Baseband signal optimization method, optimization system, equipment and medium

Abstract

The invention relates to the technical field of communication, and discloses a baseband signal optimization method, optimization system, equipment and medium, and the method comprises the steps: according to a gain matrix of a modulated signal, noise which passes through a double-color dispersion channel and is subjected to equalization processing, a time domain channel matrix, and a to-be-transmitted baseband signal of a transmitting end, obtaining a baseband signal; determining a signal to interference plus noise ratio corresponding to the communication signal; according to the power integral of the useful signal for radar sensing and the interference signal power of the radar signal, determining an integral frequency signal ratio for measuring the radar end performance; and constructing an objective function according to the signal to interference plus noise ratio and the integral frequency signal ratio, and obtaining an optimized baseband signal by maximizing the objective function on the premise of meeting constraint conditions. According to the invention, the communication and radar sensing performance of the ground end can be improved.

Description

Technical Field

[0001] This application relates to the field of communication technology, and in particular to a baseband signal optimization method, optimization system, device and medium. Background Technology

[0002] In the ground-based satellite internet for 6G, communication / sensing schemes based on hard separation and integrated implementations primarily using OFDM (Orthogonal Frequency Division Multiplexing) are constrained by the bi-dispersion effect caused by low-Earth orbit high-speed motion and ultra-wideband, resulting in inter-carrier interference (ICI) / inter-symbol interference (ISI) and inefficient coupling of gateway station / cell-level resources. Although OTFS (Orthogonal Time Frequency Space) technology in the delay-Doppler domain has excellent high dynamic robustness, its required high-density pilots and long guard intervals lead to huge delays and overheads, limiting its application in satellite-to-ground access scenarios with limited computing power. AFDM (Affine Frequency Division Multiplexing) has the advantages of low complexity and path separation, but lacks a collaborative design around multi-beam and rapid satellite-to-ground switching at the ground end, making it difficult to achieve an engineering balance between link reliability and sensing resolution. Summary of the Invention

[0003] In view of this, this application provides a baseband signal optimization method, optimization system, device and medium.

[0004] This application discloses a baseband signal optimization method, which includes: The signal-to-interference-plus-noise ratio (SINR) of the communication signal is determined based on the gain matrix of the modulated signal, the noise after passing through the bi-dispersive channel and undergoing equalization processing, the time-domain channel matrix, and the baseband signal to be transmitted at the transmitting end; the modulated signal consists of the communication signal sent to the user by the transmitting end and the radar signal used for target detection. The integral frequency-to-signal ratio, used to measure radar end performance, is determined based on the power integral of the useful signal used for radar sensing and the power of the interference signal of the radar signal. Based on the signal-to-interference-plus-noise ratio (SINR) and the integral frequency-to-signal ratio (IF), an objective function is constructed. Under the premise of satisfying the constraints, the optimized baseband signal is obtained by maximizing the objective function.

[0005] Further, the method for obtaining the gain matrix of the modulated signal includes: Based on the chirp parameters in the inverse discrete affine Fourier transform and the discrete affine Fourier transform, as well as the discrete Fourier transform matrix, the IDAFT matrix and the DAFT matrix are obtained; the discrete Fourier transform matrix is ​​determined according to the total number of subcarriers of the modulated signal; the IDAFT matrix and the DAFT matrix are transposes of each other; the modulated signal is determined based on the IDAFT matrix and the baseband signal; the modulated signal is obtained by modulating the baseband signal. The gain matrix of the modulated signal is determined based on the IDAFT matrix, the DAFT matrix, and the time-domain channel matrix.

[0006] Furthermore, the chirp parameter is related to the normalized maximum value of the Doppler frequency shift across all paths from the transmitter to the receiver, as well as the total number of subcarriers of the modulated baseband signal.

[0007] Furthermore, the method for obtaining the noise after passing through the bichromatic dispersive channel and undergoing equalization processing includes: Based on the DAFT matrix, the time-domain channel matrix, and the complex-valued additive white Gaussian noise, the noise after passing through the bichromatic channel and undergoing equalization processing is determined; the complex-valued additive white Gaussian noise follows a cyclic symmetric complex Gaussian distribution and exists in the communication link from the transmitter to the receiver.

[0008] Furthermore, the method for obtaining the time-domain channel matrix includes: The time-domain channel matrix is ​​obtained based on the normalized time delay and normalized Doppler frequency shift of all paths between the signal transmitted from the transmitter and the receiver, the diagonal matrix, and the cyclic shift matrix. The values ​​of the elements of the diagonal matrix are related to the total number of subcarriers of the modulated baseband signal, representing the effect of Doppler delay of the signal from the transmitter to the receiver. The cyclic shift matrix is ​​used to implement a cyclic left shift of the signal, representing the effect of path delay of the signal from the transmitter to the receiver in the time domain.

[0009] Further, determining the integrated frequency-to-signal ratio for measuring radar performance based on the power integral of the useful signal used for radar sensing and the interference signal power of the radar signal includes: The ratio of the power integral of the useful signal used for radar sensing to the power of the interference signal of the radar signal is used as the integral frequency-signal ratio to measure the performance of the radar.

[0010] Further, the method for obtaining the power integral of the useful signal used for radar sensing includes: Based on the baseband signal to be transmitted at the transmitting end, the gain matrix of the modulated signal, and the first matrix, the power integral of the useful signal for radar sensing is obtained; the position and total number of non-zero elements in the first matrix are related to the total number of radar signals in the modulated signal.

[0011] Furthermore, the method for obtaining the interference signal power of the radar signal includes: The interference signal power of the radar signal is obtained based on the baseband signal to be transmitted at the transmitting end, the gain matrix of the modulated signal, and the second matrix; the position and total number of non-zero elements in the second matrix are related to the total number of communication signals in the modulated signal; the interference signal power of the radar signal includes the interference power of the communication signal on the radar signal.

[0012] Furthermore, the constraints include a first constraint, a second constraint, and a third constraint; The first constraint is that the power of each subcarrier modulating the baseband signal is equal to a preset ratio; the preset ratio is the ratio of the total power of the transmitter to the total number of subcarriers modulating the baseband signal. The second constraint is: the difference between the baseband signal and the preset value is less than a preset threshold; the preset value is the product of the similarity factor and the reference signal. The third constraint condition is that the power of the useful signal obtained by the receiver demodulation is equal to the preset power.

[0013] Furthermore, the method for acquiring the reference signal includes: By introducing non-negative relaxation variables into the first constraint, the second constraint, and the third constraint, the first relaxation constraint, the second relaxation constraint, and the third relaxation constraint are obtained, respectively. An augmented objective function is constructed based on the objective function, the non-negative slack variables, and the penalty factor; the penalty factor is used to ensure that the non-negative slack variables contract until the first constraint, the second constraint, and the third constraint are restored to the first constraint, the second constraint, and the third constraint, respectively. Using the first, second, and third relaxation constraints as constraints, the augmented objective function is maximized to obtain the reference signal and the optimized non-negative relaxation variables.

[0014] This application also discloses an embodiment of a baseband signal optimization system, which includes: The first calculation module is used to determine the signal-to-interference-plus-noise ratio (SINR) of the communication signal based on the gain matrix of the modulated signal, the noise after passing through the bi-dispersive channel and undergoing equalization processing, the time-domain channel matrix, and the baseband signal to be transmitted by the transmitter; the modulated signal consists of the communication signal sent to the user by the transmitter and the radar signal used to detect the target; The second calculation module is used to determine the integral frequency-to-signal ratio, which is used to measure the performance of the radar end, based on the power integral of the useful signal used for radar sensing and the power of the interference signal of the radar signal. The baseband signal optimization module is used to construct an objective function based on the signal-to-interference-plus-noise ratio and the integral frequency signal ratio, and to obtain the optimized baseband signal by maximizing the objective function under the premise of satisfying the constraints.

[0015] This application also discloses an electronic device, including a memory and a processor, wherein the memory stores a computer program that, when executed by the processor, implements the method described above.

[0016] This application also discloses a computer-readable storage medium comprising a computer program or instructions that, when executed on a computer, cause the computer to perform the methods described above.

[0017] Due to the adoption of the above technical solution, this application has the following advantages: This application can suppress the Doppler effect and multipath effect in the dual-dispersion channel, and significantly improve the communication and radar sensing performance of the satellite Internet ground terminal. Attached Figure Description

[0018] To more clearly illustrate the technical solutions in the embodiments of this application, the accompanying drawings used in the description of the embodiments will be briefly introduced below. Obviously, the accompanying drawings described below are only some embodiments recorded in the embodiments of this application. For those skilled in the art, other drawings can be obtained based on these drawings.

[0019] Figure 1 This is a schematic diagram illustrating an application scenario of the ISAC system framework according to an embodiment of this application; Figure 2 This is a schematic flowchart of a baseband signal optimization method according to an embodiment of this application; Figure 3 This is a schematic diagram of AFDM modulation and demodulation according to an embodiment of this application; Figure 4 This is a schematic diagram illustrating the convergence characteristics of the ADPM-FPP algorithm in various modulation modes according to embodiments of this application. Figure 5This is a schematic diagram illustrating the change of the objective function of the communication-sensing integrated system with different modulation schemes based on the ADPM-FPP algorithm in an embodiment of this application, as a function of the weighting coefficients. Figure 6 This is a schematic diagram illustrating the impact of the similarity threshold on the objective function under different modulation modes and algorithms in embodiments of this application. Figure 7 This is a schematic diagram illustrating the response of INR to the objective function under different modulation modes and algorithms in embodiments of this application; Figure 8 This is a block diagram of an electronic device according to an embodiment of this application. Detailed Implementation

[0020] The present application will be further described in conjunction with the accompanying drawings and embodiments. The described embodiments are only some, not all, of the embodiments of the present application. All other embodiments obtained by those skilled in the art should fall within the protection scope of the embodiments of the present application.

[0021] See Figure 1 This application provides an embodiment of a baseband signal optimization method, which includes: Step 101: Determine the signal-to-interference-plus-noise ratio (SINR) of the communication signal based on the gain matrix of the modulated signal, the noise after passing through the bi-dispersive channel and undergoing equalization processing, the time-domain channel matrix, and the baseband signal to be transmitted at the transmitting end; the modulated signal consists of the communication signal sent to the user by the transmitting end and the radar signal used to detect the target; Among them, see Figure 2 The transmitting end (ground base station) sends signals (including communication signals and radar signals) to the user end, and the user end calculates the corresponding signal-to-interference-plus-noise ratio based on the received communication signals.

[0022] In one embodiment of this application, a method for obtaining the gain matrix of a modulated signal includes: Based on the chirp parameters in the inverse discrete affine Fourier transform and the discrete affine Fourier transform, as well as the discrete Fourier transform matrix, the IDAFT matrix and the DAFT matrix are obtained. The discrete Fourier transform matrix is ​​determined according to the total number of subcarriers of the modulated signal. The IDAFT matrix and the DAFT matrix are transposes of each other. The modulated signal is determined based on the IDAFT matrix and the baseband signal. The modulated signal is obtained by modulating the baseband signal. The gain matrix of the modulated signal is determined based on the IDAFT matrix, DAFT matrix, and time-domain channel matrix.

[0023] In one embodiment of this application, the chirp parameter is related to the normalized maximum value of the Doppler shift across all paths from the transmitter to the receiver and the total number of subcarriers of the modulated baseband signal.

[0024] In one embodiment of this application, a method for obtaining noise after passing through a dual-dispersion channel and undergoing equalization processing includes: Based on the DAFT matrix, the time-domain channel matrix, and the complex-valued additive white Gaussian noise, the noise after passing through the bichromatic channel and undergoing equalization processing is determined. The complex-valued additive white Gaussian noise follows a cyclic symmetric complex Gaussian distribution and exists in the communication link from the transmitter to the receiver.

[0025] In one embodiment of this application, a method for obtaining a time-domain channel matrix includes: The time-domain channel matrix is ​​obtained by taking the normalized time delay and normalized Doppler frequency shift of all paths between the transmitted signal and the received signal, the diagonal matrix, and the cyclic shift matrix. The values ​​of the elements of the diagonal matrix are related to the total number of subcarriers of the modulated baseband signal, representing the effect of Doppler delay from the transmitter to the receiver. The cyclic shift matrix is ​​used to implement a cyclic left shift of the signal, representing the effect of path delay from the transmitter to the receiver in the time domain.

[0026] In one possible implementation of the application, such as Figure 2 As shown, an ISAC (Integrated Sensing and Communication) system framework was designed for dual-dispersion channels, which enables the system to improve the fidelity of channel measurements by leveraging the time-frequency orthogonality and interference suppression capabilities of AFDM modulation.

[0027] In the context of an ISAC system for 6G satellite internet terrestrial terminals, a monostatic ISAC system model based on AFDM modulation under a dual-dispersion channel is as follows: Figure 2 As shown, the ground base station transmits an AFDM-modulated ISAC waveform to different users and radar targets. The signal passes through a dual-dispersion channel, and the Doppler delay and time delay of its different paths are considered fixed. The receiver uses MMSE (Minimum Mean Square Error) equalization and DAFT (Discrete Affine Fourier Transform) demodulation. At the same time, it outputs communication data and target echo for sensing. Multiple users (user 1 to user K) share the same ISAC waveform.

[0028] The modulation and demodulation diagram based on AFDM is as follows: Figure 3 As shown, the data bit stream to be transmitted by the transmitting end is an Nx1 dimensional baseband signal obtained by Quadrature Amplitude Modulation (QAM). Where N represents the total number of carriers, Let x represent a vector space of dimension N×1, containing the communication information and radar signal to be transmitted. Then, the radio frequency signal is obtained by performing Inverse Discrete Affine Fourier Transform (IDAFT) modulation on x. In sending Previously, a CPP (Chirped Periodic Prefix) needed to be added. The CPP serves the same purpose as the Cyclic Prefix (CP) in OFDM, to address multipath propagation and ensure the channel is effectively in the periodic domain. Then, after parallel-to-serial conversion... The data is transmitted to the receiving end through a two-color dispersion channel. After serial-to-parallel conversion, the CPP is removed, and then the discrete affine Fourier transform is performed for demodulation to obtain x. Finally, the parallel-to-serial conversion is performed to obtain the original data bit stream.

[0029] A vector containing N complex data symbols (Nx1 dimensional baseband signal) Using N as input, N-point IDAFT (subcarrier modulation) is performed through formula (1) to obtain a time-domain AFDM symbol consisting of N complex sample points. (Modulated signal). Details are as follows: The baseband signal x is modulated by a subcarrier to obtain the nth complex number. : (1) in Let represent the m-th complex data symbol in the baseband signal x, where c1 and c2 represent the two chirp parameters that determine IDAFT and DAFT, respectively, and are adaptively adjusted according to the specific time-delay Doppler environment. , If c1=c2=0, then IDAFT is equal to Inverse Fast Fourier Transform (IFFT), and the AFDM system is equal to the traditional OFDM system.

[0030] Will Represented in vector form: ,in and These are the IDAFT matrix and the DAFT matrix, respectively. , This represents a vector space of dimension N×N. This represents an N-point Discrete Fourier Transform (DFT) matrix, with each term being... , Indicates the row and column indices of a matrix. , ,in This represents the chirp matrix corresponding to the simulated radio frequency multiplexing.

[0031] Sending Previously, a CPP needed to be added to satisfy formula (2): (2) in This indicates the subscript of CPP. for The One element, express The One element, It is the length of CPP, and the above formula represents the result after adding CPP. The periodic relationship that is satisfied gives it a strong ability to resist time dispersion. When the signal passes through the dual-dispersion channel, the original linear convolution channel can be converted into a cyclic convolution channel at the receiving end by removing the CPP. If N is an integer and N is even, then That is, CPP equals CP at this time.

[0032] The signal transmitted from the transmitter passes through a bidispersive multipath channel and is affected by additive white Gaussian noise (AWGN). To achieve circular convolution of the channel and the signal, the chirp parameter is assumed in the following discussion. ,in Indicates the length of the protection bandwidth. This represents the normalized maximum value of the Doppler frequency shift across all paths from the transmitter to the receiver. ,Right now Set to much smaller The irrational number. Therefore, the time-domain channel matrix of the AFDM system using CPP can be obtained. This is expressed as in formula (3): (3) in Represents the channel coefficient. This represents the normalized delay of the p-th path. This represents the normalized Doppler frequency shift of the p-th path. It contains N roots of unity, defined as: ,in Indicates by A diagonal matrix composed of the elements in the matrix. Used to represent the effect of Doppler delay. This is a cyclic shift matrix, used to represent path delay in the time domain. The effect is that by right-multiplying the matrix, the signal can be cyclically shifted to the left, which can be expressed as formula (4): (4) At the receiving end, by removing the CPP, the received signal can be represented in matrix form, and any user receiver can be represented by formula (5): (5) in This indicates a signal that has been sent by the transmitting end; For complex value AWGN and ,Right now It is complex additive white Gaussian noise; The variance of additive Gaussian noise is given by: It is an identity matrix of size N×N.

[0033] The receiver performs MMSE equalization on the received signal r to reduce the effects of noise and interference, and then performs DAFT to obtain the symbol sequence as shown in formula (6): (6) in The equilibrium matrix obtained by the MMSE equilibrium criterion can be represented by formula (7) according to the general formula of MMSE: (7) in Represents the conjugate transpose of a matrix. This represents the inverse of a matrix.

[0034] (8) Set intermediate variables , , respectively, represent the gain matrix of the received signal and the noise received after passing through the bi-dispersive channel and equalization by MMSE (the noise after passing through the bi-dispersive channel and equalization). Rewriting u, the estimated symbol of the nth modulated subcarrier at the receiver can be expressed as formula (9): (9) in Indicated The nth element, i.e., the estimated value of the demodulated nth modulated subcarrier, is in the above equation. Representation matrix The elements in the nth row and ith column, express The elements in the nth row and nth column. , and Representing vectors respectively Complex information of the nth and i-th subcarriers and The nth element. It is easy to obtain from this... It can also be expressed as formula (10): (10) in It represents the Hadamah accumulation. Represents the transpose of a matrix. This represents the vector formed by taking the diagonal elements of the corresponding matrix, and the signal-to-interference-plus-noise ratio (SIR) for any nth modulated subcarrier. This can be expressed as formula (11): (11) Indicates baseband signal variance This indicates the calculation of the variance of the sequence.

[0035] This application embodiment suppresses the Doppler effect and multipath effect in the bi-dispersive channel (as shown in Equation (3)) by introducing a chirped periodic prefix structure (Equation (2)) and a parameterized inverse discrete pseudo-Fourier transform modulator (Equation (1)). Combined with the minimum mean square error equalization (MMSE) technology at the receiver, the system utilizes the time-frequency orthogonality and interference suppression characteristics of AFDM to significantly improve the communication and radar sensing performance of the 6G satellite internet ground terminal.

[0036] Step 102: Determine the integral frequency-to-signal ratio used to measure radar end performance based on the power integral of the useful signal used for radar sensing and the interference signal power of the radar signal. Among them, see Figure 2 The transmitting end (ground base station) sends signals (including communication signals and radar signals) to the target, and the target calculates the corresponding integral frequency signal ratio based on the received radar signal.

[0037] In one embodiment of this application, determining the integrated frequency-to-signal ratio for measuring radar end performance based on the power integral of the useful signal used for radar sensing and the interference signal power of the radar signal includes: The ratio of the power integral of the useful signal used for radar sensing to the power of the interference signal of the radar signal is used as the integral frequency-signal ratio to measure the performance of the radar.

[0038] In one embodiment of this application, a method for obtaining the power integral of a useful signal for radar sensing includes: Based on the baseband signal to be transmitted at the transmitting end, the gain matrix of the modulated signal, and the first matrix, the power integral of the useful signal used for radar sensing is obtained; the position and total number of non-zero elements in the first matrix are related to the total number of radar signals in the modulated signal.

[0039] In one embodiment of this application, a method for obtaining the interference signal power of a radar signal includes: The interference signal power of the radar signal is obtained based on the baseband signal to be transmitted at the transmitting end, the gain matrix of the modulated signal, and the second matrix. The position and total number of non-zero elements in the second matrix are related to the total number of communication signals in the modulated signal. The interference signal power of the radar signal includes the interference power of the communication signal on the radar signal.

[0040] Based on the above-mentioned feasible methods, due to and and Independent and unrelated, among which It is easy to prove that the SINR (Signal to Interference plus Noise Ratio) for all subcarriers is Hermitian matrix, and can be expressed as Equation (12): (12) in This represents the square of the L2 norm of a vector.

[0041] Transform SINR and define a diagonal matrix. It indicates that the construction is based on The diagonal elements are diagonal matrices.

[0042] (13) in This represents the conjugate transpose of a matrix.

[0043] and Therefore, it is determined Then we have formula (14): (14) The signal-to-interference-plus-noise ratio (SINR) can then be expressed as formula (15): (15) Define the Interference-to-Noise Ratio (INR) as: , is used as an independent variable parameter to explore the influence on the objective function shown in formula (17) during simulation.

[0044] Select the transmitted signal s Each subcarrier carrying the transmitted signal serves as the radar sensing signal, in which The remaining Nm subcarriers carrying the transmission signal are used for communication signals, thus interfering with the radar sensing signal. Therefore, the Integrated Frequency Signal Ratio (IFSR) metric used by AFDM to measure radar performance can be: (16) in It is a square matrix (the first matrix) where all elements except the element at position (p,p) are 0. The elements in the set represent the subcarrier index numbers corresponding to the selected m sensing signals; It is a square matrix (the second matrix) where all elements except the element at position (q,q) are 0. The elements in the set represent the subcarrier index numbers corresponding to the remaining Nm subcarriers; the numerator of the IFSR represents the power integral of the useful signal used for radar sensing, and the denominator represents the interference signal power of the radar signal, that is, the signal not used for radar sensing will interfere with the radar sensing signal, which is the interference power integral of the radar sensing signal.

[0045] This application proposes an Integrated Communication-Sensing-Cognition (ISAC) optimization model for 6G satellite internet ground terminals. It optimizes the SINR (Signal Indicator Radio Frequency) performance at the communication terminal and the IFSR (Indicator Indicator Radio Frequency) performance at the radar terminal. Simultaneously, it employs fractional programming theory to transform the IFSR maximization problem into a linear auxiliary variable form. Based on the MM method, the original non-convex objective function (Equation 16) is transformed into a convex objective function (Equation 22), thus converting this NP-hard problem into a solvable optimization form. This allows for more efficient optimization of the transmitted waveform, improving the measurement accuracy for 6G satellite internet ground terminals.

[0046] Step 103: Based on the signal-to-interference-plus-noise ratio and the integral frequency-to-signal ratio, construct an objective function. Under the premise of satisfying the constraints, obtain the optimized baseband signal by maximizing the objective function.

[0047] The process involves acquiring the signal-to-interference-plus-noise ratio (SINR) and integral frequency-to-signal ratio (IFNR) from the receiving end (target and user ends), constructing an objective function, and providing the optimized baseband signal to the transmitting end (ground base station). The transmitting end then performs inverse discrete affine Fourier transform modulation (IDAFT) on the optimized baseband signal to obtain the radio frequency (RF) signal, which is then transmitted to the receiving end. Figure 2 As shown.

[0048] In one embodiment of this application, the constraints include a first constraint, a second constraint, and a third constraint; First constraint: The power of each subcarrier of the modulated baseband signal is equal to a preset ratio; the preset ratio is the ratio of the total power of the transmitter to the total number of subcarriers of the modulated baseband signal. Second constraint: The difference between the baseband signal and the preset value is less than the preset threshold; the preset value is the product of the similarity factor and the reference signal; The third constraint is that the power of the useful signal obtained by demodulation at the receiving end is equal to the preset power.

[0049] In one embodiment of this application, the method for obtaining a reference signal includes: By introducing non-negative slack variables into the first, second, and third constraints, we obtain the first, second, and third slack constraints, respectively. Based on the objective function, non-negative slack variables, and penalty factor, an augmented objective function is constructed. The penalty factor is used to ensure that the non-negative slack variables contract until the first, second, and third constraints are restored to the first, second, and third constraints, respectively. Using the first, second, and third relaxation constraints as constraints, the augmented objective function is maximized to obtain the reference signal and the optimized non-negative relaxation variables.

[0050] Building upon the aforementioned feasible approaches, a dual-function optimization model is employed to jointly maximize the communication SINR and the integrated frequency signal ratio (IFSR), which serves as an indicator of the accuracy of channel parameter estimation. Fractional programming theory is used to linearize the IFSR maximization problem through auxiliary variables. Subsequently, based on a minorize-maximize (MM) scheme, a lower bound function of the objective function is found in each iteration, and its maximum value is calculated. This transforms the non-deterministic polynomial time-hard (NP-hard) problem into an easier form, directly optimizing the transmitted waveform to improve measurement accuracy.

[0051] The objective function can be expressed as formula (17): (17) in It is a weight vector factor, a constraint. The first constraint is a constant modulus constraint. It is a square matrix where all elements except the element at position (i,i) are 0. The baseband signal... The power of each subcarrier is constant. (Preset ratio) It is the total power of the transmitter, a constraint. The second constraint is a similarity constraint, enforced by a similarity factor η and a threshold δ to maintain alignment with the reference signal. Similarity, initial reference signal Random selection, final reference signal The result is then obtained using the FPP (Feasible Point Pursuit) algorithm. These methods ensure signal stability and fidelity. To ensure modulation consistency, and Preserve waveform characteristics.

[0052] right Perform a convex approximation derivation, and define... Set the formula (16) in , , The trace of the matrix is ​​represented, therefore IFSR can also be expressed as formula (18): (18) against To each and The gradient can be calculated, and the results are shown in formulas (19)-(20): (19) (20) in This indicates that the gradient is calculated, and the IFSR is... A first-order Taylor expansion is performed at the given point to construct a linear approximate lower bound substitution function as shown in equation (21): (twenty one) in , This indicates that at iteration t... , The value of .

[0053] make , Then we can obtain the first-order Taylor expansion formula of IFSR as shown in formula (22): (twenty two) Obtain the substitution function Next, use to replace , Representation matrix The conjugate transpose of . In order to solve the inherent nonconvexity in the original optimization problem (Equation (17)), a fixed numerator term is introduced into SINR of Equation (15). (Usually set to 1), this parameter represents the normalization constraint parameter of the useful signal power component at the receiver, and is introduced by a constraint condition (third constraint condition). ( This indicates the power of the useful signal obtained by demodulation at the receiving end. (Indicates preset power) to decouple optimization variables Therefore, the objective function shown in formula (17) can be expressed as formula (23): (twenty three) in yes The conjugate transpose of .

[0054] The ADPM (Alternating Direction Penalty Method) algorithm, with its adaptive penalty factors (equations (50)-(52)), ensures convergence and accelerates the convergence speed. The ADPM algorithm is used to solve the above problem (equation (23)) to obtain the optimized baseband signal, letting... ,let They are respectively represented as The real-valued form of .

[0055] Define complex vectors and complex matrix The real-valued form is: (twenty four) in This indicates taking the real and imaginary parts.

[0056] Introducing constraints corresponding to formula (23) , , Auxiliary variables , and Formula (23) can be rewritten as formula (25): (25) in For only in The value is 1 A 3D matrix Representing auxiliary variables Based on formula (25), the augmented Lagrange expression formula (26) is written as follows: (26) in These are the Lagrange multipliers related to the corresponding constraints. These are the corresponding positive penalty parameters. and They represent and The abbreviation symbol, in the specified constraint set middle, For only in The value is 1 The matrix, the ADPM algorithm iteratively performs the updates of formulas (27)-(30): (27) (28) (29) (30) in express In the The value at the next iteration express In the The value at the next iteration.

[0057] The following explains how to solve it: (1) To The update can be expressed as formula (31): (31) The first-order optimality condition of formula (31) is shown in formula (32). Solving for the first derivative yields formula (32): (32) (2) Update for any The update problem can be expressed as formula (33): (33) The closed-form solution of formula (33) is formula (34): (34) By taking the first-order partial derivative, we can obtain:

[0058] express In the The value taken in the next iteration.

[0059] (3) The update can be expressed as formula (35): (35) It is a convex problem and is solved using a proximal algorithm, i.e., formula (36): (36) express In the The value taken in the next iteration.

[0060] By taking the first-order partial derivative, we can obtain: .

[0061] right The update can be expressed as formula (37): (37) Its closed-form solution is given by formula (38): (38) in express In the The value at the next iteration can be obtained by taking the first-order partial derivative, which gives formula (39): (39) The Lagrange multiplier variables are updated according to formulas (40)-(48): (40) (41) (42) in yes In the The value at the next iteration.

[0062] (43) (44) (45) in yes In the The value at the next iteration.

[0063] (46) (47) (48) in yes In the The value at the next iteration This means taking the maximum value among them. This indicates taking the absolute value. Represents the first element in the corresponding vector. n One element, n Range of values .

[0064] Three auxiliary variables in the Lagrange method The corresponding residual during the iteration process , , As in formula (49); (49) This indicates the degree to which the current transmitted waveform violates the constant mode amplitude constraint, that is, the deviation between the actual amplitude of each transmitted symbol and the target constant mode amplitude. This indicates the degree of structural similarity deviation between the current transmitted waveform and the reference waveform; that is, the quantification of the difference between the two under a given similarity metric. It indicates the degree of deviation of the current waveform's useful signal power at the receiving end from the set normalized power, that is, the residual amount of the useful signal power normalization constraint.

[0065] Positive and negative parameters In the The update rules during iteration are as follows: (50)-(52) (50) (51) (52) in Both represent positive numbers greater than 1. express In the The value during iteration express In the The value at the next iteration.

[0066] The initial ADPM algorithm iteration points based on FPP are optimized as follows: To ensure the convergence speed and effectiveness of the ADPM algorithm, the Feasible Point Pursuit (FPP) method is adopted: under the three key constraints in formula (23), a random signal vector (reference signal) is first set. The non-convex terms are then conservatively convexized at this point (i.e., the equality constraint is transformed into a less than or equal to constraint in formula (53)). The constraints are relaxed and gradually tightened (i.e., relaxation variables are added for each constraint in formula (53)). The method iteratively solves the convex subproblem (Formula (55)) to improve convergence efficiency while ensuring feasibility. Finally, the initial feasible point (reference signal) that meets the constraints is obtained. ), which serves as the initial input vector for the ADPM algorithm.

[0067] The implementation of FPP is carried out in the following steps: To allow for more flexible handling of constraints, non-negative slack variables are introduced. This indicates that each constraint is relaxed and then gradually tightened during iteration to gradually satisfy the original constraints. Therefore, the original constraints (formula (23)) can be transformed into elastic constraints as shown in formula (53): (53) in This indicates that for constant modulus constraints (in formula (23) The set of non-negative slack variables (constraints). and Corresponding similarity constraints (in formula (23) (constraints) and useful power normalization constraints (in formula (23) The slack variable of the constraint. In formula (53) , , These are the first relaxation constraint, the second relaxation constraint, and the third relaxation constraint, respectively.

[0068] Construct the following augmented objective function: (54) in Represents the set of slack variables , The relaxation penalty factor (the factor that penalizes relaxation, i.e., the penalty factor) is much greater than 1, which is used to ensure that the relaxation variable gradually shrinks and eventually shrinks to the range of the original constraints (the three original constraints in formula (23)). Therefore, the initial iteration point, i.e. the reference signal, is input into the ADPM algorithm. The solution can be expressed as formula (55): (55) Equation (55) is expressed as Second-Order Cone Programming (SOCP), and the quadratic terms are transformed into second-order cone constraints through Cholesky decomposition. Specifically, within the SOCP framework, the positive semi-definite matrix can decompose the quadratic constraints (i.e., the first three constraints in Equation (55)) into the square form of the L2 norm. Using the interior-point method and with the aid of the cone structure, the problem can be solved efficiently regarding the... The convex subproblem (Equation (55)) is solved, and polynomial-time convergence is achieved. To ensure nonnegativity and iterative feasibility, slack variables are used. Updated using closed-threshold projection. The Cholesky decomposition decomposes a positive definite matrix into the product of a lower triangular matrix and its transpose. ), used to simplify quadratic terms.

[0069] This application proposes a joint optimization framework for AFDM-ISAC, oriented towards satellite-ground collaboration and implemented on the ground: taking the signal-to-interference-plus-noise ratio (SINR) corresponding to communication and the integral frequency signal ratio (IFSR) sensed by radar as dual objectives, it introduces a communication-sensing performance balancing strategy (i.e., formulas (15)-(17)) and an alternating direction penalty method (ADPM) solution process; and jointly optimizes the inverse discrete affine Fourier transform (IDAFT) parameters (i.e., in formula (1)) on the waveform side. and ) and combining the chirped periodic prefix CPP with the minimum mean square error MMSE to suppress bichromatic interference (i.e., in formula (3) , This approach enables complete separation of carrier signals from different paths in the delay-Doppler domain, thereby improving performance at the receiver. Furthermore, the Feasible Point Tracking (FPP) method is introduced to select the initial iteration point of the ADPM algorithm. Compared to random or empirical initialization schemes, this reduces divergence and iteration backoff caused by infeasible initial iteration points, improving initial feasibility and optimization start-up stability in time-frequency dual-dispersion channels.

[0070] This application provides an initial iteration point optimization method based on FPP, targeting the joint communication sensing index of AFDM-ISAC transmit waveform (i.e., the objective function of formula (17)) and the non-convex quadratic constraint (i.e., the constraint of formula (17)), and using the set of non-negative relaxation variables (i.e., the set of non-negative relaxation variables of formula (53)). The rigid constraints are made elastic (i.e., the first three constraints of formula (53)), and the quadratic constraints are equivalently rewritten as SOCP constraints (i.e., the constraints of formula (55)). Cholesky decomposition and interior point method are used to solve the problem (i.e., the method described below formula (55)) to obtain the initial iteration point that satisfies all constraints (i.e., the final solution obtained by solving formula (55)) and use it as the input of the subsequent ADPM algorithm. Compared to random or empirical initialization schemes, it can reduce the initial iteration point of ADPM. Divergence and iterative backoff caused by infeasibility improve initial feasibility and optimized start-up stability in dual-dispersion channels.

[0071] The efficient iterative ADPM solution framework proposed in this application, based on the joint FPP algorithm, is a set of solutions for the waveform optimization problem of Integrated Sensing and Communication (ISAC), namely, optimizing the transmitted waveform. An efficient numerical optimization method is proposed. The framework first introduces slack variables through the feasible point pursuit (FPP) mechanism (such as the parts of formula (53)-formula (55)), transforms the non-convex quadratic constraints (i.e., the constraints of formula (17)) into elastic forms (i.e., the first 3 constraints of formula (53)), and constructs a fast-solvable second-order cone programming (SOCP) subproblem (i.e., formula (55)). The final result obtained from solving the problem (i.e., the final solution obtained from solving formula (55)) is used as the initial iteration point of ADPM and also as the reference signal in the similarity constraints) as a high-quality initial iteration point for ADPM iteration. Furthermore, in the iterative loop of ADPM, the transmitted waveform, auxiliary variables and Lagrange multipliers are updated alternately (i.e., formulas (31)-(48)), and the penalty factor is dynamically adjusted according to the constraint violation residual (formula (49)) (formula (50)-(52)), thereby achieving adaptive penalty and accelerated convergence. The whole process effectively integrates the feasible region guidance of FPP and the distributed optimization capability of ADPM. Under the premise of ensuring that the constraints are satisfied, it significantly improves the solution efficiency and algorithm stability, and is especially suitable for waveform design and resource coordination problems in high-dimensional, dual-dispersion channel environments such as 6G satellite ground terminals.

[0072] In balanced operating mode, the proposed ADPM-FPP algorithm achieves superior sensing-communication integration (ISAC) performance, validating the algorithm's improvement on communication and radar sensing performance, such as... Figure 4 and Figure 5 As shown, the ADPM-FPP algorithm exhibits faster convergence speed and superior interference suppression capability compared to the traditional Alternating Direction Method of Multipliers (ADMM). Figure 6 and Figure 7 As shown, this directly enhances the reliability of the integrated communication and radar system.

[0073] like Figure 4As shown, in the highly mobile environment of 6G satellite internet terrestrial terminals, the AFDM-ISAC system based on the ADPM-FPP algorithm exhibits significant advantages in convergence and communication performance. The ADPM-FPP algorithm can achieve bi-objective convergence within approximately 40 iterations for all contrasting modulation modes (AFDM, OTFS, OFDM). Compared to OTFS and OFDM systems equipped with traditional algorithms, the AFDM system based on ADPM-FPP has the best communication performance. This is due to the adaptive multi-objective coordination mechanism of ADPM-FPP, which, by selecting appropriate initial iteration points and adaptively and dynamically adjusting penalty parameters, can fully adapt to the resistance of AFDM to bi-dispersive channels, further amplify its delay-Doppler orthogonality characteristics, and ultimately improve the communication fidelity of the terrestrial link.

[0074] like Figure 5 As shown, the AFDM system based on the ADPM-FPP algorithm achieves a superior balance between communication-side performance SINR and radar-side performance IFSR. With the increase of the weighting coefficient β, the ADPM-FPP algorithm significantly improves the convergence speed and optimization effect by adaptively adjusting the penalty parameters (Equation (50)-Equation (52)) and relaxing constraints (Equation 53) using the feasible point tracking (FPP) mechanism (Equation 55), resulting in a significant improvement in communication SINR of AFDM modulation that surpasses that of OTFS and OFDM systems. At the radar performance level, when... β In the intermediate range, ADPM-FPP, with its multi-objective coordination capability, achieves a significant improvement in SINR (Signal Indicator Ratio) of AFDM communication performance without excessively sacrificing IFSR, demonstrating the integrated gain of communication and sensing. In contrast, OTFS suffers from insufficient communication efficiency due to pilot overhead limitations; OFDM's overall performance is weaker due to the lack of a cooperative optimization mechanism. In summary, the ADPM-FPP algorithm performs well in different... β Under all conditions, it exhibits better balancing capabilities and stability. In summary, the ADPM-FPP algorithm, as a key optimization framework supporting 6G space-ground integrated sensing and communication systems, not only significantly improves the system performance of AFDM, but also provides effective algorithmic support for waveform design in future high-frequency and high-mobility scenarios.

[0075] Under different similarity thresholds δ and modulation schemes, the ADPM-FPP algorithm has significant advantages over the traditional ADMM algorithm: like Figure 6As shown, under different modulation schemes and similarity thresholds δ, the ADPM-FPP algorithm exhibits significant and stable convergence performance. All configurations achieve stable convergence, with a smaller similarity threshold δ producing a better target value. This is attributed to the Feasible Point Pursuit (FPP) mechanism, which uses initial iteration points to approximate the feasible region, effectively improving the flexibility and convergence efficiency of the optimization process. Therefore, implementing stricter waveform constraints near the reference signal x0 maximizes performance. ADPM-FPP utilizes an adaptive penalty factor... The iterative update strategy of (Formula (50)-Formula (52)) combined with closed threshold projection to handle slack variables effectively avoids premature convergence and achieves fast and stable convergence in various modulation environments. Especially when combined with AFDM, this algorithm not only significantly outperforms its combination with OTFS, but also far surpasses traditional ADMM-like methods, demonstrating its strong generalization ability under a wide range of parameter conditions. In summary, the ADPM-FPP algorithm, as an enhanced alternating direction optimization framework, has performance advantages not only in its optimal synergy with AFDM, but also in its general constraint handling mechanism and adaptive optimization logic, providing key algorithmic support for ISAC systems under high dynamic and dual-dispersion channels.

[0076] like Figure 7 As shown, under different interference-to-noise ratios (INR) (as defined below in Equation (15)), the ADPM-FPP algorithm consistently demonstrates superior system adaptability and optimization performance, significantly outperforming the traditional ADMM algorithm. Its core advantage lies in achieving efficient interference suppression and system stability maintenance within a wide INR range (5dB-30dB) through an adaptive penalty mechanism (Equation (50)-Equation (52)) and a feasible point pursuit (FPP) strategy (Equation 55). In the low INR range (5dB-15dB), ADPM-FPP dynamically adjusts the penalty parameters (as defined in Equation (50)-Equation (52)) and, in conjunction with the optimal initial iteration point found by the FPP algorithm (Equation (55)), obtains the relevant information about the problem. The algorithm effectively suppresses ICI and ISI interference caused by multipath and Doppler effects, significantly improving convergence speed and interference suppression capability. Even under high INR conditions (15dB-30dB), the algorithm maintains stable convergence of the objective function, approaching the theoretical performance limit and demonstrating excellent robustness. Furthermore, it can be seen that the ADPM-FPP algorithm fully utilizes the orthogonality of the AFDM waveform in the delay-Doppler domain and the multipath resistance potential of the CPP structure, with objective function values ​​superior to OFDM and OTFS modulation methods under the same conditions.

[0077] This application also provides an embodiment of a baseband signal optimization system, which includes: The first calculation module is used to determine the signal-to-interference-plus-noise ratio (SINR) of the communication signal based on the gain matrix of the modulated signal, the noise after passing through the bi-dispersive channel and undergoing equalization processing, the time-domain channel matrix, and the baseband signal to be transmitted by the transmitter; the modulated signal consists of the communication signal sent to the user by the transmitter and the radar signal used to detect the target; The second calculation module is used to determine the integral frequency-to-signal ratio, which is used to measure the performance of the radar end, based on the power integral of the useful signal used for radar sensing and the power of the interference signal of the radar signal. The baseband signal optimization module is used to construct an objective function based on the signal-to-interference-plus-noise ratio and the integral frequency signal ratio, and to obtain the optimized baseband signal by maximizing the objective function under the premise of satisfying the constraints.

[0078] See Figure 8 This application also provides an electronic device including a memory and a processor. The memory stores a computer program, which, when executed by the processor, implements the methods described in the above embodiments. As an example, the electronic device may include multiple processors. A processor may refer to one or more devices, circuits, and / or computing units for processing data (e.g., computer programs). The processor can invoke the computer program stored in the memory to implement the methods described in the above embodiments. Figure 8 Taking an electronic device consisting of one processor and one memory as an example, the processor and memory are used to indicate a type of device or equipment, and the quantity of each type of device or equipment can be determined according to business needs.

[0079] This application also provides a computer-readable storage medium, which includes a computer program or instructions that, when executed on a computer, cause the computer to perform the methods described in the above embodiments.

[0080] It should be noted that, in the various embodiments of this application, the order of the above-mentioned processes does not imply the order of execution. The execution order of each process should be determined by its function and internal logic, and should not constitute any limitation on the implementation process of the embodiments of this application.

[0081] Those skilled in the art should clearly understand that, for the sake of convenience and brevity, the specific working processes of the systems, electronic devices, and computer-readable storage media described in the above embodiments can be referred to the corresponding processes in the foregoing method embodiments, and will not be repeated here.

[0082] Those skilled in the art will understand that all or part of the steps of the above embodiments can be implemented by hardware, or by a program instructing the relevant hardware to implement them. The program can be stored in a computer-readable storage medium, such as a read-only memory, a disk, or an optical disk.

[0083] The above are merely optional embodiments of this application, used only to illustrate the technical solution of this application and not to limit it. Any modifications, equivalent substitutions, improvements, etc., to the specific implementation of this application without departing from the spirit and scope of this application should be covered within the protection scope of this application.

Claims

1. A baseband signal optimization method, characterized in that, include: The signal-to-interference-plus-noise ratio (SINR) of the communication signal is determined based on the gain matrix of the modulated signal, the noise after passing through the bi-dispersive channel and undergoing equalization processing, the time-domain channel matrix, and the baseband signal to be transmitted at the transmitting end; the modulated signal consists of the communication signal sent to the user by the transmitting end and the radar signal used for target detection. The integral frequency-to-signal ratio, used to measure radar end performance, is determined based on the power integral of the useful signal used for radar sensing and the power of the interference signal of the radar signal. Based on the signal-to-interference-plus-noise ratio (SINR) and the integral frequency-to-signal ratio (IF), an objective function is constructed. Under the premise of satisfying the constraints, the optimized baseband signal is obtained by maximizing the objective function.

2. The method according to claim 1, characterized in that, A method for obtaining the gain matrix of the modulated signal includes: Based on the chirp parameters in the inverse discrete affine Fourier transform and the discrete affine Fourier transform, as well as the discrete Fourier transform matrix, the IDAFT matrix and the DAFT matrix are obtained; the discrete Fourier transform matrix is ​​determined according to the total number of subcarriers of the modulated signal; the IDAFT matrix and the DAFT matrix are transposes of each other; the modulated signal is determined based on the IDAFT matrix and the baseband signal; the modulated signal is obtained by modulating the baseband signal. The gain matrix of the modulated signal is determined based on the IDAFT matrix, the DAFT matrix, and the time-domain channel matrix.

3. The method according to claim 2, characterized in that, The chirp parameter is related to the normalized maximum value of the Doppler shift across all paths from the transmitter to the receiver, as well as the total number of subcarriers of the modulated baseband signal.

4. The method according to claim 1, characterized in that, The method for obtaining the noise after passing through a dual-dispersion channel and undergoing equalization processing includes: Based on the DAFT matrix, the time-domain channel matrix, and the complex-valued additive white Gaussian noise, the noise after passing through the bichromatic channel and undergoing equalization processing is determined; the complex-valued additive white Gaussian noise follows a cyclic symmetric complex Gaussian distribution and exists in the communication link from the transmitter to the receiver.

5. The method according to any one of claims 1-4, characterized in that, The method for obtaining the time-domain channel matrix includes: The time-domain channel matrix is ​​obtained based on the normalized time delay and normalized Doppler frequency shift of all paths between the signal transmitted from the transmitter and the receiver, the diagonal matrix, and the cyclic shift matrix. The values ​​of the elements of the diagonal matrix are related to the total number of subcarriers of the modulated baseband signal, representing the effect of Doppler delay of the signal from the transmitter to the receiver. The cyclic shift matrix is ​​used to implement a cyclic left shift of the signal, representing the effect of path delay of the signal from the transmitter to the receiver in the time domain.

6. The method according to claim 1, characterized in that, The step of determining the integrated frequency-to-signal ratio, used to measure radar performance, based on the power integral of the useful signal used for radar sensing and the interference signal power of the radar signal includes: The ratio of the power integral of the useful signal used for radar sensing to the power of the interference signal of the radar signal is used as the integral frequency-signal ratio to measure the performance of the radar.

7. The method according to claim 6, characterized in that, The method for obtaining the power integral of the useful signal used for radar sensing includes: Based on the baseband signal to be transmitted at the transmitting end, the gain matrix of the modulated signal, and the first matrix, the power integral of the useful signal for radar sensing is obtained; the position and total number of non-zero elements in the first matrix are related to the total number of radar signals in the modulated signal.

8. The method according to claim 6, characterized in that, A method for obtaining the interference signal power of the radar signal includes: The interference signal power of the radar signal is obtained based on the baseband signal to be transmitted at the transmitting end, the gain matrix of the modulated signal, and the second matrix; the position and total number of non-zero elements in the second matrix are related to the total number of communication signals in the modulated signal; the interference signal power of the radar signal includes the interference power of the communication signal on the radar signal.

9. The method according to claim 1, characterized in that, The constraints include a first constraint, a second constraint, and a third constraint. The first constraint is that the power of each subcarrier modulating the baseband signal is equal to a preset ratio. The preset ratio is the ratio of the total power of the transmitting end to the total number of subcarriers modulating the baseband signal; The second constraint is: the difference between the baseband signal and the preset value is less than a preset threshold; the preset value is the product of the similarity factor and the reference signal. The third constraint condition is that the power of the useful signal obtained by the receiver demodulation is equal to the preset power.

10. The method according to claim 9, characterized in that, The method for obtaining the reference signal includes: By introducing non-negative relaxation variables into the first constraint, the second constraint, and the third constraint, the first relaxation constraint, the second relaxation constraint, and the third relaxation constraint are obtained, respectively. An augmented objective function is constructed based on the objective function, the non-negative slack variables, and the penalty factor; the penalty factor is used to ensure that the non-negative slack variables contract until the first constraint, the second constraint, and the third constraint are restored to the first constraint, the second constraint, and the third constraint, respectively. Using the first, second, and third relaxation constraints as constraints, the augmented objective function is maximized to obtain the reference signal and the optimized non-negative relaxation variables.

11. A baseband signal optimization system, characterized in that, include: The first calculation module is used to determine the signal-to-interference-plus-noise ratio (SINR) of the communication signal based on the gain matrix of the modulated signal, the noise after passing through the bi-dispersive channel and undergoing equalization processing, the time-domain channel matrix, and the baseband signal to be transmitted by the transmitter; the modulated signal consists of the communication signal sent to the user by the transmitter and the radar signal used to detect the target; The second calculation module is used to determine the integral frequency-to-signal ratio, which is used to measure the performance of the radar end, based on the power integral of the useful signal used for radar sensing and the power of the interference signal of the radar signal. The baseband signal optimization module is used to construct an objective function based on the signal-to-interference-plus-noise ratio and the integral frequency signal ratio, and to obtain the optimized baseband signal by maximizing the objective function under the premise of satisfying the constraints.

12. An electronic device, characterized in that, It includes a memory and a processor, the memory storing a computer program that, when executed by the processor, implements the method of any one of claims 1-10.

13. A computer-readable storage medium, characterized in that, The computer-readable storage medium includes a computer program or instructions that, when executed on a computer, cause the computer to perform the functions of claim 1. The method as described in any one of the 10.

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