Integrated sensing and beamforming method based on aperture allocation and saturated power amplification

Abstract

The application discloses a through-sensing integrated beam forming method based on aperture distribution and saturated power amplification, and mainly aims to solve the problems of low radar sensing performance, the need of all antennas and the simultaneous design of communication beams and radar sensing beams. The implementation steps are as follows: a transmitting array is divided into communication antennas and radar sensing antennas, communication beams and radar sensing beams are respectively designed, and communication data streams are corrected to ensure constant communication signal-to-interference-and-noise ratio. The designed beams can improve the radar sensing performance in the through-sensing integrated system, enhance the radar direction of arrival estimation performance, and ensure constant communication signal-to-interference-and-noise ratio, without the need of simultaneously designing communication beams and radar sensing beams.

Description

Technical Field

[0001] This invention belongs to the field of telecommunications technology, and further relates to a method for integrated inductive beamforming based on aperture allocation and saturated power amplification within the field of inductive technology. This invention can be used to divide a transmitting array into a communication antenna and a radar sensing antenna, and to design communication beams and radar sensing beams separately. Background Technology

[0002] In recent years, Integrated Sensing and Communication (ISAC) technology has achieved the integration and unification of communication and radar sensing tasks by sharing spectrum resources, jointly designing integrated sensing beams, and multiplexing hardware platforms and signal processing modules. Traditional integrated sensing beam design methods utilize all transmitting antennas in the transmitting array to design communication and radar sensing beams, using these beams to implement communication and radar sensing functions respectively. When designing beams, the transmit power constraints of the actual system must be met, often constraining the total transmit power of each transmitting beam or the average transmit power of each antenna in the transmitting array. However, in practical engineering applications, communication waveforms have a high peak-to-average power ratio. To avoid nonlinear distortion and clipping in power amplifiers that degrade communication system performance, each power amplifier in the integrated sensing system must operate in the linear range, and its average transmit power is much lower than its maximum transmit power, limiting the radar sensing performance of the integrated sensing system.

[0003] In their paper "Cramer-Rao Bound Optimization for Joint Radar-Communication Beamforming" (IEEE TRANSACTIONS ON SIGNAL PROCESSING, 2022, Vol. 70), Fan Liu et al. proposed a method for designing a coherent and inductive beam under total power constraints. This method minimizes the Cramer-Rao bound (CRB) of the direction of arrival (DOA) estimation while satisfying the signal-to-interference-plus-noise ratio (SINR) condition, and proposes a semidefinite programming method for solving this bound. The drawbacks of this method are that the designed coherent and inductive beam requires the use of all transmit antennas in the transmit array to achieve communication functionality, and all power amplifiers in the transmit antennas must operate in the linear range, resulting in a limited transmit power for the designed beam.

[0004] In their paper "Joint Transmit Beamforming for Multiuser MIMO Communications and MIMO Radar" (IEEE TRANSACTIONS ON SIGNAL PROCESSING, 2020, Vol. 68), Xiang Liu et al. proposed an integrated communication and radar sensing beam design method that simultaneously designs communication and radar sensing beams. The method assumes that the communication and radar sensing symbols are uncorrelated and constructs an integrated communication and radar sensing beam design model with pattern matching error as the objective function, communication signal-to-interference-plus-noise ratio (SNR) and per-antenna power constraint (PAPC) as constraints, and the covariance matrices of the communication and radar sensing beams as optimization variables. The method has a drawback: it assumes that the communication and radar sensing symbols are linearly superimposed on each transmit array element and requires the power amplifiers in the transmit array to operate in the linear range. However, the communication data stream has a large peak-to-average power ratio (PAPR). To avoid nonlinear distortion and clipping affecting communication performance, this method constrains the transmit power of the transmitting antennas to the linear amplification region, limiting the output power of the integrated communication and radar sensing system and thus limiting the radar sensing performance of the system.

[0005] Beijing University of Posts and Telecommunications disclosed a method for integrated communication and sensing beam design in its patent application, "A Method for Integrated Communication and Sensing Beam Design Based on MIMO Communication and Sensing Technology" (Patent Application No. 202311054119.2, Publication No. CN 117060954 A). The method involves establishing channel matrix diagonalization and signal-to-interference-plus-noise ratio (SIR) constraints; optimizing the error function between the transmit beam pattern and the radar beam pattern; establishing and solving a design model for the beam covariance matrix; based on the obtained optimal beam covariance matrix; and recovering the communication beam and radar sensing beam using Cholesky decomposition and QR decomposition. The advantage of this method is that it uses a simpler optimization objective function in the beam design model, reducing the computational complexity of designing the integrated communication and sensing beam. However, a remaining drawback is that, since this method uses all antennas of the transmit array in the system to achieve communication and radar sensing functions, it requires the simultaneous design of both communication and radar sensing beams to satisfy both functions. Summary of the Invention

[0006] The purpose of this invention is to address the shortcomings of existing technologies by proposing a beamforming method for integrated inductive and perceptual systems based on aperture allocation and saturated power amplification. This method solves the problems of requiring all transmitting antennas to perform communication functions in integrated inductive and perceptual systems, resulting in low radar sensing performance, and the need to simultaneously design communication and radar sensing beams.

[0007] The specific approach to achieving the objective of this invention is as follows: This invention achieves communication functionality in an integrated sensing and communication system by selecting a portion of the antennas in the transmitting array as communication antennas. It adaptively allocates the antennas in the transmitting array and designs the communication beam. The designed communication beam, under the power constraints of the communication antennas, meets the signal-to-interference-plus-noise ratio (SNR) requirements. This eliminates the need to utilize all antennas in the transmitting array to achieve communication functionality in the integrated sensing and communication system, thus solving the problem in existing technologies that require the use of all transmitting antennas. Furthermore, because this invention uses a portion of the antennas in the transmitting array as communication antennas and the remaining antennas as radar sensing antennas, and operates the radar sensing antennas in the saturation amplification range to transmit a constant envelope radar sensing waveform, the radar sensing antennas have higher transmission power compared to the communication antennas. The designed radar sensing beam enhances the system's transmission power, thereby solving the problems of limited transmission power and low radar sensing performance in existing technologies. Because this invention designs the radar sensing beam based on existing aperture allocation and communication beams, it allows the radar beam to interfere with communication users to a certain extent while meeting the communication signal-to-interference-plus-noise ratio (SNR) requirements. By modifying the communication data stream to maintain a constant SNR, it is not necessary to design both the communication beam and the radar sensing beam simultaneously, thus solving the problem of needing to design both the communication beam and the radar sensing beam at the same time.

[0008] The specific steps to achieve the objective of this invention include the following:

[0009] Step 1: Establish a communication and sensing integrated system with multiple communication users. Each transmitting antenna in the base station transmitting array is connected to its corresponding radio frequency link. The power amplifier in each radio frequency link can operate in the linear amplification range or the saturation amplification range.

[0010] Step 2: Select some antennas in the base station transmitting array as communication antennas and the rest as radar sensing antennas. The number of selected communication antennas is the minimum number of antennas required to achieve the communication function. The power amplifier of the radar sensing antenna operates in the saturation range.

[0011] Step 3: With the goal of minimizing the number of selected communication antennas and with the communication antenna transmit power and the signal-to-interference-plus-noise ratio of the communication users as constraints, construct an aperture allocation and communication beam design model;

[0012] Step 4: Using the continuous convex approximation and semi-positive definite programming method, the aperture allocation and communication beam design model are iteratively optimized to adaptively determine the number of communication antennas and generate the communication beam.

[0013] Step 5: Under the constraints of radar antenna transmit power and radar interference to communication users, maximize the transmit power of the radar beam in the direction of the radar target and construct a radar sensing beam design model.

[0014] Step 6: If the radar interference constraint on communication users is zero, the radar sensing beam design model is solved using a closed-form solution; if the radar interference constraint on communication users is not zero, the radar sensing beam design model is solved using the alternating direction multiplier method to generate the radar sensing beam.

[0015] Step 7: When the radar's interference constraint on communication users is not zero, active interference cancellation technology is used to correct the communication data stream to ensure that the communication signal-to-interference-plus-noise ratio remains constant.

[0016] Furthermore, the establishment of a multi-communication user integrated sensing system is as follows. Wherein,

[0017] The expression for the transmitted signal X of the base station in the integrated sensing system is:

[0018] X = WS + w r s r

[0019] Where W represents the beam matrix of the base station transmitted signal in the integrated sensing system. w k N represents the beam of the k-th communication user. t N represents the total number of transmitting antennas. r K represents the total number of receiving antennas, S represents the total number of antenna communication users, and S represents the communication baseband data stream. Let represent the data stream of the k-th communication user, (·) T This represents the transpose operator. This represents the sensing beam of the r-th receiving antenna of the radar. Let represent the radar sensing data stream of the r-th receiving antenna with constant envelope. The mean of the communication data stream and the radar sensing data stream is 0, and the data streams are independent of each other. The operator representing mathematical expectation, (·). H Represents the conjugate transpose operator;

[0020] Based on the transmitted signal of the integrated induction system, the signal received by each antenna communication user can be represented as:

[0021]

[0022] Among them, y k This represents the signal received by the k-th antenna communication user. w represents the channel state vector from the transmitter to the k-th communication user. i w represents the communication beam of the i-th communication user. r Indicates the radar sensing beam, s i Let s represent the communication data stream of the i-th communication user. r Represents the radar sensing data stream, nk Let the variance of the white Gaussian noise received by the k-th antenna communication user be .

[0023] The signal-to-interference-plus-noise ratio (SINR) for each communication user can be expressed as:

[0024]

[0025] Where, γ k Let |·| represent the signal-to-interference-plus-noise ratio (SINR) of the k-th communication user, and |·| represent the modulo operator.

[0026] Based on the transmitted signal from the integrated sensing system, the base station receives the radar target echo signal Y. r It can be represented as:

[0027] Y r =αa r (θ)a t (θ) T X+N r

[0028] in, This represents the path loss coefficient of the target echo. Let N represent the transmit steering vector and receive steering vector of the integrated sensing system, respectively, θ represent the angle of the radar target, and N represent the transmit steering vector and receive steering vector of the integrated sensing system. r The variance of the integrated inductive receiver is... Gaussian white noise;

[0029] The radiated power of the integrated sensing system at each radar target angle can be expressed as:

[0030]

[0031] Wherein, P(θ) represents the radiated power of the integrated sensing system located at the radar target angle θ;

[0032] The Cramer-Rao boundary (CRB) for estimating the radar target's direction of arrival angle is expressed as:

[0033]

[0034] in, Let represent the noise variance at the receiver of the integrated sensing system, and tr(·) represent the trace of the matrix. Indicates a r The derivative of (θ) with respect to θ Indicates a t (θ) is the derivative of θ, where α represents the path loss coefficient of the radar target echo, and L represents the length of the communication data stream.

[0035] Furthermore, the constraint condition of the communication antenna transmit power and the signal-to-interference-plus-noise ratio of the communication user refers to the situation where the following formula is satisfied:

[0036]

[0037] γ k ≥Γ k

[0038] Among them, w k [n] represents w k The nth element, u[n] represents the nth element in the aperture allocation vector u, where all elements in u are in the set {0,1}, P ant Γ represents the transmit power of the communication antenna. k This represents the signal-to-interference-plus-noise ratio (SIR) threshold for the k-th communication user.

[0039] Furthermore, the aperture allocation and communication beam design model is as follows:

[0040]

[0041] u[n]∈{0,1}

[0042] Where ||·||0 represents the zero norm operator, This represents any value taken within the range [1, K]. Indicates [1, N] t It can be any value taken from the range of ].

[0043] Furthermore, the steps for iteratively optimizing the aperture allocation and communication beam design model using the continuous convex approximation and semi-positive definite programming method are as follows:

[0044] The first step is to approximate the aperture allocation and communication beam design model as the objective function in the following form:

[0045]

[0046] Where log(·) represents the base-10 logarithmic operation, and μ represents the approximation error;

[0047] The second step is to use the continuous convex approximation method to perform a Taylor expansion of f(u):

[0048]

[0049] in, This indicates that in the i-th iteration, f(u) is in u (i-1) The result of the first-order Taylor expansion at the given location;

[0050] The second step is to define a matrix. The aperture allocation and communication beam design model is updated to the following form:

[0051]

[0052] 0≤u≤1

[0053] rank(W k ) = 1

[0054]

[0055] Among them, diag(W) k This indicates that the matrix W is returned in vector form. k The diagonal elements, rank(·) denote the rank of the matrix. Represents the constraint matrix W k Given a positive semi-definite matrix, the first constraint in the above model is the communication signal-to-interference-plus-noise ratio constraint, and the second constraint is the communication antenna transmit power constraint.

[0056] The third step is to use a semidefinite programming algorithm to solve the updated model.

[0057] The fourth step is to determine whether the preset maximum number of iterations has been reached. If so, the number of antennas in the current iteration is determined as the number of communication antennas and a communication beam is generated. Otherwise, the second step is executed.

[0058] Furthermore, the radar antenna transmit power constraint refers to the requirement that the radar sensing beam must meet the power constraint of the radar sensing antenna for the radar sensing beam w. r The power constraint is:

[0059]

[0060] in, Ω r Represents a collection of radar sensing antennas. Ω c The set of communication antennas, and the interference constraint of the radar sensing beam on the communication user, are as follows: Where ε represents the radar communication interference threshold.

[0061] Furthermore, the radar sensing beam design model is as follows:

[0062]

[0063] Where -P(θ) represents the minimum -P(θ) corresponding to maximizing the transmit power P(θ) in the radar target direction when designing the radar sensing beam, allowing the radar beam to have a certain degree of interference to the communication user.

[0064] Furthermore, when the radar's interference constraint on communication users is zero, the radar sensing beam design model has a closed-form solution. In this case, the optimal solution for the radar sensing beam can be expressed as:

[0065]

[0066] Where I represents the identity matrix, and U represents the diagonal matrix formed by using the elements of vector u as its diagonal. The channel matrix representing the communication users, Let a represent the pseudo-inverse of a matrix. t (θ) represents the steering vector of the transmission array, and max(·) represents the maximum value operation;

[0067] Furthermore, the steps for solving the radar sensing beam design model using the alternating direction multiplier method are as follows:

[0068] The first step is to define the auxiliary variable v. r And assume v r =w r ;

[0069] The second step is to generate the augmented Lagrangian function of the radar sensing beam design model. generated It can be represented as:

[0070]

[0071] Where ρ represents the penalty factor, Denote the Lagrange dual variable;

[0072] The third step is to use the augmented Lagrange function from the second step. With w r The following optimization model is established for the optimization variables, and the model is solved using a convex optimization algorithm:

[0073]

[0074] in,(·) * This indicates the conjugate operation;

[0075] Fourth step, based on the augmented Lagrange function in step two. With v r The following optimization model is established for the optimization variables:

[0076]

[0077] The model is solved using a convex optimization algorithm.

[0078] Fifth step, according to d r =d r +wr -v r Formula for updating the Lagrange dual variable d r ;

[0079] Step 6: Determine if the maximum number of iterations has been reached. If so, set the current iteration's w... r If it is confirmed to be a radar sensing beam, otherwise, proceed to step three.

[0080] Compared with the prior art, the present invention has the following advantages:

[0081] First, because the present invention allocates a portion of the antennas in the transmitting array as communication antennas and designs the communication beam to meet the communication signal-to-interference-plus-noise ratio requirements, it can adaptively allocate the transmitting aperture and design the communication beam to realize the communication function in the integrated sensing system. This overcomes the defect in the prior art that all antennas of the transmitting array are required to realize the communication function, so that the beam designed in the present invention only needs a portion of the antennas to realize the communication function.

[0082] Secondly, because the present invention uses the remaining antennas in the transmitting array as radar sensing antennas according to the aperture allocation result, and makes the power amplifier of the radar sensing antenna work in the saturation amplification range to obtain greater transmission power for transmitting radar sensing waveforms with constant envelope, it overcomes the defect of low transmission power in the prior art. This invention increases the transmission power of the system and can effectively improve the radar sensing performance in the integrated sensing system and enhance the radar wave direction of arrival estimation performance.

[0083] Third, because the present invention allows for a certain degree of interference from the radar beam to the communication user when designing the radar sensing beam, and constrains the interference of the radar to the communication to not exceed a certain threshold, the communication data stream is corrected at the transmitting end to eliminate the interference of the radar beam to the communication user. This overcomes the defect in the prior art that requires the simultaneous design of the communication beam and the radar sensing beam to meet the signal-to-interference-plus-noise ratio (SNR) requirement. The radar sensing beam designed in this invention can be based on the existing aperture allocation and communication beam to ensure a constant SNR at the receiving end of the communication user, without the need to design the communication beam and the radar sensing beam simultaneously. Attached Figure Description

[0084] Figure 1 This is a flowchart of the present invention;

[0085] Figure 2 This is a schematic diagram of the integrated sensing system structure designed in an embodiment of the present invention;

[0086] Figure 3 This is the beam pattern of the simulation experiment of this invention;

[0087] Figure 4 The figure shows the simulation results of aperture allocation and transmit antenna power in the simulation experiment of this invention;

[0088] Figure 5 This is a graph showing the relationship between the direction-of-arrival (DOA) estimation performance and the radar signal-to-noise ratio in the simulation experiment of this invention. Detailed Implementation

[0089] The present invention will be further described below with reference to the accompanying drawings and embodiments.

[0090] Reference Figure 1 The specific steps for implementing the embodiments of the present invention will be further described below.

[0091] Step 1. Establish a sensor-integrated system with multiple communication users:

[0092] The integrated sensing system model designed in this embodiment of the invention is as follows: Figure 2 As shown.

[0093] The integrated inductive and perceptron system consists of one base station and K single-antenna communication users. The integrated inductive and perceptron base station has N... t One transmitting antenna and N r Each base station has one receiving antenna and one transmitting antenna connected to a radio frequency (RF) link. The power amplifier in the RF link can operate in either the linear amplification range or the saturation amplification range. In this embodiment of the invention, the number of communication users K = 2, and the base station has N... t =25 transmitting antennas and N r = 25 receiving antennas.

[0094] Step 1.1, according to the integrated sensing system model, the transmitted signal X of the base station in the integrated sensing system can be expressed as:

[0095] X = WS + w r s r

[0096] Where W represents the beam matrix of the base station transmitted signal in the integrated sensing system. w k This represents the beam of the k-th communication user. Indicates the communication baseband data stream. Let represent the data stream of the k-th communication user, (·) T This indicates the transpose operation. Indicates the radar sensing beam. This represents the radar sensing data stream with constant envelope. The mean of the communication data stream and the radar sensing data stream is 0, and the data streams are independent of each other. in The operator representing mathematical expectation, (·). H This represents the conjugate transpose operator.

[0097] Step 1.2, based on the integrated sensing system model and the transmitted signal, the signal received by the k-th single-antenna communication user is represented as:

[0098]

[0099] in, This represents the channel state vector from the transmitter to the k-th communication user, where n is the number of users. k Let the variance of the white Gaussian noise received by communication user k be .

[0100] The signal-to-interference-plus-noise ratio γ for each communication user k k Represented as:

[0101]

[0102] Where, γ k This represents the signal-to-interference-plus-noise ratio (SIR) of the k-th communication user.

[0103] Step 1.3, based on the transmitted signal of the integrated sensing system, the base station receives the radar target echo signal Y. r Represented as

[0104] Y r =αa r (θ)a t (θ) T X+N r

[0105] in, This represents the path loss coefficient of the target echo. and Let N represent the transmit steering vector and receive steering vector of the integrated sensing system, respectively, θ represent the angle of the radar target, and N represent the transmit steering vector and receive steering vector of the integrated sensing system. r The variance of the integrated inductive receiver is... Gaussian white noise.

[0106] The radiated power of the integrated sensing system at each radar target angle can be expressed as:

[0107]

[0108] Where P(θ) represents the radiated power of the integrated sensing system located at the radar target angle θ.

[0109] The Cramer-Rao boundary (CRB) for estimating the radar target's direction of arrival angle is expressed as:

[0110]

[0111] Where tr(·) represents the trace of the matrix, in Indicates a r The derivative of (θ) with respect to θ Indicates a t (θ) is the derivative of θ. Thus, step 1 completes the establishment of the integrated sensory system model.

[0112] Step 2. Select some antennas in the base station transmitting array as communication antennas, and the remaining antennas as radar sensing antennas. The number of selected communication antennas is the minimum number of antennas required to achieve the communication function; the power amplifier of the radar sensing antenna operates in the saturation range.

[0113] Vectors are assigned according to aperture. The transmitting array of the integrated sensing system is divided into communication antennas and radar sensing antennas. Each element in vector u is in the set {0,1}, where 1 indicates that the antenna is assigned as a communication antenna and 0 indicates that the antenna is assigned as a radar sensing antenna.

[0114] For communication beams, the following power constraints must be met:

[0115]

[0116] Among them, w k [n] represents the vector w k The nth element, |·| represents the modulo operation, u[n] represents the nth element of vector u, P ant In this embodiment of the invention, P represents the transmission power of the communication antenna. ant =10dBW.

[0117] To achieve the communication function, the signal-to-interference-plus-noise ratio γ of the k-th communication user is... k The signal-to-interference-plus-noise ratio (SIR) Γ is not lower than the threshold of the k-th communication user. k The communication function refers to satisfying γ k ≥Γ k conditions.

[0118] Step 3. With the goal of minimizing the number of selected communication antennas and the constraints of the communication antenna transmit power and the signal-to-interference-plus-noise ratio of the communication users, construct an aperture allocation and communication beam design model.

[0119] The objective function is to minimize the number of communication antennas, i.e., to minimize ||u||0, where ||·||0 represents the zero norm. The selected communication antenna transmit power does not exceed P. ant To realize the communication function in the integrated sensing system, a signal-to-interference-plus-noise ratio (SIR) constraint is adopted to ensure that the SIR of each communication user is not lower than the threshold value Γ. k The aperture allocation and communication beam design model is constructed as follows:

[0120]

[0121] u[n]∈{0,1}

[0122] in, This represents any value taken within the range [1, K]. Indicates [1, N] t It can be any value taken from the range of ].

[0123] Step 4. Solve the aperture allocation and communication beam design model using the continuous convex approximation and semi-positive definite programming method.

[0124] The aperture allocation vector u is randomly initialized. The continuous convex approximation method is used to simplify the objective function of aperture allocation and communication beam design constructed in step 3 into an easy-to-solve optimization model, and the simplified model is solved iteratively.

[0125] Step 4.1: The optimization model constructed in Step 3 has a non-convex and discontinuous objective function. To facilitate solving, the objective function is simplified to the following form:

[0126]

[0127] Where log(·) represents the logarithmic operation to base 10, and μ represents the approximation error, which in this embodiment is μ = 0.0001. The simplified objective function is still a non-convex function, and a Taylor expansion of the objective function f(u) is performed using the continuous convex approximation method. Its expression is:

[0128]

[0129] in, This indicates that in the i-th iteration, the objective function f(u) is in u (i-1) The result of the first-order Taylor expansion at the given location.

[0130] Step 4.2, convert the communication beam vector w of each communication user k Represented in matrix form And define a new matrix The signal-to-interference-plus-noise ratio (SIR / NOT) constraint for communication can be expressed as:

[0131]

[0132] Based on the aperture allocation vector u, the transmit power of the communication antenna is constrained, and the constraint condition can be expressed as follows:

[0133]

[0134] Among them, diag(W) k This indicates that the matrix W is returned in vector form.k The diagonal elements. Combining the two constraints above with the first-order Taylor expansion formula in step 4.1. The aperture allocation vector is then relaxed to a continuous variable 0 ≤ u ≤ 1, where 0 represents a vector with all zero values ​​and 1 represents a vector with all 1 values. The model solved in the i-th iteration is expressed as:

[0135]

[0136] 0≤u≤1,

[0137] rank(W k ) = 1,

[0138]

[0139] Where rank(·) represents the rank of the matrix. Representation matrix W k It is a positive semi-definite matrix.

[0140] The model established in steps 4.3 and 4.2 is a semidefinite programming problem, and the constraint rank(W) of the matrix rank can be ignored. k With ) = 1, the following convex optimization model is obtained:

[0141]

[0142] 0≤u≤1,

[0143]

[0144] To solve the above equation, we use an existing positive semidefinite programming algorithm.

[0145] Step 4.4: Determine whether the preset maximum number of iterations has been reached. If so, determine the number of antennas in the current iteration as the number of communication antennas and generate a communication beam; otherwise, continue with step 4.2. In this embodiment of the invention, the preset maximum number of iterations is 100.

[0146] Step 5. Construct a radar sensing beam design model.

[0147] Based on the aperture allocation vector u obtained in step 4, the selected communication antennas are denoted as the set Ω. c The remaining antennas are used as radar sensing antennas and are denoted as set Ω. r The power amplifier in the radar sensing antenna operates in the saturation region. Therefore, for the radar sensing beam w... r Its transmission power is constrained to be:

[0148]

[0149] in, P sat This represents the transmit power of the radar sensing antenna, and P sat >P ant In the embodiments of the present invention, P sat =15dBW. To avoid affecting the signal-to-interference-plus-noise ratio (SNR) of communication, and to limit the interference of the radar sensing beam on communication users to a small range, the following radar communication interference constraint conditions can be established:

[0150]

[0151] Wherein, ε represents the radar communication interference threshold, and ε≥0. In the embodiments of the present invention, ε is set to 0 and 0.01.

[0152] Minimizing the Cramer-Rao boundary (CRB) of the radar target direction of arrival angle θ is equivalent to maximizing the radiated power P(θ) in the θ direction, i.e., minimizing -P(θ). Combining the above constraints and setting a radar communication interference threshold ε, the following radar sensing beam design model is established:

[0153]

[0154] Step 6. If the radar interference constraint on communication users is zero, the radar sensing beam design model is solved using a closed-form solution; if the radar interference constraint on communication users is not zero, the radar sensing beam design model is solved using the alternating direction multiplier method to generate the radar sensing beam.

[0155] Step 6.1: If the radar communication interference threshold ε = 0, then the radar sensing beam design model in Step 5 has a closed-form solution, and the optimal radar sensing beam can be expressed as:

[0156]

[0157] in, H = [h1, h2, ..., h K ], This represents the pseudo-inverse of a matrix.

[0158] Step 6.2: If the radar communication interference threshold ε>0, then the radar sensing beam design model does not have a closed-form solution. The alternating direction multiplier method is used to solve the radar sensing beam design model, introducing a new auxiliary variable v. r And assume v r =w r The radar sensing beam design model in step 5 can be reformulated as follows:

[0159]

[0160] in, (·) * This indicates the conjugate operator.

[0161] Step 6.3, the augmented Lagrangian function of the above model It can be represented as:

[0162]

[0163] Where ρ represents the penalty factor, represents the Lagrange dual variable.

[0164] Step 6.4, fix v r With d r Update w r Based on the augmented Lagrangian function in step 6.3, with w r The following optimization model is established for the optimization variables:

[0165]

[0166] The optimization model is a quadratic programming problem, so it can be solved using existing convex optimization tools.

[0167] Step 6.5, fix w r With d r Update v r Based on the augmented Lagrangian function in step 6.3, with v r The following optimization model is established for the optimization variables:

[0168]

[0169] The optimization model is a quadratic programming problem, so it can be solved using existing convex optimization tools.

[0170] Step 6.6, update the Lagrange dual variable d according to the following formula. r

[0171] d r =d r +w r -v r

[0172] Step 6.7: Determine if the maximum number of iterations has been reached. If so, set the current iteration's w... r If the signal is identified as a radar sensing beam, then proceed to step 6.4; otherwise, continue. In this embodiment of the invention, the maximum number of iterations is set to 100.

[0173] Step 7. When the radar's interference constraint on communication users is not zero, active interference cancellation technology is used to correct the communication data stream to ensure that the communication signal-to-interference-plus-noise ratio is constant.

[0174] When the radar communication interference threshold ε>0, the radar beam will affect the signal received by the communication users. According to step 1, the signals Y received by K communication users... c It can be represented as

[0175] Y c =H H WS+H H w r s r +N c

[0176] in, The channel matrix representing the communication users, This represents the noise at the communication user's receiving end. The second term on the right-hand side of the above equation represents the radar interference with the communication function, which reduces the signal-to-interference-plus-noise ratio of the communication user.

[0177] Since the transmitter of the integrated sensing system already knows the communication data stream, radar sensing data stream, and channel state vectors of each communication user, active interference cancellation technology is used to correct the communication data stream based on this prior information to avoid affecting communication functionality. The corrected communication data stream should be determined by the following formula:

[0178]

[0179] in, This represents the communication data stream obtained using active interference cancellation technology. This represents the data stream of the k-th communication user. Replacing S in step 4.8 yields the desired result. When used as a communication data stream, the signal received by the communication user is:

[0180]

[0181] According to the above formula, the signal received by the communication user no longer contains radar interference signals. The communication data stream obtained by using active interference cancellation technology can ensure that the signal-to-interference-plus-noise ratio of the communication user remains constant.

[0182] The effects of this invention will be further illustrated below with simulation experiments:

[0183] 1. Simulation conditions:

[0184] The simulation experiment of this invention was conducted using Matlab R2022a software, which ran on an Intel(R) Core(TM) i7-6700 CPU@3.40GHz CPU, 8GB of memory, and Windows 10 operating system.

[0185] Simulation Experiment Condition 1: The structure of the integrated inductive system is shown in the attached figure. Figure 2 As shown, attached Figure 2 The transmitting array in the system has a total of 25 elements. The transmitting array is a uniform linear array, and the spacing between each transmitting element is half a wavelength. The integrated inductive and perceptron system has two single-antenna communication users located at -35° and 40° respectively. The noise variance at the communication user end is... The signal strength is -50dBW, and the signal from the transmitter of the integrated sensing and communication system to the communication user experiences a path loss of 60dB. There is also a radar target located at 0°. The transmit power P of the communication antenna is... ant The radar antenna's transmit power P is 10 dBW. sat The signal-to-interference-plus-noise ratio (SIR) threshold Γ for each communication user is set to 15 dBW and μ is set to 0.001. k Set to 8dB.

[0186] In simulation experiment condition 2, except that the radar communication interference threshold ε is set to 0.01, the other conditions are the same as simulation condition 1.

[0187] 2. Simulation content and result analysis:

[0188] The simulation experiment of this invention is conducted under simulation experiment conditions 1 and 2, using the method of this invention and two existing technologies to design and generate communication beams and radar sensing beams.

[0189] The first existing technology is the method proposed by Xiang Liu et al. in their paper “Joint Transmit Beamforming for Multiuser MIMO Communications and MIMO Radar” (IEEE TRANSACTIONS ON SIGNAL PROCESSING, 2020, Vol. 68).

[0190] The second existing technology is the method proposed by Fan Liu et al. in their paper “Cramer-Rao Bound Optimization for Joint Radar-Communication Beamforming” (IEEE TRANSACTIONS ONSIGNAL PROCESSING, 2022, Vol. 70).

[0191] In the following description, the method proposed by Xiang Liu et al. is designated as PAPC, and the method proposed by Fan Liu et al. is designated as TPC. The method proposed in this invention is designated as DAP.

[0192] The following is combined Figure 3, Figure 4 , Figure 5 The advantages of the method of the present invention are verified from three aspects: beam pattern, aperture allocation and transmit antenna power, and the relationship between wave direction of arrival estimation performance and radar signal-to-noise ratio.

[0193] Based on the communication beam and the radar sensing beam Figure 3 Draw the corresponding beam pattern. Figure 3 The horizontal axis represents angle in degrees, and the vertical axis represents transmission power in dB. Figure 3 It can be seen that, compared with the prior art, the method of the present invention has a greater transmission power at 0° in the radar target direction. Furthermore, when the method of the present invention is under simulation experimental condition 2, it has a greater transmission power in the radar target sensing direction than under simulation experimental condition 1.

[0194] Based on the obtained beam vector Figure 4 The average transmit power of each antenna is shown in the figure. Figure 4 The horizontal axis represents the transmitting elements in the integrated inductive and sensory system's transmitting array, and the vertical axis represents the antenna's transmitting power, measured in dB. From... Figure 4 As can be seen, the beam obtained by the method of this invention results in varying transmit powers for the antennas in the transmitting array. The 1st, 16th, 17th, and 22nd transmitting antennas, serving as communication antennas, have lower transmit powers, with an average transmit power not exceeding 10dB. The remaining antennas function as radar sensing antennas, operating in the saturation amplification range and possessing higher transmit power. When the interference threshold ε of this invention is set to 0.01, compared to setting the interference threshold ε to 0, the radar sensing antennas have greater transmit power, but the maximum transmit power still does not exceed the saturation transmit power of 15dB. In contrast, existing radar and communication beams have power amplifiers for each antenna operating in the linear range, with each antenna having an average transmit power of around 10dB, far less than the saturation transmit power of 15dB.

[0195] Based on the obtained beam vector Figure 5 The table presents the root mean square error (RMSE) for the direction of arrival estimation. Figure 5 The horizontal axis represents the radar signal-to-noise ratio (SNR), ranging from -10:1:10, in dB. The vertical axis represents the RMSE (Rear-of-Arrival Score) of the estimated direction-of-arrival (AOA), in degrees. The maximum likelihood estimation (MLE) algorithm is used for AOA estimation. Figure 5 The present invention provides a comparison between the method of the present invention and the existing Craméro boundary (CRB). From... Figure 5As can be seen from the simulation, the method proposed in this invention has a lower direction-of-arrival estimation error (RMSE) and a lower CRB under simulation conditions 1 and 2 compared with the prior art, indicating that the method of this invention can achieve better radar perception performance compared with the prior art.

Claims

1. A co-sited beamforming method based on aperture allocation and saturated power amplification, characterized in that, The transmit array is divided into communication antennas and radar sensing antennas, and the power amplifier of the radar sensing antenna works in the saturation interval; based on the aperture allocation and beam design model and the radar sensing beam design model, the communication beam and the radar sensing beam are generated respectively; the steps of the beam forming method include the following: Step 1, an integrated sensing and communication system with multiple communication users is established, each transmit antenna in the base station transmit array is connected with its corresponding radio frequency link, and the power amplifier in each radio frequency link can work in the linear amplification interval or the saturation amplification interval; Step 2, select part of the antennas in the base station transmit array as communication antennas, and the rest as radar sensing antennas, and the number of selected communication antennas is the minimum number of antennas required to realize the communication function; The power amplifier of the radar sensing antenna works in the saturation interval; Step 3, taking the minimum number of selected communication antennas as the target, and taking the communication antenna transmit power and the signal-to-interference-and-noise ratio (SINR) of the communication user as the constraint condition, an aperture allocation and communication beam design model is constructed; Step 4, the aperture allocation and communication beam design model is iteratively optimized by using the continuous convex approximation and semi-definite programming method to adaptively determine the number of communication antennas and generate the communication beam; Step 5, under the condition of meeting the radar antenna transmit power constraint and the radar interference constraint to the communication user, the radar beam transmit power in the radar target direction is maximized to construct a radar sensing beam design model; Step 6, if the radar interference constraint to the communication user is zero, the radar sensing beam design model is solved by using the closed-form solution; if the radar interference constraint to the communication user is not zero, the radar sensing beam design model is solved by using the alternating direction multiplier method to generate the radar sensing beam; Step 7, when the radar interference constraint to the communication user is not zero, the active interference cancellation technology is used to modify the communication data stream to ensure the constant communication signal-to-interference-and-noise ratio (SINR).

2. The beamforming method of claim 1, wherein: The integrated sensing and communication system in step 1 is as follows: The expression of the transmit signal X of the base station in the integrated sensing and communication system is as follows: X = WS + w r s r wherein W denotes a beam matrix of a base station transmitting signal in the integrated sensing and communication system, w k denotes a beam of the kth communication user, t denotes a total number of transmitting antennas, r denotes a total number of receiving antennas, K denotes a total number of antenna communication users, and S denotes a communication baseband data stream, denotes a data stream of the kth communication user, T denotes a transposition operator, denotes a sensing beam of the rth receiving antenna of the radar, denotes a radar sensing data stream of the rth receiving antenna constant envelope, a communication data stream and a radar sensing data stream have a mean of 0, and the data streams are mutually independent, i.e. denotes a mathematical expectation operator, H denotes a conjugate transposition operator; According to the transmit signal of the integrated sensing and communication system, the signal received by each antenna communication user can be expressed as: where y k represents the signal received by the kth antenna communication user, represents the channel state vector from the transmitting end to the kth communication user, w i represents the communication beam of the ith communication user, w r represents the radar perception beam, s i represents the communication data stream of the ith communication user, s r represents the radar perception data stream, n k represents the Gaussian white noise received by the kth antenna communication user, with a variance of The signal-to-interference-and-noise ratio (SINR) of each communication user can be expressed as: where γ k denotes the signal-to-interference-and-noise ratio of the kth communication user, |·| denotes the modulo operator; According to the transmitting signal of the synesthesia integration system, the radar target echo signal Y received by the base station r is represented as: Y r = αa r (θ)a t (θ) T X+N r wherein, denotes a path loss coefficient of the target echo, denote a transmit steering vector and a receive steering vector of the sensor-fusion system, respectively, and θ denotes an angle of the radar target, r denotes a Gaussian white noise with variance of the sensor-fusion receiving end. The radiation power of the integrated sensing and communication system located at each radar target angle can be expressed as: Wherein, P(θ) represents the radiation power of the integrated sensing and communication system located at the radar target angle θ; The Cramer-Rao Bound (CRB) of estimating the radar target direction of arrival angle is expressed as: wherein denotes the noise variance of the receiving end of the sensory integration system, tr(·) denotes the trace of a matrix, denotes a r derivative of (θ) with respect to θ, denotes a t derivative of (θ) with respect to θ, α denotes a path loss coefficient of a radar target echo, and L denotes a length of a communication data stream.

3. The beamforming method of claim 2, wherein, The constraint condition of the communication antenna transmit power and the signal-to-interference-and-noise ratio (SINR) of the communication user in step 3 is as follows: γ k ≥Γ k wherein w k [n] denotes the nth element of w k , u[n] denotes the nth element of the aperture allocation vector u, each element of u is in the set {0, 1}, P ant denotes the transmit power of the communication antenna, Γ k denotes the signal-to-interference-plus-noise ratio threshold of the kth communication user.

4. The beamforming method of claim 3, wherein, The aperture allocation and communication beam design model in step 3 is as follows: u[n]∈{0,1} where ||•||0represents a zero norm operator, represents a value taken arbitrarily in the range [1, K], represents a value taken arbitrarily in the range [1, N t ].

5. The beamforming method of claim 4, wherein, The steps of using the continuous convex approximation and semi-definite programming method to iteratively optimize the aperture allocation and communication beam design model in step 4 are as follows: First, approximate the aperture allocation and communication beam design model as follows: Wherein, log(·) represents the logarithm operation with base 10, and μ represents the approximation error; Second, use the continuous convex approximation method to perform Taylor expansion on f(u): wherein, denotes the first order Taylor expansion of f(u) at u (i-1) in the i-th iteration; In the second step, the matrix is defined as The aperture assignment and the communication beam design model are updated as follows: 0≤u≤1 rank(W k ) = 1 W k ≥0 wherein diag(W k ) represents returning diagonal elements of the matrix W k in the form of a vector, rank(·) represents the rank of a matrix, W k ≥ 0 represents a constraint that the matrix W k is a semi-positive definite matrix, the first constraint in the above model is a communication signal-to-interference-and-noise ratio constraint, and the second constraint is a communication antenna transmit power constraint; Third, use the semi-definite programming algorithm to solve the updated model; In the fourth step, it is judged whether the preset maximum iteration number is reached. If yes, the number of antennas in the current iteration is determined as the number of communication antennas and the communication beam is generated. Otherwise, the second step is continuously executed.

6. The beamforming method of claim 5, wherein, The radar antenna transmit power constraint described in Step 5 means that the radar sensing beam needs to satisfy the power constraint of the radar sensing antenna. The power constraint for the radar sensing beam w r is: wherein Ω r denotes a set of radar sensing antennas, Ω c denotes a set of communication antennas, the interference constraint of radar sensing beams to communication users is: Wherein, ε represents the radar communication interference threshold.

7. The beamforming method of claim 6, wherein, The radar sensing beam design model in step 5 is as follows: Wherein, -P(θ) represents that when the radar sensing beam is designed, the power constraint condition of the radar sensing beam is met, the radar beam is allowed to have certain interference on the communication user, the minimum -P(θ) corresponding to the maximum transmission power P(θ) of the radar target direction is maximized.

8. The beamforming method of claim 7, wherein, When the radar interference constraint on the communication user is zero in step 6, the radar sensing beam design model has a closed-form solution, and the optimal solution of the radar sensing beam can be represented as: where I denotes an identity matrix, U denotes a diagonal matrix with the elements in vector u as the diagonal line, denotes a channel matrix of a communication user, denotes a pseudo-inverse of a matrix, a t (θ) denotes a steering vector of a transmit array, max(·) denotes a maximum value operation.

9. The beamforming method of claim 8, wherein, The steps of solving the radar sensing beam design model by using the alternating direction multiplier method in step 6 are as follows: First step, define auxiliary variable v r and assume v r = w r ; In a second step, an augmented Lagrangian function of the radar perception beam design model is generated generated may be represented as: wherein p denotes a penalty factor, denotes a Lagrange dual variable; Third step, according to the augmented Lagrange function in the second step with w r The following optimization model is established with w as the optimization variable, and a convex optimization algorithm is used to solve the model: wherein (·) * denotes a take conjugate operation; Step 4: According to the augmented Lagrange function in Step 2 with v r as the optimization variable, the following optimization model is established: The model is solved by using a convex optimization algorithm; Step 5, update the Lagrange dual variable d r = d r + w r - v r Equation, update the Lagrange dual variable d r ; Step 6, determine whether the maximum number of iterations is reached, if so, output the current iteration w r determine whether the radar perception beam is determined, otherwise, continue to perform step 3.

10. The beamforming method of claim 9, wherein, The modification of the communication data stream by using the active interference cancellation technology in step 7 is realized by the following formula: wherein denotes the communication data stream S after modification by means of active interference cancellation, denotes the data stream of the kth communication user after modification.

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