A method for generating an OFDM communication and sensing integrated signal with low sidelobe and PAPR characteristics

Abstract

This invention provides a method for generating an integrated OFDM communication and sensing signal with low sidelobes and PAPR characteristics, relating to the fields of communication and radar technology. The method includes: constructing an OFDM time-domain signal with N subcarriers; constructing an integrated communication and sensing frequency-domain signal, the integrated frequency-domain signal including a set of communication subcarriers and a set of radar sensing subcarriers; constructing a mathematical model of the integrated communication and sensing signal; constructing a Lagrange augmented function; updating the OFDM time-domain signal; updating the communication subcarriers; updating the radar subcarriers; updating the Lagrange multipliers; and repeating the above update steps to obtain the optimal result. This invention optimizes both radar sensing and communication performance under PAPR constraints, solves the non-convex problem, and achieves a good balance between sensing and communication performance.

Description

TECHNICAL FIELD

[0001] The present application relates to the technical field of radar communication, and in particular to a method for generating an OFDM communication and sensing integrated signal with low sidelobe and PAPR characteristics. BACKGROUND

[0002] Integrated sensing and communication (ISAC) technology has significant advantages in improving spectrum efficiency and network intelligence, and provides key technical support for emerging applications such as autonomous driving and unmanned systems. Therefore, ISAC has become a key research focus for future sixth generation (6G) wireless communication.

[0003] Due to the spectrum occupancy of communication systems, it becomes increasingly difficult for radars to obtain continuous spectrum. To address this challenge, integrated adaptive subcarrier (IAS) sequences based on orthogonal frequency division multiplexing (OFDM) allocate subcarriers to radars and communications respectively, and their design methods can be divided into communication-oriented and radar-oriented types according to the different priorities of the functions.

[0004] In communication-oriented design, OFDM signals often face the problem of high peak-to-average power ratio (PAPR). Although there are some methods in the prior art to alleviate PAPR, and these methods can make orthogonal frequency division multiplexing signals used for radar sensing, they inevitably limit the maximum resolvable distance of the radar.

[0005] In radar-based system design, orthogonal frequency division multiplexing (OFDM) sequences are usually transmitted in a pulse structure to expand the resolvable range. At the radar receiving end, a matched filter technology is used to improve the signal-to-noise ratio (SNR) and target detection performance. In order to realize the joint function, a part of the subcarriers will be reserved for communication, thereby realizing spectrum coexistence. In this case, achieving low autocorrelation integrated sidelobes (SLLs) is crucial for radar performance. Researchers have studied methods based on the combination of Gerchberg-Saxton (GS) algorithm and convex optimization under spectrum constraints to reduce the PAPR of the sequence while maintaining the optimized low autocorrelation characteristics, reducing inter-symbol interference (ISI) and peak-to-average power ratio (PAPR). However, other researchers have proposed joint optimization of the transmitted sequence and the receiving filter to suppress SLLs. However, these methods often ignore the impact of embedded communication signals, which can cause PAPR to rise and radar performance to decline in ISAC systems. SUMMARY

[0006] To address the aforementioned issues, this invention proposes a method for generating OFDM integrated communication and sensing signals with low sidelobes and PAPR characteristics. By designing an intelligent adaptive cyclic sequence based on Pulsed OFDM, this sequence balances autocorrelation integral sidelobes (SLLs) and communication performance under the constraint of power-weighted average peak-to-average power ratio (PAPR), thereby improving power efficiency. Furthermore, to solve the resulting non-convex optimization problem, an algorithm based on the Alternating Directional Multiplier (ADMM) method is designed to alternately optimize the sequence on radar subcarriers and communication subcarriers, achieving a good balance between radar sensing and communication performance.

[0007] A method for generating an integrated OFDM communication and sensing signal with low sidelobe and PAPR characteristics, specifically comprising the following steps:

[0008] Step S1, constructing OFDM time-domain signal with 1 subcarrier;

[0009] Step S2: Establish an integrated frequency domain signal for communication and sensing, which includes a set of communication subcarriers and a set of radar sensing subcarriers;

[0010] Step S3: Construct a mathematical model of the integrated communication and sensing signal. The model satisfies the following constraints: apply a constant modulus constraint in the frequency domain to the radar sensing subcarrier; restrict the communication subcarrier to belong to the discrete coded sequence set A; and restrict the power of the time-domain waveform.

[0011] Step S4: Construct the Lagrange augmenting function and the variable update process based on the ADMM algorithm;

[0012] Step S5: Update the OFDM time domain signal;

[0013] Step S6: Update the communication subcarrier;

[0014] Step S7, update radar subcarriers;

[0015] Step S8, update the Lagrange multipliers;

[0016] Step S9: Repeat steps S5 to S8 until the maximum number of iterations is reached.

[0017] Further, the frequency domain signal of OFDM in step S1 is represented as follows: X = [ X 1 , … , X n ] T ,in, n ∈ [ 1 ， N ] , Indicates the first The frequency domain signal of each subcarrier, and the OFDM time domain signal are: ,in, x = [ x 1 , … , x N ] T ∈ ℂ N × 1 Represents the sampling points of a discrete signal. This indicates that all elements in the variable are constants. The IDFT matrix is ​​represented as:

[0018] F I = 1 N [ 1 1 1 ⋯ 1 1 e j 2 π N e j 2 π N ⋅ 2 ⋯ e j 2 π N ( N − 1 ) 1 e j 2 π N ⋅ 2 e j 2 π N ⋅ 4 ⋯ e j 2 π N ⋅ 2 ( N − 1 ) ⋮ ⋮ ⋮ ⋱ ⋮ 1 e j 2 π N ( N − 1 ) e j 2 π N ⋅ 2 ( N − 1 ) ⋯ e j 2 π N ( N − 1 ) 2 ] ;

[0019] in, For the number of subcarriers, For a complex exponent, It is the imaginary unit.

[0020] Furthermore, the integrated communication-sensing frequency domain signal constructed in step S2 is: ,in, Indicates the first frequency band in the communication band Data on each subcarrier Indicates the first frequency band in the radar frequency band Data on each subcarrier Represents the communication subcarrier set, This represents the radar sensing subcarrier set.

[0021] Furthermore, the mathematical model of the integrated communication and sensing signal constructed in step S3 is as follows:

[0022] ;

[0023] in, This represents the Hermitian conjugate operator. Indicates condition, For the frequency domain sequence corresponding to the communication subcarrier, This is the frequency domain sequence corresponding to the radar sensing subcarrier. Indicates the total number of communication subcarriers. For a given communication subcarrier, the phase-coded symbol for ideal transmission. OFDM time-domain signal The elements in The weighting factor represents the adjustment factor for communication and sensing. It is a set of discrete coded sequences. It is a PAPR constraint. This represents the average energy of the time-domain signal. This indicates taking the absolute value. Represents the L2 norm, The time-shift matrix is ​​represented as follows:

[0024] J p = [ 0 ⋯ 0 1 0 0 0 0 ⋯ 0 0 1 0 0 ⋮ ⋮ ⋮ ⋱ ⋮ 0 ⋯ 0 0 0 0 1 0 ⋯ 0 ︸ p zeros 0 0 0 0 ] N × N ;

[0025] in, express One zero, denotes the discrete-time delay index.

[0026] Further, the Lagrangian augmented function constructed in the step S4 is:

[0027] ;

[0028] wherein, is a penalty factor, is a scaled Lagrange multiplier;

[0029] In the i-th iteration, the ADMM algorithm consists of the following update processes:

[0030] ;

[0031] ;

[0032] ;

[0033] ;

[0034] wherein, is the OFDM time-domain signal in the i-th iteration, is the OFDM time-domain signal in the i-th iteration, is the frequency-domain sequence corresponding to the communication subcarriers in the i-th iteration, is the frequency-domain sequence corresponding to the communication subcarriers in the i-th iteration, is the frequency-domain sequence corresponding to the radar sensing subcarriers in the i-th iteration, is the frequency-domain sequence corresponding to the radar sensing subcarriers in the i-th iteration, is the Lagrange multiplier in the i-th iteration, is the Lagrange multiplier in the i-th iteration, the set , and are defined as: ; ; ;

[0035] ;

[0036] .

[0037] .

[0038] ​​​​​​Furthermore, in step S5, the Lagrange augmented function with respect to the OFDM time-domain signal... The optimization problem for finding the minimum value is expressed as:

[0039] ;

[0040] in, This means minimizing the objective function. This indicates the operation of taking the real part. Q = σ ⋅ ∑ p =− N + 1 , p ≠ 0 N − 1 [ J p F I ( X c ( k ) + X r ( k ) ) ( X c ( k ) + X r ( k ) ) H F I H J P H ] , is with irrelevant items This represents the Hermitian conjugate operator. , Represents the identity matrix;

[0041] Then, the above equation is solved using the gradient projection method. Setting the gradient to zero, the solution is:

[0042] ;

[0043] at last, Updated by the following formula:

[0044] .

[0045] Furthermore, in step S6, for a given set Lagrange augmented function with respect to The optimization problem for finding the minimum value is expressed as:

[0046] ;

[0047] in, Indicates the total number of communication subcarriers. For a given communication subcarrier, the phase-coded symbol for ideal transmission. for Hermitian conjugate operation;

[0048] The coordinate descent method (CD) is used to solve the above equation, and the variable to be optimized is... elements in That is, the signal on the communication subcarrier is used in an iterative manner. The 3D optimization problem is decomposed into a 1D optimization problem. For the 1D optimization problem... A one-dimensional optimization problem, fixed , No. The values ​​of each communication subcarrier are obtained through a search set. Find the values ​​of all discrete communication symbols in the equation, and find the value that makes the Lagrange augmented function relativistic about... Minimize the sign value ,get After the solution, let .

[0049] Further, the optimization problem of the minimum value of the Lagrange augmented function about in step S7 is expressed as:

[0050] ;

[0051] wherein, represents the i-th element of the radar perception signal, is the conjugate of , , let the i-th element of the vector be 0, and other elements be the same as , the i-th element of the vector be 1, and other elements be 0; Let , , then the optimization problem of the minimum value of the Lagrange augmented function about is changed to:

[0052] ;

[0053] ;

[0054] When is the optimal solution, so there is:

[0055] ;

[0056] wherein, is a complex exponential, is an imaginary unit, and are phase angles.

[0057] Further, the updating method of the Lagrange multiplier in step S8 is: .

[0058] Further, if the residual error of the algorithm converges in the process of optimization iteration, the optimization cycle of the algorithm is ended.

[0059] ​​​The beneficial technical effect of the present application is that the present application designs an ISAC sequence based on pulse OFDM, optimizes radar sensing and communication performance under PAPR constraint, balances autocorrelation SLLs and communication quality through a weighting factor, uses ADMM algorithm to efficiently separate the non-convex problem into a convex optimization sub-problem, uses CD algorithm and gradient projection method to solve the sub-problem, and achieves a good balance between sensing and communication performance, so that it is suitable for actual ISAC scenarios with strict requirements for spectrum and power efficiency. BRIEF DESCRIPTION OF DRAWINGS

[0060] In order to more clearly illustrate the technical solutions in the embodiments of the present application or the prior art, the following will briefly introduce the drawings needed to be used in the embodiments or prior art description. Obviously, the drawings in the following description are some embodiments of the present application, and other drawings can also be obtained by those skilled in the art without creative labor.

[0061] Figure 1 is a flowchart of a method for generating an OFDM communication sensing integrated signal with low sidelobe and PAPR characteristics provided by an embodiment of the present application;

[0062] Figure 2 is an iteration curve diagram of the residual of the optimization variable and the optimization objective function value in the method described in the present application, wherein (a) is the original residual, (b) is the dual residual, and (c) is the ADMM iteration curve;

[0063] Figure 3 is a comparison diagram of the autocorrelation sidelobe of a random OFDM signal and the signal optimized by the method described in the present application provided by an embodiment of the present application;

[0064] Figure 4 is a diagram showing the change of PAPR with the number of iterations provided by an embodiment of the present application;

[0065] Figure 5 is a curve diagram of the change of the SER of the communication sensing integrated signal with the SNR provided by an embodiment of the present application. DETAILED DESCRIPTION

[0066] The technical solutions in the embodiments of the present application will be described clearly and completely below with reference to the drawings in the embodiments of the present application. Obviously, the described embodiments are only some of the embodiments of the present application, not all. Based on the embodiments in the present application, all other embodiments obtained by those skilled in the art without creative labor are within the scope of protection of the present application.

[0067] In order to better describe, first define as follows:

[0068] ADMM: Alternating Direction Method of Multipliers, a numerical algorithm for solving separable convex optimization problems;

[0069] Autocorrelation function: a mathematical function used to characterize the similarity between a signal or sequence of events and its own shifted version by different time;

[0070] SLLs: Self-correlation integral side lobe level, a performance indicator used to characterize the relative high or low total energy of the side lobe region outside the main peak of the autocorrelation function;

[0071] CD: Coordinate Descent, a numerical algorithm for solving optimization problems;

[0072] Convex optimization problem: a problem whose local optimal solution is also the global optimal solution.

[0073] A method for generating an OFDM communication and perception integrated signal with low side lobe and PAPR characteristics, as shown in Figure 1 , the method comprises the following steps:

[0074] Step 1, constructing an OFDM time domain signal with N subcarriers, the time domain signal vector has rows columns.

[0075] An OFDM symbol has subcarriers, and the frequency domain signal of OFDM is represented as X = [ X 1 , … , X n ] T , wherein n ∈ [ 1 ， N ] , represents the frequency domain signal of the th subcarrier, and the OFDM time domain signal is: , wherein x = [ x 1 , … , x N ] T ∈ ℂ N × 1 represents the discrete signal sampling point, represents that all elements in the variable are constants, is the IDFT matrix, and is represented as:

[0076] F I = 1 N [ 1 1 1 ⋯ 1 1 e j 2 π N e j 2 π N ⋅ 2 ⋯ e j 2 π N ( N − 1 ) 1 e j 2 π N ⋅ 2 e j 2 π N ⋅ 4 ⋯ e j 2 π N ⋅ 2 ( N − 1 ) ⋮ ⋮ ⋮ ⋱ ⋮ 1 e j 2 π N ( N − 1 ) e j 2 π N ⋅ 2 ( N − 1 ) ⋯ e j 2 π N ( N − 1 ) 2 ] ;

[0077] , wherein represents that all elements in the variable are constants.

[0078] Step 2, constructing a communication and perception integrated frequency domain signal.

[0079] The signal has a carrier frequency band for communication, and other frequency bands for radar detection performance optimization, let represent the communication subcarrier set, represent the radar perception subcarrier set, Nc represents the total number of communication subcarriers, Nr represents the total number of radar sensing subcarriers, and the frequency domain sequences corresponding to the communication subcarriers and the radar sensing subcarriers are respectively defined as , , , only has a value on the communication subcarriers and is 0 on the rest of the subcarriers, only has a value on the radar subcarriers and is 0 on the rest of the subcarriers, and the constructed communication-sensing integrated frequency domain signal is represented as: , where represents the data on the th subcarrier in the communication frequency band, represents the data on the th subcarrier in the radar frequency band.

[0080] Step 3, construct the mathematical model of the communication-sensing integrated signal, the specific process is as follows:

[0081] The autocorrelation function of the communication-sensing integrated signal is:

[0082] ;

[0083] wherein is an element in the OFDM time domain signal , represents the conjugate of , and the time shift matrix is defined as:

[0084] J p = [ 0 ⋯ 0 1 0 0 0 0 ⋯ 0 0 1 0 0 ⋮ ⋮ ⋮ ⋱ ⋮ 0 ⋯ 0 0 0 0 1 0 ⋯ 0 ︸ p zeros 0 0 0 0 ] N × N ;

[0085] wherein p ∈ [ − N + 1 , N − 1 ] , represents zeros, represents the discrete time delay index, and the sidelobe of the filtered output of the communication-sensing integrated signal is: ;

[0086] The integral sidelobe level of the autocorrelation function of the transmit waveform of the communication-sensing integrated signal is:

[0087] ;

[0088] Considering single-user communication, the frequency domain representation of the communication signal received at the user is:

[0089] ;

[0090] wherein Y = [ Y 1 , … , Y N ] T ​​​​​​​​​​​​​​​​​​the received frequency domain signal at the user, whose elements , n ∈ [ 1 , N ] the frequency domain signal of the th subcarrier, the channel coefficient from the integrated system to the user, a Gaussian white noise matrix.

[0091] Assuming that the communication-sensing integrated system can accurately estimate its channel state information, and the receiving end has compensated the channel, the phase-coded symbol of the ideal transmission on the communication subcarrier is given by Since the OFDM subcarriers are orthogonal to each other, the communication-sensing integrated system designs the transmitted signal so that the frequency domain sequence corresponding to the communication subcarrier approximates the phase-coded symbol .

[0092] The design is expected to balance the minimization of the integral sidelobe level of the radar signal autocorrelation function and the minimization of the difference between the communication received signal vector and the transmission symbol, and to satisfy the following constraints: 1. The frequency domain constant modulus constraint is imposed on the radar detection subcarrier to ensure that the transmitted signal amplitude is constant; 2. Limiting the communication subcarrier to belong to the discrete code sequence set ; 3. Limiting the power of the time domain waveform to reduce the PAPR, avoiding the excessive power of the communication band signal causing nonlinear distortion. Therefore, the band-limited OFDM signal waveform design problem is modeled as:

[0093] ;

[0094] wherein denotes the Hermitian conjugate operator, denotes the condition, denotes the absolute value, denotes the two-norm, denotes the weight adjustment factor of communication and sensing, is the discrete code sequence set, is the PAPR constraint, denotes the average energy of the time domain signal. Since the original problem is a quartic non-convex problem, it is difficult to obtain a closed solution directly, so the constraint is substituted into the above model, replacing one of , to obtain the optimization problem:

[0095] ;

[0096] Substituting the communication-sensing integrated frequency domain signal into the above optimization problem, replacing , the mathematical model of the communication-sensing integrated signal is obtained as:

[0097] ;

[0098] Step 4: Construct the Lagrange augmented function, expressed as:

[0099] ;

[0100] in, As a penalty factor, These are scaled Lagrange multipliers;

[0101] In the In the next iteration, the ADMM algorithm consists of the following update process:

[0102] ;

[0103] ;

[0104] ;

[0105] ;

[0106] in, For the first OFDM time-domain signal of the next iteration For the first OFDM time-domain signal of the next iteration For the first The frequency domain sequence corresponding to the communication subcarrier in the next iteration. For the first The frequency domain sequence corresponding to the communication subcarrier in the next iteration. For the first The frequency domain sequence corresponding to the radar sensing subcarrier in the next iteration. For the first The frequency domain sequence corresponding to the radar sensing subcarrier in the next iteration. For the first The Lagrange multipliers of the next iteration, For the first The Lagrange multipliers of the next iteration, set , and They are defined as follows:

[0107] ;

[0108] ;

[0109] ;

[0110] Step 5: Update the OFDM time domain signal :

[0111] For a given set , the optimization problem of the minimum value of the Lagrangian function with respect to the OFDM time-domain signal is:

[0112] ;

[0113] wherein denotes that the objective function takes the minimum value, the first term in the optimization problem of the minimum value with respect to the OFDM time-domain signal is the integral sidelobe level, and is denoted as:

[0114] σ ⋅ ∑ p =− N + 1 , p ≠ 0 N − 1 | x H J p F I ( X c ( k ) + X r ( k ) ) | 2 = σ ⋅ ∑ p =− N + 1 , p ≠ 0 N − 1 [ x H J p F I ( X c ( k ) + X r ( k ) ) ] [ x H J p F I ( X c ( k ) + X r ( k ) ) ] H = x H { σ ⋅ ∑ p =− N + 1 , p ≠ 0 N − 1 [ J p F I ( X c ( k ) + X r ( k ) ) ( X c ( k ) + X r ( k ) ) H F I H J P H ] } x = x H Qx ;

[0115] wherein Q = σ ⋅ ∑ p =− N + 1 , p ≠ 0 N − 1 [ J p F I ( X c ( k ) + X r ( k ) ) ( X c ( k ) + X r ( k ) ) H F I H J P H ] is a term independent of ;

[0116] In addition, the second term in the optimization problem of the minimum value with respect to the OFDM time-domain signal is expanded as:

[0117] ρ 2 ‖ x − F I ( X c ( k ) + X r ( k ) ) + u ( k ) ‖ 2 2 = ρ 2 [ x − F I ( X c ( k ) + X r ( k ) ) + u ( k ) ] H [ x − F I ( X c ( k ) + X r ( k ) ) + u ( k ) ] = ρ 2 x H x − ρ R e ( x H b ) + c o n s t ;

[0118] wherein denotes the real part operation, is a constant term, is defined by:

[0119] ;

[0120] In combination with the above derivation, ignoring the constant term, the optimization problem of the minimum value of the Lagrangian function with respect to the OFDM time-domain signal is equivalent to:

[0121] ;

[0122] This problem is a quadratic convex optimization problem, and the optimal solution of the unconstrained optimization problem is considered first, and then projected, that is, solved by the gradient projection method, and the gradient thereof is denoted as:

[0123] ;

[0124] Let the gradient be zero, and the solution is obtained as:

[0125] ;

[0126] Finally, is updated by:

[0127] .

[0128] Step 6, update the communication subcarriers:

[0129] For a given set , the optimization problem of the minimum of the Lagrangian augmented function with respect to is:

[0130] ;

[0131] The above equation is solved by using the coordinate descent method (CD). The variables to be optimized are the elements in , i.e., the signals on the communication subcarriers. The -dimensional optimization problem is decomposed into one-dimensional optimization problems in an iterative manner. For the th one-dimensional optimization problem, the value of is fixed, and the value of the th communication subcarrier is obtained by searching all the discrete communication symbols in the set and finding the symbol value that minimizes the Lagrangian augmented function with respect to . After obtaining the solutions, the value of is updated.

[0132] Step 7, update the radar subcarriers:

[0133] For a given set , the optimization problem of the minimum of the Lagrangian augmented function with respect to is:

[0134] ;

[0135] The first term in the above optimization problem with respect to the minimum of is expanded to obtain:

[0136] σ ⋅ ∑ p =− N + 1 , p ≠ 0 N − 1 | x H ( k + 1 ) J p F I ( X c ( k + 1 ) + X r ) | 2 = σ ⋅ ∑ p =− N + 1 , p ≠ 0 N − 1 [ x ( k + 1 ) H J p F I ( X c ( k + 1 ) + X r ) ] H [ x ( k + 1 ) H J p F I ( X c ( k + 1 ) + X r ) ] = σ ⋅ ∑ p =− N + 1 , p ≠ 0 N − 1 ( X c ( k + 1 ) + X r ) H F I H J P H x ( k + 1 ) x ( k + 1 ) H J p F I ( X c ( k + 1 ) + X r ) = ( X c ( k + 1 ) + X r ) H M 1 ( X c ( k + 1 ) + X r ) = X r H M 1 X r + 2 Re ( X r H M 1 X c ( k + 1 ) ) + X c ( k + 1 ) H M 1 X c ( k + 1 ) ;

[0137] where , the second term in the above optimization problem with respect to the minimum of is expanded to obtain:

[0138] ;

[0139] where , is the inverse Fourier transform matrix and satisfies , is the identity matrix. Due to the constant modulus constraint, there is Ignoring the constant term, the optimization problem of the minimum of the Lagrangian augmented function with respect to is equivalent to:

[0140] ;

[0141] The coordinate descent method CD is used to solve the above equation, and the variables to be optimized are the elements in , i.e., the signals on the radar subcarriers. The dimensional optimization problem is decomposed into one-dimensional optimization problems in an iterative manner. For the th one-dimensional optimization problem, fix , and optimize . Let the th element of the vector be 0, and the other elements be the same as . Let the th element of the vector be 1, and the other elements be 0. Since , the first term in the above equation is expressed as:

[0142] ;

[0143] where is a constant term, and represents the th element of the frequency domain perception signal, i.e., the radar signal. The second term in the above equation is expressed as:

[0144] ;

[0145] The third term in the above equation is expressed as:

[0146] ;

[0147] Then the objective function is simplified as:

[0148] 2 R e ( X r n * [ Ε ˜ n H M 1 X ¯ n + Ε ˜ n H M 1 X c ( k + 1 ) − ρ 2 Ε ˜ n H F I H M 2 ] ) + c o n s t = 2 Re ( X r n * d n ) + const ;

[0149] where , ignoring the constant term, the optimization problem of the minimum of the Lagrangian augmented function with respect to is further expressed as:

[0150] ;

[0151] Let , , then the optimization problem with respect to the minimum of becomes:

[0152] ;

[0153] When is the optimal solution, so we have:

[0154] ;

[0155] where, is a complex exponential, is the imaginary unit, and are phase angles.

[0156] Step 8, update the Lagrange multiplier:

[0157] The Lagrange multiplier is updated by:

[0158] .

[0159] Step 9, take the updated new result as the initial value of the next iteration, repeat steps 5 to 8, generally 80 to 100 times.

[0160] Through the above iterative updating process, the ADMM algorithm can continuously find the optimal solution under the premise of meeting the constraint condition, and the finally output global optimal solution balances the minimization of the sidelobe level of the integral of the radar signal autocorrelation function and the minimization of the difference between the communication received signal vector and the transmission symbol.

[0161] If the residual error of the algorithm converges in the process of optimization iteration, the optimization cycle of the ADMM algorithm is ended, and the required transmission signal is obtained.

[0162] The application proposes an ISAC sequence design method based on pulse OFDM, which simultaneously optimizes radar sensing and communication performance under PAPR constraint, a weighted factor balances autocorrelation SLLs and communication quality, ADMM algorithm is used to split the optimization problem into several convex optimization problems, CD algorithm and gradient projection algorithm are used to solve in the sub-problems, and the non-convex problem generated thereby is efficiently solved.

[0163] The simulation verification is carried out on the generation method of the OFDM communication sensing integrated signal with low sidelobe and PAPR characteristics proposed in the application, and the following results are obtained:

[0164] Figure 2 It is the iteration curve diagram of the residual error of the optimization variable and the optimization objective function value in the method described in the application, wherein (a) is the original residual error, (b) is the dual residual error, and (c) is the ADMM iteration curve, it can be seen from the figure that the residual error and the objective function converge; Figure 3A comparison chart of autocorrelation sidelobes of a random OFDM signal and the signal optimized by the method of the application, from which it can be seen that the method of the application effectively reduces the autocorrelation sidelobes of the signal compared with the random OFDM signal; Figure 4 A maximum value of PAPR that can be reduced by different signal average energies when the fixed weight factor is 0.5 in the method of the application; Figure 5 A curve chart of the bit error rate SER of the method of the application versus the signal-to-noise ratio SNR.

[0165] The simulation results show that the method of the application can realize sidelobe suppression below -30dB, reduce the PAPR to about 1.5, and maintain stable low bit error rate performance under various weighting coefficients, which demonstrates a good balance between sensing and communication performance, making it suitable for practical ISAC scenarios with strict requirements for spectrum and power efficiency.

[0166] Meanwhile, the optimization search method of the application is not limited to the ADMM algorithm.

[0167] Finally, it should be noted that: the above embodiments are only used to illustrate the technical solutions of the application, and not to limit them; although the application has been described in detail with reference to the foregoing embodiments, those skilled in the art should understand that: it can still modify the technical solutions recorded in the foregoing embodiments, or make equivalent replacement for part or all of the technical features; and these modifications or replacements do not make the essence of the corresponding technical solutions deviate from the scope of the technical solutions of the embodiments of the application.

Claims

1. A method for generating an OFDM communication and sensing integrated signal with low sidelobe and PAPR characteristics, characterized in that, The method comprises: Step S1, constructing an OFDM time domain signal with N subcarriers; Step S2, a communication-aware integrated frequency domain signal is established, the integrated frequency domain signal includes a communication subcarrier set and a radar-aware subcarrier set, and the communication-aware integrated frequency domain signal is specifically: Wherein, represents data on the nth subcarrier in the communication frequency band, represents data on the nth subcarrier in the radar frequency band, Ω c represents the communication subcarrier set, Ω r represents the radar-aware subcarrier set; Step S3, constructing a mathematical model of the communication and perception integrated signal, the constraint condition met by the model being: imposing a frequency domain constant modulus constraint on the radar perception subcarriers, limiting the communication subcarriers to belong to a discrete code sequence set A, and limiting the power of the time domain waveform; The mathematical model of the constructed communication and perception integrated signal is specifically: where (·) H denotes the Hermitian conjugate operator, s.t. denotes the condition, X c is the frequency domain sequence corresponding to the communication subcarriers, X r is the frequency domain sequence corresponding to the radar perception subcarriers, N c denotes the total number of communication subcarriers, S c is the phase encoded symbol of the ideal transmission on a given communication subcarrier, x n is the element in the OFDM time domain signal x, 0≤σ≤1 denotes the weight adjustment factor for communication and perception, A is the set of discrete code sequences, λ is the PAPR constraint, P denotes the average energy of the time domain signal, |·| denotes the absolute value, ||·||2 denotes the two-norm, J p is the time shift matrix denoted as: Wherein, pzeros represents p zeros, and p represents a discrete time delay index; Step S4, constructing a Lagrange augmented function and a variable updating process based on the ADMM algorithm: The constructed Lagrange augmented function is: wherein, denotes the Lagrangian augmented function, p is a penalty factor, and u is the scaled Lagrangian multiplier; At the k+1th iteration, the ADMM algorithm is composed of the following updating process: where x (k) is the OFDM time domain signal at the kth iteration, x (k+1) is the OFDM time domain signal at the (k+1)th iteration, X c (k) is the frequency domain sequence corresponding to the communication subcarriers at the kth iteration, X c (k+1) is the frequency domain sequence corresponding to the communication subcarriers at the (k+1)th iteration, X r (k) is the frequency domain sequence corresponding to the radar sensing subcarriers at the kth iteration, X r (k+1) is the frequency domain sequence corresponding to the radar sensing subcarriers at the (k+1)th iteration, u (k) is the Lagrange multiplier at the kth iteration, u +k+1) is the Lagrange multiplier at the (k+1)th iteration, the set and are defined as: Step S5, updating the OFDM time domain signal, specifically: The optimization problem of the minimum value of the Lagrange augmented function with respect to the OFDM time domain signal x is represented as: where arg min(·) denotes a minimization operation, Re(·) denotes a real part operation, is a term independent of x, (·) H denotes a Hermitian conjugate operator, I denotes an identity matrix; Then, the above formula is solved by the gradient projection method, and the gradient is set to zero, and the solution is obtained as: Finally, x (k+1) is updated by the following equation: Step S6, updating the communication subcarriers, specifically: For a given set {x (k+1) , X r (k) , u (k)}, the optimization problem of the minimum value of the Lagrangian augmented function with respect to X c is expressed as: where N c represents the total number of communication subcarriers, S c is a phase encoded symbol for an ideal transmission on a given communication subcarrier, x (k +1)H is the Hermitian conjugate operation on x (k+1) ; The above equation is solved by using the coordinate descent method CD, and the optimization variable is X c in the equation The signal on the communication sub-carrier is denoted by X c The N dimensional optimization problem is decomposed into one-dimensional optimization problems in an iterative manner. For the nth one-dimensional optimization problem, the value of the nth communication sub-carrier is fixed c The value of the symbol is searched from all discrete communication symbols in the set A, and the symbol value that minimizes the Lagrangian augmented function with respect to X After N c solutions are obtained, X Step S7, updating the radar subcarriers, specifically: The optimization problem of the minimum of the Lagrangian augmented function with respect to X r is expressed as: Where Re(·) denotes the real part operation, This represents the nth element of the radar sensing signal. for conjugate, Let vector The nth element is 0, and the other elements are the same as X. r Same, vector The nth element is 1, and all other elements are 0. H Represents the Hermitian conjugate operator; Let X rn = e jθ , d n = |d n |e jφ , then the optimization problem of the minimum value of the Lagrange augmented function about X r is changed into: When θ=φ-π, it is the optimal solution, so there is: where e j(·) is the complex exponential, j is the imaginary unit, and θ and φ are phase angles. Step S8, update the Lagrange multiplier, the update mode is: u (k+1) = u (k) + x (k+1) - F I (X r (k+1) + x c (k+1) ); Step S9, repeating steps S5 to S8 until the maximum number of iterations is reached.

2. The method of claim 1, wherein, The frequency domain signal of the OFDM in the step S1 is represented as X = [X1,..., XN]T. n ] T wherein n ∈ [1, N], X n represents the frequency domain signal of the nth subcarrier, and the OFDM time domain signal is x = F I X, wherein, represents a discrete signal sampling point, represents that all elements in the variable are constants, is an IDFT matrix, and is represented as: where N is the number of subcarriers, e j(·) is the complex exponential, and j is the imaginary unit.

3. The method of claim 2, wherein, If the residual error of the algorithm converges in the process of optimization iteration, the optimization cycle of the algorithm is ended.

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