Smart reflector assisted OFDM-ISAC system waveform optimization method

Abstract

This invention relates to the field of integrated communication and sensing technology, specifically disclosing a waveform optimization method for an OFDM-ISAC system assisted by an intelligent reflector. The method includes constructing a system architecture where a base station transmits a composite signal superimposed with a dedicated sensing signal. This composite signal is then modulated by an intelligent reflector and delivered to the communication user and illuminates the target. A waveform optimization problem is constructed using the communication signal vector, the sensing signal vector, and the phase shift matrix of the intelligent reflector as optimization variables. The objective function is the weighted sum and minimization of spatial-spectrum matching error and communication mutual information. Constraints include the total transmit power budget, sensing signal power allocation, peak sidelobe level, and constant modulus of the reflector unit. The problem is decomposed into three sub-problems using alternating optimization and iterated sequentially. Within each sub-problem, a convex quadratic surrogate function is constructed using a minimization-maximization method, and then solved using an alternating direction penalty method until the objective function converges. This invention effectively coordinates communication and sensing performance, improving the overall system efficiency.

Description

Technical Field

[0001] This invention relates to the field of integrated communication and sensing technology, and in particular to a waveform optimization method for an OFDM-ISAC system assisted by an intelligent reflector. Background Technology

[0002] With the rapid convergence of wireless communication and radar sensing technologies, communication systems are no longer limited to information transmission; they also need to possess environmental awareness, target detection, and parameter estimation capabilities. Traditionally, communication and radar systems are deployed separately, with separate hardware platforms, antenna resources, and spectrum resources to avoid interference between communication and radar signals. While this approach is structurally clear and simple to implement, it suffers from low spectrum utilization, insufficient hardware reuse, and limited system integration, making it difficult to meet the demands of future wireless networks for high spectrum efficiency, high sensing accuracy, and multi-functional integration.

[0003] In recent years, Integrated Sensing and Communication (ISAC) systems have become a research hotspot. This system enables base stations to simultaneously perform multi-user communication and active radar sensing tasks on a single platform by sharing spectrum resources, transmitted waveforms, antenna arrays, and signal processing modules. In a typical OFDM-ISAC system, the base station usually employs a multiple-input multiple-output (MIMO) antenna structure, utilizing spatial degrees of freedom to perform directional beamforming for multiple communication users while simultaneously radiating sensing signals to the target area. OFDM waveforms possess advantages such as good subcarrier orthogonality and strong resistance to frequency-selective fading. Their broadband characteristics are beneficial for improving radar range resolution, and their multi-symbol time-domain structure can also support Doppler estimation, making them suitable for scenarios where communication and sensing coexist.

[0004] In real-world wireless propagation environments, communication links are easily affected by building obstructions, terrain barriers, and complex scattering environments, leading to a decline in the quality of the direct link between the base station and the user, or even its interruption. To improve the propagation environment, a Reconfigurable Intelligent Surface (RIS) is introduced as an auxiliary control method. An IRS consists of a large number of tunable reflective elements. By adjusting the phase shift of each reflective element, the incident electromagnetic wave can be reflected in a controlled manner, thereby constructing an auxiliary propagation path between the base station and the user. By rationally designing the phase shift parameters of the RIS, the quality of the communication link can be enhanced, while also providing the system with additional spatial control freedom, allowing it to participate in communication beam optimization and sensing beam design.

[0005] In a RIS-assisted orthogonal frequency division multiplexing (OFDM) integrated communication and sensing system, the base station typically overlays communication and sensing signals onto the same time-frequency resources. On each subcarrier and resource unit corresponding to each symbol, the transmitted signal consists of multiple communication signal components oriented towards the communication users and a dedicated sensing signal component. The communication signal carries user data and enables multi-user transmission, while the sensing signal serves as a known reference signal for illuminating the target area. The base station receives the target echo while transmitting the composite signal and constructs distance and velocity information through matched filtering and two-dimensional transformation, thereby achieving target detection and parameter estimation. For system performance evaluation, communication mutual information is typically used to measure communication performance. Space-spectrum matching error is used to describe the deviation between the transmitted beam and the desired beam, and peak sidelobe levels constrain the sidelobe levels of the sensing waveform in the time delay and Doppler dimensions, thus providing a comprehensive assessment of the system's sensing performance.

[0006] However, existing RIS-assisted orthogonal frequency division multiplexing (OFDM) integrated communication and sensing systems still have several shortcomings. First, communication signals have random modulation characteristics, while sensing functions require deterministic transmitted waveforms with good low sidelobe characteristics. These two requirements are inherently contradictory in waveform design, easily leading to increased sidelobes in the sensing waveform, thus affecting the detection performance of weak targets. Second, the superposition of communication and sensing signals on the same time-frequency resources introduces mutual interference. With limited total system power and spatial degrees of freedom, it is difficult to simultaneously achieve both communication and sensing performance. Furthermore, existing sensing performance evaluation methods often focus on a single indicator, making it difficult to simultaneously consider spatial beam quality and time-delay-Doppler sidelobe characteristics, resulting in an incomplete description of sensing performance. Finally, there is a strong coupling relationship between the phase shift of the communication signal, sensing signal, and intelligent reflector, and the optimization problem is usually non-convex, making the joint design process complex and difficult to solve. Summary of the Invention

[0007] This invention provides a waveform optimization method for an OFDM-ISAC system assisted by an intelligent reflector. The technical problem it solves is: how to jointly optimize communication signals, sensing signals and IRS parameters under a unified framework, so as to coordinate communication and sensing performance under limited resource conditions and improve the overall system performance and adaptability to complex environments.

[0008] To address the above technical problems, this invention provides a waveform optimization method for an OFDM-ISAC system assisted by an intelligent reflector, comprising the following steps:

[0009] An architecture for an orthogonal frequency division multiplexing (OFDM) integrated communication and sensing system assisted by an intelligent reflector is constructed. The architecture includes an integrated communication and sensing base station equipped with multiple antennas, multiple single-antenna communication users, an intelligent reflector equipped with multiple passive reflective elements, and one or more targets to be detected. The integrated communication and sensing base station transmits a composite signal formed by superimposing communication signals and dedicated sensing signals. After being modulated by the intelligent reflector, the signal is simultaneously delivered to the communication users and illuminates the targets to be detected. The integrated communication and sensing base station receives the target echo to complete the sensing. The communication users receive the downlink signal superimposed by the direct link and the reflected link.

[0010] Based on the architecture, a waveform optimization problem is constructed. The waveform optimization problem uses the communication signal vector, the sensing signal vector, and the phase shift matrix of the intelligent reflector as optimization variables, the weighted sum of space-spectrum matching error and communication mutual information as the objective function, and the total transmit power budget, sensing signal power allocation, peak sidelobe level, and constant mode of the reflector unit as constraints.

[0011] Using alternating optimization as the outer framework, the waveform optimization problem is decomposed into three sub-problems: sensing signal, communication signal, and intelligent reflector phase shift, and updated iteratively in sequence. Within each sub-problem, a convex quadratic surrogate function is constructed using the minimax method, and then the surrogate sub-problems are solved using the alternating direction penalty method. The inner and outer double-layer iteration continues until the objective function converges.

[0012] Furthermore, in each round of outer layer iteration, the latest communication signal vector and the intelligent reflector phase shift matrix are fixed first, and the sensing signal vector is updated.

[0013] After the sensing signal vector is updated, the updated sensing signal vector and the current intelligent reflector phase shift matrix are fixed, and the communication signal vector is updated.

[0014] After the communication signal vector is updated, the updated communication signal vector and sensing signal vector are fixed, and the phase shift matrix of the intelligent reflector is updated.

[0015] After updating the above three sub-problems, determine whether the objective function has converged. If it has not converged, proceed to the next round of outer iteration. If it has converged, stop the iteration and output the current optimization result.

[0016] Furthermore, the step of fixing the latest communication signal vector and the intelligent reflector phase shift matrix, and updating the sensing signal vector, includes:

[0017] In the current outer-layer iterative sensing signal subproblem, the communication signal vector and the phase shift matrix of the intelligent reflector are fixed;

[0018] For the original non-convex objective function consisting of space-spectrum matching error and communication mutual information, convex quadratic surrogate functions for both are constructed at the current iteration point of the sensing signal vector.

[0019] The constructed convex quadratic surrogate functions are added together, and constant terms that are irrelevant to the sensing signal vector are discarded to form a convex surrogate optimization problem for the sensing signal subproblem. This problem takes a quadratic function as the objective and retains the peak sidelobe level constraint, total transmit power budget constraint, and fixed allocation constraint of sensing signal power in the original problem.

[0020] The convex proxy optimization problem is solved using the alternating direction penalty method to update the sensing signal vector.

[0021] Furthermore, the step of solving the convex surrogate optimization problem using the alternating direction penalty method to update the sensing signal vector includes:

[0022] The convex proxy optimization problem of the sensing signal is transformed into an equivalent real-valued optimization problem;

[0023] In the real-valued optimization problem, corresponding auxiliary variables are introduced for the peak sidelobe level constraint, the total transmit power budget constraint, and the fixed allocation constraint of the sensing signal power, and equality constraints are established between each auxiliary variable and the original sensing signal vector variable.

[0024] Construct the augmented Lagrangian function for the real-valued optimization problem;

[0025] In the inner iteration of the alternating direction penalty method, variables are updated sequentially through the following steps: Fixing other variables, a system of linear equations with positive definite coefficient matrices is solved to update the sensing signal vector variable in a closed loop; auxiliary variables corresponding to the peak sidelobe level constraint, total transmit power budget constraint, and fixed allocation constraint of sensing signal power are updated respectively; Lagrange multiplier vectors corresponding to each equality constraint are updated; and penalty parameters corresponding to each equality constraint are updated. The update of the auxiliary variables corresponding to the peak sidelobe level constraint is achieved by solving a second-order cone programming problem. The constraint condition of this second-order cone programming problem is that the norm of the sensing signal vector after the time-delay-Doppler transformation matrix does not exceed the product of the preset peak sidelobe level threshold, the number of subcarriers, and the number of symbols.

[0026] Repeat the above inner-layer iteration steps until the inner-layer convergence condition is met, thus completing the update of the sensing signal vector.

[0027] Furthermore, the step of fixing the updated sensing signal vector and the current intelligent reflector phase shift matrix, and updating the communication signal vector, includes:

[0028] In the current outer-layer iterative communication signal subproblem, the sensing signal vector and the intelligent reflector phase shift matrix are fixed;

[0029] For the original non-convex objective function consisting of space-spectrum matching error and communication mutual information, convex quadratic surrogate functions for both are constructed at the current communication signal vector iteration point.

[0030] The constructed convex quadratic surrogate functions are added together, and constant terms that are irrelevant to the communication signal vector are discarded to form a convex surrogate optimization problem for the communication signal subproblem. This problem takes a quadratic function as the objective and retains the total transmit power budget constraint in the original problem.

[0031] The convex proxy optimization problem is solved using the alternating direction penalty method to update the communication signal vector.

[0032] Furthermore, the step of solving the convex surrogate optimization problem using the alternating direction penalty method to update the communication signal vector includes:

[0033] The convex proxy optimization problem of the communication signal is transformed into an equivalent real-valued optimization problem;

[0034] In the real-valued optimization problem, a corresponding auxiliary variable is introduced to constrain the total transmit power budget, and an equality constraint is established between this auxiliary variable and the sum of the communication signal vectors on all subcarriers, all symbols, and all users, plus the sum of the fixed sensing signal vectors.

[0035] Construct the augmented Lagrangian function for the real-valued optimization problem;

[0036] In the inner iteration of the alternating direction penalty method, the variables are updated sequentially through the following steps: fixing other variables, solving a system of linear equations for each user on each resource element to update the communication signal vector variable of each user on each resource element in a closed loop; updating the auxiliary variables corresponding to the total transmit power budget constraint; updating the Lagrange multiplier vectors corresponding to the equality constraints; and updating the penalty parameters.

[0037] Repeat the above inner-layer iteration steps until the inner-layer convergence condition is met, thus completing the update of the communication signal vector.

[0038] Furthermore, the step of fixing the updated communication signal vector and sensing signal vector, and updating the phase shift matrix of the intelligent reflector, includes:

[0039] In the current outer-layer iterative intelligent reflective surface problem, the communication signal vector and the sensing signal vector are fixed;

[0040] Since the space-spectrum matching error is independent of the phase shift matrix of the smart reflector, it is treated as a constant term and only the communication mutual information part is processed.

[0041] At the current iteration point of the phase shift vector of the intelligent reflector, a convex quadratic surrogate function with negative communication mutual information is constructed using the gradient Lipschitz continuity of the communication mutual information with respect to the phase shift vector, as a substitute for the original objective function in this subproblem.

[0042] After removing the constant terms in the convex quadratic surrogate function that are irrelevant to the phase shift vector, and combining them with the constant mode constraints of each reflection unit of the smart reflector, a surrogate optimization problem for the phase shift subproblem is formed.

[0043] The phase shift proxy optimization problem is solved using the alternating direction penalty method to update the phase shift vector of the smart reflector.

[0044] Furthermore, the step of solving the phase shift proxy optimization problem using the alternating direction penalty method to update the phase shift vector of the intelligent reflector includes:

[0045] An auxiliary phase shift variable is introduced into the phase shift vector in the phase shift proxy optimization problem, and an equality constraint is established between the auxiliary variable and the original phase shift variable. At the same time, the constant mode constraint of the reflection unit is transferred to the auxiliary variable.

[0046] Construct the augmented Lagrangian function for the phase shift problem after introducing auxiliary variables;

[0047] In the inner iteration of the alternating direction penalty method, the variables are updated sequentially through the following steps: fix other variables, solve a system of linear equations to update the original phase shift vector variable in a closed loop; fix other variables, update the auxiliary phase shift vector by projecting each component of the auxiliary variable onto the unit circle on the complex plane; update the Lagrange multiplier vector corresponding to the equality constraints; update the penalty parameters.

[0048] Repeat the above inner-layer iteration steps until the inner-layer convergence condition is met, thus completing the update of the phase shift vector of the intelligent reflector.

[0049] Furthermore, the inner and outer double-layer iterations until the objective function converges include:

[0050] In each iteration of the outer layer alternating optimization, the sensing signal vector, the communication signal vector, and the intelligent reflective surface phase shift vector are updated sequentially.

[0051] After a complete update, calculate the current objective function value and compare it with the objective function value obtained in the previous outer iteration.

[0052] If the relative change of the current objective function value with respect to the previous objective function value is less than the preset convergence threshold, or the number of outer iterations reaches the preset maximum number of iterations, then the objective function is determined to have converged and the iteration is stopped.

[0053] If the above convergence conditions are not met, continue to the next round of outer layer iteration.

[0054] Furthermore, the waveform optimization problem, constrained by total transmit power budget, sensing signal power allocation, peak sidelobe level, and constant modulus of the reflection unit, also includes:

[0055] The total transmit power budget constraint is used to limit the total transmit signal power on all subcarriers and symbols from exceeding the preset power budget value;

[0056] The sensing signal power allocation constraint is used to limit the sum of the power of all sensing signal vectors to a preset fixed power value.

[0057] The peak sidelobe level constraint is used to limit the peak amplitude of the sidelobe of the sensed signal in the time-delay-Doppler two-dimensional plane to not exceed a preset sidelobe level threshold.

[0058] The constant modulus constraint of the reflection unit is used to limit the modulus of the reflection coefficient of each reflection unit on the smart reflection surface to 1.

[0059] The waveform optimization method for an OFDM-ISAC system assisted by an intelligent reflector provided by this invention first constructs an intelligent reflector-assisted system architecture, clarifies the superimposed composite signal structure of the base station's transmitted communication signal and dedicated sensing signal, and incorporates the RIS phase shift into the optimization variables, providing a unified framework for jointly controlling the spatial beam and signal waveform. Based on this, the waveform optimization problem is constructed as follows: the communication signal vector, sensing signal vector, and RIS phase shift matrix are used as joint optimization variables; the objective function is the weighted sum minimization of space-spectrum matching error and communication mutual information; and constraints are introduced, including total transmit power budget, sensing signal power allocation, peak sidelobe level, and constant mode of the reflector unit, transforming the contradiction between sensing and communication performance into a quantitatively optimizable mathematical problem. For this non-convex problem, alternating optimization is used to decompose it into three sub-problems, which are iteratively updated sequentially. Within each sub-problem, a convex quadratic surrogate function is constructed using the minimax method, and then solved using the alternating direction penalty method, transforming the original problem into a rigorously solvable sequence of convex sub-problems, ensuring that the algorithm converges to a high-quality stable solution. This invention achieves comprehensive gains in beam pointing accuracy, sidelobe suppression, and communication rate through a complete path of architecture design, problem modeling, and hierarchical solution. Compared with existing methods, this invention can more effectively coordinate communication and sensing performance, improve the overall resource utilization efficiency of the system, target detection reliability, and adaptability in complex environments. Attached Figure Description

[0060] Figure 1 A flowchart illustrating the waveform optimization method for an OFDM-ISAC system assisted by an intelligent reflective surface provided in an embodiment of the present invention;

[0061] Figure 2A schematic diagram of the architecture of the intelligent reflective surface-assisted OFDM-ISAC system provided in an embodiment of the present invention;

[0062] Figure 3 A comparison chart of normalized space-spectrum matching error (SSME) convergence curves with and without intelligent reflector (RIS) assistance provided in embodiments of the present invention;

[0063] Figure 4 A comparison chart of the total mutual information (MI) convergence curves of the system with and without the assistance of a smart reflector (RIS) provided in an embodiment of the present invention;

[0064] Figure 5 A comparison chart of the convergence curves of the total objective function with and without the assistance of a Smart Reflector (RIS) provided in an embodiment of the present invention;

[0065] Figure 6 A comparison of the convergence curves of the objective function under different configurations of the number of intelligent reflective surface (RIS) reflective units provided in the embodiments of the present invention;

[0066] Figure 7 The heatmap of the pre-optimized sensing signal delay-Doppler two-dimensional ambiguity function provided in this embodiment of the invention;

[0067] Figure 8 The optimized sensing signal delay-Doppler two-dimensional ambiguity function heatmap provided in this embodiment of the invention;

[0068] Figure 9 This is a three-dimensional surface plot of the amplitude of the normalized fuzzy function of the optimized sensing signal provided in an embodiment of the present invention.

[0069] Figure 10 A comparison of normalized spatial beam patterns after optimized convergence with and without the assistance of a Smart Reflector (RIS) provided in an embodiment of the present invention;

[0070] Figure 11 The graph showing the relationship between communication and sensing performance and weighting factors is provided in the embodiments of the present invention.

[0071] Figure 12 A comparison of the objective function convergence curves of the algorithm of this invention and the comparison algorithms (SQP algorithm, SSCA algorithm) provided for embodiments of this invention. Detailed Implementation

[0072] The embodiments of the present invention are described in detail below with reference to the accompanying drawings. The embodiments are given for illustrative purposes only and should not be construed as limiting the present invention. The accompanying drawings are for reference and illustration only and do not constitute a limitation on the scope of patent protection of the present invention, because many changes can be made to the present invention without departing from the spirit and scope of the present invention.

[0073] The waveform optimization method for OFDM-ISAC system assisted by intelligent reflector surface provided in this embodiment of the invention, such as... Figure 1 The flowchart shown includes the following steps:

[0074] S1. Constructing an architecture for an orthogonal frequency division multiplexing (OFDM) integrated communication and sensing system assisted by an intelligent reflector; the architecture includes an integrated communication and sensing base station equipped with multiple antennas, multiple single-antenna communication users, an intelligent reflector equipped with multiple passive reflective elements, and one or more targets to be detected; the integrated communication and sensing base station transmits a composite signal formed by superimposing communication signals and dedicated sensing signals, which is simultaneously delivered to the communication users and illuminates the targets to be detected after being modulated by the intelligent reflector; the integrated communication and sensing base station receives the target echo to complete the sensing; and the communication users receive the downlink signal superimposed by the direct link and the reflected link.

[0075] S2. Based on the architecture, construct a waveform optimization problem. The waveform optimization problem uses the communication signal vector, the sensing signal vector, and the phase shift matrix of the intelligent reflector as optimization variables, the weighted sum of space-spectrum matching error and communication mutual information as the objective function, and the total transmit power budget, sensing signal power allocation, peak sidelobe level, and constant mode of the reflector unit as constraints.

[0076] S3. Using alternating optimization as the outer framework, the waveform optimization problem is decomposed into three sub-problems: sensing signal, communication signal, and intelligent reflector phase shift, and updated iteratively in sequence. Within each sub-problem, a convex quadratic surrogate function is constructed using the minimax method, and then the surrogate sub-problems are solved using the alternating direction penalty method. The inner and outer double-layer iteration continues until the objective function converges.

[0077] (1) Step S1: Constructing the system architecture

[0078] System architecture such as Figure 2 As shown, the system consists of a device equipped with Integrated communication and sensing base station with root antenna A single-antenna communication user, a user with The intelligent reflective surface of each passive reflective unit and It consists of several targets to be detected. An orthogonal frequency division multiplexing frame contains... Subcarriers and The base station obtains the direct channel from the base station to the user, the channel from the base station to the smart reflector, and the channel from the smart reflector to the user through channel estimation, and sets the desired beam template based on the prior information of the target direction.

[0079] In integrated communication and sensing systems, communication signals need to carry random modulation symbols, while radar sensing requires transmitted waveforms to have stable correlation characteristics. If random communication symbols are used directly for sensing, the time delay-Doppler sidelobes will fluctuate with changes in the communication symbols, and strong target sidelobes may mask nearby weak targets. Therefore, this invention sets up separate communication signal components and dedicated sensing signal components, and transmits them superimposed on the same time-frequency resource. In the... The subcarrier, the first At each symbol, the base station transmits a composite signal consisting of a communication component and a dedicated sensing component superimposed on each other. :

[0080] (1)

[0081] in, To send to users The communication signal vector, which includes user data modulation symbols and their spatial precoding, is responsible for carrying information transmission tasks; These are dedicated sensing signal vectors. Both types of signals are continuous vector optimization variables, which can be jointly designed under a unified optimization framework. By adjusting their respective spatial orientation and power allocation, the performance trade-off between sensing and communication can be flexibly controlled.

[0082] For a monostatic communication and sensing integrated system, the base station transmits composite signals while simultaneously using a receiving antenna array to collect target echoes to complete radar sensing. Assume that there are targets within the detection area... The target point, the first The distance between each target and the base station is Radial velocity is The corresponding two-way delay and Doppler frequency shift are respectively and ( At the speed of light, (For carrier frequency). The echo signal received by the base station is at the [number]th [frequency]. Each resource element can be represented as:

[0083] (2)

[0084] in, For the first The complex scattering coefficient of a target comprehensively reflects the effects of path loss and radar cross-section. For subcarrier spacing, For OFDM symbol period, Additive white Gaussian noise at the receiver ( For receiver noise power, This indicates that the mean is 0 and the variance is 0. (complex Gaussian distribution) The natural base. Due to the perceived signal Given a deterministic sequence, the base station performs matched filtering on the echo signal and then constructs a range-velocity profile through a two-dimensional discrete Fourier transform, thereby achieving target detection and parameter estimation.

[0085] To evaluate the quality of spatial beamforming, the base station is defined on the subcarrier. and spatial sampling direction The actual transmitted beam power is:

[0086] (3)

[0087] in, The base station provides the steering vector for the base station array at the corresponding frequency and direction. The base station pre-sets the desired beam template based on the target's prior direction information. The value is 1 within the direction of the target and 0 in other directions. This represents the conjugate transpose. The Spatial-Spectral Matching Error (SSME) measures the deviation between the actual beam and the desired template.

[0088] (4)

[0089] in, This represents the number of discrete sampling points in the spatial direction. SSME is a scaling factor for dimensional alignment. The smaller the SSME, the more concentrated the energy is in the target direction and the less energy is leaked in non-target directions.

[0090] Communication users In subcarrier The equivalent downlink channel consists of the superposition of the direct link from the base station to the user and the auxiliary reflection link formed by the smart reflector:

[0091] (5)

[0092] in, For base station to user direct transmission channel For the channel from the base station to the smart reflector, For intelligent reflective surfaces to users The channel, Let be the phase shift matrix, and each reflection coefficient satisfy... , This represents a diagonal matrix.

[0093] user In the The received signals on each resource element are:

[0094] (6)

[0095] in, It is additive white Gaussian noise. For users Noise power.

[0096] In the ISAC system, users Other users (users) , The communication and sensing signals are considered as interference, and their covariance matrix is ​​as follows:

[0097] (7)

[0098] in, yes The identity matrix. This covariance matrix includes multi-user interference terms and radar system interference to users. Interference items caused and users The noise term received by the receiver.

[0099] When using single-user detection, the user In the The reachability mutual information (MI) on each resource unit is as follows:

[0100] (8)

[0101] in, Represents a determinant. Represents the identity matrix.

[0102] The system sums the total mutual information for all users, subcarriers, and symbols:

[0103] (9)

[0104] in, It will serve as the core indicator for measuring communication performance in the objective function, and together with SSME, it will constitute the joint optimization objective function. Increasing the sensing signal power is generally beneficial for target detection, but it will also increase the interference experienced by communication users and reduce mutual information. Therefore, a joint trade-off needs to be made between communication capability and sensing quality.

[0105] Simply controlling the spatial beam direction cannot guarantee resolution in both range and velocity dimensions. To suppress the obscuring of nearby weak targets by the sidelobes of strong targets, the sensing signal... towards the target direction Projection, to obtain the first Effective perceived scalar on each resource element:

[0106] (10)

[0107] because For deterministic signals, It is about The deterministic linear function, and therefore the fuzzy function, are entirely determined by the optimization variables and can be precisely controlled within the optimization framework. All Each projection value is expanded into a vector. (vec(⋅) denotes the vectorization operator), where Then the fuzzy function at the time delay grid points Doppler grid points The sampled value at that location is:

[0108] (11)

[0109] in, Apply a time delay phase offset to the subcarrier dimension to achieve the transformation from the frequency domain to the time delay domain; A Doppler phase shift is applied to the symbol dimension to achieve the transformation from the time domain to the Doppler domain.

[0110] set up To exclude the main peak location After the time delay-Doppler sidelobe region, the peak sidelobe level is defined as:

[0111] (12)

[0112] Here, `max` represents maximization. This is achieved by limiting the peak sidelobe level to no more than a preset threshold. This can reduce false peaks on the range-velocity plane and improve the reliability of weak target detection.

[0113] (2) Step S2: Construct the optimization problem

[0114] Considering both spatial perception and communication performance, this invention employs a weighted combination objective function design strategy, which integrates SSME (Spatial Sense Medium) and the total system mutual information (MI) through weighting factors. Unify and incorporate them into the same optimization objective, and jointly optimize the communication signal vector. Sensing signal vector and RIS phase shift The optimization criterion is to minimize the SSME and maximize the MI. At the same time, PSL is added as a hard constraint to ensure that the sidelobe level of the sensed waveform in the time delay-Doppler dimension does not exceed a preset threshold. Based on the above analysis, the joint optimization problem is modeled as follows:

[0115] (13)

[0116] in, As a weighting factor between sensing and communication performance, For the total system transmit power budget, A fixed power allocation value for the sensed signal; min represents minimization. Adjustment. This can change the system's emphasis on communication and sensing performance. Among these... to These constraints are: total transmit power budget constraint, sensed signal power allocation constraint, peak sidelobe level constraint, and constant modulus constraint for reflector elements. The total transmit power budget constraint limits the total transmit signal power across all subcarriers and symbols to a preset power budget value. The sensed signal power allocation constraint ensures the sum of the powers of all sensed signal vectors equals a preset fixed power value. The peak sidelobe level constraint limits the peak amplitude of the sidelobes of the sensed signal in the time-delay-Doppler two-dimensional plane to a preset sidelobe level threshold. The constant modulus constraint for reflector elements limits the magnitude of the reflection coefficient of each reflector element on the smart reflector surface to 1.

[0117] (3) Step S3: Solve the optimization problem

[0118] The non-convexity of the optimization problem in this invention mainly stems from three coupled factors: first, the SSME exhibits a fourth-order non-convex structure with respect to the transmitted signal; second, the mutual information is non-convex under vector parameterization conditions; and third, the RIS constant modulus constraint constitutes a non-convex feasible set. These coupled non-convex factors make the original optimization problem difficult to solve directly using traditional convex optimization methods.

[0119] Specifically, in each round of outer layer iteration, the latest communication signal vector and the intelligent reflector phase shift matrix are fixed first, and the sensing signal vector is updated.

[0120] After the sensing signal vector is updated, the updated sensing signal vector and the current intelligent reflector phase shift matrix are fixed, and the communication signal vector is updated.

[0121] After the communication signal vector is updated, the updated communication signal vector and sensing signal vector are fixed, and the phase shift matrix of the intelligent reflector is updated.

[0122] After updating the above three sub-problems, determine whether the objective function has converged. If it has not converged, proceed to the next round of outer iteration. If it has converged, stop the iteration and output the current optimization result.

[0123] Therefore, this invention employs a joint optimization algorithm combining alternating optimization and minimization methods. Based on the physical meaning of the optimization variables, the original joint optimization problem is decomposed into three sub-problems: sensing signals, communication signals, and phase shifting of intelligent reflectors. In each outer iteration, two sets of variables are fixed, while the other set is updated. Within each sub-problem, the minimization method is used to transform the non-convex objective function into a strictly convex quadratic surrogate function, and the closed-form update result or the solution to the standard convex sub-problem is obtained through the alternating direction penalty method.

[0124] 1) Sensing signals Optimization

[0125] The optimization of the sensing signal includes fixing the communication signal vector and the phase shift matrix of the smart reflector in the current outer-layer iterative sensing signal subproblem;

[0126] For the original non-convex objective function consisting of space-spectrum matching error and communication mutual information, convex quadratic surrogate functions for both are constructed at the current iteration point of the sensing signal vector.

[0127] The constructed convex quadratic surrogate functions are added together, and constant terms that are irrelevant to the sensing signal vector are discarded to form a convex surrogate optimization problem for the sensing signal subproblem. This problem takes a quadratic function as the objective and retains the peak sidelobe level constraint, total transmit power budget constraint, and fixed allocation constraint of sensing signal power in the original problem.

[0128] The alternating direction penalty method is used to solve the convex surrogate optimization problem to update the sensing signal vector, including:

[0129] The convex proxy optimization problem of the sensing signal is transformed into an equivalent real-valued optimization problem;

[0130] In the real-valued optimization problem, corresponding auxiliary variables are introduced for the peak sidelobe level constraint, the total transmit power budget constraint, and the fixed allocation constraint of the sensing signal power, and equality constraints are established between each auxiliary variable and the original sensing signal vector variable.

[0131] Construct the augmented Lagrangian function for the real-valued optimization problem;

[0132] In the inner iteration of the alternating direction penalty method, variables are updated sequentially through the following steps: Fixing other variables, a system of linear equations with positive definite coefficient matrices is solved to update the sensing signal vector variables in a closed loop; auxiliary variables corresponding to the peak sidelobe level constraint, total transmit power budget constraint, and fixed allocation constraint of sensing signal power are updated respectively; Lagrange multiplier vectors corresponding to each equality constraint are updated; and penalty parameters corresponding to each equality constraint are updated. The update of the auxiliary variables corresponding to the peak sidelobe level constraint is achieved by solving a second-order cone programming problem. The constraint condition of this second-order cone programming problem is that the norm of the sensing signal vector after the time-delay-Doppler transformation matrix does not exceed the product of the preset peak sidelobe level threshold, the number of subcarriers, and the number of symbols.

[0133] Repeat the above inner-layer iteration steps until the inner-layer convergence condition is met, thus completing the update of the sensing signal vector.

[0134] Specifically, through fixed communication signals and RIS phase variables For the perceived signal Optimization is performed. Quadratic surrogate functions are constructed for SSME and mutual information at the current iteration point. After merging and removing constant terms irrelevant to the sensed signal, the surrogate optimization problem for the sensed signal is expressed as:

[0135] (14)

[0136] in, Indicates the real part.

[0137] To include the quadratic terms in the mutual information expression Rewritten in matrix form for easier construction of surrogate functions, defining the first... Users on each subcarrier The equivalent channel outer product matrix ( (represented as), then the quadratic coefficient matrix and the linear coefficient vector are respectively... and ,in This represents the Lipschitz constant representing the gradient of SSME with respect to the sensed signal. This represents the matrix obtained by weighting the current sensing beam residuals. This represents a positive coefficient calculated based on the current multi-user interference power, perceived interference power, and desired signal power. Indicates the first The current iteration (i.e., the current iteration).

[0138] To reduce the complexity of complex-valued operations and avoid numerical instability, this invention transforms the sensing signal subproblem into an equivalent real-valued form for solution. To simplify subsequent descriptions, the steering vector in the target direction is... Abbreviated as Furthermore, by splitting the complex-valued variable into its real and imaginary parts, the real-valued form of the sensing signal vector is defined as follows: Similarly, for the steering vector... The quadratic coefficient matrix in the surrogate function and linear coefficient vector Perform real-value conversion on each part to obtain the corresponding real-valued form. , and .

[0139] At the same time, auxiliary variables are introduced. , , Representing the original constraints, the problem is ultimately transformed into an equivalent real-valued optimization problem:

[0140] (15)

[0141] in, It is the real-valued form of the fixed communication beam combination vector. for The corresponding real-valued matrix, , To exclude the main peak location The time delay-Doppler sidelobe region after that, The discrete Fourier transform matrix of the Doppler dimension (its i) The elements are ), The discrete Fourier transform matrix with time delay dimension (its i) The elements are ).

[0142] Next, we construct the augmented Lagrange function:

[0143] (16)

[0144] in, This represents the Lagrange multiplier vector related to the constraints, while This represents the penalty coefficient in the augmented Lagrange function. Within the iterative framework of the alternating direction multiplier method, if the current iteration is the... In the next iteration, with other variables fixed, the update result of the sensed signal variable is:

[0145] (17)

[0146] in, This refers to the coefficient matrix in the closed-form update of the sensed signal. It is a vector consisting of the current auxiliary variable, Lagrange multipliers, and linear surrogate terms.

[0147] The peak sidelobe auxiliary variable is updated by solving the following second-order cone programming problem:

[0148] (18)

[0149] in, .

[0150] The total transmit power auxiliary variable is updated as follows:

[0151] (19)

[0152] in, .

[0153] The sensed signal power auxiliary variable is updated as follows:

[0154] (20)

[0155] in, .

[0156] The three Lagrange multiplier subvectors are updated according to the following formula:

[0157] ,(twenty one)

[0158] in, , , .

[0159] The penalty parameters are updated according to the following formula:

[0160] ,(twenty two)

[0161] Among them, residual term , , ,for , , .

[0162] 2) Communication signal Optimization

[0163] The optimization of the communication signal includes fixing the sensing signal vector and the smart reflector phase shift matrix in the communication signal subproblem of the current outer iteration;

[0164] For the original non-convex objective function consisting of space-spectrum matching error and communication mutual information, convex quadratic surrogate functions for both are constructed at the current communication signal vector iteration point.

[0165] The constructed convex quadratic surrogate functions are added together, and constant terms that are irrelevant to the communication signal vector are discarded to form a convex surrogate optimization problem for the communication signal subproblem. This problem takes a quadratic function as the objective and retains the total transmit power budget constraint in the original problem.

[0166] The alternating direction penalty method is used to solve the convex surrogate optimization problem to update the communication signal vector, including:

[0167] The convex proxy optimization problem of communication signals is transformed into an equivalent real-valued optimization problem;

[0168] In the real-valued optimization problem, a corresponding auxiliary variable is introduced to constrain the total transmit power budget, and an equality constraint is established between this auxiliary variable and the sum of the communication signal vectors on all subcarriers, all symbols, and all users, plus the sum of the fixed sensing signal vectors.

[0169] Construct the augmented Lagrangian function for the real-valued optimization problem;

[0170] In the inner iteration of the alternating direction penalty method, the variables are updated sequentially through the following steps: fixing other variables, solving a system of linear equations for each user on each resource element to update the communication signal vector variable of each user on each resource element in a closed loop; updating the auxiliary variables corresponding to the total transmit power budget constraint; updating the Lagrange multiplier vectors corresponding to the equality constraints; and updating the penalty parameters.

[0171] Repeat the above inner-layer iteration steps until the inner-layer convergence condition is met, thus completing the update of the communication signal vector.

[0172] Next, fix the sensing signal and RIS phase variables Extract communication signals Subproblems:

[0173] ,(twenty three)

[0174] in, This represents the set of all user communication signal vectors across all resource elements. Equivalent channel Because the phase variable is fixed. In this subproblem, both the sensing signal and the RIS phase shift take the fixed values ​​updated in the previous subproblem.

[0175] Following the same surrogate function construction method as for sensing signals, the communication signal subproblem is transformed into:

[0176] ,(twenty four)

[0177] The quadratic coefficient matrix and the linear coefficient vector are respectively:

[0178] (25)

[0179] This represents the Lipschitz constant representing the gradient of SSME with respect to the communication signal. The Lipschitz constant represents the gradient of mutual information with respect to the communication signal. Indicates user The MI gradient coefficient matrix at the current iteration point In this subproblem, it represents the matrix formed by weighting the residuals of the current communication beam.

[0180] Perform an equivalent real-valued transformation, let , and They represent , and The real numerical form of the total transmit power is introduced, and an auxiliary variable for total transmit power is introduced. ,get:

[0181] (26)

[0182] Construct its augmented Lagrangian form:

[0183] (27)

[0184] in, Let Lagrange multiplier variables be the variables. The penalty parameter is used. Within the iterative framework of the alternating direction multiplier method, if the current iteration is the... In the next iteration, the closed-form update result of the communication signal variable is:

[0185] (28)

[0186] The total transmit power auxiliary variable is updated as follows:

[0187] (29)

[0188] in, .

[0189] The Lagrange multiplier vectors are updated according to the following formula:

[0190] (30)

[0191] The penalty parameters are updated according to the following formula:

[0192] (31)

[0193] Here, residual term The residual decay coefficient satisfies Penalty parameter amplification factor .

[0194] 3) RIS phase shift variables Optimization

[0195] Updates to the RIS phase shift variables include:

[0196] In the current outer-layer iterative intelligent reflective surface problem, the communication signal vector and the sensing signal vector are fixed;

[0197] Since the space-spectrum matching error is independent of the phase shift matrix of the smart reflector, it is treated as a constant term and only the communication mutual information part is processed.

[0198] At the current iteration point of the phase shift vector of the intelligent reflector, a convex quadratic surrogate function with negative communication mutual information is constructed using the gradient Lipschitz continuity of the communication mutual information with respect to the phase shift vector, as a substitute for the original objective function in this subproblem.

[0199] After removing the constant terms in the convex quadratic surrogate function that are irrelevant to the phase shift vector, and combining them with the constant mode constraints of each reflection unit of the smart reflector, a surrogate optimization problem for the phase shift subproblem is formed.

[0200] The alternating direction penalty method is used to solve the phase shift surrogate optimization problem to update the phase shift vector of the smart reflector.

[0201] Finally, within the framework of alternating optimization, the sensing signal is fixed. and communication signals , to perform variable The solution includes:

[0202] An auxiliary phase shift variable is introduced into the phase shift vector in the phase shift proxy optimization problem, and an equality constraint is established between the auxiliary variable and the original phase shift variable. At the same time, the constant mode constraint of the reflection unit is transferred to the auxiliary variable.

[0203] Construct the augmented Lagrangian function for the phase shift problem after introducing auxiliary variables;

[0204] In the inner iteration of the alternating direction penalty method, the variables are updated sequentially through the following steps: fix other variables, solve a system of linear equations to update the original phase shift vector variable in a closed loop; fix other variables, update the auxiliary phase shift vector by projecting each component of the auxiliary variable onto the unit circle on the complex plane; update the Lagrange multiplier vector corresponding to the equality constraints; update the penalty parameters.

[0205] Repeat the above inner-layer iteration steps until the inner-layer convergence condition is met, thus completing the update of the phase shift vector of the intelligent reflector.

[0206] Due to SSME and Since it is irrelevant, it is a constant and can be considered a constant in this subproblem. Therefore, the phase shift optimization problem is:

[0207] (32)

[0208] Among them, the objective function is subject to the gradient Lipschitz continuity at the current iteration point. Reaching the global upper bound:

[0209] (33)

[0210] The equal sign is at It must be strictly established at that time, satisfying the MM tightness condition. Among them, yes Lipschitz constant, Wirtinger gradient This represents the gradient of the total mutual information with respect to the phase shift conjugate vector at the current phase shift iteration point.

[0211] Removal and After removing irrelevant constant terms, the proxy problem for the phase shift of the smart reflector is expressed as:

[0212] (34)

[0213] in, , Gradient-driven term, This is the Lipschitz proximal anchoring term. Next, we introduce an auxiliary phase shift variable to rewrite the objective function subproblem:

[0214] (35)

[0215] Similarly, construct an augmented Lagrangian function for it:

[0216] (36)

[0217] in, Let Lagrange multiplier vectors be used. This is the penalty parameter. In the... In the next inner iteration, the phase-shifted original variable is updated to:

[0218] (37)

[0219] make The problem of updating the auxiliary phase shift variable is as follows:

[0220] (38)

[0221] Among them, the constraint set Regarding the independence of each component, the above formula applies to each... Completely separable, it can be solved by projecting each component onto the unit circle of the complex plane, and its closed-form update result is:

[0222] (39)

[0223] The Lagrange multipliers of the phase shifter problem are updated as follows:

[0224] (40)

[0225] The penalty parameters are updated according to the following formula:

[0226] (41)

[0227] Here, residual term , , Thus, the ADPM algorithm has been used to solve the problem. Completed.

[0228] After completing one round of updates to the phase shift variables of the sensing signal, communication signal, and intelligent reflector, the current result is used as the input for the next round of alternating optimization, and the solution process of the above three sub-problems is repeated in sequence.

[0229] In each iteration of the outer layer alternating optimization, the sensing signal vector, communication signal vector, and intelligent reflector phase shift vector are updated sequentially. After a complete update, the current objective function value is calculated and compared with the objective function value obtained in the previous outer layer iteration. If the relative change of the current objective function value with respect to the previous objective function value is less than a preset convergence threshold, or the number of outer layer iterations reaches the preset maximum number of iterations, the objective function is determined to have converged, and the iteration stops. If the above convergence conditions are not met, the next outer layer iteration continues.

[0230] In summary, to address the problem of limited system efficiency caused by mutual interference between communication and sensing signals and high coupling of optimization variables in RIS-assisted OFDM-ISAC systems, this invention provides a waveform optimization method for intelligent reflector-assisted OFDM-ISAC systems. First, an intelligent reflector-assisted system architecture is constructed, clarifying the superimposed composite signal structure of the base station's transmitted communication signal and dedicated sensing signal. The RIS phase shift is then incorporated into the optimization variables, providing a unified framework for jointly controlling the spatial beam and signal waveform. Based on this, the waveform optimization problem is constructed as follows: the communication signal vector, sensing signal vector, and RIS phase shift matrix are used as joint optimization variables. The objective function is the weighted sum and minimization of spatial-spectrum matching error and communication mutual information. Constraints are introduced, including total transmit power budget, sensing signal power allocation, peak sidelobe level, and constant mode of the reflector unit. This transforms the contradiction between sensing and communication performance into a quantitatively optimizable mathematical problem. For this non-convex problem, an alternating optimization approach is used to decompose it into three subproblems, which are then iteratively updated sequentially. Within each subproblem, a convex quadratic surrogate function is constructed using a minimax method, and then solved using an alternating direction penalty method. This transforms the original problem into a rigorously solvable sequence of convex subproblems, ensuring the algorithm converges to a high-quality, stable solution. This invention achieves comprehensive gains in improving beam pointing accuracy, sidelobe suppression capability, and communication rate through a complete path encompassing architecture design, problem modeling, and hierarchical solution.

[0231] Simulation verification is then performed. In the waveform joint optimization design of the RIS-assisted OFDM-ISAC system studied, the base station is equipped with... A uniform linear array of antennas, with an antenna spacing of half a wavelength, and a carrier frequency of... GHz, subcarrier spacing MHz, OFDM frame contains Subcarriers and A symbol. System service. For a single-antenna user, RIS is equipped with There are [number] reflector units (excluding the RIS unit number comparison experiment). The total base station transmit power budget is [number]. Among them, the sensing signal power Receiver noise power Perception-communication weighting factor PSL threshold dB (excluding PSL threshold comparison experiments). The channel model uses a Ricean channel, with the Ricean factor of the base station-user direct channel. Path gain coefficient 0.5 (simulating weaker non-line-of-sight components); Rice factor of base station-RIS and RIS-user channels. Path gain factor 1.5 (simulating a strong line-of-sight link). Desired main lobe direction set as... , and Three intervals. All simulation results are based on the above parameters.

[0232] Figure 3 The convergence curves of the normalized SSME with and without RIS assistance are given. Figure 3 As shown, this method significantly reduces the normalized SSME and improves the accuracy of sensing beamforming. The results show that by jointly optimizing the phase shift of the intelligent reflector and the base station transmission signal, the present invention enables the reflective link and the direct link to be coordinated and controlled in the spatial direction, which can make the actual radiation beam closer to the desired beam template, enhance the main lobe energy focusing capability in the target direction, and reduce the side lobe leakage in the non-target direction.

[0233] Figure 4 The convergence curves of total mutual information (MI) with and without RIS assistance are presented. From Figure 4 It can be seen that, with Figure 3 The normalized SSME curve shown shows a downward trend, while the MI curve monotonically rises from an initial low value to a stable level, reflecting the algorithm's continuous optimization of communication performance.

[0234] Figure 5 The convergence curves of the overall objective function with and without RIS assistance are presented. From Figure 5 As can be seen, both curves start from positive values ​​and decrease monotonically until they eventually stabilize, verifying the convergence of the proposed algorithm.

[0235] This invention can further improve system performance by increasing the number of intelligent reflective surface reflective units. Figure 6 By comparison The convergence curves of the objective function under five configurations are presented, and the impact of RIS scale on system performance is analyzed. Figure 6 The results show that as the number of reflection units increases, the system performance continues to improve, the objective function converges better and faster, indicating that more reflection units can provide higher spatial control degrees of freedom, thereby enhancing communication and sensing performance.

[0236] This invention significantly reduces the time-delay Doppler sidelobe level and improves the detection capability of multiple weak targets. Figure 7 , Figure 8 By comparing the time-delay-Doppler blur function heatmaps before and after optimization, the blur function characteristics of the sensing waveform before and after introducing PSL hard constraints are intuitively compared, demonstrating the suppression effect of the proposed algorithm on the sidelobes of the sensing waveform. Figure 7 and Figure 8 As shown, the optimized waveform can effectively suppress the sidelobe level, make the ambiguity function present a concentrated main peak structure, reduce the interference of strong targets on weak targets, and thus improve the detection reliability in multi-target scenarios.

[0237] This invention can improve the ability of sensing waveforms to distinguish in the dimensions of distance and velocity. Figure 9 The amplitude of the normalized ambiguity function of the optimized sensing signal on the time-delay-Doppler plane is further illustrated using a three-dimensional surface. As shown in the figure, the optimized ambiguity function exhibits an ideal "thumbtack-shaped" characteristic, with a prominent main peak and low side lobes, indicating that it can effectively improve the range and velocity resolution and reduce mutual occlusion between targets.

[0238] This invention can improve the quality of spatial beam pattern, enabling sensing energy to more accurately cover the target area. Figure 10 The normalized spatial beam pattern after optimized convergence is shown for the RIS-assisted scheme and the baseline without RIS. As shown in the figure, the present invention can form a more concentrated and directional main lobe, while effectively suppressing sidelobes in non-target directions, demonstrating that more accurate spatial energy distribution can be achieved through intelligent reflector optimization.

[0239] This invention can flexibly adjust the trade-off between communication performance and sensing performance according to different application requirements. Figure 11 The weighting coefficients are displayed. The impact on sensing performance (SSME) and communication performance (MI) (since the objective function is to minimize the overall performance, where MI is negative). Figure 11 As shown, by adjusting the weighting factor, a flexible balance can be achieved between communication performance and sensing performance, providing adjustable performance configuration capabilities for different application scenarios.

[0240] The hierarchical iterative optimization algorithm used in this invention has superior solution performance. Figure 12 The convergence curves of the objective function of the two proposed algorithms, Sequential Quadratic Programming (SQP) and Stochastic Successive Convex Approximation (SSCA), were compared under the same initialization conditions. Figure 12 As shown, the algorithm of this invention outperforms the comparative algorithms in terms of optimization effect, can obtain better objective function results, and has good computational efficiency; further, by combining it with the depth unfolding method, the computational complexity can be reduced and the inference efficiency in practical applications can be improved.

[0241] In summary, this invention achieves significant improvements in communication performance, spatial beam matching quality, time-delay-Doppler sidelobe suppression capability, and algorithm convergence performance by jointly optimizing the phase shift of communication signals, sensing signals, and intelligent reflectors. Compared with existing methods, this invention can more effectively coordinate communication and sensing performance, improve the overall resource utilization efficiency of the system, target detection reliability, and adaptability in complex environments.

[0242] The above embodiments are preferred embodiments of the present invention, but the embodiments of the present invention are not limited to the above embodiments. Any changes, modifications, substitutions, combinations, or simplifications made without departing from the spirit and principle of the present invention shall be considered equivalent substitutions and shall be included within the protection scope of the present invention.

Claims

1. A waveform optimization method for an OFDM-ISAC system assisted by a smart reflector, characterized in that, Including the following steps: An architecture for an OFDM-ISAC (Orthogonal Frequency Division Multiplexing) integrated communication and sensing system assisted by an intelligent reflector is constructed. This architecture includes an integrated communication and sensing base station equipped with multiple antennas, multiple single-antenna communication users, an intelligent reflector equipped with multiple passive reflective elements, and one or more targets to be detected. The integrated communication and sensing base station transmits a composite signal formed by superimposing communication signals and dedicated sensing signals. After being modulated by the intelligent reflector, this signal is simultaneously delivered to the communication users and illuminates the targets to be detected. The integrated communication and sensing base station receives the target echo to complete the sensing, and the communication users receive the downlink signal superimposed from the direct and reflected links. Based on the architecture, a waveform optimization problem is constructed. The waveform optimization problem uses the communication signal vector, the sensing signal vector, and the phase shift matrix of the intelligent reflector as optimization variables, the weighted sum of space-spectrum matching error and communication mutual information as the objective function, and the total transmit power budget, sensing signal power allocation, peak sidelobe level, and constant mode of the reflector unit as constraints. Using alternating optimization as the outer framework, the waveform optimization problem is decomposed into three sub-problems: sensing signal, communication signal, and intelligent reflector phase shift, and updated iteratively in sequence. Within each sub-problem, a convex quadratic surrogate function is constructed using the minimax method, and then the surrogate sub-problems are solved using the alternating direction penalty method. The inner and outer double-layer iteration continues until the objective function converges.

2. The waveform optimization method for an OFDM-ISAC system assisted by a smart reflector as described in claim 1, characterized in that: In each round of outer layer iteration, the latest communication signal vector and the phase shift matrix of the intelligent reflector are fixed first, and the sensing signal vector is updated. After the sensing signal vector is updated, the updated sensing signal vector and the current intelligent reflector phase shift matrix are fixed, and the communication signal vector is updated. After the communication signal vector is updated, the updated communication signal vector and sensing signal vector are fixed, and the phase shift matrix of the intelligent reflector is updated. After updating the above three sub-problems, determine whether the objective function has converged. If it has not converged, proceed to the next round of outer iteration. If it has converged, stop the iteration and output the current optimization result.

3. The waveform optimization method for an OFDM-ISAC system assisted by a smart reflector as described in claim 2, characterized in that, The process of fixing the latest communication signal vector and the intelligent reflector phase shift matrix, and updating the sensing signal vector, includes: In the current outer-layer iterative sensing signal subproblem, the communication signal vector and the phase shift matrix of the intelligent reflector are fixed; For the original non-convex objective function consisting of space-spectrum matching error and communication mutual information, convex quadratic surrogate functions for both are constructed at the current iteration point of the sensing signal vector. The constructed convex quadratic surrogate functions are added together, and constant terms that are irrelevant to the sensing signal vector are discarded to form a convex surrogate optimization problem for the sensing signal subproblem. This problem takes a quadratic function as the objective and retains the peak sidelobe level constraint, total transmit power budget constraint, and fixed allocation constraint of sensing signal power in the original problem. The convex proxy optimization problem is solved using the alternating direction penalty method to update the sensing signal vector.

4. The waveform optimization method for an OFDM-ISAC system assisted by a smart reflector as described in claim 3, characterized in that, The method of using alternating direction penalty to solve the convex proxy optimization problem to update the sensing signal vector includes: The convex proxy optimization problem of the sensing signal is transformed into an equivalent real-valued optimization problem; In the real-valued optimization problem, corresponding auxiliary variables are introduced for the peak sidelobe level constraint, the total transmit power budget constraint, and the fixed allocation constraint of the sensing signal power, and equality constraints are established between each auxiliary variable and the original sensing signal vector variable. Construct the augmented Lagrangian function for the real-valued optimization problem; In the inner iteration of the alternating direction penalty method, variables are updated sequentially through the following steps: Fixing other variables, a system of linear equations with positive definite coefficient matrices is solved to update the sensing signal vector variable in a closed loop; auxiliary variables corresponding to the peak sidelobe level constraint, total transmit power budget constraint, and fixed allocation constraint of sensing signal power are updated respectively; Lagrange multiplier vectors corresponding to each equality constraint are updated; and penalty parameters corresponding to each equality constraint are updated. The update of the auxiliary variables corresponding to the peak sidelobe level constraint is achieved by solving a second-order cone programming problem. The constraint condition of this second-order cone programming problem is that the norm of the sensing signal vector after the time-delay-Doppler transformation matrix does not exceed the product of the preset peak sidelobe level threshold, the number of subcarriers, and the number of symbols. Repeat the above inner-layer iteration steps until the inner-layer convergence condition is met, thus completing the update of the sensing signal vector.

5. The waveform optimization method for an OFDM-ISAC system assisted by a smart reflector as described in claim 2, characterized in that, The step of fixing the updated sensing signal vector and the current intelligent reflector phase shift matrix, and updating the communication signal vector, includes: In the current outer-layer iterative communication signal subproblem, the sensing signal vector and the intelligent reflector phase shift matrix are fixed; For the original non-convex objective function consisting of space-spectrum matching error and communication mutual information, convex quadratic surrogate functions for both are constructed at the current communication signal vector iteration point. The constructed convex quadratic surrogate functions are added together, and constant terms that are irrelevant to the communication signal vector are discarded to form a convex surrogate optimization problem for the communication signal subproblem. This problem takes a quadratic function as the objective and retains the total transmit power budget constraint in the original problem. The convex proxy optimization problem is solved using the alternating direction penalty method to update the communication signal vector.

6. The waveform optimization method for an OFDM-ISAC system assisted by a smart reflector as described in claim 5, characterized in that, The method of using alternating direction penalty to solve the convex surrogate optimization problem to update the communication signal vector includes: The convex proxy optimization problem of the communication signal is transformed into an equivalent real-valued optimization problem; In the real-valued optimization problem, a corresponding auxiliary variable is introduced to constrain the total transmit power budget, and an equality constraint is established between this auxiliary variable and the sum of the communication signal vectors on all subcarriers, all symbols, and all users, plus the sum of the fixed sensing signal vectors. Construct the augmented Lagrangian function for the real-valued optimization problem; In the inner iteration of the alternating direction penalty method, the variables are updated sequentially through the following steps: fixing other variables, solving a system of linear equations for each user on each resource element to update the communication signal vector variable of each user on each resource element in a closed loop; updating the auxiliary variables corresponding to the total transmit power budget constraint; updating the Lagrange multiplier vectors corresponding to the equality constraints; and updating the penalty parameters. Repeat the above inner-layer iteration steps until the inner-layer convergence condition is met, thus completing the update of the communication signal vector.

7. The waveform optimization method for an OFDM-ISAC system assisted by a smart reflector as described in claim 2, characterized in that, The step of fixing the updated communication signal vector and sensing signal vector, and updating the phase shift matrix of the intelligent reflector, includes: In the current outer-layer iterative intelligent reflective surface problem, the communication signal vector and the sensing signal vector are fixed; Since the space-spectrum matching error is independent of the phase shift matrix of the smart reflector, it is treated as a constant term and only the communication mutual information part is processed. At the current iteration point of the phase shift vector of the intelligent reflector, a convex quadratic surrogate function with negative communication mutual information is constructed using the gradient Lipschitz continuity of the communication mutual information with respect to the phase shift vector, as a substitute for the original objective function in this subproblem. After removing the constant terms in the convex quadratic surrogate function that are irrelevant to the phase shift vector, and combining them with the constant mode constraints of each reflection unit of the smart reflector, a surrogate optimization problem for the phase shift subproblem is formed. The phase shift proxy optimization problem is solved using the alternating direction penalty method to update the phase shift vector of the smart reflector.

8. The waveform optimization method for an OFDM-ISAC system assisted by a smart reflector as described in claim 7, characterized in that, The method of using alternating direction penalty to solve the phase shift proxy optimization problem to update the phase shift vector of the smart reflector includes: An auxiliary phase shift variable is introduced into the phase shift vector in the phase shift proxy optimization problem, and an equality constraint is established between the auxiliary variable and the original phase shift variable. At the same time, the constant mode constraint of the reflection unit is transferred to the auxiliary variable. Construct the augmented Lagrangian function for the phase shift problem after introducing auxiliary variables; In the inner iteration of the alternating direction penalty method, the variables are updated sequentially through the following steps: fix other variables, solve a system of linear equations to update the original phase shift vector variable in a closed loop; fix other variables, update the auxiliary phase shift vector by projecting each component of the auxiliary variable onto the unit circle on the complex plane; update the Lagrange multiplier vector corresponding to the equality constraints; update the penalty parameters. Repeat the above inner-layer iteration steps until the inner-layer convergence condition is met, thus completing the update of the phase shift vector of the intelligent reflector.

9. The waveform optimization method for an OFDM-ISAC system assisted by a smart reflector as described in claim 1, characterized in that, The inner and outer double-layer iterations until the objective function converges include: In each iteration of the outer layer alternating optimization, the sensing signal vector, the communication signal vector, and the intelligent reflective surface phase shift vector are updated sequentially. After a complete update, calculate the current objective function value and compare it with the objective function value obtained in the previous outer iteration. If the relative change of the current objective function value with respect to the previous objective function value is less than the preset convergence threshold, or the number of outer iterations reaches the preset maximum number of iterations, then the objective function is determined to have converged and the iteration is stopped. If the above convergence conditions are not met, continue to the next round of outer layer iteration.

10. The waveform optimization method for an OFDM-ISAC system assisted by a smart reflector as described in claim 1, characterized in that, The waveform optimization problem, constrained by total transmit power budget, sensing signal power allocation, peak sidelobe level, and constant modulus of the reflection unit, also includes: The total transmit power budget constraint is used to limit the total transmit signal power on all subcarriers and symbols from exceeding the preset power budget value; The sensing signal power allocation constraint is used to limit the sum of the power of all sensing signal vectors to a preset fixed power value. The peak sidelobe level constraint is used to limit the peak amplitude of the sidelobe of the sensed signal in the time-delay-Doppler two-dimensional plane to not exceed a preset sidelobe level threshold. The constant modulus constraint of the reflection unit is used to limit the modulus of the reflection coefficient of each reflection unit on the smart reflection surface to 1.

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