A communication and perception integrated waveform design method for vehicle networking

Abstract

The application provides a communication and sensing integrated waveform design method for Internet of Vehicles, and belongs to the technical field of wireless communication. By minimizing the weight sum of multi-user interference, designing the similarity of the waveform and the reference waveform and the Cramer-Rao bound, the ISAC waveform can realize peak performance, enhance radar capability and ensure efficient communication. The optimization with the total transmission power and the peak-to-average power ratio as constraints converts the non-convex problem into a convex problem, and the alternating direction multiplier method algorithm is used for solving. The simulation result shows that the ISAC waveform has good communication and target detection capability, and can improve the spectrum utilization rate of V2X. The method can detect targets when communicating with downlink users, minimize the sum of MUI, CRB and waveform similarity, introduce a trade-off parameter, realize flexible trade-off between communication and sensing under the constraints of total power and peak-to-average power ratio, better adapt to the high dynamic scene of V2X, and reduce the mutual interference caused by the separation of traditional sensing and communication functions.

Description

TECHNICAL FIELD

[0001] The present application relates to the technical field of wireless communication, and in particular to a communication and sensing integrated waveform design method for vehicle networking. BACKGROUND

[0002] Due to the rapid deployment of 5G networks, the sharp increase in the number of vehicles, and the continuous progress of vehicle-to-everything (V2X) technology, spectrum resources are facing unprecedented pressure. At the same time, V2X applications have strict requirements on delay, but the transmission of a large amount of sensing and communication data hinders real-time communication between vehicles and the surrounding environment, which exacerbates the contradiction between limited communication and sensing resources of networked vehicle devices. In this case, Integrated Sensing and Communication (ISAC) has become a key solution in V2X applications. ISAC is a technology that combines sensing and communication, which can sense details such as direction, distance, and speed while transmitting information, has advantages such as improving spectrum utilization, reducing hardware deployment costs, and alleviating electromagnetic interference between communication and sensing, thereby realizing the complementarity of communication and sensing functions. On the one hand, sensing can enhance communication through more accurate channel modeling, channel estimation, beam management, and multi-vehicle resource joint management; on the other hand, communication can also enhance sensing. ISAC not only meets the communication needs between vehicles, but also collects accurate environmental information using its sensing capabilities. By efficiently utilizing limited spectrum resources, ISAC improves the performance of communication and sensing, and provides a strong guarantee for more intelligent traffic management and safe control of vehicles.

[0003] At present, ISAC based on V2X has been deeply researched in many aspects, but the research on ISAC waveform design in V2X is still in a blank state. Waveform design is a key aspect of ISAC, which determines the performance boundary that the ISAC system can achieve. V2X has more stringent requirements for communication and sensing capabilities. The existing ISAC waveform design method only considers the weighted optimization of MUI and waveform similarity, and does not take into account the sensing and communication problems brought by high dynamic changes in V2X, so it cannot well adapt to the V2X environment. The ISAC collaborative design waveform method involves creating a new waveform that seamlessly integrates communication and sensing functions. This requires the waveform to perform sensing tasks such as parameter estimation and target detection, while supporting communication through information data transmission. SUMMARY

[0004] To address the shortcomings of existing technologies, this invention aims to provide an integrated communication and sensing waveform design method for vehicle-to-everything (V2X) networks. A waveform design scheme for a V2X MIMO-ISAC system is proposed. By minimizing the weighted sum of multi-user interference (MUI), the similarity between the designed waveform and the reference waveform, and the Cramér-Rao bound (CRB), the ISAC waveform achieves peak performance while enhancing radar capabilities and ensuring efficient communication. An optimization scheme constrained by total transmitted power and peak-to-average power ratio (PAPR) is designed. This waveform exhibits good communication and sensing performance, transforming a non-convex problem into a convex one, which is solved using the alternating direction method of multipliers (ADMM) algorithm. Simulation results show that the designed ISAC waveform has good communication and target detection capabilities, and can improve the spectral efficiency of V2X.

[0005] To solve the above-mentioned technical problems, the technical solution provided by the present invention is as follows:

[0006] A waveform design method integrating communication and sensing for the Internet of Vehicles includes the following steps:

[0007] S1. By defining the ISAC base station, the communication and sensing capabilities of the transmitted waveform, the vehicle-to-everything (V2X) scenario, and the target of interest, a multi-input multi-output integrated communication and sensing system model for V2X is constructed.

[0008] S2. Based on the communication and sensing integrated system model constructed in S1, the communication model is established by defining the user received signal and the waveform communication performance indicators MUI and PAPR that affect the transmission.

[0009] S3. Based on the communication and sensing integrated system model constructed in S1, a sensing model is established by defining the received signal of the target of interest received by the ISAC base station and the waveform similarity and CRB indicators that affect the waveform sensing performance of the transmission.

[0010] S4. Combining the communication model established in S2 and the perception model established in S3, construct an optimization problem that minimizes the weighted sum of MUI, CRB and waveform similarity, and is constrained by total transmission power and PAPR. Transform the optimization problem into matrix form, making it a QCQP problem with quadratic equation constraints and quadratic inequality constraints.

[0011] S5. Based on the QCQP problem described in S4, auxiliary variables are introduced to convert the non-convex problem into a convex problem, and the ADMM algorithm is used to solve the optimal waveform X by fixing different parameters and alternately iterating each parameter variable.

[0012] Further, the ISAC base station in S1 is composed of a uniform linear array, including root transmitting antennas and root receiving antennas.

[0013] The ISAC base station communicates with mobile users such as vehicles and mobile terminals, and the detected target of interest is the surrounding buildings, roadside pedestrians, and vehicles.

[0014] Further, S2 includes the following steps:

[0015] S2.1 The signal matrix received by the communication user ,

[0016] ;

[0017] wherein, is a complex matrix, wherein represents the length of the communication frame; represents the downlink communication channel matrix, assuming experiences flat Rayleigh fading and can be perfectly estimated; represents the transmission signal matrix; represents the additive white Gaussian noise (AWGN) of the downlink user;

[0018] S2.2 Rewrite the received signal matrix described in S2.1 as:

[0019] ;

[0020] MUI is represented as:

[0021] ;

[0022] In order to maximize the sum rate, the MUI is minimized; the signal-to-noise ratio of each user in each frame and the achievable sum rate are calculated;

[0023] ;

[0024] wherein, is the set average with respect to the time index, is the th item in , indicating the signal transmitted between the th and th communication user, indicating the signal transmitted between the Signals transmitted in each time slot;

[0025] The realizable sum and rate of a downlink mobile user are represented as follows:

[0026] ;

[0027] S2.3 Considering the impact of PAPR on the effectiveness of the communication system, PAPR is controlled to provide sufficient transmission distance and reliability, based on the signal matrix received by the communication user as described in S2.1. The formula for calculating PAPR is:

[0028] ;

[0029] in, It is a vector The One element, , indicating that the matrix The vector obtained after vectorization The threshold representing PAPR, and the total transmit power of the ISAC waveform. for:

[0030] ;

[0031] The right half of equation (7) above is rewritten as:

[0032] ;

[0033] in .

[0034] Further, step S3 includes the following steps:

[0035] S3.1 For radar sensing, assuming the propagation path of the transmitted waveform is a line-of-sight path, then in the direction... The signal matrix received by the far-field point target Represented as:

[0036] ;

[0037] in, Indicates the first The reflection coefficient of the target; This indicates the angle of the radar-detected target relative to the ISAC base station. and These are the guide vectors for the transmitting and receiving antennas, respectively; half-wavelength ULA is used between adjacent components; It is an AWGN with MIMO radar;

[0038] The transmit direction and the arrival direction of a monostatic radar are the same, assuming that both the DOA and the DOD are and is expressed as

[0039] ;

[0040] ;

[0041] S3.2 Waveform similarity constraint is introduced in ISAC waveform design to affect its sensing performance; waveform similarity is expressed as

[0042] ;

[0043] wherein is the reference waveform matrix; minimizing can approximately obtain the expected radar beam pattern;

[0044] S3.3 CRB is used to measure the sensing performance, providing a lower bound of mean square error and having a closed-form expression; for radar point target detection, CRB is expressed as

[0045] ;

[0046] wherein , is the derivative of , denotes the reflection coefficient; equation (13) is further equivalent to

[0047] ;

[0048] For convenience of calculation, it is assumed that , obtaining ; CRB can be expressed as

[0049] .

[0050] Further, the S4 comprises the following steps:

[0051] S4.1 The optimization problem is expressed as

[0052] ;

[0053] wherein is a trade-off parameter, which can affect the characteristics of the waveform by adjusting it; it can be further expressed as

[0054] ;

[0055] S4.2 Further simplifying the optimization problem;

[0056] S4.2.1 Let:

[0057] ,

[0058] where is a zero matrix, the optimization problem is transformed into:

[0059] ;

[0060] S4.2.2 Transform the objective function into matrix form:

[0061] ;

[0062] Let , the objective equation can be expressed as:

[0063] ;

[0064] Let , and vectorize into a diagonal matrix , vectorize into , and let ;

[0065] The objective equation can be rewritten as:

[0066] ;

[0067] where .

[0068] Further, the S5 comprises the following steps:

[0069] S5.1 By introducing variables and , the original optimization problem is expressed as

[0070] ;

[0071] From the above optimization problem, the augmented Lagrangian expression is obtained, expressed as:

[0072] ;

[0073] where is a penalty factor, and the augmented Lagrangian function can also be regarded as a non-augmented Lagrangian function of the following optimization problem:

[0074] ;

[0075] S5.2 update ;

[0076] In the iteration process of ADMM algorithm, the variable update expression of the th iteration is as follows:

[0077] (25);

[0078] By deriving equation (25) and setting its gradient to 0, the update expression of is obtained.

[0079] The gradient is obtained by deriving the augmented Lagrangian function:

[0080] (26);

[0081] Let the gradient be equal to zero, and the update equation of is obtained by rearranging:

[0082] ;

[0083] S5.3 update ;

[0084] After updating , the auxiliary variable is updated, and the variable update expression of the th iteration is as follows:

[0085] (28);

[0086] is expressed as the following optimization problem:

[0087] ;

[0088] Similarly, the Lagrangian expression of it is obtained, as follows:

[0089] (30);

[0090] Similar to the update of , the following Lagrangian expression is obtained for calculating the gradient of ;

[0091] (31);

[0092] And let obtain the update equation of :

[0093] (32);

[0094] S5.4 update ;

[0095] updating auxiliary variables ; similarly, the variable updating expression of the second iteration is:

[0096] (23);

[0097] The optimization problem can be expressed as:

[0098] ;

[0099] If the constraint condition is satisfied, its Lagrange function and gradient are calculated, expressed as:

[0100] ;

[0101] ;

[0102] Let , the updating expression of is obtained:

[0103] (37);

[0104] If the constraint is not satisfied, project to an area that satisfies the constraint; set a scaling factor , so that , and obtain:

[0105] ;

[0106] S5.5 updating auxiliary variables:

[0107] By iterating the auxiliary variables, the optimal solution is obtained, expressed as:

[0108] (39);

[0109] .

[0110] The beneficial effects of the present application are:

[0111] ​The application provides a MIMO-ISAC transmission waveform design method for a V2X scene, which can detect targets when communicating with downlink users, minimize the sum of MUI, CRB and waveform similarity, and further introduce a trade-off parameter to realize flexible trade-off between communication and sensing under total power and peak-to-average power ratio constraints. The waveform design scheme can better adapt to the high dynamic scene of V2X, reduce the mutual interference caused by the separation of traditional sensing and communication functions, and realize seamless integration of communication and sensing. The simulation results verify the performance of the designed ISAC waveform, significantly improve the information transmission rate and accuracy in communication, and realize superior target detection performance in sensing, thereby maximizing the sensing performance of V2X on the basis of ensuring effective transmission of vehicle sensing information. BRIEF DESCRIPTION OF DRAWINGS

[0112] The accompanying drawings are included to provide a further understanding of the application, and constitute a part of the specification, illustrate the application, and are used to explain the application together with the embodiments of the application, and do not constitute a limitation on the application. In the drawings:

[0113] Figure 1 The flowchart is built for the communication and sensing integrated waveform design system of the application facing the Internet of Vehicles

[0114] Figure 2 The schematic diagram of the multiple-input multiple-output integrated sensing and communication system model is for the application

[0115] Figure 3 The ISAC base station is for

[0116] Figure 4 The average achievable sum rate of different user numbers is for

[0117] Figure 5 The radar pulse compression performance under different ISAC waveform designs is for DETAILED DESCRIPTION

[0118] The preferred examples of the application are described below in combination with the drawings, and it should be understood that the following examples are given only for the purpose of illustration, and are not used to limit the scope of the application. Those skilled in the art can make various modifications and replacements to the application without departing from the spirit and principles of the application.

[0119] The application aims to provide a communication and sensing integrated waveform design method for vehicle networking, which balances and optimizes ISAC waveform, is a MIMO-ISAC transmission waveform design method for V2X scene, can detect targets when communicating with downlink users, minimizes the sum of MUI, CRB and waveform similarity, and introduces a trade-off parameter to realize flexible trade-off between communication and sensing under total power and PAPR constraints.

[0120] The optimization problem is a non-convex quadratic constraint quadratic programming problem, and the ADMM algorithm is used to solve the optimization problem. The waveform design method can better adapt to the high dynamic scene of V2X, reduce the mutual interference caused by the separation of traditional sensing and communication functions, and realize seamless integration of communication and sensing. The simulation results verify the performance of the designed ISAC waveform, significantly improve the information transmission rate and accuracy in communication, and realize superior target detection performance in sensing, on the basis of ensuring effective transmission of vehicle sensing information, maximize the sensing performance of V2X.

[0121] The application is a communication and sensing integrated waveform design method for vehicle networking, comprising the following steps:

[0122] S1. Construct a multi-input multi-output integrated communication and sensing system model for vehicle networking by defining ISAC base station, communication and sensing capability of the transmitted waveform, vehicle networking scene and target of interest;

[0123] S2. Based on the communication and sensing integrated system model constructed in S1, a communication model is established by defining user received signal and indicators MUI and PAPR affecting the communication performance of the transmitted waveform;

[0124] S3. Based on the communication and sensing integrated system model constructed in S1, a sensing model is established by defining the received signal of the ISAC base station received by the target of interest and indicators waveform similarity and CRB affecting the sensing performance of the transmitted waveform;

[0125] S4. Combine the communication model established in S2 and the sensing model established in S3 to construct an optimization problem of minimizing the weighted sum of MUI, CRB and waveform similarity, and taking total transmission power and PAPR as constraints, convert the optimization problem into a matrix form, so that it becomes a QCQP problem of quadratic equation constraint and quadratic inequality constraint;

[0126] S5. Based on the QCQP problem described in S4, auxiliary variables are introduced to convert the non-convex problem into a convex problem, and the ADMM algorithm is used to solve the optimal waveform X by fixing different parameters and alternately iterating each parameter variable.

[0127] Specifically,

[0128] S1. Design a MIMO-ISAC system model for V2X.

[0129] The application designs a multiple-input multiple-output integrated sensing and communication (MIMO-ISAC) system model for V2X. The system model transmits ISAC waveforms, which can not only communicate with mobile users such as vehicles and mobile terminals, but also detect targets of interest such as surrounding buildings, roadside pedestrians and vehicles. The ISAC base station is composed of a uniform linear array (ULA), including root transmitting antennas and root receiving antennas. The system model is shown in Figure 2 , and the ISAC base station is shown in Figure 3 .

[0130] S2. Build a communication model

[0131] S2.1 The signal matrix received by the communication user ,

[0132] ;

[0133] wherein, is a complex matrix, wherein represents the length of the communication frame; represents the downlink communication channel matrix, which is assumed to experience flat Rayleigh fading and can be perfectly estimated; represents the transmission signal matrix; represents the Additive White Gaussian Noise (AWGN) of the downlink user.

[0134] S2.2 To maximize the sum rate, MUI needs to be minimized. By rewriting the received signal matrix as:

[0135] ;

[0136] MUI can be represented as:

[0137] ;

[0138] and accordingly calculate the signal-to-noise ratio of each user in each frame and the achievable sum rate.

[0139] ;

[0140] wherein, is the set average with respect to time index, is the th element in , represents the signal transmitted between the th and th communication users, represents the signal transmitted in the th time slot. Thus, the achievable sum rate of downlink mobile users can be represented as follows:

[0141] ;

[0142] S2.3 Considering the impact of PAPR on the effectiveness of the communication system, PAPR must be properly controlled to provide sufficient transmission distance and reliability.

[0143] The formula for calculating PAPR is:

[0144] ;

[0145] wherein, is the th element of the vector , , represents the vector obtained after vectorizing the matrix , represents the threshold value of PAPR. The total transmit power of the ISAC waveform is:

[0146] ;

[0147] Then, the right half of the above formula can be rewritten as:

[0148] ;

[0149] wherein .

[0150] S3. Constructing a perception model

[0151] S3.1 For radar perception, assuming that the propagation path of the transmitted waveform is a line-of-sight path, the signal matrix received by a far-field point target located in direction can be represented as:

[0152] ;

[0153] wherein, represents the the reflection coefficient of the target. denotes the angle of the radar detected target with respect to the ISAC base station, and are the steering vectors of the transmit and receive antennas, respectively. In addition, half- wavelength ULA is used between adjacent elements. is the AWGN of MIMO radar.

[0154] Since a monostatic radar is used, the Direction of Departure (DOD) and the Direction of Arrival (DOA) are the same. Assume that both the DOA and the DOD are .

[0155] Then, and can be expressed as:

[0156] ;

[0157] ;

[0158] S3.2 Waveform similarity constraints are introduced in the ISAC waveform design to affect its sensing performance. The waveform similarity constraint represents the difference between the designed waveform and the reference waveform. The waveform similarity is expressed as:

[0159] ;

[0160] where is the reference waveform matrix. Minimizing can approximate the expected radar beam pattern.

[0161] S3.3 The CRB can be used to measure the sensing performance, providing a lower bound of the mean square error and having a closed-form expression.

[0162] For radar point target detection, the CRB can be expressed as:

[0163] ;

[0164] where is the derivative of , denotes the reflection coefficient. Therefore, (13) can be further equivalent to:

[0165] ;

[0166] For convenience of calculation, assume , from which we can get Thus, the CRB can be expressed as:

[0167] .

[0168] S4. Establishing the optimization problem

[0169] With the above communication and sensing models, an optimization problem is constructed with the total transmission power and PAPR as constraints. The objective function of the optimization problem includes the weighted sum of MUI, CRB and waveform similarity, and the relative importance between each term is adjusted by introducing a trade-off parameter.

[0170] S4.1 The optimization problem is expressed as:

[0171] ;

[0172] wherein is a trade-off parameter, which can affect the characteristics of the waveform by adjusting it.

[0173] Further, it can be expressed as:

[0174] ;

[0175] Obviously, the optimization problem is a non-convex optimization problem, which is difficult to solve.

[0176] S4.2 In order to further solve the optimization problem, the optimization problem needs to be further simplified.

[0177] First, let:

[0178] ;

[0179] wherein is a zero matrix, and the optimization problem is converted to:

[0180] ;

[0181] Then, the objective function needs to be converted into a matrix form;

[0182] ;

[0183] Let , then the objective equation can be expressed as:

[0184] ;

[0185] Let , and is vectorized into a diagonal matrix , and is vectorized into , and let .

[0186] The target equation can be rewritten as:

[0187] ;

[0188] where .

[0189] The above optimization problem is a QCQP problem consisting of quadratic equation constraints and quadratic inequality constraints. It is solved by using the ADMM algorithm. This algorithm is an effective iterative method for handling non-convex optimization problems. It can decompose the original problem into multiple sub-problems and update the solutions of each sub-problem through alternating iteration, eventually converging to the optimal solution or approximate optimal solution of the original problem.

[0190] S5. Solving using ADMM algorithm

[0191] S5.1 Introducing variables and , the original optimization problem can be represented as:

[0192] ;

[0193] From the above optimization problem, an augmented Lagrangian expression can be obtained, represented as:

[0194] ;

[0195] where is the penalty factor. This augmented Lagrangian function can also be considered as the non-augmented Lagrangian function of the following optimization problem,

[0196] ;

[0197] S5.2 Updating ,

[0198] In the iteration process of the ADMM algorithm, the variable update expression of the th iteration is as follows:

[0199] (25);

[0200] By taking the derivative of equation (25) and setting its gradient to zero, the update expression of can be obtained. First, by taking the derivative of the augmented Lagrangian function, the gradient

[0201] (26),

[0202] Setting the gradient to zero and rearranging the update equation for is:

[0203] ;

[0204] S5.3 Update ,

[0205] Now, after updating , the auxiliary variable , the variable update expression for the th iteration is as follows,

[0206] (28),

[0207] which can be represented as the following optimization problem:

[0208] ,

[0209] Similarly, its Lagrangian expression can be obtained as follows,

[0210] (30);

[0211] Similar to the update , the next set of Lagrangian expressions for the gradient can be obtained:

[0212] (31),

[0213] and let the update equation for can be obtained:

[0214] (32),

[0215] S5.4 Update ,

[0216] Next, the auxiliary variable is updated. Similarly, the variable update expression for the th iteration is:

[0217] (23),

[0218] The optimization problem can be represented as:

[0219] ;

[0220] If the constraint condition is satisfied, its Lagrangian function and gradient can be calculated, represented as:

[0221] ,

[0222] ,

[0223] Therefore, the update expression of can be obtained as

[0224] (37);

[0225] If this constraint is not satisfied, the usual practice is to project to a region that satisfies the constraint. Set a scaling factor , so that , so that

[0226] .

[0227] S5.5 Update auxiliary variables

[0228] By iterating the auxiliary variables, the optimal solution can be obtained.

[0229] Can be expressed as:

[0230] (39),

[0231] ;

[0232] Simulation parameters:

[0233] The performance of the method proposed in the application is demonstrated by numerical simulation. It is assumed that the number of transmitting antennas and receiving antennas is the same and is 9, the communication frame length , the total transmitting power , the carrier frequency is 32GHz and the communication symbol uses QPSK. In addition, the sum of the trade-off parameters is set to 1, usually , and .

[0234] As shown in Figure 3 , it is an ISAC base station composed of a uniform linear array, including transmitting antennas and receiving antennas, which can communicate with mobile users such as vehicles and mobile terminals by sending ISAC waveforms, and can also detect targets of interest such as surrounding buildings, roadside pedestrians and vehicles, representing the downlink communication channel.

[0235] As shown in Figure 4 ​As shown, the horizontal axis represents the number of communication users, and the vertical axis represents the communication rate. The blue curve represents the ideal radar waveform, the orange curve represents the traditional ISAC waveform, and the purple curve represents our proposed ISAC waveform. The results show that the communication rate increases with the increase in the number of downlink mobile communication users. Furthermore, the communication performance of our proposed ISAC waveform is higher than that of the ideal radar waveform but lower than that of the traditional ISAC waveform, indicating that increasing the degrees of freedom and the number of communication users can effectively alleviate MUI and further optimize communication performance.

[0236] like Figure 5 As shown, the horizontal axis represents the index of each output sample during the IFFT transform, and the vertical axis represents the pulse compression gain. The blue curve in the figure represents the proposed ISAC waveform, and the yellow curve represents the ideal radar waveform. The results show that the designed ISAC waveform exhibits a pulse compression result that is highly similar to the ideal radar waveform, and the pulse compression gains almost overlap, indicating that it has robust pulse compression performance.

[0237] The contents not described in detail in this specification are existing technologies known to those skilled in the art.

[0238] Finally, it should be noted that the above descriptions are merely preferred embodiments of the present invention and are not intended to limit the present invention. Although the present invention has been described in detail with reference to the foregoing embodiments, those skilled in the art can still modify the technical solutions described in the foregoing embodiments or make equivalent substitutions for some of the technical features. Any modifications, equivalent substitutions, improvements, etc., made within the spirit and principles of the present invention should be included within the protection scope of the present invention.

Claims

1.A method for designing a communication and sensing integrated waveform for vehicle-to-everything (V2X), characterized in that, Comprising the following steps: S1. Constructing a multi-input multi-output integrated communication and sensing system model for vehicle networking by defining ISAC base stations, communication and sensing capabilities of transmitted waveforms, vehicle networking scenarios, and targets of interest; S2. Based on the communication and sensing integrated system model constructed in S1, a communication model is established by defining user received signals and indicators MUI and PAPR affecting the communication performance of the transmitted waveform; S3. Based on the communication and sensing integrated system model constructed in S1, a sensing model is established by defining the received signals of the ISAC base station received from the target of interest and indicators waveform similarity and CRB affecting the sensing performance of the transmitted waveform; S4. Combining the communication model established in S2 and the sensing model established in S3, an optimization problem is constructed for minimizing the weighted sum of MUI, CRB, and waveform similarity, with total transmission power and PAPR as constraints, and the optimization problem is converted into a matrix form to become a QCQP problem with quadratic equation constraints and quadratic inequality constraints; S5. Based on the QCQP problem in S4, auxiliary variables are introduced to convert the non-convex problem into a convex problem, and ADMM algorithm is used to fix different parameters and iteratively update each parameter variable, and finally the optimal waveform X is solved; The ISAC base station in S1 consists of a uniform linear array, including a root transmit antenna and a root receive antenna; The ISAC base station communicates with vehicles and mobile terminals, and the detected target of interest is surrounding buildings, roadside pedestrians, and vehicles; The S2 comprises the following steps: S2.1 Communication user received signal matrix ; ; wherein is a complex matrix, wherein denotes the length of the communication frame, denotes the number of downlink communication users; denotes the downlink communication channel matrix, assuming experiences flat Rayleigh fading and can be perfectly estimated; denotes the transmit signal matrix; denotes the additive white Gaussian noise, AWGN, of the downlink users; S2.2 rewriting the received signal matrix in S2.1 as ; MUI is represented as ; In order to maximize the sum rate, MUI is minimized; the signal-to-noise ratio of each user in each frame and the achievable sum rate are calculated; ； wherein, is a set average over time index, is is the th element in j is a signal transmitted between the th and th communication users, is a signal transmitted in the th time slot; The achievable sum rate of the downlink mobile user is represented as ; S2.3 Taking into account the impact of PAPR on the effectiveness of the communication system, controlling PAPR to provide sufficient transmission distance and reliability, based on the signal matrix received by the communication user described in S2.1 The formula for calculating PAPR is ; in, It is a vector The One element, , indicating that the matrix The vector obtained after vectorization The threshold representing PAPR, and the total transmit power of the ISAC waveform. for ; The right half of the above formula (7) is rewritten as ; wherein ; The S3 comprises the following steps: S3.1 For radar perception, assuming the propagation path of the transmitted waveform is a line-of-sight path, the signal matrix received by a far-field point target located in direction is represented as ​ ; where U is the number of targets of interest, denotes the reflection coefficient of the target; denotes the angle of the radar detected target with respect to the ISAC base station, and are the steering vectors of the transmit and receive antennas, respectively; half- wavelength ULA is used between adjacent elements; is the AWGN of the MIMO radar; The transmit direction and the arrival direction of a monostatic radar are the same, assuming that both the DOA and the DOD are and are represented as ; ; S3.2 introducing waveform similarity constraints in ISAC waveform design to affect its sensing performance; waveform similarity is represented as ; wherein, is a reference waveform matrix; minimizing The expected radar beam pattern can be approximated; S3.3 CRB is used to measure the sensing performance, providing a lower bound of mean square error and having a closed-form expression; for radar point target detection, CRB is represented as ; wherein is derivative of denotes the reflection coefficient; Formula (13) is further equivalent to ; For ease of calculation, assume , we get ; the CRB can be expressed as 。

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