An envelope peak-to-average ratio optimization method for a large-bandwidth OFDM radar-communication integrated waveform

Abstract

The application provides a PMEPR optimization method of a large-bandwidth OFDM radar communication integrated waveform, and the method is based on a reserved subcarrier method, an l p norm is introduced to remodel PMEPR under a high reservation rate as a target function that can be used for gradient analysis, the PRP conjugate gradient descent method is used to efficiently and quickly solve the target function, and the radar communication integrated waveform with good PMEPR reduction performance is obtained. The application has an important role in the actual application of the radar communication integrated waveform.

Description

Technical Field

[0001] This invention belongs to the field of radar-communication integration technology, specifically relating to a method for optimizing the envelope peak-to-average power ratio of a large-bandwidth OFDM radar-communication integrated waveform. Background Technology

[0002] To achieve efficient transmission of communication data while simultaneously detecting radar targets, OFDM signals are widely used in radar-communication integration due to their advantages such as high communication rate, high spectral efficiency, and good pulse compression performance. Furthermore, the design of OFDM-based integrated radar-communication waveforms is a hot topic in radar-communication integration research. However, a typical drawback of OFDM is its high peak-to-average power ratio (PMEPR). This causes a certain degree of nonlinear distortion when the designed integrated waveform passes through nonlinear devices such as power amplifiers, resulting in spectral distortion and a decrease in radar and communication performance.

[0003] Currently, many methods exist for reducing the PMEPR of OFDM waveforms. Among them, the reserved subcarrier-based method is a widely adopted and effective approach in the communications field, but its reservation rate (the ratio of reserved subcarriers to the total number of subcarriers) is generally low. Since large-bandwidth OFDM radar-communication integrated waveforms need to simultaneously achieve good radar detection and communication performance, the performance requirements for PMEPR reduction are high, and increasing the reservation rate is an effective technical means. Traditional reserved subcarrier-based methods generally have poor PMEPR reduction performance at high reservation rates. Therefore, it is necessary to research new PMEPR optimization methods under high reservation rates to improve the integrated performance of radar and communications. Summary of the Invention

[0004] In view of this, the present invention provides a PMEPR optimization method for a large-bandwidth OFDM radar communication integrated waveform. This method is mainly based on the reserved subcarrier method, by introducing l p - Norm, remodeling PMEPR under high reservation rate into an objective function that can be used for gradient analysis, and using the Polak-Ribière-Polyak (PRP) conjugate gradient descent method to solve the objective function efficiently and quickly, to obtain radar-communication integrated waveform with good PMEPR reduction performance, which plays an important role in the practical application of radar-communication integrated waveform.

[0005] A method for optimizing the peak-to-average power ratio (PAPR) of the envelope of a large-bandwidth OFDM radar-communication integrated waveform includes the following steps:

[0006] Step 1: Construct an integrated OFDM radar-communication signal model, specifically as follows:

[0007] For a complex-valued OFDM signal, assuming it has N subcarriers, with N of them reserved... r One subcarrier is used for communication data transmission, and the remaining subcarriers are used for communication data transmission; Let... This represents the set of indices for the reserved subcarriers among N subcarriers. Corresponding to its complement; the discrete-time OFDM signal s(n) after being upsampled by J times is:

[0008]

[0009] Where J≥4; X k and C k Let X and C represent the k-th complex modulation symbol of the communication symbol vector and the reserved symbol vector C, respectively, and satisfy the condition that... X k =0, when C k =0.

[0010] set up Formula (1) can be written in matrix form as follows:

[0011] s = s c +F R C (2)

[0012] Among them, s c =F I X represents the initial transmitted signal; F I From IDFT matrix middle The matrix F is composed of column vectors. R From IDFT matrix middle It consists of column vectors;

[0013] The PMEPR of signal s is defined as the ratio of maximum instantaneous power to average power, i.e.:

[0014]

[0015] in, P represents the average power. c This represents the total energy of the communication symbol vector X;

[0016] Step 2: Obtain the PMEPR optimization problem under high reservation rate:

[0017] Introducing l p - Norm, the PMEPR optimization problem is remodeled as follows:

[0018]

[0019] Where O(C) represents the objective function with respect to the reserved symbol vector C; s c (n) represents s c The nth element, F R,n F represents R The nth row;

[0020] Step 3: Obtain the conjugate gradient of the objective function O(C) in the optimization problem represented by formula (4) with respect to the reserved sign vector C.

[0021]

[0022] in, F R H F represents R The conjugate transpose of . Represents the Hadamard product;

[0023] Step 4: Solve the optimization problem represented by formula (4) using the conjugate gradient descent method. The update rule for the reserved symbol vector C during the iteration process is as follows:

[0024] C l+1 =C l +μ l d l (6)

[0025] Where l is the iteration number, C l and C l+1 Let d represent the reserved symbol vectors for the l-th and (l+1)-th iterations, respectively. l Indicates the direction of descent, μ l This represents the step size of the reserved symbol vector in the l-th iteration;

[0026]

[0027] in,

[0028] After each update of the reserved symbol vector C according to formula (6), determine whether the termination condition of the iterative calculation of the reserved symbol vector is met:

[0029]

[0030] The threshold ξ is selected based on the actual system requirements;

[0031] If satisfied, output the current reserved symbol vector C; if not satisfied, update the iteration count to l = l + 1, and obtain the conjugate gradient according to formula (5). Substitute into formula (7) to calculate the descent direction d lThen, the reserved symbol vector is updated according to formula (6), and so on, until the termination condition of the iterative calculation is met.

[0032] Furthermore, it also includes calculating the optimal step size of the reserved symbol vector in each iteration:

[0033] Solving for the step size can be characterized as a minimization problem, namely:

[0034]

[0035] Wherein, step size μ l The update rules are as follows:

[0036]

[0037] Where i = 1, 2, ... represents the iteration number of the step size, h'(μ l ) and h" (μ l ) are the objective functions h(μ) l Regarding step size μ l The first and second derivatives, λ∈(0,1] are the downhill factor;

[0038] According to formula (9), the step size is continuously updated during the iteration process until the iteration termination condition is met. Obtain the optimal step size

[0039] Preferably, the adjustment of the downhill factor λ satisfies the following relationship:

[0040] The present invention has the following beneficial effects:

[0041] This invention provides a PMEPR optimization method for integrated waveforms of large-bandwidth OFDM radar communication, based on the reserved subcarrier method, by introducing l p The PMEPR norm is used to remodel the PMEPR under high reservation rate into an objective function that can be used for gradient analysis. The PRP conjugate gradient descent method is then used to efficiently and quickly solve the objective function, resulting in an integrated radar-communication waveform with good PMEPR reduction performance. This plays an important role in the practical application of integrated radar-communication waveforms. Attached Figure Description

[0042] Figure 1 Flowchart of the method of this invention;

[0043] Figure 2 To optimize the time-domain plots of the waveforms before and after;

[0044] Figure 3 The iterative curve of PMEPR versus the objective function;

[0045] Figure 4 CCDF curves of PMEPR under different reservation rates. Detailed Implementation

[0046] To make the objectives, technical solutions, and advantages of the embodiments of the present invention clearer, the technical solutions of the embodiments of the present invention will be clearly and completely described below with reference to the accompanying drawings.

[0047] Consider a complex-valued OFDM signal with N subcarriers, where N are reserved. r One subcarrier is used to reduce PMEPR, and the remaining subcarriers are used for communication data transmission. The reservation rate is defined as R = N. r / N. Let This represents the index set of reserved subcarriers in {-N / 2,…,N / 2-1}. Corresponding to its complement. The discrete-time OFDM signal s(n) after being upsampled by a factor of J (J≥4) is:

[0048]

[0049] in, and Let X and C represent the k-th complex modulation symbol of the communication symbol vector and the reserved symbol vector C, respectively, and satisfy the condition that... X k =0, when C k =0.

[0050] set up Formula (1) can be written in matrix form as follows:

[0051] s = s c +F R C (2)

[0052] Among them, s c =F I X represents the initial transmitted signal. F I From IDFT matrix middle The matrix F is composed of column vectors. R From IDFT matrix middle It consists of column vectors.

[0053] The PMEPR of signal s is defined as the ratio of maximum instantaneous power to average power, i.e.:

[0054]

[0055] in, P represents the average power. cThis represents the total energy of the communication symbol vector X. According to formula (3), given the communication symbol vector X, PMEPR is only related to the reserved symbol vector C.

[0056] For the traditional PMEPR optimization problem, the reserve factor R is usually very small. In the average power calculation, we generally have E[|s(n)| 2 ]≈P c Therefore, the traditional PMEPR optimization problem is expressed as:

[0057]

[0058] in, s c (n) represents s c The nth element, F R,n F represents R The nth line.

[0059] For high-bandwidth OFDM radar-communication integrated waveforms, a feasible approach to simultaneously achieve good radar detection and communication performance is to increase the reservation rate, i.e., reserving more subcarriers to reduce PMEPR while still having enough subcarriers for communication. However, traditional methods generally perform poorly in optimizing PMEPR under high reservation rates.

[0060] Based on this, this invention proposes an efficient PMEPR optimization method based on conjugate gradients for PMEPR optimization under high reservation rates, such as... Figure 1 As shown, the specific process is as follows:

[0061] Step 1: Construct an integrated OFDM radar-communication signal model, as shown in formula (2);

[0062] Step 2: Obtain the PMEPR optimization problem under high reservation rate:

[0063] Introducing l p - Norm, the PMEPR optimization problem under high reservation rate is remodeled as follows:

[0064]

[0065] Where O(C) represents the objective function with respect to the reserved symbol vector C;

[0066] Step 3: Obtain the conjugate gradient of the objective function in problem (5) with respect to the reserved symbol vector C.

[0067]

[0068] in, F R HF represents R The conjugate transpose of . This represents the Hadamard product.

[0069] Step 4: Solve the optimization problem (5) using the conjugate gradient descent method. The update rule for the reserved symbol vector C during the iteration process is as follows:

[0070] C l+1 =C l +μ l d l (7)

[0071] Where l is the iteration number, C l and C l+1 Let d represent the reserved symbol vectors for the l-th and (l+1)-th iterations, respectively. l Indicates the direction of descent, μ l This represents the step size of the reserved symbol vector in the i-th iteration.

[0072] During the iteration process, to ensure the effective implementation of the PMEPR optimization method, a modified descent direction is adopted, namely the PRP descent direction:

[0073]

[0074] in,

[0075] After each update of the reserved symbol vector C, determine whether the termination condition for the iterative calculation of the reserved symbol vector is met:

[0076]

[0077] The threshold ξ is selected based on the actual system requirements.

[0078] If the condition is not met, the update iteration count is l = l + 1, and the conjugate gradient is obtained according to formula (6). Substitute into formula (8) to calculate the descent direction d l Then, the reserved symbol vector is updated according to formula (7), and so on, until the termination condition of the iterative calculation is met. If the condition is met, the current reserved symbol vector C is output, and the OFDM radar communication integrated transmission signal can be obtained.

[0079] In this invention, to increase the PMEPR optimization rate, a method is also provided for calculating the optimal step size of the reserved symbol vector in each iteration. The method is as follows:

[0080] To quickly obtain the optimal step size, the step size solution is characterized as a minimization problem, namely:

[0081]

[0082] The Newton downhill method is used to solve problem (9). Among them, the step size μ l is updated according to the following rule:

[0083]

[0084] Here, i = 1, 2,... represents the iteration number sequence of the step size μ l , h'(μ l ) and h”(μ l ) are the first-order derivative and second-order derivative of the objective function h(μ l ) with respect to the step size μ l respectively. λ ∈ (0, 1] is the downhill factor, which needs to be dynamically adjusted to meet

[0085] According to formula (10), by continuously updating the step size during the iteration until it meets the iteration termination condition the optimal step size can be obtained

[0086] In the present invention, at a high reservation rate, since the denominator in formula (3) is irreducible, it is difficult to directly optimize PMEPR. By introducing the l p -norm, an optimization problem (5) that can be subjected to gradient analysis is obtained. Here, according to the definition of the l p -norm, there is That is, by approximating PMEPR with the l p -norm with a relatively large p, PMEPR < O(C) can be obtained, where p < ∞. Therefore, according to steps 3 - step 4, by solving problem (5), a lower PMEPR can be obtained.

[0087] Next, the method of the present invention is verified by simulation. The specific parameters of the simulation are shown in Table 1:

[0088] Table 1 Simulation parameters

[0089] Parameter numerical values unit Pulse width 10 μs bandwidth 100 MHz Sampling rate 400 MHz Number of subcarriers 1000 indivual Communication symbol modulation method 16QAM reservation rate R

[0090] Let Randomly generate 10 5 initial OFDM symbols modulated by 16QAM, where the reserved symbol vector is 0, that is, C 0 = 0. Let ξ be the peak value of the initial OFDM symbol.

[0091] 1. Simulation results with a reservation rate R = 50%

[0092] Let p = 20. Randomly select an initial OFDM symbol, and obtain the time-domain diagrams of the waveforms before and after optimization, as shown in Figure 2As shown, the PMEPR of the optimized waveform decreased from 9.2dB to 1.5dB, the peak power remained almost the same as before optimization, and the average power increased significantly. This indicates that the method described in this invention can effectively reduce PMEPR, improve power amplifier efficiency, and thus achieve better radar detection performance. Furthermore, since the communication data remains unchanged before and after optimization, this also demonstrates that the method proposed in this invention does not degrade communication bit error rate performance.

[0093] The PMEPR and objective function of optimization problem (5) obtained by the method of this invention, and the iteration curves with respect to the number of iterations are as follows: Figure 3 As shown, the objective function decreases monotonically with the number of iterations (as shown on the right axis), and the PMEPR (as shown on the left axis) remains below the objective function value. This is consistent with the theoretical analysis above, and the performance improvement achieved by reducing the PMEPR can be obtained with only a small number of iterations.

[0094] 2. Simulation results under different reservation rates

[0095] The reduction level of PMEPR was analyzed at different reservation rates, namely R=10%, R=50%, and R=90%. PMEPR is typically evaluated using the Complementary Cumulative Distribution Function (CCDF). The resulting CCDF curve is shown below. Figure 4 As shown in the figure. It can be seen that under the three reservation rates, CCDF=10 -4 At that time, the PMEPR of the initial OFDM symbols did not differ significantly. The PMEPR obtained using the method of this invention decreased with increasing reservation rate, by 5.5 dB, 3.2 dB, and 2.4 dB, respectively. This indicates that, depending on the different requirements of the system for radar and communication performance, the method of this invention can achieve good PMEPR reduction performance.

[0096] The simulation results above show that, under a high reservation rate, the method of this invention can efficiently generate radar-communication integrated waveforms with low PMEPR.

[0097] In summary, this invention proposes a PMEPR optimization method for a large-bandwidth OFDM radar-communication integrated waveform, which can obtain a radar-communication integrated waveform with better PMEPR reduction performance, and plays an important role in the practical application of radar-communication integrated waveforms.

[0098] In summary, the above are merely preferred embodiments of the present invention and are not intended to limit the scope of protection of the present invention. Any modifications, equivalent substitutions, improvements, etc., made within the spirit and principles of the present invention should be included within the scope of protection of the present invention.

Claims

1. A method for optimizing the envelope peak-to-average power ratio of a large-bandwidth OFDM radar-communication integrated waveform, characterized in that, Comprising the following steps: Step 1, constructing an OFDM radar communication integrated signal model, specifically: For a complex-valued OFDM signal, let it have N subcarriers, of which N r subcarriers are reserved, and the remaining subcarriers are used for data transmission; Let S denote the set of indices of the reserved subcarriers among the N subcarriers, and S its complement. The discrete-time OFDM signal s(n) after J times upsampling is: where J > 4; X k and C k denote the kth complex modulation symbol of the communication symbol vector X and the reserved symbol vector C, respectively, and satisfy X X k = 0 when C k = 0; Let Equation (1) can be written in matrix form as: s = s c +F R C (2) Among them, s c =F I X represents the initial transmitted signal; F I From IDFT matrix middle The matrix F is composed of column vectors. R From IDFT matrix middle It consists of column vectors; The PMEPR of the signal s is defined as the ratio of the maximum instantaneous power to the average power, that is: wherein, denotes the average power, P c denotes the total energy of the communication symbol vector X; Step 2, obtaining the PMEPR optimization problem under high reservation rate: Introduction l p - norm, the PMEPR optimization problem is reformulated as: where O(C) denotes an objective function with respect to the reserved symbol vector C; s c (n) denotes the nth element of s c F R,n denotes the nth row of F R ​ Step 3, obtain the conjugate gradient of the objective function O(C) with respect to the reserved symbol vector C in the optimization problem represented by equation (4) wherein F R H denotes the conjugate transpose of F R "o" denotes the Hadamard product;​ Step 4, solving the optimization problem represented by formula (4) by using the conjugate gradient descent method, and the update rule of the reserved symbol vector C in the iteration process is: C l+1 = C l + μ l d l (6) where l is the iteration number, C l and C l+1 denote the reserved symbol vectors at the lth and (l+1)th iteration, respectively, d l denotes the descent direction, μ l denotes the step size of the reserved symbol vector at the lth iteration; wherein After updating the reserved symbol vector C according to formula (6) each time, it is judged whether the termination condition of the reserved symbol vector iteration calculation is satisfied: Wherein, the threshold value ξ is selected according to the actual system requirement; If satisfied, output the current reserved sign vector C; if not satisfied, update the iteration number as l = l + 1, and obtain the conjugate gradient d according to formula (5) Substitute formula (7) to calculate the descending direction d l , and then update the reserved sign vector according to formula (6), and so on until the termination condition of the iteration calculation is satisfied.

2. The method of claim 1, wherein the PAPR of the large bandwidth OFDM radar communication integrated waveform is optimized by, Also including calculating the optimal step size of the reserved symbol vector in each iteration process: The step size solving is characterized as a minimization problem, that is: wherein the step size μ l The update rule is: wherein i = 1, 2,... represents the iteration number of the step size, h'(μ l ) and h''(μ l ) are the first and second derivatives of the objective function h(μ l ) with respect to the step size μ l , and λ ∈ (0, 1] is the step-down factor; According to formula (9), by constantly updating the step size in the iteration process until it meets the iteration termination condition get the optimal step size 3. The method of claim 2, wherein the PAPR of the large bandwidth OFDM radar communication integrated waveform is optimized by, The adjustment of the hill factor λ satisfies the following relationship:

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