Omnidirectional intelligent metasurface assisted mimo sensing and communication integrated system transmission beamforming method

Abstract

The application discloses a kind of omni-directional intelligent metasurface assisted MIMO integrated system transmission beamforming method, for simultaneously realizing line-of-sight target detection and non-line-of-sight multi-user communication.By introducing STARS into MIMO integrated transmission system, using its independent control ability to reflected signal and transmitted signal, additional signal path is provided for beamforming, and non-line-of-sight link is constructed for communication users to guarantee service quality.The matching error between radar expected power pattern and actual pattern is used as the objective function, and block coordinate descent combined with alternating direction penalty method and distance optimization algorithm is used for solving.The application realizes full space coverage, while ensuring the quality of communication service, compared with conventional intelligent metasurface assisted MIMO integrated system, has better beam matching performance.

Description

Technical Field

[0001] This invention belongs to the field of sensor-integrated communication, specifically relating to a beamforming method for transmitting beams in a MIMO sensor-integrated communication system assisted by an omnidirectional intelligent metasurface (STARS), used to realize line-of-sight target detection and non-line-of-sight multi-user communication. Background Technology

[0002] Integrated Sensing and Communication Acquisition (ISAC) systems, capable of simultaneously detecting targets and transmitting information, demonstrate significant potential in terms of spectral efficiency and hardware integration, making them a key technology for next-generation wireless communication (such as 6G). Beamforming designs for ISAC systems can be broadly categorized into three types: 1. Radar performance-centric design: Prioritizing radar sensing performance while maintaining minimum communication requirements. Its advantage is reliable radar performance, but its disadvantage is that the communication data rate is limited by the radar's pulse repetition period, resulting in a lower communication speed. 2. Communication performance-centric design: Prioritizing communication performance and utilizing communication signals for sensing. Its advantage is guaranteed communication performance, but its disadvantages include poor autocorrelation and cross-correlation of communication signals and low design freedom, limiting the improvement of sensing capabilities. In contrast, joint radar and communication performance design overcomes the limitations of these two centralized designs, offering greater freedom, more effective utilization of time, frequency, and spatial resources, flexible trade-offs between communication and sensing performance, and the potential for higher system integration gain.

[0003] However, the effectiveness of traditional ISAC systems is highly dependent on the availability of the line-of-sight (LoS) path—radar detection requires precise acquisition of target angle and distance information via a direct beam, while communication quality is limited by channel strength and interference levels. In densely populated urban areas with tall buildings and complex indoor environments, obstacles such as buildings and vegetation can easily cause LoS path attenuation or even blockage, leading to decreased sensing accuracy and the risk of communication interruption. Traditional solutions rely on dense base station deployment to improve coverage, but this significantly increases hardware costs and energy consumption. Summary of the Invention

[0004] The purpose of this invention is to propose a method for transmitting beamforming in an omnidirectional intelligent metasurface-assisted MIMO sensing integrated system.

[0005] The technical solution to the problem of this invention is: a method for transmitting beamforming in an omnidirectional intelligent metasurface-assisted MIMO sensing integrated system, the specific implementation steps of which are as follows:

[0006] Step 1: Based on minimizing the matching error between the desired power pattern and the actual pattern, and constrained by the signal-to-noise ratio requirement of symbol-level precoding, constant-mode transmit waveform, and the physical characteristics of STARS reflection and transmission coefficients, a joint optimization model for transmit beamforming of the STARS-assisted MIMO inductive system is constructed, specifically as follows:

[0007] ,

[0008] In the formula, The radar's desired power pattern. This is the actual direction chart. The number of grid cells for angle discretization. For angle Weighting factor at the location, Scaling factor For modulo operation; The number of transmit antennas in a MIMO inductive integrated system. The number of snapshots for the transmitted waveform. The available transmit power of the transmitting antenna; For the first The transmitted waveform of a quick snapshot is as follows: , For the first The transmitting antenna is at the 1st The emission waveform during a quick snapshot for The transmitted waveform within a single snapshot Let be the complex field, and its superscript denotes the dimension of the complex field. This is the conjugate transpose operation. This is a transpose operation; Is with the first The minimum signal-to-noise ratio required for decoding by a communication user and the coefficients related to the modulation scheme. For STARS and the Channel between individual communication users This is the channel between the transmitter and STARS. For real part operations; STARS contains M metasurface units that simultaneously reflect and transmit light. Let be the reflection coefficient of the m-th metasurface unit. Let be the transmission coefficient of the m-th metasurface unit. and These are the corresponding reflection coefficient matrix and transmission coefficient matrix, respectively. It is an operator that transforms a vector into a diagonal matrix;

[0009] Step 2: Determine the actual radiation pattern in the joint optimization model of transmit beamforming for the STARS-assisted MIMO inductive system;

[0010] Step 3: Introduce auxiliary variables The objective function of the joint optimization model for transmit beamforming of the STARS-assisted MIMO sensing system in step 1 is reduced to a quadratic function of the transmit waveform, and the optimization problem after the transformation is determined.

[0011] Step 4: Using the block coordinate descent framework, the transformed optimization problem is decomposed into four sub-problems that can be solved iteratively;

[0012] Step 5: Solve the four sub-problems formed in Step 4 to obtain the optimal scaling factor, auxiliary variables, transmitted waveform, reflection coefficient, and transmission coefficient, thereby achieving STARS-assisted MIMO inductive system transmit beamforming with minimal power pattern matching error.

[0013] Compared with the prior art, the significant advantages of this invention are as follows: the introduction of STARS expands the coverage of the integrated sensing system and increases the system's degrees of freedom, making beamforming more flexible and efficient; by optimizing the transmitted waveform, scaling factor, STARS reflection coefficient, and transmission coefficient, this invention obtains a desired power pattern with low matching error; and by optimizing the algorithm design, this invention reduces computational complexity and improves the feasibility of practical applications. Attached Figure Description

[0014] Figure 1 The curve represents the convergence of the objective function.

[0015] Figure 2 This is the beam pattern of a single main lobe flat-top beam.

[0016] Figure 3 This is the beam pattern of a double main lobe flat-top beam.

[0017] Figure 4 The curve showing the impact of communication service quality on beam matching error.

[0018] Figure 5 The curve shows the effect of the number of STARS cells on beam matching error.

[0019] Figure 6 This is a flowchart of the present invention. Detailed Implementation

[0020] The present invention, namely a method for transmitting beamforming in an omnidirectional intelligent metasurface-assisted MIMO sensing integrated system, is further described below with reference to the accompanying drawings and examples.

[0021] This invention presents a transmit beamforming method for a MIMO integrated sensing and communication system assisted by an omnidirectional intelligent metasurface (STARS), used for line-of-sight target detection and non-line-of-sight multi-user communication. By introducing STARS into the MIMO transmit system, and using the matching error between the radar's desired power pattern and the actual pattern as the objective function, the method employs block coordinate descent (BCD) combined with alternating direction penalty method (ADPM) and range optimization algorithm under constraints of constant modulus of the transmit waveform, STARS energy, and symbol-level precoded constructive interference from communication users. First, by introducing auxiliary variables, the fourth-order problem is reduced to a second-order problem. Then, within the BCD framework, the scaling factor, auxiliary variables, transmit waveform, reflection coefficient, and transmission coefficient are alternately optimized. The scaling factor and auxiliary variables directly derive closed-form solutions; the transmit waveform is solved using the ADPM algorithm; and the reflection and transmission coefficients are solved using the range optimization algorithm. Figure 6 As shown, the specific implementation steps are as follows:

[0022] Step 1: In a STARS-assisted MIMO sensing system, a STARS is deployed near a conventional MIMO radar transmitter array. Assume the phase center of the MIMO radar transmitter array is located at the origin of the coordinate system, and the coordinates of the phase center of the STARS are... These coordinates uniquely determine the spatial location of STARS. STARS divides the entire space into two regions: the region where the radar target is located is called the radar side, situated on one side of the MIMO transmitting array; the other side contains... There are 10 communication users, and this area is called the communication side. The transmitting array is composed of... STARS is a uniform linear array composed of antenna elements, while STARS is composed of... The system is composed of intelligent metasurface units, arranged in a uniform linear array. During operation, the transmitting array sends narrowband signals under far-field transmission conditions. Two signal transmission paths exist between the transmitting array and the radar target: a line-of-sight (LoS) path and a non-line-of-sight (NLoS) path. The LoS path directly transmits the radiated signal from the transmitting array to the radar target, while the NLoS path requires signal reflection via STARS before reaching the radar target. Only one signal path exists between the transmitting array and the communication user: the non-line-of-sight link, which transmits the signal via STARS.

[0023] The STARS in this invention uses an energy splitting model to synchronously reflect and transmit signals, and its unit number is... .definition and These are the reflection and transmission coefficient matrices of STAR, respectively, specifically expressed as follows: ,in Let be the reflection coefficient of the m-th metasurface unit. Let be the transmission coefficient of the m-th metasurface unit. This is an operator that transforms a vector into a diagonal matrix. Based on minimizing the matching error between the desired power pattern and the actual pattern, and constrained by the signal-to-noise ratio requirements of symbol-level precoding, constant-mode transmit waveform, and the physical characteristics of STARS reflection and transmission coefficients, the joint optimization model for transmit beamforming in a STARS-assisted MIMO inductive system is as follows:

[0024]

[0025] In the formula, The radar's desired power pattern. This is the actual direction chart. The number of grid cells for angle discretization. For angle Weighting factor at the location, Scaling factor For modulo operation; The number of transmit antennas in a MIMO inductive integrated system. The number of snapshots for the transmitted waveform. The available transmit power of the transmitting antenna; For the first The transmitted waveform of a quick snapshot is as follows: , For the first The transmitting antenna is at the 1st The emission waveform during a quick snapshot for The transmitted waveform within a single snapshot Let be the complex field, and its superscript denotes the dimension of the complex field. This is the conjugate transpose operation. This is a transpose operation; Is with the first The minimum signal-to-noise ratio required for decoding by a communication user and the coefficients related to the modulation scheme. For STARS and the Channel between individual communication users This is the channel between the transmitter and STARS. This is an operation to extract the real part.

[0026] Actual direction map The specific expression is:

[0027]

[0028] in, , For the transmission array in Directional guidance vector, For STARS Directional guidance vector, It represents the angular difference between the radar's line-of-sight illumination direction and its non-line-of-sight illumination direction.

[0029] Step 2: Introduce auxiliary variables By reducing the objective function to a quadratic function of the transmitted waveform, the joint optimization model for transmit beamforming in the STARS-assisted MIMO inductive system is transformed into the following problem:

[0030]

[0031] In the formula, , For Kronecker product, For the Euclidean norm, The number of grid cells for angle discretization. The radar's desired power pattern. From the perspective of discretization.

[0032] Step 3: Using the BCD method, decompose the transformed problem into four subproblems that can be solved iteratively, namely the scaling factor. Sub-problems, auxiliary variables Sub-problem, transmitted waveform Subproblems, STARS coefficients Sub-problems:

[0033]

[0034]

[0035]

[0036]

[0037] Among them, all superscripts are The variable is the first The result of the round of iterations, all superscripts are The variable is the first The result of rounds of iteration.

[0038] In the During each iteration, the above four sub-problems are solved separately to obtain the optimal scaling factor, auxiliary variables, emission waveform, reflection coefficient, and transmission coefficient. The specific process is as follows:

[0039] 1. Regarding scaling factors The subproblem has the following closed-form optimal solution:

[0040]

[0041] In the formula, To obtain the conjugate operation, For angle Weighting factor at the location.

[0042] 2. For auxiliary variables The subproblem has the following closed-form optimal solution:

[0043]

[0044] 3. Regarding the transmitted waveform The subproblem is solved using the ADPM algorithm, specifically as follows:

[0045] First, introduce constant modulus auxiliary variables. The transmitted waveform The subproblem is equivalently described as the following problem without a summation term:

[0046]

[0047] in, ,

[0048] , , Introducing constant modulus auxiliary variables The problem of having no summation term is transformed into the following variable separation and reconstruction problem:

[0049]

[0050] Secondly, define the augmented Lagrangian function. ,in As a penalty factor, These are Lagrange multipliers. Based on the principles of the ADPM algorithm, the variable separation and reconstruction problem is transformed into the following augmented Lagrange problem:

[0051]

[0052] The solution is obtained iteratively according to the following process, where the superscript... Indicates the first Next iteration, superscript Indicates the first Next iteration:

[0053] Step 3.1: Fix , , The following problem is solved using convex optimization techniques. :

[0054]

[0055] Step 3.2: Fix , , According to the following formula, :

[0056]

[0057] Step 3.3: Define the residual Update the penalty factor as follows: :

[0058]

[0059] in, , .

[0060] Step 3.4: Update the Lagrange multipliers as follows. :

[0061]

[0062] Step 3.5: Determine if the ADPM algorithm meets the termination condition. ,in This is the termination tolerance. If satisfied, stop the iteration and output the result. Find the optimal solution; otherwise, return to step 3.1.

[0063] 4. Regarding the STAR coefficient The subproblem is solved using a distance optimization algorithm, specifically:

[0064] First, regarding the STARS coefficients The objective function and inequality constraints in the subproblem are transformed to explicitly represent the reflection coefficient.

[0065] definition Expand the STAR coefficients The objective function of the subproblem, after removing irrelevant terms, yields:

[0066]

[0067] right Perform an equivalent transformation to obtain

[0068] ,

[0069] in, ,

[0070] , .

[0071] Rewrite the STARS coefficients The inequality constraints in the subproblem allow the transmission coefficient to be expressed explicitly, i.e.:

[0072] ,

[0073] In the formula, , .

[0074] Secondly, the STARS coefficients The subproblem is equivalently described by explicitly representing the subproblem as follows:

[0075]

[0076] in,

[0077] ,

[0078] ,

[0079] Furthermore, the explicit representation subproblem is transformed into a real-valued subproblem:

[0080]

[0081] In the formula,

[0082] , ,

[0083] , ,

[0084] ,

[0085] This represents the real number field, where the superscript indicates the dimension. This indicates the operation of taking the real part. This indicates the operation of taking the imaginary part; Indicates the first One element, Indicates the first Each element.

[0086] Next, the constraints in the real-valued subproblem are incorporated into the objective function using the Courant penalty method, and the problem is redefined as the following distance function subproblem:

[0087] Step 3.4.6: Incorporate the constraints into the objective function using the Courant penalty method, and reformulate the real-valued subproblem as the following distance function subproblem:

[0088] ,

[0089] In the formula, , , , , For the feasible set of real-valued subproblems, express In the set Projection on;

[0090] Then, the distance function subproblem is transformed into a series of easily solvable convex subproblems using the MM technique. The specific form of the convex subproblem is as follows:

[0091]

[0092] In the formula,

[0093]

[0094] yes The projection onto the feasible set formed by the inequality constraints. and They are and The projection onto the feasible set formed by equality constraints, with subscripts The first MM technology The next iteration.

[0095] Based on the first-order optimality condition of the convex subproblem, the closed-form optimal solution of the convex subproblem is obtained as follows:

[0096]

[0097] In the formula,

[0098]

[0099]

[0100] Finally, using the Nesterov acceleration algorithm, the explicit representation subproblem is solved iteratively according to the closed-form optimal solution of the convex subproblem to obtain the optimal STARS reflection coefficient and transmission coefficient.

[0101] Step 4: Determine whether the BCD algorithm satisfies the iteration termination condition, i.e., whether it meets the condition.

[0102] ,

[0103] in This is the termination tolerance of the algorithm. If it is satisfied, the loop stops, and the transmitted waveform, reflection coefficient, and transmission coefficient obtained in the current iteration are output as the optimal solution of BCD; otherwise, step 3 is repeated.

[0104] Example

[0105] The method for transmitting beamforming in an omnidirectional intelligent metasurface-assisted MIMO inductive integrated system, as described in this invention, is further illustrated through Matlab simulation.

[0106] 1) Simulation system parameter settings

[0107] Unless otherwise specified, the number of base station transmit antennas All array elements are uniformly distributed with an element spacing of half a wavelength. STARS element number Number of transmitted signals in quick snapshots Available transmission power is Launch direction exist Uniform sampling within the range, number of sampling points Weight Number of communication users Assuming each user has the same communication symbols and QoS requirements, the noise power at the user is... The minimum signal-to-noise ratio requirement is The distance between the base station and STARS is... The distance between STARS and the user is Channel Employing a small-scale Ricean fading model, the channel It follows the small-scale Rayleigh fading model.

[0108] 2) Beam plotting

[0109] To visually demonstrate the STARS-assisted transmit beamforming effect, this embodiment will... Each unit only reflects RIS and A transmissive RIS array of 1 unit was deployed adjacent to each other as a control group, and compared with a STARS array of M units under the same experimental conditions. Only the reflective RIS array was used for radar target detection, and only the transmissive RIS array was used for serving communication users. The horizontal axis of the beammap represents the angular range of [-90°, 90°), and the vertical axis of the beammap is in dB.

[0110] 3) Measurement indicators

[0111] In this invention, it is necessary to measure the effect of the final beamforming. In addition to plotting beammaps in radar-only and Information-Sensing Integration (ISAC) scenarios to show the difference from the desired beammap, peak sidelobe level (PSL) and integral sidelobe level (ISL) are used to quantitatively measure the sidelobe level of the transmitted beamformation. Under the same initial conditions, the smaller the PSL and ISL, the better the formed beam pattern performance.

[0112] 4) Results Analysis

[0113] The present invention has verified the convergence of the algorithm and conducted simulations of four examples. Figure 1 It is the convergence curve of the objective function. Figure 2 This is a comparison of single main lobe flat-top beam patterns. Figure 3 It is a comparison of the beam patterns of dual main lobe flat-top beams. Figure 4 The curve showing the impact of communication service quality on beam matching error. Figure 5 The curve shows the effect of the number of STARS cells on beam matching error.

[0114] exist Figure 1 In the figure, the horizontal and vertical axes represent the number of iterations and the power pattern matching error, respectively. Experiments were conducted to compare and analyze the convergence behavior of STARS and RIS under conditions with and without communication requirements: (i) radar detection only; (ii) communication service quality constraints. Experimental results show that the objective function value converges to a stable state within 120 iterations in both cases, and the convergence trajectory exhibits a monotonically decreasing characteristic, verifying the convergence of the proposed algorithm under conditions of no communication requirement.

[0115] Figure 2 The normalized single mainlobe transmit power patterns are shown under different constraints. In the radar-specific scenario, the PSL of STARS and RIS are -5.97dB and -5.91dB, respectively, and the ISL is 4.36dB and 4.47dB, respectively. When communication constraints are introduced, the PSL of STARS is -4.96dB, an improvement of 1.55dB compared to RIS's -3.41dB; the ISL difference reaches 3.22dB. This indicates that STARS can still maintain the concentration of radar mainlobe energy under strict communication requirements, while RIS, due to the separation of transmission / reflection elements, has limited degrees of freedom and cannot well balance the joint optimization requirements of high communication service quality and low sidelobes.

[0116] Figure 3 The normalized dual-main-lobe transmit power patterns are shown under different constraints. In the radar-specific scenario, the PSL of STARS and RIS are -7.68dB and -7.63dB, respectively, and the ISL is 6.82dB and 7.05dB, respectively. When communication constraints are introduced, the PSL of STARS is -6.37dB, an improvement of 2.21dB compared to RIS's -4.16dB; the ISL difference reaches 5.15dB. The data shows that when the desired pattern shape is more complex, STARS can provide a more significant improvement in beamforming performance compared to RIS.

[0117] Figure 4 The relationship between radar pattern matching error and communication service quality in a STARS and RIS-assisted MIMO sensing integrated system was revealed. The results show that: 1) When the demand for communication service quality increases (i.e. When the number of STARS and RIS units increases, the pattern matching error exhibits a monotonically increasing trend. This is because the base station and STARS / RIS need to consume more degrees of freedom to meet stricter quality of service constraints, resulting in a decrease in radar detection performance. 2) Compared with the RIS-assisted scheme, the pattern matching error of the STARS-assisted MIMO sensing system did not show a significant increase when the communication service quality requirements improved. This phenomenon is more pronounced when the number of STARS and RIS units is small. This phenomenon is as expected because the RIS is limited by its component allocation strategy in the detection space and communication space and cannot achieve a degree of freedom comparable to that of STARS.

[0118] Figure 5 This paper demonstrates the relationship between radar pattern matching error and the number of elements in a STARS-assisted and RIS-assisted MIMO sensing integrated system. The horizontal axis represents the number of STARS elements. The results show that: 1) The pattern matching error monotonically decreases with increasing STARS element count. This is because increasing the element count significantly enhances the following capabilities: for STARS, it simultaneously enhances the ability to reflect and transmit signals, while traditional RIS enhances the reflection capability of reflective RIS and the transmission capability of transmission-type RIS, respectively. This hardware performance improvement allows the system to improve radar detection performance while maintaining communication service quality. 2) Under the same communication service quality constraints, the pattern matching error of the STARS-assisted system is consistently lower than that of the traditional RIS system.

[0119] In summary, the method described in this invention exhibits excellent overall performance. Compared to conventional RIS (Resonance Injection System), the proposed method achieves near-optimal main lobe gain performance in commonly used beams while ensuring low PSL (Power Strain Level). When applied to integrated sensing systems, this invention can significantly reduce hardware costs and computational complexity with minimal performance loss, demonstrating high practical value.

Claims

1. A method for transmitting beamforming in an omnidirectional intelligent metasurface-assisted MIMO sensing integrated system, characterized in that, The specific implementation steps are as follows: Step 1: Based on minimizing the matching error between the desired power pattern and the actual power pattern, and constrained by the signal-to-noise ratio requirements of symbol-level precoding, constant-mode transmit waveform, and the physical characteristics of STARS reflection and transmission coefficients, a joint optimization model for transmit beamforming of the STARS-assisted MIMO inductive system is constructed, specifically as follows: ， In the formula, The radar's desired power pattern. This is the actual direction chart. The number of grid cells for angle discretization. For angle Weighting factor at the location, Scaling factor For modulo operation; The number of transmit antennas in a MIMO inductive integrated system. The number of snapshots for the transmitted waveform. The available transmit power of the transmitting antenna; For the first The transmitted waveform of a quick snapshot is as follows: , For the first The transmitting antenna is at the 1st The emission waveform during a quick snapshot for The transmitted waveform within a single snapshot Let be the complex field, and its superscript denotes the dimension of the complex field. This is the conjugate transpose operation. This is a transpose operation; Is with the first The minimum signal-to-noise ratio required for decoding by a communication user and the coefficients related to the modulation scheme. For STARS and the Channel between individual communication users This is the channel between the transmitter and STARS. For real part operations; STARS contains M metasurface units that simultaneously reflect and transmit light. Let be the reflection coefficient of the m-th metasurface unit. Let be the transmission coefficient of the m-th metasurface unit. and These are the corresponding reflection coefficient matrix and transmission coefficient matrix, respectively. It is an operator that transforms a vector into a diagonal matrix; Step 2: Determine the actual radiation pattern in the joint optimization model of transmit beamforming for the STARS-assisted MIMO inductive system; Step 3: Introduce auxiliary variables The objective function of the joint optimization model for transmit beamforming of the STARS-assisted MIMO sensing system in step 1 is reduced to a quadratic function of the transmit waveform, and the optimization problem after the transformation is determined. Step 4: Using a block coordinate descent framework, the transformed optimization problem is decomposed into four iterative subproblems, namely scaling factors. Sub-problems, auxiliary variables Sub-problem, transmitted waveform Subproblems, STARS coefficients Sub-problems: scaling factor Sub-problems: ， Auxiliary variables Sub-problems: ， Transmit waveform Sub-problems: ， STARS coefficient Sub-problems: ， Among them, the superscript is The variable is the first The result of the round of iterations, all superscripts are The variable is the first The result of round iteration; Step 5: Solve the four sub-problems formed in Step 4 to obtain the optimal scaling factor, auxiliary variables, transmitted waveform, reflection coefficient, and transmission coefficient, thereby achieving STARS-assisted MIMO inductive system transmit beamforming with minimal power pattern matching error.

2. The method for transmitting beamforming in an omnidirectional intelligent metasurface-assisted MIMO sensing integrated system according to claim 1, characterized in that, Actual radiation pattern in the joint optimization model of transmit beamforming for STARS-assisted MIMO inductive system Specifically: ， in , For the transmission array in Directional guidance vector, For STARS Directional guidance vector, It represents the angular difference between the radar's line-of-sight illumination direction and its non-line-of-sight illumination direction.

3. The method for transmitting beamforming in an omnidirectional intelligent metasurface-assisted MIMO sensing integrated system according to claim 1, characterized in that, Introducing auxiliary variables The objective function of the joint optimization model for transmit beamforming of the STARS-assisted MIMO sensing system in step 1 is reduced to a quadratic function of the transmit waveform, specifically: ， In the formula, , For Kronecker product, For the Euclidean norm, The number of grid cells for angle discretization. The radar's desired power pattern. From the perspective of discretization.

4. The method for transmitting beamforming in an omnidirectional intelligent metasurface-assisted MIMO sensing integrated system according to claim 1, characterized in that, The specific process of iteratively solving the four sub-problems is as follows: Step 3.1: Solve for the scaling factor Subproblems ， Obtain the Scaling factor for round iteration, From the perspective of discretization Weighting factor at the location; Step 3.2: Solve for auxiliary variables Subproblems ， Obtain the Auxiliary variables for round iteration; Step 3.3: Solve the transmitted waveform using the alternating direction penalty method algorithm. Subproblems, to obtain the first The emission waveform of the round iteration; Step 3.4: Solve for the STARS coefficients using a distance optimization algorithm. Subproblems, to obtain the first The STARS reflection and transmission coefficients of the round iteration; Step 3.5: Determine whether the BCD algorithm satisfies the iteration termination condition, i.e., whether it meets the condition. ， in This is the termination tolerance of the algorithm; if it is satisfied, the loop stops, and the transmitted waveform, reflection coefficient, and transmission coefficient obtained in the current iteration are output as the optimal solution obtained by the BCD algorithm; otherwise, return to step 3.

1.

5. The method for transmitting beamforming in an omnidirectional intelligent metasurface-assisted MIMO sensing integrated system according to claim 4, characterized in that, For the scaling factor in step 3.1 The subproblem is obtained in the following way: Closed-form optimal solution for round-by-round iteration: ， In the formula, This is for taking the conjugate operation.

6. The method for transmitting beamforming in an omnidirectional intelligent metasurface-assisted MIMO sensing integrated system according to claim 4, characterized in that, For the auxiliary variables in step 3.2 The subproblem is obtained in the following way: Closed-form optimal solution for round-by-round iteration: 。 7. The method for transmitting beamforming in an omnidirectional intelligent metasurface-assisted MIMO sensing integrated system according to claim 4, characterized in that, For the transmitted waveform in step 3.3 Sub-problem solving: ADPM is used to solve the equivalent transformed transmit waveform sub-problem to obtain the first... The specific process of the emitted waveform in the round iteration is as follows: First, transmit waveform The subproblem is equivalently transformed into the following problem without a summation term: ， in, , , , Introducing constant modulus auxiliary variables The problem of having no summation term is transformed into the following variable separation and reconstruction problem: ， Secondly, the ADPM algorithm is used to solve the variable separation and reconstruction problem, and the augmented Lagrangian function is defined as follows: ， in, As a penalty factor, For Lagrange multipliers, the specific update process of the ADPM algorithm is as follows, with superscripts used in the following process. Indicates the first Next iteration: Step 3.3.1: Fix , , Using standard convex optimization techniques, such as the interior-point method, the following subproblem is solved to obtain... : ， Step 3.3.2: Fix , , In this case, solving the following subproblem yields the following result. : ， The closed-form solution to this problem is: ， Step 3.3.3: Define the residual Update the penalty factor as follows: ， in , ; Step 3.3.4: Update the Lagrange multipliers as follows: ， Step 3.3.5: Determine whether the iteration termination condition is met, i.e., whether it is satisfied. , This is the termination tolerance of the algorithm. If it is satisfied, the loop stops, and the resulting transmitted waveform is the optimal transmitted waveform obtained by the ADPM algorithm.

8. The method for transmitting beamforming in an omnidirectional intelligent metasurface-assisted MIMO sensing integrated system according to claim 4, characterized in that, For the STARS reflection and transmission coefficient subproblems in step 3.4, a distance optimization algorithm is used to solve the equivalent transformed subproblem, obtaining the... The specific process for calculating the reflection coefficient and transmission coefficient in the round iteration is as follows: Step 3.4.1: Definition Expand the STAR coefficients The objective function of the subproblem, after removing irrelevant terms, is obtained as follows: ， Step 3.4.2: For Perform an equivalent transformation to make the reflection coefficient explicitly expressible: ， in, , ， ； Step 3.4.3: Rewrite the inequality constraints to make the transmission coefficient explicitly expressed: ， In the formula, , ; Step 3.4.4: Set the STARS coefficients The subproblem is equivalently described by explicitly representing the subproblem as follows: ， in, ， ， Step 3.4.5: Transform the explicit representation subproblem into a real-valued subproblem: ， In the formula, ， ， ， ， ， This represents the real number field, where the superscript indicates the dimension. This indicates the operation of taking the real part. This indicates the operation of taking the imaginary part; Indicates the first One element, Indicates the first One element; Step 3.4.6: Incorporate the constraints into the objective function using the Courant penalty method, and reformulate the real-valued subproblem as the following distance function subproblem: ， In the formula, , , , , For the feasible set of real-valued subproblems, express In the set Projection on; Step 3.4.7: Use the MM technique to transform the distance function subproblem into a series of easily solvable convex subproblems. The specific form of the convex subproblems is as follows: ， In the formula, ， yes The projection onto the feasible set formed by the inequality constraints. and They are and The projection onto the feasible set formed by equality constraints, with subscripts Indicates the first The next iteration; Step 3.4.8: Based on the first-order optimality condition of the convex subproblem, the closed-form optimal solution of the convex subproblem is given as follows: ， In the formula ， ， Step 3.4.9: Using the Nesterov acceleration algorithm, iteratively solve the explicit representation subproblem according to the closed-form optimal solution of the convex subproblem to obtain the optimal STARS reflection coefficient and transmission coefficient.

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