Hybrid beam forming method based on terahertz large-scale MIMO-ISAC system

Abstract

The invention relates to a hybrid beam forming method based on a terahertz large-scale MIMO-ISAC system, and belongs to the technical field of wireless communication. The method comprises the following steps: firstly, determining channel state information of a base station side and a user side and the direction of a target; solving an optimal communication beam former and an optimal radar beam former according to the channel state information and the target user direction; combining the communication performance index-spectrum efficiency and the radar performance index-space spectrum matching error by using a weight factor to construct an optimization problem; then, the optimization problem is converted into Euclidean distance minimization, in the process, unitary matrix assistance is introduced, and an optimal communication beam former, an optimal radar beam former and a hybrid beam former are unified to the same dimension; and finally, solving the hybrid beam former by adopting an alternating optimization algorithm. According to the invention, high energy consumption caused by hardware introduction is reduced, high array gain loss caused by a beam splitting effect is eliminated, and the implementation mechanism is simple.

Description

Technical Field

[0001] The invention belongs to the technical field of wireless communications and relates to a hybrid beamforming method based on a terahertz large-scale MIMO-ISAC system. Background Art

[0002] To meet the demand for ultra-high-speed transmission and new applications in future wireless communications, the communications community is exploring new spectrum opportunities and functions for the sixth generation (6G) wireless network. It is expected that 6G networks will achieve a peak data transmission rate of Tbits / s, and terahertz (THz) has attracted widespread attention as a key enabling technology to achieve this goal. However, THz signals face serious losses during propagation. Therefore, combining THz with large-scale multiple-input multiple-output (MIMO) technology to generate high-gain directional beams through beamforming is expected to solve this problem. However, traditional all-digital beamforming relies on a large number of expensive and high-power RF links, making it difficult to be widely used in THz large-scale MIMO. Therefore, hybrid beamforming technology came into being and has been widely adopted in millimeter wave communication systems. At the same time, Integrated Sensing and Communication (ISAC) as an innovative technical solution integrates communication and radar sensing functions to enable wireless networks to have sensing capabilities. Therefore, THz massive MIMO-ISAC technology is expected to achieve ultra-precise perception and ultra-high-speed data transmission in future wireless communications.

[0003] Typical hybrid beamforming consists of a digital beamformer and an analog beamformer, where the analog beamformer usually relies on a phase shifter. For broadband MIMO-ISAC systems based on orthogonal frequency division multiplexing (OFDM), the goal is to jointly optimize the communication spectrum efficiency and the radar spatial spectrum matching error. For this scheme, some researchers have adopted an algorithm based on the consensus alternating direction multiplier method to achieve the collaborative function of communication and perception; by optimizing the beamformers at the transmitter and receiver, the weighted minimum mean square error (WMMSE), the exact penalty term (EPM-RCG) and the continuous convex approximation (SCA) methods are used to eliminate inter-user, intra-user and radar-communication interference. However, due to the broadband characteristics, the analog beam based on the phase shifter will have severe beam splitting at different subcarrier frequencies, resulting in severe gain loss of the large-scale MIMO array, making the above scheme no longer applicable. Therefore, how to effectively deal with the beam splitting problem has become a key challenge facing broadband large-scale MIMO-ISAC systems.

[0004] In response to the beam splitting problem in broadband massive MIMO systems, researchers have proposed a variety of solutions to improve system performance. The core idea is to optimize the hybrid beamformer through an algorithm to improve the beam splitting effect. These methods have achieved significant results in alleviating array gain degradation and improving system spectral efficiency. However, for broadband THz massive MIMO-ISAC systems with wider bandwidths and more antennas, the beams of different subcarriers are split into completely different physical directions, which significantly reduces the applicability of these methods.

[0005] In order to solve the beam splitting problem in broadband THz massive MIMO-ISAC systems, researchers have proposed using delay devices to replace traditional phase shifters to achieve frequency-dependent phase shift control, thereby optimizing beam steering. The You Li team from Southeast University and the Gao Feifei team from Tsinghua University proposed to completely replace the phase shifters with delay devices to eliminate the beam splitting effect. Although these solutions have achieved remarkable results in solving the beam splitting problem, the delay devices used in equal amounts as phase shifters will lead to high power consumption problems in the system. To meet this challenge, researchers have proposed the concept of delayed phase precoding. For example, the method of Dai Linglong's team alleviates beam splitting in the analog domain by introducing a low-dimensional delay network between the RF chain and the phase shifter. However, existing research is still in its initial stage, and the exploration of time-phase joint technology in beam splitting mitigation is still relatively limited. Therefore, introducing the time-phase joint beamforming system into the massive MIMO-ISAC system for in-depth research is still a frontier issue that needs to be solved urgently. Summary of the invention

[0006] In view of this, the purpose of the present invention is to provide a hybrid beamforming method based on a terahertz massive MIMO-ISAC system. By introducing a frequency-dependent low-dimensional delay network into the system, signal processing is optimized to effectively alleviate the beam splitting effect while controlling power consumption, thereby significantly improving system performance.

[0007] In order to achieve the above object, the present invention provides the following technical solutions:

[0008] A hybrid beamforming method based on a terahertz massive MIMO-ISAC system, the method comprising the following steps:

[0009] Step 1: Obtain channel state information based on beam tracking and determine the optimal communication beamformer using singular value decomposition;

[0010] Step 2: According to the multi-signal classification MUSIC algorithm, the direction information of the target is obtained and the optimal radar perception beamformer is constructed;

[0011] Step 3: According to the weight factor, the spectrum efficiency that measures the communication performance and the beam space spectrum matching error that measures the radar performance are combined together to construct an optimization problem;

[0012] Step 4: Using the property that the unitary matrix does not cause beam distortion, the joint optimization problem of spectral efficiency and spatial spectrum matching error is transformed into the weighted sum of the Euclidean distances between the hybrid beamformer and the optimal communication beamformer / optimal radar beamformer.

[0013] Step 5: Using the constant mode characteristics of the time delayer and phase shifter, the digital beamformer, the time delay beamformer and the phase shift beamformer are solved respectively by using the alternating minimization method;

[0014] A small number of delay devices are introduced between the RF chain and the phase shifter, and the frequency-related characteristics of the delay devices are utilized to solve the beam splitting problem. At the same time, a small number of delay devices is also beneficial to reduce system power consumption.

[0015] Furthermore, the step 1 and step 2 specifically include:

[0016] a. Use channel state information to find the optimal communication beamforming matrix F C,m :

[0017] H m =U m Σ m V m H ,in

[0018]

[0019] Among them, F C,m represents the optimal communication beamforming matrix of the mth subcarrier, the subscript C represents the abbreviation of the communication system; H m represents the channel of the mth subcarrier, U m ,Σ m , V m Respectively represent H m Do singular value decomposition of the left unitary matrix, singular value matrix, right unitary matrix; () H is the conjugate transpose of the matrix; and is the matrix V m The block matrix, M is the number of subcarriers, and m = 1, 2, M; [] represents the construction of the matrix;

[0020] b. Use target direction information to construct the optimal radar beamforming matrix F S,m :

[0021] F S,m =[f m (θ1),fm (θ2),…,f m (θ K )]

[0022] Among them, F S,m represents the optimal sensing beamforming matrix of the mth subcarrier, the subscript S represents the abbreviation of the radar sensing system, and f m (θ k ) represents the optimal sensing beam vector in the kth target direction, θ k represents the direction of the kth target, and k=1,...,K.

[0023] Further, in the step 4, the spectrum efficiency SE for measuring the communication performance and the spatial spectrum matching error SSME of the beam for measuring the radar performance are combined by the weight factor, specifically including:

[0024] a. Spectral efficiency SE of communication:

[0025]

[0026] Where R m represents the spectrum efficiency of the mth subcarrier; N r Indicates the number of antennas at the user end, Indicates dimension N r ×N r The identity matrix; ρ is the average received power; σ 2 is the additive white Gaussian noise power; represents the delay beamforming matrix T at the mth subcarrier m and the phase shift beamforming matrix A PS The hybrid beamforming matrix is ​​composed of P is a P×1 vector of all ones. The symbol ⊙ represents the Hadamard product. PS The abbreviation for phase shifter; symbol It is represented by Kronecker product; log2(||) means finding the logarithm of the determinant of the matrix with base 2, ∑ means summation operation;

[0027] b. Radar-perceived spatial spectrum matching error SSME:

[0028]

[0029] where f m Represents the frequency of the mth subcarrier; R opt It is represented as the covariance matrix of the optimal radar sensing beam, and the subscript opt ​​represents the abbreviation of the English word optimal; R m represents the covariance matrix of the hybrid beam on the mth subcarrier; G(f m ,θ k ,Ropt ) and G(f m ,θ k ,R m ) respectively represent the k The optimal spatial spectrum and actual spatial spectrum of the mth subcarrier in the direction; | | 2 It represents the square of the matrix modulus;

[0030] c. Combine steps a and b and use the weight factor ζ∈[0,1] to construct the following optimization problem:

[0031]

[0032] Where max means maximizing the objective function under the following constraints; st means satisfying the constraints; A PS (i,j) Represents the matrix A PS The element in the i-th row and j-th column of ; It represents the delay value of the tth delay device on the nth RF chain, and n=1,2,...,N RF and t=1,2,...,T,N RF represents the number of RF chains, T represents the number of delay devices connected to each RF chain; τ max Indicates the maximum delay value of the delay device; N s Indicates the number of transmitted data streams; | | is a modulo operation; It means to find the square of the F norm of the matrix; represents any value; when ζ is 1 or 0, the system is only communicating or sensing.

[0033] Furthermore, in step 4, the optimal radar beamforming matrix, the optimal communication beamforming matrix and the hybrid beamforming matrix are unified into the same dimension by utilizing the characteristic that the unitary matrix does not distort the beam, specifically:

[0034] a. In order to maximize the communication spectrum efficiency, the problem is transformed into the problem of minimizing the Euclidean distance between the optimal communication beamforming matrix and the hybrid beamforming matrix, specifically:

[0035]

[0036] Where min means minimizing the objective function under the following constraints;

[0037] b. In order to minimize the radar perception spatial spectrum matching error, the problem is transformed into a problem of minimizing the Euclidean distance between the optimal radar beamforming matrix and the hybrid beamforming matrix, using the auxiliary matrix U m Unify the dimensions of the optimal radar beamforming matrix, the optimal communication beamforming matrix, and the hybrid beamforming matrix, specifically:

[0038]

[0039]

[0040] c. According to the optimization methods in step a and step b, the joint optimization problem of maximizing the communication spectrum and minimizing the radar spatial spectrum matching error is transformed into the problem of minimizing the Euclidean distance between the optimal communication beamforming matrix, the optimal radar sensing beamforming matrix and the hybrid beamforming matrix, specifically:

[0041]

[0042] Where F(U m ,A PS ,T m ,D m )for:

[0043]

[0044] Furthermore, by utilizing the unitary matrix characteristics and the transverse modulus of the delay and phase shift matrix being 1, an alternating minimization method is used to respectively obtain the optimal digital beamforming matrix, the delay beamforming matrix, and the phase shift beamforming matrix; the steps of alternating optimization are as follows:

[0045] a. For the unitary matrix U m , by fixing the digital beamforming matrix D m , delay beamforming matrix T m and the phase-shifted beamforming matrix A PS , using the characteristics of the unitary matrix, the problem is transformed into an orthogonal Prucker problem, and the optimal unitary matrix U is obtained m ;

[0046] b. For the digital beamforming matrix D m , by fixing the auxiliary matrix U m , delay beamforming matrix T m and the phase-shifted beamforming matrix A PS ; Using the mutual orthogonality of the columns of the optimal communication beamforming matrix and the optimal radar sensing beamforming matrix, constraints are imposed so that the columns of the digital beamforming matrix satisfy quasi-orthogonality, that is, in With D m is a unitary matrix with the same dimension; the digital beamforming matrix optimization problem is a deformation of the orthogonal Prucker problem, and the optimal digital beamforming matrix D is obtained. m ;

[0047] Where η is a positive scaling factor, To define symbols;

[0048] c. Fixed auxiliary matrix U m , digital beamforming matrix D m and the phase-shifted beamforming matrix A PS , using the characteristic that the modulus value of each element in the delay beamforming matrix is ​​always 1, solve the delay beamforming matrix T m ;

[0049] d. Fixed auxiliary matrix U m , digital beamforming matrix D m and the delay beamforming matrix T m , using the characteristic that the modulus of each element in the phase-shift beamforming matrix is ​​always 1, the phase-shift beamforming matrix A is obtained PS .

[0050] The beneficial effects of the present invention are as follows: first, the optimal communication beamforming matrix and the optimal radar sensing beamforming matrix are constructed through channel state information and the direction of the target; then the communication performance index-spectral efficiency and the radar performance index-spatial spectrum matching error are used to construct the competitive relationship between the two using weight factors; then this competitive relationship is converted into minimization of the Euclidean distance. Because the dimensions of the optimal radar beamformer and the hybrid beamformer are not uniform, a unitary matrix is ​​introduced to unify the optimal radar beamforming matrix and the hybrid beamforming matrix to the same dimension; finally, the hybrid beamformer is solved by an alternating optimization algorithm through the unitary matrix characteristics and the transverse modulus values ​​of the delayer and the phase shifter being 1. The present invention not only eliminates the high array gain loss caused by the beam splitting effect, but also controls the high energy consumption caused by the introduction of hardware.

[0051] Other advantages, objectives and features of the present invention will be described in the following description to some extent, and to some extent, will be obvious to those skilled in the art based on the following examination and study, or can be taught from the practice of the present invention. The objectives and other advantages of the present invention can be realized and obtained through the following description. BRIEF DESCRIPTION OF THE DRAWINGS

[0052] In order to make the purpose, technical solutions and advantages of the present invention more clear, the present invention will be described in detail below in conjunction with the accompanying drawings, wherein:

[0053] Figure 1 The specific implementation flow chart of the hybrid beamforming method for the terahertz massive MIMO-ISAC system;

[0054] Figure 2 This is a model diagram of the terahertz massive MIMO-ISAC system;

[0055] Figure 3 Flowchart for solving each hybrid beamformer;

[0056] Figure 4 The original beam splitting diagram and the beam diagram optimized by the method proposed in the present invention. DETAILED DESCRIPTION

[0057] The following describes the embodiments of the present invention by specific examples, and those skilled in the art can easily understand other advantages and effects of the present invention from the contents disclosed in this specification. The present invention can also be implemented or applied through other different specific embodiments, and the details in this specification can also be modified or changed in various ways based on different viewpoints and applications without departing from the spirit of the present invention. It should be noted that the illustrations provided in the following embodiments only illustrate the basic concept of the present invention in a schematic manner, and the following embodiments and features in the embodiments can be combined with each other without conflict.

[0058] Among them, the drawings are only used for illustrative explanations, and they only represent schematic diagrams rather than actual pictures, and should not be understood as limitations on the present invention. In order to better illustrate the embodiments of the present invention, some parts of the drawings may be omitted, enlarged or reduced, and do not represent the size of actual products. For those skilled in the art, it is understandable that some well-known structures and their descriptions in the drawings may be omitted.

[0059] The same or similar numbers in the drawings of the embodiments of the present invention correspond to the same or similar parts; in the description of the present invention, it should be understood that if the terms "upper", "lower", "left", "right", "front", "rear", etc. indicate the orientation or position relationship, they are based on the orientation or position relationship shown in the drawings, which is only for the convenience of describing the present invention and simplifying the description, rather than indicating or implying that the device or element referred to must have a specific orientation, be constructed and operate in a specific orientation. Therefore, the terms describing the position relationship in the drawings are only used for illustrative purposes and cannot be understood as limiting the present invention. For ordinary technicians in this field, the specific meanings of the above terms can be understood according to specific circumstances.

[0060] Figure 1 The specific implementation flow chart of the hybrid beamforming method for the terahertz massive MIMO-ISAC system is described in detail as follows.

[0061] On the one hand, the existing algorithms cannot effectively alleviate the beam splitting effect under terahertz broadband. On the other hand, if we simply rely on introducing hardware to solve the beam splitting problem, it will bring very high power consumption. Therefore, by inserting a small number of delays between the RF chain and the phase shifter, a hybrid beamforming method for terahertz massive MIMO-ISAC system is proposed under the condition of tolerable power consumption. In this method, the beam splitting problem is solved by optimizing the hybrid beamforming design.

[0062] A terahertz massive MIMO-ISAC system hybrid beamforming method comprises the following steps:

[0063] Step 1: Obtain channel state information based on beam tracking and determine the optimal communication beamformer using singular value decomposition;

[0064] Step 2: According to the multiple signal classification (MUSIC) algorithm, the direction information of the target is obtained and the optimal radar perception beamformer is constructed;

[0065] Step 3: Based on the weight factor, the spectrum efficiency that measures the communication performance and the beam space spectrum matching error that measures the radar performance are combined together to construct an optimization problem.

[0066] Step 4: Taking advantage of the property that the unitary matrix does not cause beam distortion, the joint optimization problem of spectral efficiency and spatial spectrum matching error is transformed into the weighted sum of the Euclidean distances between the hybrid beamformer and the optimal communication beamformer / optimal radar beamformer.

[0067] Step 5: Using the constant mode characteristics of the time delayer and phase shifter, the digital beamformer, the time delay beamformer and the phase shift beamformer are solved respectively by the alternating minimization method.

[0068] like Figure 2 For a terahertz massive MIMO-ISAC system, a t Antennas and N RF The base station (BS) of the RF chain uses orthogonal frequency division multiplexing (OFDM) to connect an N r The antenna provides communication services to the user (UE) and detects K targets of interest at the same time. In this paper, it is assumed that both the BS and the UE use uniform linear arrays (ULA) and the spacing between antenna elements is d. The mth subcarrier signal at the transmitter can be modeled as:

[0069]

[0070] in Represents the digital beamforming matrix of the mth subcarrier, with dimension N RF ×N s , Represents the delayed network beamforming matrix of the mth subcarrier, with dimension T×N RF , Represents the phase shift beamforming matrix of the mth subcarrier, with dimension N t ×N RF , superscript PS It represents the abbreviation of phase shifter. ⊙ is the Hadamard product of the matrix; For Kronek. 1 Pis a P×1 vector of all 1s. P represents the number of phase shifters connected to each delay, T represents the number of delays connected to each RF chain, and m=1,2,...,M, is the dimension of the complex matrix.

[0071] Step 1: Obtain channel state information based on beam tracking and determine the optimal communication beamformer using singular value decomposition;

[0072] like Figure 2 As shown, under the communication system, the detailed process is as follows:

[0073] a. After the signal transmitted by the base station passes through the channel, the downlink received signal at the user end at the mth subcarrier It is expressed as:

[0074]

[0075] Where ρ is the average received power; is the frequency domain channel at the mth subcarrier, with dimension N r ×N t ; is the additive Gaussian white noise at the mth subcarrier that follows a Gaussian distribution and satisfies where σ 2 Represents the noise power, dimension is N r ×1,N r Indicates the number of antennas at the user point; Represents the square root of a number.

[0076] b. Define the achievable spectral efficiency (SE) as:

[0077]

[0078] Where R m represents the spectrum efficiency of the mth subcarrier; Indicates dimension N r ×N r The identity matrix of represents the delayed beamforming matrix T at the mth subcarrier m and the phase shift beamforming matrix A PS The hybrid beamforming matrix is ​​constructed, log2(||) represents the logarithm of the determinant of the matrix with base 2, ∑ represents the summation operation, () H Represents the conjugate transpose of a matrix.

[0079] Step 2: According to the multiple signal classification (MUSIC) algorithm, the direction information of the target is obtained and the optimal radar perception beamformer is constructed;

[0080] like Figure 2As shown in the radar perception system, the detailed process is as follows: a. According to the known target user information, the optimal radar perception beamforming matrix is

[0081] F S,m = pf m (θ1),f m (θ2),...,f m (θ K )]

[0082] where f m (θ k ) indicates that the mth subcarrier is in the kth target direction θ k The optimal radar beam. Therefore, the ideal covariance matrix can be constructed as Subscript opt represents the optimal value abbreviation, subscript S Abbreviation for radar perception.

[0083] b. According to the terahertz massive MIMO radar system, the transmit beam pattern is a key task to ensure the maximum power transmitted at the target location. Therefore, in the perception model, the mth subcarrier is in the kth target direction θ k The spatial spectrum G(f m ,θ k ,R m ) is expressed as:

[0084]

[0085] in Indicates the physical direction angle θ corresponding to the target k The steering vector on the mth subcarrier, f m Represents the frequency of the mth subcarrier; R m is the covariance matrix of the transmitted signal:

[0086]

[0087] in It means to find the expectation of a matrix.

[0088] c. Combining the analysis of a and b, define the spatial spectrum matching error (SSME) of the optimal radar beamformer and the hybrid beamformer,

[0089]

[0090] where | | 2 represents the square of the modulus, G(f m ,θ k ,R opt ) represents the physical direction angle θ of the corresponding targetk The optimal spatial spectrum on the mth subcarrier.

[0091] Step 3: Based on the weight factor, the spectrum efficiency that measures the communication performance and the beam space spectrum matching error that measures the radar performance are combined together to construct an optimization problem.

[0092] a. According to the SE and SSME indicators defined in step 1 and step 2, the following optimization problem is constructed through the weight factor ζ∈[0,1]:

[0093]

[0094] Among them, max means to perform maximization operation according to the constraint conditions.

[0095] Step 4: Using the property that the unitary matrix does not distort the beam, the joint optimization problem of SE and MMSE is transformed into the weighted sum of the Euclidean distances between the hybrid beamformer and the optimal communication beamformer / optimal radar beamformer.

[0096] a. To maximize the SE of communication, it is necessary to minimize the Euclidean distance between the optimal communication beamforming matrix and the hybrid beamforming matrix, which is specifically expressed as:

[0097]

[0098] in represents the square of the norm of the matrix F, where min represents the minimization operation under the constraint conditions, and the subscript C Indicates communication abbreviation.

[0099] b. According to the method in a, the formal equivalent conversion relationship between SSME and Euclidean distance minimization under the radar beam pattern is established:

[0100]

[0101] Where (a) is derived from the Cauchy-Schwarz inequality, F m =A m D m ; Tr(·) represents the matrix trace; Similarly, the SSME of the radar beam pattern is transformed into the following Euclidean distance optimization:

[0102]

[0103] The auxiliary matrix is a unitary matrix to match F S,m and A m D mThe joint optimization of maximizing communication SE and minimizing SSME is thus transformed into minimizing the Euclidean distance between the hybrid beamformer and the optimal communication beamformer / optimal radar beamformer.

[0104]

[0105] Where F(U m ,A PS ,T m ,D m )for:

[0106]

[0107] Step 5: Using the constant mode characteristics of the time delayer and phase shifter, the digital beamformer, the time delay beamformer and the phase shift beamformer are solved respectively by the alternating minimization method.

[0108] like Figure 3 As shown, the digital beamformer, delay beamformer and phase shift beamformer are solved by alternating minimization, which is specifically expressed as:

[0109] a. For the unitary matrix U m , by fixing the digital beamforming matrix D m , delay beamforming matrix T m and the phase-shifted beamforming matrix A PS , using the characteristics of the unitary matrix, the problem is transformed into an orthogonal Prucker problem, and the optimal unitary matrix U can be obtained m .

[0110]

[0111] The optimization problem satisfies the orthogonal Prucker problem (OPP). Therefore, we can obtain in yes The singular value decomposition of is to take the left unitary matrix V before N s columns, Σ is the singular value matrix, and P is the right unitary matrix. st is a constraint condition, and there must be an optimization method for the auxiliary matrix.

[0112] b. For the digital beamforming matrix D m , by fixing the auxiliary matrix U m , delay beamforming matrix T m and the phase-shifted beamforming matrix A PS , the optimization in step 4 is equivalent to:

[0113]

[0114] in and By using the mutual orthogonality of the columns of the optimal communication beamforming matrix and the optimal radar sensing beamforming matrix, constraints are imposed so that the columns of the digital beamforming matrix satisfy quasi-orthogonality, that is, in With D m are unitary matrices with the same dimensions. Therefore, The solution becomes:

[0115]

[0116] Where η is a positive scaling factor, is the definition symbol. The optimization problem satisfies a variant of the orthogonal Pluck problem, so we get in and B m H V m The left unitary matrix and right unitary matrix after singular value decomposition truncation. Then use normalization The optimization method of obtaining the optimal digital beamforming matrix is ​​obtained. It means taking the F norm of the matrix, where It means taking the real part of the function.

[0117] c. Fixed auxiliary matrix U m , digital beamforming matrix D m and the phase-shifted beamforming matrix A PS , using the characteristic that the modulus value of each element in the delay beamforming matrix is ​​always 1, the delay beamforming matrix T is obtained m . Specifically expressed as:

[0118]

[0119] in and

[0120] i) Using the Cauchy-Schwarz inequality, the above optimization problem is reduced to:

[0121]

[0122] in Represents the pseudoinverse of a matrix.

[0123] ii) Using the characteristic that the modulus value of each element in the delay beamforming matrix is ​​always 1, the optimization problem is transformed into:

[0124]

[0125] in() * Denotes taking the conjugate of a matrix.

[0126] iii) Based on Medium delay matrix T m Size, convert the problem into independent sub-problems on each delayer for optimization:

[0127]

[0128] iv) For iii is a known value. For the maximization in iii, it is only necessary to calculate the actual delay interval of the delay device [0,τ max Specifically, let V represent the number of search steps, and get the search set make τ v =vΔτ. Finally, the optimization method of the delay beamforming matrix is ​​obtained.

[0129] d. Fixed auxiliary matrix U m , digital beamforming matrix D m and the delay beamforming matrix T m , using the characteristic that the modulus of each element in the phase-shift beamforming matrix is ​​always 1, the phase-shift beamforming matrix A is obtained PS . Specifically expressed as:

[0130]

[0131] According to the properties of the F norm, to maximize the optimization problem, we must make in is a known matrix, where J m(i,j) Represents the matrix J m The i-th row and j-th column element of . Through optimization, the phase-shifted beamforming matrix is ​​obtained

[0132] By alternately optimizing the above steps a, b, c, and d, an optimized hybrid beamformer is finally obtained. Figure 4 The normalized array gain of the traditional hybrid beamforming structure and the optimized phase joint beamforming structure of the present invention at different subcarrier frequencies is given. In the terahertz frequency band, we can observe that the traditional hybrid beamforming structure has the lowest frequency f1 and the highest frequency f M and the center carrier frequency f c In the case of , the physical directions of the beams do not overlap, resulting in beam splitting; however, after adding the delay, the beams of different subcarrier frequencies can better align with the physical direction of the target. In particular, the beams of the lowest carrier frequency and the highest carrier frequency achieve a good match with the target direction.

[0133] Finally, it should be noted that 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 can be modified or replaced by equivalents without departing from the purpose and scope of the technical solution, which should be included in the scope of the claims of the present invention.

Claims

1. A hybrid beamforming method based on a terahertz massive MIMO-ISAC system, characterized in that: The method comprises the following steps: Step 1: Obtain channel state information based on beam tracking and determine the optimal communication beamformer using singular value decomposition; Step 2: According to the multi-signal classification MUSIC algorithm, the direction information of the target is obtained and the optimal radar perception beamformer is constructed; Step 3: According to the weight factor, the spectrum efficiency that measures the communication performance and the beam space spectrum matching error that measures the radar performance are combined together to construct an optimization problem; Step 4: Using the property that the unitary matrix does not cause beam distortion, the joint optimization problem of spectral efficiency and spatial spectrum matching error is transformed into the weighted sum of the Euclidean distances between the hybrid beamformer and the optimal communication beamformer / optimal radar beamformer. Step 5: Using the constant mode characteristics of the time delayer and phase shifter, the digital beamformer, the time delay beamformer and the phase shift beamformer are solved respectively by using the alternating minimization method; A small number of delay devices are introduced between the RF chain and the phase shifter, and the frequency-related characteristics of the delay devices are utilized to solve the beam splitting problem. At the same time, a small number of delay devices is also beneficial to reduce system power consumption.

2. The hybrid beamforming method based on terahertz massive MIMO-ISAC system according to claim 1, characterized in that: The steps 1 and 2 specifically include: a. Use channel state information to find the optimal communication beamforming matrix F C,m : H m =U m S m V m H , among them where F C,m represents the optimal communication beamforming matrix of the mth subcarrier, the subscript C represents the abbreviation of the communication system; H m represents the channel of the mth subcarrier, U m ,Σ m , V m Respectively represent H m Do singular value decomposition of the left unitary matrix, singular value matrix, right unitary matrix; () H is the conjugate transpose of the matrix; and is the matrix V m The block matrix, M is the number of subcarriers, and m = 1, 2, M; [] represents the construction of the matrix; b. Use target direction information to construct the optimal radar beamforming matrix F S,m : F S,m =[f m (θ1),f m (θ2),...,f m (i K )] where F S,m represents the optimal sensing beamforming matrix of the mth subcarrier, the subscript S represents the abbreviation of the radar sensing system, and f m (θ k ) represents the optimal sensing beam vector in the kth target direction, θ k represents the direction of the kth target, and k=1,...,K.

3. The hybrid beamforming method based on terahertz massive MIMO-ISAC system according to claim 1, characterized in that: In the step 4, the spectrum efficiency SE for measuring communication performance and the spatial spectrum matching error SSME of the beam for radar performance are combined by weight factors, specifically including: a. Spectral efficiency SE of communication: Where R m represents the spectrum efficiency of the mth subcarrier; N r Indicates the number of antennas at the user end, I Nr Indicates that the dimension is N r ×N r The identity matrix; ρ is the average received power; σ 2 is the additive white Gaussian noise power; Denotes the delay beamforming matrix T at the mth subcarrier m and the phase shift beamforming matrix A PS The hybrid beamforming matrix is ​​composed of P is a P×1 vector of all ones. The symbol ⊙ represents the Hadamard product. PS The abbreviation for phase shifter; symbol It is represented as Kronecker product; log2(||) represents the logarithm of the determinant of the matrix with base 2, and Σ represents the sum operation; b. Radar-perceived spatial spectrum matching error SSME: where f m Represents the frequency of the mth subcarrier; R opt It is represented as the covariance matrix of the optimal radar sensing beam, subscript opt Abbreviation for "best" in English; R m represents the covariance matrix of the hybrid beam on the mth subcarrier; G(f m ,θ k ,R opt ) and G(f m ,θ k ,R m ) respectively represent the k The optimal spatial spectrum and actual spatial spectrum of the mth subcarrier in the direction; | | 2 It represents the square of the matrix modulus; c. Combine steps a and b and use the weight factor ζ∈[0,1] to construct the following optimization problem: Where max means maximizing the objective function under the following constraints; st means satisfying the constraints; A PS (i,j) Represents the matrix A PS The element in the i-th row and j-th column of ; It represents the delay value of the tth delay device on the nth RF chain, and n=1,2,...,N RF and t=1,2,...,T,N RF represents the number of RF chains, T represents the number of delay devices connected to each RF chain; τ max Indicates the maximum delay value of the delay device; N s Indicates the number of transmitted data streams; | | is a modulo operation; It means to find the square of the F norm of the matrix; represents any value; when ζ is 1 or 0, the system is only communicating or sensing.

4. The hybrid beamforming method based on terahertz massive MIMO-ISAC system according to claim 1, characterized in that: In step 4, the optimal radar beamforming matrix, the optimal communication beamforming matrix and the hybrid beamforming matrix are unified into the same dimension by utilizing the characteristic that the unitary matrix does not cause beam distortion, which is specifically: a. In order to maximize the communication spectrum efficiency, the problem is transformed into the problem of minimizing the Euclidean distance between the optimal communication beamforming matrix and the hybrid beamforming matrix, specifically: Where min means minimizing the objective function under the following constraints; b. In order to minimize the radar perception spatial spectrum matching error, the problem is transformed into a problem of minimizing the Euclidean distance between the optimal radar beamforming matrix and the hybrid beamforming matrix, using the auxiliary matrix U m Unify the dimensions of the optimal radar beamforming matrix, the optimal communication beamforming matrix, and the hybrid beamforming matrix, specifically: c. According to the optimization methods in step a and step b, the joint optimization problem of maximizing the communication spectrum and minimizing the radar spatial spectrum matching error is transformed into the problem of minimizing the Euclidean distance between the optimal communication beamforming matrix, the optimal radar sensing beamforming matrix and the hybrid beamforming matrix, specifically: Where F(U m ,A PS ,T m ,D m )for:

5. The hybrid beamforming method based on terahertz massive MIMO-ISAC system according to claim 1, characterized in that: By using the unitary matrix characteristics and the transverse modulus of the delay and phase shift matrix being 1, the optimal digital beamforming matrix, the delay beamforming matrix and the phase shift beamforming matrix are respectively obtained by using the alternating minimization method; the steps of alternating optimization are as follows: a. For the unitary matrix U m , by fixing the digital beamforming matrix D m , delay beamforming matrix T m and the phase-shifted beamforming matrix A PS , using the characteristics of the unitary matrix, the problem is transformed into an orthogonal Prucker problem, and the optimal unitary matrix U is obtained m ; b. For the digital beamforming matrix D m , by fixing the auxiliary matrix U m , delay beamforming matrix T m and the phase-shifted beamforming matrix A PS ; Using the mutual orthogonality of the columns of the optimal communication beamforming matrix and the optimal radar sensing beamforming matrix, constraints are imposed so that the columns of the digital beamforming matrix satisfy quasi-orthogonality, that is, in With D m are unitary matrices with the same dimensions; The digital beamforming matrix optimization problem is a deformation of the orthogonal Prucker problem. The optimal digital beamforming matrix D is obtained. m ; Where η is a positive scaling factor, To define symbols; c. Fixed auxiliary matrix U m , digital beamforming matrix D m and the phase-shifted beamforming matrix A PS , using the characteristic that the modulus value of each element in the delay beamforming matrix is ​​always 1, solve the delay beamforming matrix T m ; d. Fixed auxiliary matrix U m , digital beamforming matrix D m and the delay beamforming matrix T m , using the characteristic that the modulus of each element in the phase-shift beamforming matrix is ​​always 1, the phase-shift beamforming matrix A is obtained PS .

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