A Hybrid Beamforming Method for Integrated Communication and Radar Based on Overlapping Subarrays

Abstract

This invention discloses a hybrid beamforming method for integrated MIMO communication and radar based on overlapping subarrays. Under the conditions of hybrid analog-digital arrays, including overlapping subarray structure, transmit power, and constant mode constraints, a joint problem of maximizing communication spectral efficiency and minimizing radar beam pattern matching error is established. This joint problem is relaxed into a weighted summation minimization problem, where the designed hybrid beamformer minimizes the Euclidean distance to the optimal communication / radar beamformer. This invention decomposes the hybrid beamforming design problem into three subproblems and develops an efficient alternating minimization algorithm. The proposed hybrid beamforming design based on overlapping subarray structure offers flexibility and effectiveness in terms of spectral efficiency and radar beam pattern performance.

Description

Technical Field

[0001] This invention pertains to beamforming technology, specifically a hybrid beamforming method for MIMO communication and radar integration based on overlapping subarrays. Background Technology

[0002] Due to its enhanced sensing capabilities and reduced hardware power consumption and cost, Integrated Communication-Sensing (ISAC) has become one of the key technologies for future sixth-generation (6G) wireless communication systems. Massive Multiple-Input Multiple-Output (MIMO) technology, equipped with a large number of antennas, offers significant improvements in spatial degrees of freedom. The combination of MIMO and ISAC promises to improve spectral efficiency and sensing capabilities, supporting emerging applications such as drones and connected vehicles.

[0003] However, due to the large number of antennas with dedicated radio frequency (RF) chains, large-scale MIMO-ISAC using traditional all-digital beamforming architectures requires excessive power consumption and hardware costs. Hybrid beamforming (HBF) architecture is considered a feasible solution for balancing system performance and hardware efficiency in large-scale MIMO systems. In parallel with communications, a similar hybrid architecture in radar sensing, called subarray MIMO radar, also offers a performance trade-off between phased array and MIMO radar. This has prompted recent research to incorporate hybrid structures into the beamforming design of large-scale MIMO-ISAC systems. Previous studies have investigated sub-connected structures, designing hybrid beamformers by balancing communication and radar sensing beams. Since the antenna array is divided into multiple non-overlapping subarrays in a sub-connected structure (SC), this inevitably leads to a loss of communication and sensing performance. To provide more degrees of freedom for large-scale MIMO-ISAC systems, some researchers have studied the hybrid beamforming design problem of fully connected structures (FC), where radar beam performance and communication service quality are guaranteed at the cost of more phase shifters. Summary of the Invention

[0004] To explore the application of overlapping subarrays in MIMO-ISAC, this invention proposes a hybrid beamforming method for MIMO communication radar integration based on overlapping subarrays.

[0005] The technical solution to achieve the purpose of this invention is: a hybrid beamforming method for MIM0 communication radar based on overlapping subarrays, the specific steps of which are as follows:

[0006] Step 1: Establish a user-received signal model and calculate the spectral efficiency of the communication;

[0007] Step 2: Construct an ideal radar beam pattern and calculate the mean square error of the beam pattern as the radar sensing model;

[0008] Step 3: Construct the overlapping subarray structure and determine the simulated beamforming matrix;

[0009] Step 4: Model the maximization of communication spectrum efficiency and the minimization of radar beam pattern matching error as a joint problem, and then transform it into a weighted Euclidean distance minimization problem of hybrid beamformer and optimal communication / radar beamformer;

[0010] Step 5: Decompose the weighted Euclidean distance minimization problem into three subproblems and solve them separately: digital beamformer, auxiliary unitary matrix, and analog beamformer.

[0011] Preferably, the user received signal model is as follows:

[0012]

[0013] In the formula, ρ represents the transmission power. To simulate a beamformer, For digital beamformers, N BS N represents the number of base station antennas. RF N represents the number of radio frequency chains. s For data stream numbers, Represents complex Gaussian noise, σ z Represents noise variance. It is of dimension N UE unit array, N represents the communication channel. UE This refers to the number of user antennas.

[0014] Preferably, the communication channel is specifically:

[0015]

[0016] In the formula, L represents the number of propagation paths, and α l N represents the gain of the l-th propagation path. BS N represents the number of base station antennas. UE For the number of user antennas, the transmit and receive array steering vectors represent a, respectively. BS (θ l ) and a UE (ψ l ), θ l and ψ l These represent the angle of arrival and the angle of departure, respectively.

[0017] Preferably, the spectral efficiency of the communication is as follows:

[0018]

[0019] In the formula, For dimension N UEThe identity matrix, where ρ represents the transmission power. Represents the communication channel, σ z Represents noise variance. To simulate a beamformer, For digital beamformers, N BS N represents the number of base station antennas. RF N represents the number of radio frequency chains. s For data stream numbers.

[0020] Preferably, the transmitted beam pattern is represented as follows:

[0021]

[0022] In the formula, The covariance matrix representing the transmitted signal. Represents the transmission array steering vector. To simulate a beamformer, For digital beamformers, N BS N represents the number of base station antennas. RF N represents the number of radio frequency chains. s For data stream number;

[0023] The radar sensing model, specifically the mean square error of the beam pattern, is as follows:

[0024]

[0025] In the formula, N p Represents the number of discrete angles. Represents an ideal beam pattern. The covariance matrix representing the transmitted signal, N BS The number of base station antennas. F R It is a radar beamformer.

[0026] Preferably, the simulated beamforming matrix is ​​as follows:

[0027]

[0028] In the formula, (F RF ) i,n =f i,n , n = 1, ..., N RF , represents the element in the i-th row and n-th column of the simulated beamforming matrix, M represents the number of phase shifters connected to a single RF chain, Δ M N represents the subarray offset. RF This represents the number of radio frequency chains.

[0029] Preferably, the specific method for modeling maximizing communication spectral efficiency and minimizing radar beam pattern matching error as a joint problem, and then transforming it into a weighted Euclidean distance minimization problem of a hybrid beamformer and an optimal communication / radar beamformer, is as follows:

[0030] Maximizing communication spectrum efficiency and minimizing radar beam pattern matching error are modeled as a joint problem, specifically expressed as:

[0031]

[0032]

[0033]

[0034] In the formula, η∈[0,1] represents the weighting factor, SE is the spectral efficiency of communication, and MSE is the mean square error of the beam pattern. To simulate a beamformer, For digital beamformers, N BS N represents the number of base station antennas. RF N represents the number of radio frequency chains. s Here, i and n represent the number of data streams, and i and n represent the i-th row and n-th column of the simulated beamformer.

[0035] The problem of maximizing communication spectral efficiency is transformed into minimizing the Euclidean distance between the hybrid beamforming matrix and the optimal communication beamforming matrix, specifically expressed as:

[0036]

[0037] To simulate a beamformer, For digital beamformers, N represents optimal communication beamforming. BS N represents the number of base station antennas. RF N represents the number of radio frequency chains. s For data stream numbers.

[0038] The beam pattern average error is transformed into the minimum Euclidean distance between the hybrid beamforming matrix and the radar beamforming matrix. The formula for the beam pattern average error is then expanded as follows:

[0039]

[0040] Transmit beam pattern Represents an ideal beam pattern. The covariance matrix representing the transmitted signal. F R For radar beamformers, N p The number of discrete angles represents the number of angles, and the transmission array steering vector represents a.BS (θ l ).

[0041] In the second equation, F = F RF F BB Inequality (a) in the formula satisfies the Cauchy-Schwarz inequality. Expanding the above formula further...

[0042]

[0043] F R For radar beamformers, N s Let Tr(·) represent the trace operation; inequality (a) in the formula satisfies the Cauchy-Schwarz inequality, and the last equation in the formula... With constant power, in the formula Representing F and F R The square chord distance on the Gaussian manifold, when F and F R When the dimensions are consistent, use the Euclidean distance on the manifold. Instead of the squared chord distance; when N s >K, introduce an auxiliary unitary matrix Without affecting the performance of the radar beam pattern, make F and F R Consistent dimensions;

[0044] The minimum Euclidean distance between the hybrid beamforming matrix and the radar beamforming matrix is ​​expressed as:

[0045]

[0046] To simulate a beamformer, For digital beamformers, Represents a radar beamformer, auxiliary unitary matrix N BS N represents the number of base station antennas. RF N represents the number of radio frequency chains. s K represents the number of data streams, and K represents the target number.

[0047] The weighted Euclidean distance minimization problem for hybrid beamformers and optimal communication / radar beamformers is expressed as:

[0048]

[0049]

[0050]

[0051]

[0052] To simulate a beamformer, For digital beamformers, auxiliary unitary matrix N BS N represents the number of base station antennas. RF N represents the number of radio frequency chains. s Let g be the number of data streams, K be the target number, and i and n represent the i-th row and n-th column of the simulated beamformer. In the formula, g(F RF ,F BB The weighted Euclidean distance minimization problem (U) is specifically represented as:

[0053]

[0054] η∈[0,1] represents the weighting factor. To simulate a beamformer, For digital beamformers, auxiliary unitary matrix N BS N represents the number of base station antennas. RF N represents the number of radio frequency chains. s K represents the number of data streams, and K represents the target number.

[0055] Preferably, the weighted Euclidean distance minimization problem is decomposed into three subproblems for separate solving: digital beamformer, auxiliary unitary matrix, and analog beamformer. The specific method is as follows:

[0056] Step 5.1: With the auxiliary unitary matrix fixed and the beamformer simulated, the subproblem of solving the digital beamformer is expressed as:

[0057]

[0058] To simulate a beamformer, For digital beamformers, auxiliary unitary matrix N BS N represents the number of base station antennas. RF N represents the number of radio frequency chains. s Let K be the number of data streams and K be the target number. and The subproblem of digital beamformers is restated as follows:

[0059]

[0060] To simulate a beamformer, For digital beamforming, N BS N represents the number of base station antennas. RF N represents the number of radio frequency chains. s For data streams, each column of the optimal communication / radar beamformer is orthogonal; inspired by this structure, F is assigned...BB Quasi-orthogonality, that is:

[0061]

[0062] In the formula, β is a positive scaling factor, and F DD It is a unitary matrix that satisfies I Ns For dimension N UE The subproblem of a unit array and a digital beamformer is equivalent to:

[0063]

[0064] and To simulate a beamformer, For digital beamformers, auxiliary unitary matrix Indicates optimal communication beamforming, N represents a radar beamformer. BS N represents the number of base station antennas. RF N represents the number of radio frequency chains. s Let K be the number of data streams and K be the target number. The last term in the formula is further expressed as:

[0065]

[0066] In the formula F DD It is a unitary matrix. For dimension N UE The identity matrix, the second equation utilizes eigenvalue decomposition. The subproblem of digital beamformers is equivalent to:

[0067]

[0068] In the formula, and To simulate a beamformer, For digital beamformers, auxiliary unitary matrix Indicates optimal communication beamforming, N represents a radar beamformer. BS N represents the number of base station antennas. RF N represents the number of radio frequency chains. s Where K is the number of data streams, F is the target number, and F is the target number. DD It is a unitary matrix. For dimension N UE The above problem concerns the identity matrix, specifically the orthogonal Pluke problem, F. DDObtained through the following:

[0069] F DD =ΦV H ,

[0070] In the formula, and They are respectively through A H Perform singular value decomposition on T, obtaining truncated left and right singular value matrices, and then apply this to F. DD Normalization is performed to obtain the digital beamformer F DD ;

[0071] Step 5.2: With the digital beamformer and analog beamformer fixed, the subproblem of solving the auxiliary unitary matrix is ​​expressed as:

[0072]

[0073] To simulate a beamformer, For digital beamformers, auxiliary unitary matrix N represents a radar beamformer. BS N represents the number of base station antennas. RF N represents the number of radio frequency chains. s Where K is the number of data streams, and K is the target number. For dimension N UE The above problem is non-convex, and can be equivalent to the identity matrix. Only the last term in the equation contains the auxiliary unitary matrix. This problem is also an orthogonal Pluke problem, and the auxiliary unitary matrix can be obtained as follows:

[0074]

[0075] In the formula, and They are respectively through the F RF F BB Perform singular value decomposition to obtain the truncated left and right singular value matrices;

[0076] Step 5.3: With the digital beamformer and auxiliary unitary matrix fixed, solve the subproblem of the analog beamformer as follows:

[0077]

[0078] definition and To simulate a beamformer, For digital beamformers, auxiliary unitary matrix N represents a radar beamformer. BS N represents the number of base station antennas. RF N represents the number of radio frequency chains. s Let K be the number of data streams, i and n be the number of objectives, and i and n be the i-th row and n-th column of the simulated beamformer. The subproblem of the simulated beamformer is expressed in compact form as follows:

[0079]

[0080] Due to the special structure and constant mode constraint of the simulated beamformer, the above problems are minimized, and the simulated beamformer F... RF satisfy

[0081]

[0082] In the formula, φ i,n Yes (F) RF ) i,n phase, D n,: and Y i,: These are the nth and ith rows of D and Y, respectively. and To simulate a beamformer, For digital beamformers, auxiliary unitary matrix N represents a radar beamformer. BS N represents the number of base station antennas. RF N represents the number of radio frequency chains. s Where K is the number of data streams and K is the target number, the phase is then bit-quantized:

[0083]

[0084] In the formula, D n,: and Y i,: These are the nth and ith rows of D and Y, respectively. and To simulate a beamformer, For digital beamformers, auxiliary unitary matrix N represents a radar beamformer. BS N represents the number of base station antennas. RF N represents the number of radio frequency chains. s Given the number of data streams and K as the target number, we obtain the simulated beamformer:

[0085]

[0086] Compared with the prior art, the significant advantages of this invention are:

[0087] The proposed method, based on alternating iterative minimization, relaxes the joint problem of maximizing communication spectral efficiency and minimizing radar beam pattern averaging error into a weighted Euclidean distance minimization problem. This problem is then decomposed into three sub-problems, solved separately: a digital beamformer, an auxiliary unitary matrix, and an analog beamformer. Compared to traditional methods, the proposed hybrid beamforming design based on an overlapping subarray structure offers greater flexibility and effectiveness in terms of spectral efficiency and radar beam pattern performance.

[0088] Other features and advantages of the invention will be set forth in the following description, and will be apparent in part from the description, or may be learned by practicing the invention. The objects and other advantages of the invention may be realized and obtained by means of the structures particularly pointed out in the written description, claims, and drawings. Attached Figure Description

[0089] The accompanying drawings are for illustrative purposes only and are not intended to limit the invention. Throughout the drawings, the same reference numerals denote the same parts.

[0090] Figure 1 This is a diagram of the system model of hybrid beamforming based on large-scale MIMO-ISAC studied in this invention.

[0091] Figure 2 This is a diagram of the overlapping subarray architecture of the present invention, taking an example with 6 antennas, 2 radio frequency chains, and a subarray offset of 2.

[0092] Figure 3 This is a comparison chart of the spectral efficiency of the overlapping subarray structure, the fully connected structure, and the subconnected structure used in this invention.

[0093] Figure 4 This is a comparison chart of the spectral efficiency of the overlapping subarray structure of the phase shifter with the phase connection structure with the infinite bit resolution phase shifter used in this invention.

[0094] Figure 5 This is a comparison chart of the beam pattern performance of different connection structures used in this invention. Figure 5 In (a), the beam pattern performance of the fully connected structure is shown. Figure 5 (b) shows the beam pattern performance of the overlapping subarray structure. Figure 5 (c) represents the beam pattern performance of the sub-connection structure.

[0095] Figure 6 This is a comparison diagram of the beam pattern performance of the overlapping subarray structure of the 1-bit resolution phase shifter and the sub-connection structure of the infinite-bit resolution phase shifter used in this invention. Detailed Implementation

[0096] It is readily understood that, based on the technical solution of this invention, various embodiments of the invention can be conceived by those skilled in the art without altering the essential spirit of the invention. Therefore, the following detailed embodiments and accompanying drawings are merely illustrative examples of the technical solution of this invention and should not be considered as the entirety of the invention or as limitations or restrictions on the technical solution of this invention. Rather, these embodiments are provided to enable those skilled in the art to gain a more thorough understanding of the invention. Preferred embodiments of the invention are described below in conjunction with the accompanying drawings, which form part of this application and, together with the embodiments of the invention, serve to illustrate the innovative concept of the invention.

[0097] A hybrid beamforming method for MIMO communication radar based on overlapping subarrays, the specific steps of which are as follows:

[0098] Step 1: Establish a user-received signal model and calculate the spectral efficiency of the communication;

[0099] Initialize system parameters, including the number of base station antennas N. BS RF chain number N RF Data stream number N s Number of user antennas N UE There are K targets, and the azimuth angle of the k-th target is...

[0100] The base station transmits the following signals:

[0101] x = F RF F BB s,

[0102] In the formula, To simulate a beamformer, For a digital beamformer, the user received signal model is determined as follows:

[0103]

[0104] In the formula, ρ represents the transmission power. Represents complex Gaussian noise, where σ z Represents noise variance. Representing a communication channel, specifically as follows:

[0105]

[0106] In the formula, L represents the number of propagation paths, and α l The gain represents the propagation path l.

[0107] The transmit and receive array steering vectors represent a, respectively. BS (θ l ) and a UE (ψl ), where θ l and ψ l These represent the angle of arrival and the angle of departure, respectively, and the number of antennas is N. BS The guiding vector of a uniform linear array is represented as:

[0108]

[0109] In the formula, d and λ represent the antenna spacing and signal wavelength, respectively.

[0110] Furthermore, the spectral efficiency of communication is expressed as:

[0111]

[0112] Step 2: Construct an ideal radar beam pattern and calculate the mean square error of the beam pattern as the radar sensing model;

[0113] For a specific azimuth angle Its transmitted beam pattern can be represented as:

[0114]

[0115] In the formula, The covariance matrix representing the transmitted signal is specifically expressed as follows:

[0116]

[0117] In the formula, the last equation is removed Given an ideal covariance matrix R R .

[0118] The similarity between the ideal beam pattern and the designed beam pattern can be measured by the mean square error, which is calculated as follows:

[0119]

[0120] In the formula, N p Represents the number of discrete angles. Represents an ideal beam pattern, where the ideal covariance matrix is ​​formed by... The structure, in which the radar beamformer is represented as:

[0121]

[0122] In the formula, This indicates the location of K targets.

[0123] Step 3: Construct an overlapping subarray structure. The RF chain connects the antenna subarrays through phase shifters. Overlap between antenna subarrays is allowed, but the resolution of each phase shifter is limited.

[0124] In the overlapping subarray architecture, each RF chain is connected to a subset of antennas via a phase shifter; the antenna index vector connected to the nth RF chain can be represented as:

[0125] ν n =[(n-1)Δ M +1,…,(n-1)Δ M +M]

[0126] In the formula, Δ M M represents the subarray offset, and M represents the number of phase shifters connected to each RF chain.

[0127] The simulated beamforming matrix can be represented as:

[0128]

[0129] In the formula, (F RF ) i,n =f i,n , n = 1, ..., N RF Let represent the element in the i-th row and n-th column of the simulated beamforming matrix. The phase shifter used in the simulated beamforming matrix has finite resolution. The non-zero elements of the simulated beamforming matrix can be represented as... in, This represents the B-bit quantization phase.

[0130] Step 4: Model the maximization of communication spectrum efficiency and the minimization of radar beam pattern matching error as a joint problem, and then transform it into a weighted Euclidean distance minimization problem of hybrid beamformer and optimal communication / radar beamformer;

[0131] Maximizing communication spectrum efficiency and minimizing radar beam pattern matching error are modeled as a joint problem, which can be specifically expressed as:

[0132]

[0133]

[0134]

[0135] In the formula, η∈[0,1] represents a weighting factor that can balance the performance of radar and communication. Due to the overlapping subarray structure, power, and constant mode constraints, the above problem is a non-convex problem. First, the problem of maximizing communication spectral efficiency is transformed into finding the minimum Euclidean distance between the hybrid beamforming matrix and the optimal communication beamforming matrix, specifically expressed as:

[0136]

[0137] Similarly, the beam pattern average error is transformed into the minimum Euclidean distance between the hybrid beamforming matrix and the radar beamforming matrix. First, the formula for the beam pattern average error is expanded:

[0138]

[0139] In the second equation, F = F RF F BB Inequality (a) in the formula satisfies the Cauchy-Schwarz inequality. Expanding the above formula further...

[0140]

[0141] Inequality (a) in the formula satisfies the Cauchy-Schwarz inequality, and the last equation in the formula... and The power is constant. In the formula... Representing F and F R The square chord distance on the Gaussian manifold. When F and F R When the dimensions are consistent, use the Euclidean distance on the manifold. Instead of the squared chord distance. For the general case, i.e., N s >K, introduce an auxiliary unitary matrix Without affecting the performance of the radar beam pattern, make F and F R The dimensions are consistent. The minimum Euclidean distance between the hybrid beamforming matrix and the radar beamforming matrix can be expressed as:

[0142]

[0143] The weighted Euclidean distance minimization problem between hybrid beamformers and optimal communication / radar beamformers can be expressed as:

[0144]

[0145]

[0146]

[0147]

[0148] In the formula, g(F) RF ,F BB The weighted Euclidean distance minimization problem (U) is specifically represented as:

[0149]

[0150] Step 5: Decompose the weighted Euclidean distance minimization problem into three subproblems and solve them separately: digital beamformer, auxiliary unitary matrix, and analog beamformer.

[0151] Step 5.1: With the auxiliary unitary matrix fixed and the beamformer simulated, the subproblem of solving the digital beamformer is expressed as:

[0152]

[0153] definition and The subproblem of digital beamformers is restated as follows:

[0154]

[0155] Inspired by the fact that each column of the optimal communication / radar beamformer is orthogonal, F... BB Quasi-orthogonality, that is:

[0156]

[0157] In the formula, β is a positive scaling factor, and F DD It is a unitary matrix that satisfies The subproblem of digital beamformers is equivalent to:

[0158]

[0159] The last term in the formula can be further expressed as:

[0160]

[0161] In the formula, the second equation utilizes eigenvalue decomposition. The subproblem of digital beamformers is equivalent to:

[0162]

[0163] The above problem is the orthogonal Pluke problem, F DD It can be obtained as follows:

[0164] F DD =ΦV H ,

[0165] In the formula, and They are respectively through A H Perform singular value decomposition on T, obtaining truncated left and right singular value matrices, and then apply this to F. DD Normalization is performed to obtain the digital beamformer F DD .

[0166] Step 5.2: With the digital beamformer and analog beamformer fixed, the subproblem of solving the auxiliary unitary matrix is ​​expressed as:

[0167]

[0168] The above problem is non-convex, and the problem is equivalent to... Only the last term in the equation contains the auxiliary unitary matrix. This problem is also an orthogonal Pluke problem, and we can obtain the auxiliary unitary matrix as follows:

[0169]

[0170] Step 5.2 in the formula: With the digital beamformer and the analog beamformer fixed, the subproblem of solving the auxiliary unitary matrix is ​​expressed as:

[0171] In the formula, and They are respectively through the F RF F BB Perform singular value decomposition to obtain truncated left and right singular value matrices.

[0172] Step 5.3: With the digital beamformer and auxiliary unitary matrix fixed, solve the subproblem of the analog beamformer as follows:

[0173]

[0174] definition and The compact form of the subproblem of simulating beamformers can be expressed as:

[0175]

[0176] Due to the special structure and constant mode constraint of the simulated beamformer, the above problems are minimized, and the simulated beamformer F... RF Need to meet

[0177]

[0178] In the formula, φ i,n Yes (F) RF ) i,n phase, D n,: and Y i,: These are the nth and ith rows of D and Y, respectively. Next, bit quantization is performed on the phase:

[0179]

[0180] A simulated beamformer can be obtained:

[0181]

[0182] Example 1

[0183] This invention is mainly verified using computer simulation methods, and all steps and conclusions have been verified to be correct using MATLAB.

[0184] Initialization system parameters include: the number of base station transmit antennas N BS =64, RF chain number N RF =8, Number of data streams N s =4, Number of user antennas N UE =4, number of spatial propagation paths L=10, propagation path gain The angles of arrival and departure are uniformly distributed in the range [0, 2π), with two targets set, distributed at 60° and 120°. The signal-to-noise ratio is defined as...

[0185] Step 1: Establish a communication transmission model, construct a communication channel, and calculate the spectral efficiency of the communication;

[0186] Initialize system parameters, including the number of base station antennas N. BS RF chain number N RF Data stream number N s Number of user antennas N UE There are K targets, and the azimuth angle of the k-th target is... .

[0187] The base station transmits the following signals:

[0188] x = F RF F BB s,

[0189] In the formula, To simulate a beamformer, For a digital beamformer, the user receives the following signal:

[0190]

[0191] In the formula, ρ represents the transmission power. Represents complex Gaussian noise, where σ z Represents noise variance. The channel matrix is ​​represented as follows:

[0192]

[0193] In the formula, L represents the number of propagation paths, and α l The gain of the l-th propagation path is represented by the receiving and transmitting array steering vectors, respectively representing a. UE (θ l ) and a BS (ψ l ), where θ l and ψ lThese represent the angle of arrival and the angle of departure, respectively, and the number of antennas is N. BS The guiding vector of a uniform linear array is represented as:

[0194]

[0195] In the formula, d and λ represent the antenna spacing and signal wavelength, respectively. Furthermore, the achievable spectral efficiency is expressed as:

[0196]

[0197] Step 2: Establish a radar perception model. After obtaining the perception azimuth, construct an ideal radar beam pattern and calculate the mean square error of the beam pattern.

[0198] Establish a radar perception model for a specific azimuth angle. Its transmitted beam pattern can be represented as:

[0199]

[0200] In the formula, The covariance matrix representing the transmitted signal is specifically expressed as follows:

[0201]

[0202] In the formula, the last equation is removed Given an ideal covariance matrix R R The similarity between the ideal beam pattern and the designed beam pattern can be measured by the mean square error, which is calculated as follows:

[0203]

[0204] In the formula, N p Represents the number of discrete angles. Represents an ideal beam pattern, where the ideal covariance matrix is ​​formed by... The structure, in which the radar beamformer is represented as:

[0205]

[0206] In the formula, This indicates the location of K targets.

[0207] Step 3: Design an overlapping subarray structure, where the resolution of each phase shifter is finite;

[0208] In an overlapping subarray architecture, each RF chain connects to a subset of antennas via a phase shifter. The antenna index vector connected to the nth RF chain can be represented as:

[0209]

[0210] In the formula, Δ M The subarray offset is represented by M, where M represents the number of phase shifters connected to each RF chain. The analog beamforming matrix can be expressed as:

[0211]

[0212] In the formula, (F RF ) i,n =f i,n , n = 1, ..., N RF Let represent the element in the i-th row and n-th column of the simulated beamforming matrix. The phase shifter used in the simulated beamforming matrix has finite resolution. The non-zero elements of the simulated beamforming matrix can be represented as... in, This represents the B-bit quantization phase.

[0213] Step 4: Model the maximization of communication spectral efficiency and the minimization of radar beam pattern matching error as a joint problem, then transform it into a weighted Euclidean distance minimization problem between the hybrid beamformer and the optimal communication / radar beamformer; the modeling of the maximization of communication spectral efficiency and the minimization of radar beam pattern matching error as a joint problem can be specifically expressed as:

[0214]

[0215]

[0216]

[0217] In the formula, η∈[0,1] represents a weighting factor that can balance the performance of radar and communication. Due to the overlapping subarray structure, power, and constant mode constraints, the above problem is a non-convex problem. First, the problem of maximizing communication spectral efficiency is transformed into finding the minimum Euclidean distance between the hybrid beamforming matrix and the optimal communication beamforming matrix, specifically expressed as:

[0218]

[0219] Similarly, the beam pattern average error is transformed into the minimum Euclidean distance between the hybrid beamforming matrix and the radar beamforming matrix. First, the formula for the beam pattern average error is expanded:

[0220]

[0221] In the second equation, we define F = F RF F BB Inequality (a) in the formula satisfies the Cauchy-Schwarz inequality. Expanding the above formula further...

[0222]

[0223] Inequality (a) in the formula satisfies the Cauchy-Schwarz inequality, and the last equation in the formula... and The power is constant. In the formula... Representing F and F R The square chord distance on the Gaussian manifold. When F and F R When the dimensions are consistent, use the Euclidean distance on the manifold. Instead of the squared chord distance. For the general case, i.e., N s >K, introduce an auxiliary unitary matrix Without affecting the performance of the radar beam pattern, make F and F R The dimensions are consistent. The minimum Euclidean distance between the hybrid beamforming matrix and the radar beamforming matrix can be expressed as:

[0224]

[0225] The weighted Euclidean distance minimization problem between hybrid beamformers and optimal communication / radar beamformers can be expressed as:

[0226]

[0227]

[0228]

[0229]

[0230] In the formula, g(F) RF ,F BB The weighted Euclidean distance minimization problem (U) is specifically represented as:

[0231]

[0232] Step 5: Decompose the weighted Euclidean distance minimization problem into three subproblems and solve them separately: digital beamformer, auxiliary unitary matrix, and analog beamformer.

[0233] Step 5.1: With the auxiliary unitary matrix fixed and the beamformer simulated, the subproblem of solving the digital beamformer is expressed as:

[0234]

[0235] definition and The subproblem of digital beamformers is restated as follows:

[0236]

[0237] Inspired by the fact that each column of the optimal communication / radar beamformer is orthogonal, F... BB Quasi-orthogonality, that is:

[0238]

[0239] In the formula, β is a positive scaling factor, and F DD It is a unitary matrix that satisfies The subproblem of digital beamformers is equivalent to:

[0240]

[0241] The last term in the formula can be further expressed as:

[0242]

[0243] In the formula, the second equation utilizes eigenvalue decomposition. The subproblem of digital beamformers is equivalent to:

[0244]

[0245] The above problem is the orthogonal Pluke problem, F DD It can be obtained as follows:

[0246] F DD =ΦV H ,

[0247] In the formula, and They are respectively through A H Perform singular value decomposition on T, obtaining truncated left and right singular value matrices, and then apply this to F. DD Normalization is performed to obtain the digital beamformer F DD .

[0248] Step 5.2: With the digital beamformer and analog beamformer fixed, the subproblem of solving the auxiliary unitary matrix is ​​expressed as:

[0249]

[0250] The above problem is non-convex, and the problem is equivalent to... Only the last term in the equation contains the auxiliary unitary matrix. This problem is also an orthogonal Pluke problem, and we can obtain the auxiliary unitary matrix as follows:

[0251]

[0252] Step 5.2 in the formula: With the digital beamformer and the analog beamformer fixed, the subproblem of solving the auxiliary unitary matrix is ​​expressed as:

[0253] In the formula, and They are respectively through the F RF F BB Perform singular value decomposition to obtain truncated left and right singular value matrices.

[0254] Step 5.3: With the digital beamformer and auxiliary unitary matrix fixed, solve the subproblem of the analog beamformer as follows:

[0255]

[0256] definition and Simulated beam

[0257] The compact form of the subproblem of the forming machine can be expressed as:

[0258]

[0259] Due to the special structure and constant mode constraint of the simulated beamformer, the above problems are minimized, and the simulated beamformer F... RF Need to meet

[0260]

[0261] In the formula, φ i,n Yes (F) RF ) i,n phase, D n,: and Y i,: These are the nth and ith rows of D and Y, respectively. Next, bit quantization is performed on the phase:

[0262]

[0263] A simulated beamformer can be obtained:

[0264]

[0265] To better evaluate the performance of the proposed hybrid beamforming scheme with overlapping subarrays, the performance of the adopted structure is verified by comparing it with both fully connected (FC) and sub-connected (SC) structures. Figure 3 As shown, the weights η are set to 1, 0.6, and 0.4 respectively, and the subarray offset Δ of the Overlapping Subarray (OSA) is set. M =5, the spectral efficiency of each connection structure decreases as η decreases because the weights favor radar sensing. The proposed hybrid beamforming design with overlapping subarray structures achieves an intermediate spectral efficiency performance between fully connected and sub-connected structures. For example... Figure 4As shown, the spectral efficiency performance of the overlapping subarray structure under different phase shifter resolutions B was studied. The subarray offset Δ of the overlapping subarray was set. M =5. Lower phase shifter resolution will inevitably reduce spectral efficiency performance. Nevertheless, the overlapping subarray structure with weight η = 0.6 and phase shifter resolution B = 1 still has better spectral efficiency performance than the subconnection structure with infinite phase shifter resolution and weight η = 1. Figure 5 (a) to (c) compare the performance of radar sensing beam patterns with different hybrid beamforming structures, setting the subarray offset Δ of the overlapping subarray. M =5. As the weighting coefficient η decreases, the beam pattern generated by the designed hybrid beamforming gradually approaches the ideal beam pattern. As a compromise between the fully connected structure and the sub-connected structure, the overlapping subarray structure achieves satisfactory beam pattern performance with far fewer phase shifters than the FC structure. Figure 6 The beam pattern performance of the overlapping subarray structure with a phase shifter resolution of 1 and the sub-connection structure with an infinite phase shifter resolution were compared, and the performance of the overlapping subarray structure was more competitive.

[0266] The above description is only a preferred embodiment of the present invention, but the scope of protection of the present invention is not limited thereto. Any changes or substitutions that can be easily conceived by those skilled in the art within the scope of the technology disclosed in the present invention should be included within the scope of protection of the present invention.

[0267] It should be understood that, in order to simplify the present invention and help those skilled in the art understand its various aspects, in the above description of exemplary embodiments of the present invention, various features of the present invention are sometimes described in a single embodiment or with reference to a single figure. However, the present invention should not be construed as including all features in the exemplary embodiments as essential technical features of the claims of this patent.

[0268] It should be understood that the modules, units, components, etc., included in the device of one embodiment of the present invention can be adaptively changed to be placed in a device different from that embodiment. Different modules, units, or components included in the device of the embodiment can be combined into a single module, unit, or component, or they can be divided into multiple sub-modules, sub-units, or sub-components.

Claims

1. A hybrid beamforming method for MIMO communication radar based on overlapping subarrays, characterized in that, The specific steps are as follows: Step 1: Establish a user-received signal model and calculate the spectral efficiency of the communication; Step 2: Construct an ideal radar beam pattern and calculate the mean square error of the beam pattern as the radar sensing model; Step 3: Construct the overlapping subarray structure and determine the simulated beamforming matrix; Step 4: Model maximizing communication spectral efficiency and minimizing radar beam pattern matching error as a joint problem, then transform it into a weighted Euclidean distance minimization problem between the hybrid beamformer and the optimal communication / radar beamformer. Specifically, this is represented as: In the formula, Represents the weighting factor, SE is the spectral efficiency of communication, and MSE is the mean square error of the beam pattern. To simulate a beamformer, For digital beamformers, The number of base station antennas. For the number of radio frequency chains, Here, i and n represent the number of data streams, and i and n represent the i-th row and n-th column of the simulated beamformer. The problem of maximizing communication spectral efficiency is transformed into minimizing the Euclidean distance between the hybrid beamforming matrix and the optimal communication beamforming matrix, specifically expressed as: To simulate a beamformer, For digital beamformers, Indicates optimal communication beamforming. The number of base station antennas. For the number of radio frequency chains, For data stream number; The beam pattern average error is transformed into the minimum Euclidean distance between the hybrid beamforming matrix and the radar beamforming matrix. The formula for the beam pattern average error is then expanded as follows: Transmit beam pattern , Represents an ideal beam pattern. The covariance matrix representing the transmitted signal. , For radar beamformers, The number of discrete angles is represented by the transmission array steering vector. ; The second equation in the formula is defined as follows: Inequality (a) in the formula satisfies the Cauchy-Schwarz inequality. Expanding the above formula further... For radar beamformers, For data stream numbers, The trace operation is represented; inequality (a) in the formula satisfies the Cauchy-Schwarz inequality, and the last equality in the formula... and With constant power, in the formula represent and The square chord distance on the Gaussian manifold, when and When the dimensions are consistent, use the Euclidean distance on the manifold. Instead of square chord distance; when Introducing an auxiliary unitary matrix Without affecting the performance of the radar beam pattern, and Consistent dimensions; The minimum Euclidean distance between the hybrid beamforming matrix and the radar beamforming matrix is ​​expressed as: To simulate a beamformer, For digital beamformers, Represents a radar beamformer, auxiliary unitary matrix , The number of base station antennas. For the number of radio frequency chains, K represents the number of data streams, and K represents the target number. The weighted Euclidean distance minimization problem for hybrid beamformers and optimal communication / radar beamformers is expressed as: To simulate a beamformer, For digital beamformers, auxiliary unitary matrix , The number of base station antennas. For the number of radio frequency chains, Where K is the number of data streams, i and n represent the i-th row and n-th column of the simulated beamformer; in the formula, The weighted Euclidean distance minimization problem is specifically represented as: Represents weighting factors. To simulate a beamformer, For digital beamformers, auxiliary unitary matrix , The number of base station antennas. For the number of radio frequency chains, K represents the number of data streams, and K represents the target number. Step 5: Decompose the weighted Euclidean distance minimization problem into three subproblems and solve them separately: digital beamformer, auxiliary unitary matrix, and analog beamformer.

2. The MIMO communication radar integrated hybrid beamforming method based on overlapping subarrays according to claim 1, characterized in that, The user-received signal model is specifically as follows: In the formula, Indicates transmission power. To simulate a beamformer, For digital beamformers, The number of base station antennas. For the number of radio frequency chains, For data stream numbers, Represents complex Gaussian noise. Represents noise variance. It is a dimension of unit array, Represents the communication channel. This refers to the number of user antennas.

3. The MIMO communication radar integrated hybrid beamforming method based on overlapping subarrays according to claim 2, characterized in that, The communication channel is specifically as follows: In the formula, L represents the number of propagation paths. The gain representing the propagation path l. The number of base station antennas. For the number of user antennas, the transmit and receive array steering vectors represent respectively and , and These represent the angle of arrival and the angle of departure, respectively.

4. The integrated hybrid beamforming method for MIMO communication radar based on overlapping subarrays according to claim 2, characterized in that, The specific spectral efficiency of communication is as follows: In the formula, For dimension unit array, Indicates transmission power. Represents the communication channel. Represents noise variance. To simulate a beamformer, For digital beamformers, The number of base station antennas. For the number of radio frequency chains, For data stream numbers.

5. The MIMO communication radar integrated hybrid beamforming method based on overlapping subarrays according to claim 1, characterized in that, The transmitted beam pattern is represented as follows: In the formula, The covariance matrix representing the transmitted signal. Represents the transmission array steering vector. To simulate a beamformer, For digital beamformers, The number of base station antennas. For the number of radio frequency chains, For data stream number; The radar sensing model, specifically the mean square error of the beam pattern, is as follows: In the formula, Represents the number of discrete angles. Represents an ideal beam pattern. The covariance matrix representing the transmitted signal. The number of base station antennas. , It is a radar beamformer.

6. The MIMO communication radar integrated hybrid beamforming method based on overlapping subarrays according to claim 1, characterized in that, The simulated beamforming matrix is ​​as follows: In the formula, , , , represents the element in the i-th row and n-th column of the simulated beamforming matrix, and M represents the number of phase shifters connected to a single RF chain. Represents the subarray offset. This represents the number of radio frequency chains.

7. The MIMO communication radar integrated hybrid beamforming method based on overlapping subarrays according to claim 1, characterized in that, The specific method for decomposing the weighted Euclidean distance minimization problem into three subproblems—digital beamformer, auxiliary unitary matrix, and analog beamformer—is as follows: Step 5.1: With the auxiliary unitary matrix fixed and the beamformer simulated, the subproblem of solving the digital beamformer is expressed as: To simulate a beamformer, For digital beamformers, auxiliary unitary matrix , The number of base station antennas. For the number of radio frequency chains, Let K be the number of data streams and K be the target number. and The subproblem of digital beamformers is restated as follows: To simulate a beamformer, For digital beamforming, The number of base station antennas. For the number of radio frequency chains, For data streams, each column of the optimal communication / radar beamformer is orthogonal; inspired by this structure, [the following is a separate, unrelated sentence:] ... Quasi-orthogonality, that is: In the formula, A proportionality factor that is positive. It is a unitary matrix that satisfies , For dimension The subproblem of a unit array and a digital beamformer is equivalent to: and , To simulate a beamformer, For digital beamformers, auxiliary unitary matrix , Indicates optimal communication beamforming. Indicates radar beamformer, The number of base station antennas. For the number of radio frequency chains, Let K be the number of data streams and K be the target number. The last term in the formula is further expressed as: In the formula , It is a unitary matrix. For dimension The identity matrix, the second equation utilizes eigenvalue decomposition. The subproblem of digital beamformers is equivalent to: In the formula, and , To simulate a beamformer, For digital beamformers, auxiliary unitary matrix , Indicates optimal communication beamforming. Indicates radar beamformer, The number of base station antennas. For the number of radio frequency chains, Where K is the number of data streams, and K is the target number. It is a unitary matrix. For dimension The above problem concerns the orthogonal Pluke problem, which deals with the identity matrix. Obtained through the following: In the formula, and They are respectively through the Perform singular value decomposition to obtain truncated left and right singular value matrices. Normalization is performed to obtain a digital beamformer ; Step 5.2: With the digital beamformer and analog beamformer fixed, the subproblem of solving the auxiliary unitary matrix is ​​expressed as: To simulate a beamformer, For digital beamformers, auxiliary unitary matrix , Indicates radar beamformer, The number of base station antennas. For the number of radio frequency chains, Where K is the number of data streams, and K is the target number. For dimension The above problem is non-convex, and can be equivalent to the identity matrix. The equation contains only the last term, which is an auxiliary unitary matrix. This problem is also an orthogonal Pluke problem. The auxiliary unitary matrix can be obtained as follows: In the formula, and They are respectively through the Perform singular value decomposition to obtain the truncated left and right singular value matrices; Step 5.3: With the digital beamformer and auxiliary unitary matrix fixed, solve the subproblem of the analog beamformer as follows: definition and , To simulate a beamformer, For digital beamformers, auxiliary unitary matrix , Indicates radar beamformer, The number of base station antennas. For the number of radio frequency chains, Let K be the number of data streams, i and n be the number of objectives, and i and n be the i-th row and n-th column of the simulated beamformer. The subproblem of the simulated beamformer is expressed in compact form as follows: Due to the special structure and constant mode constraint of the simulated beamformer, the above problems are minimized. satisfy In the formula, yes phase, and They are and The nth and ith rows; and , To simulate a beamformer, For digital beamformers, auxiliary unitary matrix , Indicates radar beamformer, The number of base station antennas. For the number of radio frequency chains, Where K is the number of data streams and K is the target number, the phase is then bit-quantized: In the formula, , , and They are and The nth and ith rows; and , To simulate a beamformer, For digital beamformers, auxiliary unitary matrix , Indicates radar beamformer, The number of base station antennas. For the number of radio frequency chains, Given the number of data streams and K as the target number, we obtain the simulated beamformer: 。

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