteration The first-order Taylor expansion of can be expressed as:

[0205]

[0206] in, It is expressed as:

[0207]

[0208] Obviously, About W k,i Affine, further expressed as:

[0209]

[0210] According to the results, the problem is transformed 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 solution algorithm is shown in Table 2:

[0213] Table 6 Algorithm for solving user terminal transmit beamforming

[0214]

[0215]

[0216] Step S6, using Lagrange dual transformation and fractional transformation method to convert the achievable rate function into a concave function, and considering the covariance matrix of the dedicated radar perception signal; then, using the 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 the iterative optimization method to solve the optimization problem to obtain the covariance matrix of the dedicated radar perception signal transmitted by the UT.

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

[0218]

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

[0220]

[0221] Function Transformed into the covariance matrix of the transmitting dedicated radar signal The concave function of , constraint C1 can be expressed as:

[0222]

[0223] in, represents the covariance matrix of all transmitted signals, Represented as the covariance matrix of the transmitted communication signal, R k,i Expressed as the covariance matrix of the transmitted signal perceived by the dedicated radar, represents the covariance matrix of the signal-correlated clutter of UT(k,i), Represents the covariance matrix of UT(k,i) interfered by other users’ radar echoes;

[0224] Use differential convex approximation to solve constraint C1, define So Around the feasible solution point at the nth iteration The first-order Taylor expansion of can be expressed as:

[0225]

[0226] in, About R k,i The constraint C1 is further expressed as:

[0227]

[0228] The optimization problem of maximizing user terminals and rates is transformed into a convex optimization problem, and the calculation formula is:

[0229]

[0230] The iterative optimization method is used to solve the optimization problem to obtain the covariance matrix of the user terminal transmitting dedicated radar perception signal. The specific solution algorithm is shown in Table 3:

[0231] Table 7 Algorithm for solving the covariance matrix of the user terminal radar dedicated signal

[0232]

[0233] Step S8: construct an optimization problem to maximize the ratio of the user terminal radar signal to clutter, interference and noise, and use the generalized Rayleigh entropy method to obtain the user terminal radar receiving beamforming matrix.

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

[0235]

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

[0237]

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

[0239]

[0240] Among them, eig(·) is the generalized eigenvector corresponding to the maximum generalized eigenvalue, so it is further expressed as a normalized closed solution:

[0241]

[0242] Step S9, use Lagrange dual transformation and fractional transformation method to convert the intra-cluster sum rate function into a concave function, and consider the base station side receive beamforming matrix; then, use the sequential rank-one constraint relaxation method to solve the rank-one requirement; finally, use the iterative optimization method to solve the optimization problem to obtain the base station side receive beamforming matrix.

[0243] Specifically, we first construct an optimization problem to maximize the sum rate within the user terminal cluster. The sum rate of each user terminal cluster is It is expressed as:

[0244]

[0245] Next, the Lagrange dual transformation and fractional transformation method are used to transform the achievable rate function into a concave function, and the rate function can be further transformed into:

[0246]

[0247] set up The objective function is equivalently expressed as:

[0248]

[0249] Among them, Tr(·) function is a convex function, in order to make the sum rate function For a concave function, the first term is approximated using differential convex approximation definition Then h(P k ) around the feasible solution point at the nth iteration The first-order Taylor expansion of can be expressed as:

[0250]

[0251] in, It's about P k Affine of ;

[0252] Will Substituting in the sum rate function The calculation formula is

[0253]

[0254] For γ, and Every set of is concave. When the precoding matrix and auxiliary variables are given, the problem can be transformed into:

[0255]

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

[0257] Then, the sequential rank-one constraint relaxation method is used to handle the rank-one constraint. Therefore, the rank-one constraint is transformed into:

[0258]

[0259] in, is the solution obtained at the nth iteration, Represents the maximum eigenvalue The corresponding eigenvector, ε (n) ∈[0,1] is the limit Tr(P k ) value, gradually increasing ε during the iteration process (n) value, until ε (n) =1 to obtain a feasible solution that meets the rank one requirement. Then, the relaxation coefficient at the n+1th iteration is expressed as:

[0260]

[0261] in, For the matrix The maximum eigenvalue of (n+1) is represented as the update step size of the relaxation coefficient. Therefore, in the n+1th iteration, problem (23) can be further transformed into:

[0262]

[0263] The optimization problem is solved using an iterative optimization method to obtain the base station receive beamforming vector. The specific algorithm for solving the base station beamforming vector is shown in Table 4:

[0264] Table 4 Algorithm for solving base station beamforming vectors

[0265]

[0266]

[0267] In summary, the present invention proposes a NOMA-assisted multi-ISAC user terminal communication and perception system solution. Multiple user terminals can be grouped into clusters to simultaneously perform radar perception and communication in the same spectrum, and effectively reduce interference between user terminals. The requirements of radar perception and communication transmission are met by solving the transmit-receive beamforming matrix.

[0268] The above embodiments are only used to illustrate the technical solution of the present invention rather than to limit it. Although the present invention has been described in detail with reference to the preferred embodiments, those skilled in the art should understand that the technical solution of the present invention may be modified or replaced by equivalents without departing from the spirit and scope of the technical solution of the present invention.

Claims

1. A NOMA-assisted multi-ISAC user terminal joint transmit-receive beamforming method, It is characterized in that The steps include: Construct a NOMA communication and perception fusion architecture supporting multiple ISAC user terminals, wherein the fusion architecture includes multiple user terminals, a base station, and a detection target, wherein each of the multiple user terminals has a radar perception function and a communication function, wherein the radar perception function and the communication function share a spectrum and a common hardware device; the base station obtains a transmission signal sent by the user terminal, wherein the transmission signal is a communication signal and a dedicated radar perception signal, both of which are used for radar sensing; Construct the user terminal transmission signal model, the wireless transmission reception signal model between the user terminal and the base station based on NOMA technology, the user terminal radar perception reception beamforming model and the user terminal interference model of the target echo signal of other user terminals; Determine the evaluation index of multi-user terminal grouping using NOMA technology, and determine the multi-user terminal grouping algorithm process according to the evaluation index; Construct an optimization problem of maximizing the user terminal and rate, and solve the optimization problem to obtain the user terminal transmit beamforming matrix; Construct an optimization problem for maximizing the user terminal and rate, and solve the optimization problem to obtain the covariance matrix of the user terminal dedicated radar perception signal; Construct an optimization problem to maximize the ratio of the user terminal radar signal to clutter, interference and noise, and solve the optimization problem to obtain the radar receiving beamforming matrix of the user terminal; Construct an optimization problem for maximizing the sum rate within the user terminal cluster, and solve the optimization problem to obtain the base station receive beamforming matrix; The calculated beamforming matrix satisfies the convergence condition. If not, the optimization problem is solved iteratively until convergence.

2. The method according to claim 1, It is characterized in that The user terminal, UT, can be divided into K clusters and can be represented as a set The base station has M antennas, each UT has N antennas, the i-th user terminal in the k-th cluster can be represented as UT(k,i), and the UTs in the k-th cluster can be represented as the set The transmission signal model of the user terminal is specifically expressed as follows: X k,i =W k,i s k,i +D k,i (1) in, represents the precoding matrix of the communication symbol of the i-th user terminal of the k-th cluster, represents the d parallel communication symbols to be sent by the i-th user terminal of the k-th cluster to the base station, where s k,i [n] Satisfaction represents the dedicated radar sensing signal sent by the i-th user terminal of the k-th cluster, which follows the distribution Where R k,i It is a special radar sensing signal C k,i The positive semidefinite covariance matrix of .

3. The method according to claim 1, It is characterized in that The wireless transmission and reception signal model between the user terminal and the base station, the specific calculation formula is: in, represents the base station receive beamforming matrix of the kth cluster, represents the channel matrix from the ith user terminal of the kth cluster to the base station, represents the precoding matrix of the communication symbol of the i-th user terminal of the k-th cluster, represents the d parallel communication symbols to be sent by the i-th user terminal of the k-th cluster to the base station, where s k,i [n] Satisfaction represents the dedicated radar sensing signal sent by the i-th user terminal of the k-th cluster, which follows the distribution Where R k,i It is a special radar sensing signal C k,i The semi-positive definite covariance matrix of ; The i-th user terminal of the k-th cluster can be represented as UT(k,i). The data rate expression between UT(k,i) and the base station is specifically: The user terminal radar perception receiving signal model, the specific calculation formula is: in, represents the reflection coefficient between UT(k,i) and its radar target, represents the radar receive beamforming matrix of UT(k,i), and are the transmit and receive array steering vectors of UT(k,i), n k represents the sum of the propagation delays to and from the destination at UT(k,i), represents the interference channel from UT(k,i) to UT(j,c), represents the clutter signal experienced by UT(k,i), whose covariance matrix is ​​R c,(k,i) , z k,i [n] represents the AWGN vector, obeying The user terminal is interfered by the target echo signal of other user terminals. The specific formula is: Among them, β (j,c),(k,i) represents the reflection coefficient and path loss from UT(j,c) to its radar Target(j,c) and then to UT(k,i), and are the sending and receiving array steering vectors from UT(j,c) to its radar Target(j,c) and from radar Target(j,c) to UT(k,i), respectively. Target(j,c) represents the radar detection target of the jth UT of the cth cluster.

4. The method according to claim 1, It is characterized in that Determining the evaluation index for multi-user terminal grouping using NOMA technology includes the following steps: Determine the evaluation indicators for user terminal grouping based on NOMA technology, including channel correlation and channel gain difference; The specific formula of the channel correlation is: in, represents the communication channel from the mth user terminal to the base station; The specific formula of the channel gain difference is: Taking into account the channel correlation and channel gain difference evaluation indicators, the specific calculation formula is: c(m,n)={Corr(m,n)+d(m,n)|Corr(m,n)≥ρ,d(m,n)≥ζ} (16) Among them, c(m,n) represents the utility expression that comprehensively considers the channel correlation and channel gain difference evaluation indicators.

5. The method according to claim 1, It is characterized in that The optimization problem of maximizing user terminals and rates is as follows: Among them, the definition set Constraint C1 represents the minimum SCINR requirement of UT(k,i), and constraint C2 represents that the transmit power of UT(k,i) cannot exceed P max , constraint C3 represents the modulus-1 restriction of the UT(k,i) radar receiving beamforming matrix, constraint C4 represents the modulus-1 restriction of the base station receiving beamforming matrix, wherein in constraint C1, the ratio of the user terminal radar signal to clutter, interference and noise is calculated as: in, Represents the ratio function of the user terminal radar signal to clutter, interference and noise.

6. The method according to claim 4, It is characterized in that Solving the optimization problem to obtain the user terminal transmit beamforming matrix specifically includes the following steps: The Lagrange dual transformation method is used to transform the rate function R k,i , and rate It can be expressed as: in, represents a collection of auxiliary variables, Indicates the total channel interference plus noise of the user terminal; When the precoding matrix and the base station receive beamforming matrix are given, we can derive Optimal γ k,i , the calculation formula is: Use fractional transformation to transform the sum rate function. Recalculate to: in, Represents a collection of auxiliary variables; When the precoding matrix and auxiliary variable γ are given, we can derive The optimal y k,i , the calculation formula is: N k,i Substituting in the sum rate function The calculation formula is: Among them, ||·|| 2 The function is a convex function, in order to make the sum rate function For a concave function, the first term is approximated using differential convex approximation definition Then g k,i (W k,i ) around the feasible solution point at the nth iteration The first-order Taylor expansion of can be expressed as: in, It's about W k,i Affine of ; Will Substituting in the sum rate function The calculation formula is Function Transformed into the transmit precoding matrix The concave function of , constraint C1 can be expressed as: in, represents the covariance matrix of all transmitted signals, represents the covariance matrix of the transmitted communication signal, R k,i Expressed as the covariance matrix of the transmitted signal perceived by the dedicated radar, represents the covariance matrix of the signal-correlated clutter of UT(k,i), Represents the covariance matrix of UT(k,i) interfered by other users’ radar echo signals; Use differential convex approximation to solve constraint C1, define So Around the feasible solution point at the nth iteration The first-order Taylor expansion of can be expressed as: in, It's about W k,i The constraint C1 is further expressed as: The optimization problem of maximizing user terminals and rates is transformed into a convex optimization problem, and the calculation formula is: An iterative optimization method is used to solve the optimization problem to obtain the user terminal transmit beamforming matrix.

7. The method according to claim 1, It is characterized in that Solving the optimization problem to obtain the covariance matrix of the dedicated radar sensing signal transmitted by the user terminal specifically includes the following steps: The Lagrange dual transformation method and fractional transformation are used to transform the sum rate function and recalculate the sum rate formula as follows: Among them, ||·|| 2 function, Tr(·) function is a convex function, and rate function Also about Concave function of ; Function Transformed into the transmit precoding matrix The concave function of , constraint C1 can be expressed as: in, represents the covariance matrix of all transmitted signals, Represented as the covariance matrix of the transmitted communication signal, R k,i Expressed as the covariance matrix of the transmitted signal perceived by the dedicated radar, represents the covariance matrix of the signal-correlated clutter of UT(k,i), Represents the covariance matrix of UT(k,i) interfered by other users’ radar echoes; Use differential convex approximation to solve constraint C1, define So Around the feasible solution point at the nth iteration The first-order Taylor expansion of can be expressed as: in, About R k,i The constraint C1 is further expressed as: The optimization problem of maximizing user terminals and rates is transformed into a convex optimization problem, and the calculation formula is: The optimization problem is solved by iterative optimization method to obtain the covariance matrix of the radar-specific signal transmitted by the user terminal.

8. The method according to claim 1, It is characterized in that An optimization problem of maximizing the ratio of the user terminal radar signal to clutter, interference and noise is constructed, and the radar receiving beamforming matrix of the user terminal is obtained by solving the optimization problem. Specifically, the following steps are included: An optimization problem of maximizing the ratio of the user terminal radar signal to clutter, interference, and noise is constructed, and the optimization problem is decomposed into sub-optimization problems. The specific formula is: Among them, J k,i It represents the radar signal clutter and interference plus noise of UT(k,i). The specific formula is: The generalized Rayleigh entropy method is used to obtain the closed-form solution of the radar receive beamforming matrix of the user terminal. The specific formula is: Where, eig(·) represents the generalized eigenvector corresponding to the maximum generalized eigenvalue; 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:

9. The method according to claim 1, It is characterized in that Construct an optimization problem for maximizing the sum rate within the user terminal cluster, and solve the optimization problem to obtain the base station receive beamforming matrix, which specifically includes the following steps: Construct an optimization problem to maximize the sum rate within a user terminal cluster. The sum rate of each user terminal cluster The specific formula is: The sum rate of the user terminal cluster is converted using the Lagrange dual transformation and fractional transformation method. The specific formula is: set up The objective function is equivalently expressed as: Among them, Tr(·) function is a convex function, in order to make the sum rate function For a concave function, the first term is approximated using differential convex approximation definition Then h(P k ) around the feasible solution point at the nth iteration The first-order Taylor expansion of can be expressed as: in, It's about P k Affine of ; Will Substituting in the sum rate function The calculation formula is For γ, and Every set of is concave. When the precoding matrix and auxiliary variables are given, the problem is transformed into: The rank-one constraint is processed using the sequential rank-one constraint relaxation method. The rank-one constraint is transformed into: in, represents the solution obtained at the nth iteration, Represents the maximum eigenvalue The corresponding eigenvector, ε (n) ∈[0,1] represents the restriction Tr(P k ) value, gradually increasing ε during the iteration process (n) value, until ε (n) =1, the specific formula of the relaxation coefficient at the n+1th iteration is: in, Representation Matrix The maximum eigenvalue of (n+1) represents the update step of the relaxation coefficient. In the n+1th iteration, the problem is further transformed into: An iterative optimization method is used to solve the optimization problem to obtain the base station receive beamforming matrix.

Images