Waveform design method based on joint imaging and radar perception system

Abstract

This invention discloses a waveform design method based on a joint imaging and radar sensing system, specifically including the following steps: constructing a joint imaging and radar sensing system model; using the sum of the directional power of the target radar beams to measure radar sensing performance and the channel condition number to measure imaging performance; constructing an overall optimization problem for the joint imaging and radar sensing system; transforming the objective function of the overall optimization problem and simplifying the diagonalization operation in the objective function; using the positive semidefinite relaxation method to solve the optimization problem to obtain the optimal beamforming vector; using the least squares method to recover the scattering coefficients of the received signal formed by the solved optimal waveform vector, and then performing imaging. The optimization method proposed in this invention can recover the image well and ensure that the radar sensing function is not affected.

Description

Technical Field

[0001] This invention relates to the field of joint imaging and radar sensing technology, and in particular to a waveform design method based on a joint imaging and radar sensing system. Background Technology

[0002] With the continuous development and progress of society, people's demand for intelligent, efficient, safe, and reliable production and lifestyles is becoming increasingly urgent. To address the limitations of 5G and meet the needs of future communication systems, the Sixth Generation (6G) mobile communication system has emerged. In addition to providing high-speed, high-quality mobile communication services, the next-generation wireless communication system will enable many emerging applications such as vehicle-to-everything (V2X), telemedicine, and holographic imaging. It will also allow for the deployment of different functions on the same platform, enabling functional segmentation. These applications all require high-quality wireless communication technology and high-precision sensing capabilities, making 6G a truly intelligent wireless system.

[0003] Multiple Input Multiple Output (MIMO) systems, by leveraging spatial resources, can achieve scene perception capabilities and are currently applied in imaging and sensing fields. Imaging technology is also a form of perception. Depending on the specific circumstances, when detecting target objects in the surrounding environment, sometimes it's necessary to clearly identify the target object—that is, to perform an image reconstruction process—while other times it's sufficient to know that an obstacle exists at a certain location. In such cases, a complex imaging process to reconstruct the object is unnecessary. The joint imaging and radar sensing system proposed in this invention deploys these two distinct functions on the same hardware platform. This allows for the application of imaging or simple perception / judgment functions to different target objects based on actual needs, thereby improving the overall efficiency of the detection system.

[0004] Compared to separate imaging and radar sensing designs, the integrated system proposed in this invention saves spectrum resources and hardware costs. In imaging processing, the illumination beam typically provides continuous coverage of the region of interest, which is beneficial for continuous radar sensing of the surrounding environment. However, current research on joint imaging and radar sensing is still in its early stages, and existing integrated systems have some unresolved issues. For example, integrating imaging and radar sensing onto a single hardware platform does not strictly distinguish between the illumination imaging signal and the radar sensing signal; that is, using a single waveform to achieve both imaging and radar sensing functions means that the beam design of the transmitted signal may benefit either the imaging or radar sensing component. It is clear that when the transmitted signal beam design is more favorable for image recovery, it inevitably leads to a decrease in radar sensing performance; conversely, when the transmitted signal beam design is more favorable for radar sensing, imaging performance will decline. Therefore, this invention, through beam design of the integrated imaging and radar sensing system, aims to maximize imaging performance with minimal impact on radar sensing functionality. Summary of the Invention

[0005] The purpose of this invention is to integrate imaging and radar sensing, two originally independent functions, onto the same hardware platform. This allows a multi-input multi-output antenna to simultaneously possess the dual functions of computational imaging and radar sensing of target objects. This invention studies a joint imaging and radar sensing system, in which the region of interest (ROI) is located in the near-field region of the transmitting antenna. By optimizing the transmitted beam of the illumination signal, a balance and consideration of imaging and radar sensing functions are achieved. The specific technical solution is as follows:

[0006] A waveform design method based on a joint imaging and radar sensing system specifically includes the following steps:

[0007] Construct a joint imaging and radar sensing system model;

[0008] The sum of the directional power of the target radar beam is used to measure the radar's sensing performance, and the channel condition number is used to measure its imaging performance.

[0009] The overall optimization problem of constructing a joint imaging and radar sensing system;

[0010] The objective function of the overall optimization problem is transformed, and the diagonalization operation in the objective function is simplified.

[0011] The optimal beamforming vector is obtained by solving the optimization problem using the positive semidefinite relaxation method.

[0012] The scattering coefficients are recovered from the received signal formed by the optimal waveform vector obtained by solving the least squares method, and then imaging is performed.

[0013] Furthermore, a joint imaging and radar sensing system model is constructed, including: a discrete antenna array for transmitting and receiving is located at the same position and equipped with N antennas. This array images the ROI region by transmitting signals and maximizing the radar beam power in the expected direction. The position formula of the nth antenna is:

[0014]

[0015] In the joint imaging and radar sensing system model, the formula for calculating the base station's transmitted signal is defined as follows:

[0016]

[0017] in, s represents the beamforming vector for imaging and radar sensing. n Let each symbol represent an emitted illumination signal, where each symbol is independent and uncorrelated, and satisfies the following conditions: Let the covariance matrix of the transmitted signal be... Right now in, P is the maximum power of the signal transmitted by the nth antenna element. t This indicates the maximum total transmit power of the base station;

[0018] The ROI region is divided into M grids of size Δ. The specific location of the m-th grid is determined by the following formula:

[0019]

[0020] The characteristic of the m-th grid is represented by the scattering coefficient γ. m This indicates and sets the scattering coefficient for that region.

[0021] G=diag(γ)=diag(γ1,g2,...,g M );

[0022] Define the channel from the transmitting antenna to the ROI region as TX-ROI, and use... This indicates that the channel from the ROI region to the receiving antenna is ROI-RX, using... The specific formula for the received signal is as follows:

[0023]

[0024] in, n is the variance σ 2 Additive white Gaussian noise.

[0025] Furthermore, the beam direction and gain of the radar sensing section are set, specifically including: the detection angle range of the radar sensing coverage is [-π / 2, π / 2], and the baseband signal calculation formula in the θ direction is:

[0026] y(q)=a H (q)x (5)

[0027] Where a(q)=[1,e j2πdsin(q) ,...,e j2π(N-1)dsin(q) ] represents the array direction vector in the q direction, d is the spacing between adjacent antenna elements, and the formula for calculating the beam energy in the q direction is:

[0028]

[0029] The sum of power based on the expected beam direction In measuring the performance of radar sensing, q t Let P represent the direction of the radar-sensing target t-th, and express the sum of the powers of the expected beam directions in matrix form. d =trace(A H RA), where Let T be the array matrix representing the directions of T radar-sensing targets, and let trace(g) represent the trace of the matrix.

[0030] Defining the channel condition number specifically includes: For the rank-deficient problem in near-field environments, defining the condition number of the channel matrix:

[0031]

[0032] Where, λ max and λ min Let cond represent the largest and smallest eigenvalues ​​of the channel matrix H, respectively. If the channel has random defects, cond approaches infinity; if the channel matrix is ​​well-conditioned, cond approaches 1.

[0033] Furthermore, the overall optimization problem of the joint imaging and radar sensing system is constructed, with the specific formula as follows:

[0034]

[0035] Where μ represents the minimum sum of the directional power of the target radar beam.

[0036] Furthermore, the objective function of the overall optimization problem is transformed, and the diagonalization operation in the objective function is simplified, specifically including:

[0037] Based on the equivalence between the condition number and the trace of the channel minimization problem, the implicit expression of the objective function with respect to the optimization variable x is converted into an explicit expression, transforming the global optimization problem (8) into:

[0038]

[0039] The diagonalization operation in the objective function makes the analysis of x difficult. By simplifying it through matrix vectorization, the overall optimization problem (9) is transformed into:

[0040]

[0041] The specific calculation formula for matrix vectorization is as follows:

[0042]

[0043] in, This indicates that vec(diag(G)) should be ignored. T Calculations related to zero elements in x).

[0044] Furthermore, the optimal beamforming vector is obtained by solving the optimization problem using the positive semidefinite relaxation method, specifically including:

[0045] The overall optimization problem (10) is rewritten as an equivalent quadratic semidefinite programming problem with rank-one constraints:

[0046]

[0047] Due to the non-convex rank-one constraint, optimization problem (12) is a non-convex optimization problem. Removing the rank-one constraint, optimization problem (12) is transformed into:

[0048] m R in trace(G T H G R H G R G T R)+h(trace(R)-||R||2) (13)

[0049] sttrace(A H RA)3m

[0050] trace(R) = P t

[0051] R±0

[0052] The 2-norm ||R||2 in the objective function of optimization problem (13) is taken as the lower bound by the first-order Taylor expansion using the successive convex approximation method. The specific formula is as follows:

[0053]

[0054] Based on formula (14), the final optimization problem is transformed into:

[0055]

[0056] The optimal beamforming vector x is obtained by solving the optimization problem (15) using a convex optimization solver.

[0057] Furthermore, the received signal obtained from the optimal beamforming vector is:

[0058] y = Hg + n (16)

[0059] Where H = G R diag(G T x), using the least squares method The scattering coefficient is recovered and displayed in an image.

[0060] According to one aspect of the present invention, a storage medium is provided, wherein the storage medium stores instructions that, when read by a computer, cause the computer to execute the waveform design method based on the joint imaging and radar sensing system described in any of the preceding claims.

[0061] According to another aspect of the present invention, an electronic device is provided, comprising a processor and the aforementioned storage medium, wherein the processor executes instructions in the storage medium.

[0062] Compared with the prior art, the beneficial effects of the present invention are as follows:

[0063] 1. Compared with the traditional approach of deploying imaging and radar sensing functions independently on different hardware platforms, the system designed in this invention enables the multi-input multi-output antenna to simultaneously possess the dual functions of computational imaging and radar sensing of target objects, reducing hardware costs, improving spectrum utilization, and solving the spectrum congestion problem.

[0064] 2. By optimizing the beam design of the illumination signal, this invention achieves the best possible imaging performance while minimizing the impact on radar sensing capabilities. This solves the problem of balancing the two functions in an integrated system, thus achieving a balance between imaging and radar sensing capabilities. Attached Figure Description

[0065] Other features, objects, and advantages of the invention will become more apparent from the following detailed description of non-limiting embodiments with reference to the accompanying drawings:

[0066] Figure 1 This is a schematic diagram of the overall process of an embodiment of the present invention.

[0067] Figure 2 This is an overall system model diagram of an embodiment of the present invention.

[0068] Figure 3 The image shows the simulation results of imaging restoration according to an embodiment of the present invention.

[0069] Figure 4 This is a graph showing the relationship between imaging and radar sensing performance in an embodiment of the present invention.

[0070] Figure 5 This is an optimized radar beam pattern for an embodiment of the present invention. Detailed Implementation

[0071] To make the objectives, technical solutions, and advantages of this invention clearer, the invention will be described in detail below with reference to the accompanying drawings and specific embodiments.

[0072] The embodiments of the present invention will be further described in detail below with reference to the accompanying drawings:

[0073] like Figure 1 As shown, the present invention specifically includes the following steps:

[0074] Construct a joint imaging and radar sensing system model;

[0075] The sum of the directional power of the target radar beam is used to measure the radar's sensing performance, and the channel condition number is used to measure its imaging performance.

[0076] The overall optimization problem of constructing a joint imaging and radar sensing system;

[0077] The objective function of the overall optimization problem is transformed, and the diagonalization operation in the objective function is simplified.

[0078] The optimal beamforming vector is obtained by solving the optimization problem using the positive semidefinite relaxation method.

[0079] The scattering coefficients are recovered from the received signal formed by the optimal waveform vector obtained by solving the least squares method, and then imaging is performed.

[0080] The specific implementation process includes the following steps:

[0081] Step 1: Construct a system model for joint imaging and radar sensing, setting the base station transmitted signal, the scattering coefficient of the region of interest, and the expression for the channel between the base station and the region of interest;

[0082] Step 2: Set the beam direction and gain of the radar sensing part, and evaluate the radar sensing performance by analyzing the radar power in the expected direction.

[0083] Step 3: By analyzing the relationship between the spatial characteristics of the MIMO channel and the condition number in the near-field communication system, we can see that if the channel matrix is ​​well-conditioned, the condition number is close to 1; if the channel has random defects, the condition number is close to infinity. Therefore, the channel condition number is used to measure imaging performance.

[0084] Step 4: Under the constraint of base station transmit power, construct the overall optimization problem of the joint imaging and radar sensing system;

[0085] Step 5: To transform the objective function into an explicit expression of the optimization variables, the objective function of the optimization problem is transformed into a trace representation of a matrix;

[0086] Step 6: Simplify the diagonalization operation in the objective function;

[0087] Step 7: Rewrite the problem as an equivalent quadratic semidefinite programming problem with rank 1 constraints using auxiliary variables;

[0088] Step 8: Remove the rank-1 constraint, and use the first-order Taylor expansion of the 2-norm in the objective function as its lower bound using the SCA method, and use the positive semidefinite relaxation method to solve for the optimal beamforming vector;

[0089] Step 9: The scattering coefficients are recovered from the received signal formed by the optimal waveform vector obtained by solving the least squares method, and then imaging is performed.

[0090] In step 1 above, a system model for joint imaging and radar sensing is constructed. The transmit and receive discrete antenna arrays (TX / RX) are located at the same position and equipped with N antennas. The position of the nth antenna is:

[0091]

[0092] The array images the region of interest (ROI) by transmitting signals and maximizes the power of the radar beam in the desired direction.

[0093] The base station transmits the following signals:

[0094]

[0095] in s represents the beamforming vector for imaging and radar sensing. n The symbols representing the emitted illumination signals are assumed, for ease of subsequent research and analysis, to be independent and uncorrelated, and to satisfy the following conditions: Define the covariance matrix of the transmitted signal as follows: Right now P is the maximum power of the signal transmitted by the nth antenna element. t This represents the maximum total transmit power of the base station.

[0096] The TX transmit signal illuminates the region of interest (ROI), which is divided into M grids of size Δ, located as follows:

[0097]

[0098] The feature of the m-th cell is the scattering coefficient γ. m This indicates that if there is no target cell Δ in the region, then the scattering coefficient γ m =0, if a cell exists, this value is related to the radar cross section (RCS) of the scatterer. And the magnitude of the scattering coefficient |γ m | Subject to the maximum cross-section Δ 2 The limitation corresponds to the scattering cross section of a perfect electrical conductor (PEC) with the same area, i.e. Therefore, the present invention has |γ m |￡D. Scattering coefficient of this region , G=diag(γ)=diag(γ1,g2,...,g M ).

[0099] The channel from the transmit antenna TX to the region of interest ROI is TX-ROI: The channel from the region of interest (ROI) to the receiving antenna is ROI-RX: The signal received by RX is y = G R ΓG T x+w, the above equation can be further written as:

[0100]

[0101] in, n is the variance σ 2 Additive white Gaussian noise.

[0102] In step 2 above, the detection angle range covered by the radar sensing is [-π / 2, π / 2], and the baseband signal in the θ direction can be expressed as:

[0103] y(q)=a H (q)x (5)

[0104] Where a(q)=[1,e j2πdsin(q) ,...,e j2π(N-1)dsin(q) ] represents the array direction vector in the q direction, d is the spacing between adjacent antenna elements, and the formula for calculating the beam energy in the q direction is:

[0105]

[0106] Among them, the sum of the power in the expected beam direction. To measure the quality of radar sensing performance, θ t The direction of the t-th radar-sensing target is represented by matrix P. d =trace(A H RA), where This represents the array matrix for T radar-sensing target directions.

[0107] In step 3 above, in the near-field environment, G T and G R Since H might be rank-deficient, directly using the least squares method to recover the scattering coefficient γ and then analyzing the imaging performance using the mean square error (MSE) would make the optimization problem very complex and difficult to design the signal. Therefore, the condition number is chosen as the metric for imaging performance. The condition number is defined as follows:

[0108]

[0109] Where, λ max and λ min Let represent the largest and smallest eigenvalues ​​of the channel matrix H, respectively. If the channel has random defects, then cond approaches infinity; if the channel matrix is ​​well-conditional, then cond approaches 1.

[0110] In step 4 above, since the system designed in this invention uses the emitted illumination signal for both imaging and radar sensing, better imaging performance results in weaker radar sensing capability, and vice versa. Therefore, the overall optimization problem can be written as follows:

[0111]

[0112] μ represents the minimum sum of the directional power of the target radar beam.

[0113] In step 5 above, there is no obvious relationship between x and the condition number cond. Since the condition number and the trace of the channel minimization problem are equivalent, the implicit expression of the objective function with respect to the optimization variable x is converted into an explicit expression. Therefore, the above optimization problem can be written in the following form:

[0114]

[0115] In step 6 above, the diagonalization operation in the objective function makes the analysis of x difficult. Simplification through matrix vectorization yields:

[0116]

[0117] The specific process of matrix vectorization is as follows:

[0118]

[0119] in, This indicates that vec(diag(G)) should be ignored. T Calculations related to zero elements in x).

[0120] In step 7 above, the constraint problem involves quadratic equality constraints, making it non-convex and difficult to solve. To address this issue, this invention uses the semidefinite relaxation (SDR) method to transform the optimization problem. According to the definition of R, the above equation can be rewritten as an equivalent quadratic semidefinite programming (QSDP) problem with rank-one constraints.

[0121]

[0122] In step 8 above, due to the non-convex rank-one constraint, the above equation is still a non-convex optimization problem. Therefore, by removing the rank-one constraint, the optimization problem can be written as:

[0123] m R in trace(G T H G R H G R G T R)+h(trace(R)-||R||2) (13)

[0124] sttrace(A H RA)3m

[0125] trace(R) = P t

[0126] R±0

[0127] Since the objective function contains the 2-norm ||R||2, it remains non-convex. Therefore, this invention utilizes the successive convex approximation method (SCA) to use its first-order Taylor expansion as its lower bound.

[0128]

[0129] The final optimization problem is transformed as follows, which is a typical QSDP problem. It is convex and can be solved directly using existing convex optimization solvers (such as the CVX toolkit).

[0130]

[0131] In step 9 above, the received signal obtained from the optimal beamforming vector is:

[0132] y = Hg + n (16)

[0133] Where H = GR diag(G T x), using the least squares method The scattering coefficient is recovered and displayed in an image.

[0134] like Figure 2 As shown, an overall system model is constructed, and the maximum total transmit power of the base station is set to P. max =1W, the center frequency of the transmitted carrier is f c =28GHz, signal bandwidth is 120kHz, wavelength is A square antenna array is deployed in the YOZ plane, with N = 13 × 13 = 169 antennas and an antenna spacing of [missing information]. The center of the antenna array is located at (0, 0.09m, 0.09m), and the noise power spectral density is σ. 2 = -170dBm / Hz. The plane of interest (ROI) is set at 2m parallel to the YOZ plane and modeled as a square grid with a side length Δ = 0.1m and a number of grids M = 10 × 10 = 100. Therefore, the center position of the ROI is (2, 0.45m, 0.45m). To minimize the overlap between imaging power and radar sensing beam power, the expected radar beam direction is set to [-85°, 70°].

[0135] exist Figure 3 The figures above visually demonstrate the feasibility of the system proposed in this invention and the effectiveness of the waveform optimization method for image restoration. For comparison, an experiment was conducted with a random signal image (image only, without waveform optimization) and an image (image only, with waveform optimization). The fourth figure shows the imaging result of the combined imaging and radar sensing system with beam optimization. It can be seen that the imaging performance of the combined imaging and radar sensing system designed in this invention, compared to the original region of interest, only suffers from color distortion. It can completely detect every pixel in the region of interest. Furthermore, the imaging performance of the integrated system is far superior to that of the random waveform illumination signal, and the detection of the surrounding environment of the target area is closer to reality. This demonstrates the effectiveness of the waveform optimization method proposed in this invention and proves the feasibility of the proposed combined imaging and radar sensing system.

[0136] exist Figure 4 The paper demonstrates the trade-off between the performance of imaging and radar sensing functions deployed on the same hardware platform. As radar sensing performance improves, imaging performance decreases to some extent. Furthermore, when the sum of the target radar beam powers approaches the theoretical maximum, that is, when radar sensing performance reaches its theoretical optimum, the imaging mean square error increases significantly, and imaging performance deteriorates sharply.

[0137] exist Figure 5The paper intuitively demonstrates the system and waveform optimization method proposed in this invention, which can maximize the sum of beam power in the expected direction while taking into account imaging performance.

[0138] The above embodiments are only used to illustrate the technical solutions of the present invention and are not intended to limit it. Although the present invention has been described in detail with reference to preferred embodiments, those skilled in the art should understand that modifications or equivalent substitutions can be made to the technical solutions of the present invention without departing from the spirit and scope of the technical solutions of the present invention.

Claims

1. A waveform design method based on a joint imaging and radar sensing system, characterized in that, Specifically, the following steps are included: Construct a joint imaging and radar sensing system model; The sum of the directional power of the target radar beam is used to measure the radar's sensing performance, and the channel condition number is used to measure its imaging performance. The overall optimization problem of constructing a joint imaging and radar sensing system; The objective function of the overall optimization problem is transformed, and the diagonalization operation in the objective function is simplified. The optimal beamforming vector is obtained by solving the optimization problem using the positive semidefinite relaxation method. The scattering coefficients are recovered from the received signal formed by the optimal waveform vector obtained by solving the least squares method, and then imaging is performed.

2. The method according to claim 1, characterized in that, A joint imaging and radar sensing system model is constructed, including: a discrete antenna array for transmitting and receiving is located at the same position and equipped with N antennas. This array images the ROI region by transmitting signals and maximizing the radar beam power in the expected direction, where the Nth antenna is the most powerful. The formula for the position of each antenna is: (1) In the joint imaging and radar sensing system model, the formula for calculating the base station's transmitted signal is defined as follows: (2) in, This represents the beamforming vector for imaging and radar sensing. Let each symbol represent an emitted illumination signal, where each symbol is independent and uncorrelated, and satisfies the following conditions: The covariance matrix of the transmitted signal is set as follows: ,Right now ,in, The maximum power of the transmitted signal of the nth antenna element. This indicates the maximum total transmit power of the base station; The ROI region is divided into areas of size [missing information]. of The grid, the first The formula for the specific location of each grid is: (3) Among them, the The characteristics of each grid are represented by the scattering coefficient. This indicates and sets the scattering coefficient for that region. , ; Define the channel from the transmitting antenna to the ROI region as TX-ROI, and use... This indicates that the channel from the ROI region to the receiving antenna is ROI-RX, using... The specific formula for the received signal is as follows: (4) in, , , , The variance is Additive white Gaussian noise.

3. The method according to claim 2, characterized in that, The beam direction and gain of the radar sensing section are set, specifically including the detection angle range covered by the radar sensing. , The formula for calculating the baseband signal in the direction is: (5) in, express The direction vector of the array. It is the spacing between adjacent antenna elements. The formula for calculating beam energy in a given direction is: (6) The sum of power based on the expected beam direction Among the factors used to measure the quality of radar sensing performance are... Indicates the first The direction of the radar-sensing target is represented by the sum of the powers of the expected beam directions in matrix form. ,in express An array matrix for radar to sense the direction of targets. Represents the trace of a matrix; Defining the channel condition number specifically includes: For the rank-deficient problem in near-field environments, defining the condition number of the channel matrix: (7) in, and Representing the channel matrix respectively The maximum and minimum eigenvalues, if the channel has random defects, then Approaching infinity; if the channel matrix conditions are good, then Close to 1.

4. The method according to claim 3, characterized in that, The overall optimization problem for constructing a joint imaging and radar sensing system is given by the following formula: (8) in, This represents the minimum sum of the directional power of the target radar beam.

5. The method according to claim 4, characterized in that, The objective function of the overall optimization problem is transformed, and the diagonalization operation in the objective function is simplified, specifically including: Based on the equivalence between the condition number and the trace of the channel minimization problem, the objective function is expressed with respect to the optimization variables. The implicit expression is converted into an explicit expression, transforming the overall optimization problem (8) into: (9) The diagonalization operation in the objective function makes the... The analysis becomes difficult. By simplifying through matrix vectorization, the overall optimization problem (9) is transformed into: (10) The specific calculation formula for matrix vectorization is as follows: (11) in, Indicates to ignore Calculations related to zero elements in the calculations.

6. The method according to claim 5, characterized in that, The optimal beamforming vector is obtained by solving the optimization problem using the positive semidefinite relaxation method, specifically including: The overall optimization problem (10) is rewritten as an equivalent quadratic semidefinite programming problem with rank-one constraints: (12) Due to the non-convex rank-one constraint, optimization problem (12) is a non-convex optimization problem. Removing the rank-one constraint, optimization problem (12) is transformed into: (13) The 2-norm exists in the objective function of optimization problem (13). Using the successive convex approximation method, the first-order Taylor expansion is taken as its lower bound, and the specific formula is as follows: (14) Based on formula (14), the final optimization problem is transformed into: (15) The optimal beamforming vector is obtained by solving the optimization problem (15) using a convex optimization solver. .

7. The method according to claim 6, characterized in that, The received signal obtained from the optimal beamforming vector is: (16) in, The least squares method is used. The scattering coefficient is recovered and displayed in an image.

8. A storage medium, characterized in that, The storage medium stores instructions that, when read by a computer, cause the computer to execute the waveform design method based on a joint imaging and radar sensing system as described in any one of claims 1 to 7.

9. An electronic device, characterized in that, It includes a processor and the storage medium of claim 8, wherein the processor executes instructions in the storage medium.

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