Satellite-ground communication inductance integrated waveform design method based on subcarrier optimization

Abstract

The invention discloses a subcarrier optimization-based satellite-to-ground sensing integrated waveform design method, which comprises the following steps of: 1, modeling an OFDM (Orthogonal Frequency Division Multiplexing) signal: for a frequency domain sequence of the OFDM signal, utilizing inverse Fourier transform to obtain a corresponding time domain sequence; step 2, establishing constraint conditions of communication subcarrier and radar subcarrier sequence modeling and optimization problems; the communication index comprises a bit error rate and a communication rate, and the radar index is an integral sidelobe ratio; constraint conditions of the optimization problem comprise total energy constraint and PAPR constraint; step 3, optimizing communication subcarrier and radar subcarrier resources; 4, on the basis of resource optimization of the communication subcarrier and the radar subcarrier, frequency domain sequence optimization is carried out; and step 5, according to the resource optimization result of the communication subcarrier and the radar subcarrier obtained in the step 3 and the time domain sequence optimization result obtained in the step 4, obtaining a communication and inductance integrated waveform. The method provided by the invention can obtain the integrated waveform design with compatible performance, cost and feasibility at the same time.

Description

Technical Field

[0001] The present invention belongs to the field of integrated communication and sensing waveform design, and particularly relates to a space-ground integrated communication and sensing waveform design method based on subcarrier optimization. This method combines subcarrier division and the degrees of freedom of sequence symbols, and completes the integrated communication and sensing waveform design by first performing subcarrier resource allocation and then optimizing sequence symbols. After appropriate modification, it is also applicable to other integrated waveform design criteria and has broad application prospects. Background Technique

[0002] In order to meet the information-based combat requirements for the future, one of the development trends of military electronic systems is the integration of multi-functional electronic systems. As a typical representative, the integration of communication and radar has important application values in weaponry, civil aviation, networked radars, etc. It can achieve resource sharing, save platform space, and reduce mutual interference between electronic systems, thereby enhancing the comprehensive effectiveness of electronic systems. Waveform design is the key technology for realizing the integration of communication and radar, and its design goal is that the integrated waveform can both transmit information and be used for radar sensing. If the integrated waveform design is classified from the perspective of signal processing, it can be divided into integrated waveform design mainly for communication functions, integrated waveform design mainly for radar functions, and integrated waveform design combining communication and radar functions. Among these three categories, the integrated waveform design mainly for communication can be compatible with existing communication networks, has low implementation cost, and is conducive to engineering implementation. In this type of design, the orthogonal frequency division multiplexing (OFDM) waveform has advantages such as high spectral efficiency and the ability to combat inter-symbol interference. Therefore, the integrated design based on the OFDM waveform has received extensive attention.

[0003] Communication and radar are two of the most representative typical applications in modern radio systems. Communication is mainly used to transmit information between different devices, and the key is to transmit information efficiently and correctly; while radar is mainly used for target detection, and the key is to be able to capture targets timely and effectively. Communication and radar have many similarities, such as both obtaining information by receiving and processing transmitted signals; both using radio electromagnetic waves as the carrier of information, etc. At the same time, there are many differences between them, such as the purpose of communication is to recover the transmitted signal, while radar emphasizes more on the extraction of target information; communication needs to transmit random signals, while radar needs to transmit deterministic signals, etc.

[0004] With the development of modern radio technology, on the one hand, the hardware systems of communication and radar equipment tend to be the same whether in the radio frequency front-end architecture or the data acquisition at the receiving end; on the other hand, the exponential increase in modern electronic devices has led to frequency band congestion in terms of transmission bandwidth and spectrum allocation. In this context, the integrated communication and radar technology is one of the typical development trends of future electronic systems. The integrated communication and sensing technology can significantly improve the spectrum utilization rate, and at the same time achieve the goals of reducing production and maintenance costs, saving platform space, and reducing system energy consumption by sharing equipment. In the military aspect, the integrated technology can meet the diverse needs of future battlefield operations, while in the civilian aspect, the autonomous driving driven by the integrated technology is bringing a new revolution to the traditional transportation mode.

[0005] The integrated communication and sensing technology can be classified from multiple perspectives. Here, from the perspective of signal processing waveform design, it is divided into three types, namely, the integrated waveform design mainly for communication functions, the integrated waveform design mainly for radar functions, and the integrated waveform design combining communication and radar functions.

[0006] In the integrated waveform design mainly for communication, radar sensing is integrated into the existing communication system as an auxiliary function. It may be necessary to improve and enhance the existing communication infrastructure, but the core communication signals and communication protocols generally remain unchanged. The integrated design mainly for communication can be further divided into three categories: based on spread spectrum technology, based on OFDM waveform, and based on communication standards. The characteristic of constant modulus of the sequence in spread spectrum technology is particularly suitable for high-power radar detection, but the hardware implementation cost is high; the OFDM waveform has the advantages of high spectrum efficiency and the ability to combat inter-symbol interference, and is widely used in the communication field. Levanon et al. first studied the method of using the OFDM waveform for detection. The peak-to-average ratio of the OFDM waveform is relatively high, which limits its own power efficiency in high-power radar detection. The system based on communication standards uses the pilots in the current standards for detection, including the common communication standards IEEE 802.11p and IEEE 802.11ad. However, due to the use of some pilots, the detection power is also limited to a certain extent in power-constrained scenarios.

[0007] In the integrated waveform design dominated by radar, noting that the advantage of the radar system is the ability to perform long-range detection up to hundreds of kilometers, one of the advantages brought by this type of design is the ability to perform low-latency and long-range communication. However, the data rate of the integrated system under this type of design is often limited by the radar waveform. The radar-based waveform integration design can be further divided into two categories: original waveform modification and index modulation. Original waveform modification can embed communication information in the time-frequency domain, coding domain, and spatial domain. Maintaining the constant modulus condition of the waveform will compromise unambiguous detection and communication rate, while destroying the constant modulus condition of the waveform will make the waveform inapplicable to high-power transmission scenarios. The resources of index modulation include carrier frequency, transmission time slot, antenna selection, and orthogonal waveforms, etc. However, the index modulation demodulation process is complex, and the system performance will be affected. The integrated design based on radar waveforms needs to use radar waveform decoding for communication, which increases the complexity of the communication receiver and cannot be compatible with existing communication systems. Therefore, this type of design is more used as a supplement to waveform design methods.

[0008] In the integrated waveform design of joint communication-radar functions, there is no clear boundary with the previous two design schemes, and there is more freedom in terms of signal and system design. This type of design is not limited by existing communication and radar systems and can be designed and optimized to balance communication and radar requirements. The integrated waveform design of joint communication-radar functions can be further divided into three categories: waveform optimization type, spatial domain beamforming type, and time-frequency joint design type. The waveform optimization type jointly designs the communication-sensing integrated waveform through some typical performance criteria of radar and communication, such as optimization based on signal to interference-plus-noise ratio (SINR), optimization based on Cramer-Rao lower bound (CRLB), optimization based on mutual information, and optimization based on similarity, etc. The spatial domain beamforming type can overcome the spectrum congestion problem in the communication-sensing integrated waveform. Typical methods include precoding design, multi-beam optimization, and hybrid beamforming, etc. The time-frequency joint design type designs the communication-sensing integrated waveform from the perspective of time domain and frequency domain division, including modifying the time domain communication frame signal, dividing the frequency domain subcarriers, etc. Generally speaking, the integrated waveform design of joint communication-radar functions is more complex, but at the same time, it is demand-driven in design and thus more flexible.

[0009] Among the above three types of waveform designs, the integrated waveform design dominated by communication can be compatible with existing communication networks, greatly reducing costs and improving engineering feasibility. The OFDM waveform has the advantages of high spectral efficiency and the ability to combat inter-symbol interference, etc., and has received extensive attention. However, the existing communication-sensing waveform integration design methods focus on the condition of fixed subcarrier division and do not consider the benefits brought by subcarrier division to the integrated waveform design.

[0010] To this end, the present invention combines subcarrier division and the degrees of freedom of sequence symbols to optimize the integrated communication radar waveform design. By first allocating communication subcarriers and radar subcarriers in the frequency band and then optimizing the sequence symbols, a space-ground integrated communication and sensing waveform design method based on subcarrier optimization is proposed to obtain an integrated communication and sensing waveform design that can simultaneously be compatible with performance, cost, and feasibility. Summary of the Invention

[0011] The technical problem solved by the present invention is: by first allocating communication subcarriers and radar subcarriers in the frequency band and then optimizing the sequence symbols, a space-ground integrated communication and sensing waveform design method based on subcarrier optimization is proposed to obtain an integrated communication and sensing waveform design that can simultaneously be compatible with performance, cost, and feasibility.

[0012] The technical solution of the present invention is:

[0013] A space-ground integrated communication and sensing waveform design method based on subcarrier optimization specifically includes the following steps:

[0014] Step 1, OFDM signal modeling: For the frequency-domain sequence of the OFDM signal, use the inverse Fourier transform to obtain the corresponding time-domain sequence;

[0015] Step 2, modeling of communication subcarrier and radar subcarrier sequences and constraint conditions for the optimization problem; communication metrics include bit error rate and communication rate, and the radar metric is the integrated side lobe ratio; the constraint conditions for the optimization problem include total energy constraint and PAPR constraint;

[0016] Step 3, optimization of communication subcarrier and radar subcarrier resources;

[0017] Step 4, based on the optimization of communication subcarrier and radar subcarrier resources, perform frequency-domain sequence optimization;

[0018] Step 5, according to the resource optimization results of communication subcarriers and radar subcarriers obtained in Step 3 and the time-domain sequence optimization results of Step 4, obtain the integrated communication and sensing waveform.

[0019] The beneficial effects of the present invention compared with the prior art are:

[0020] (1) A method for optimizing the ISLR of the integrated communication and sensing waveform by combining subcarrier division and the degrees of freedom of sequence symbols under PAPR constraint conditions is proposed. This method additionally introduces the degrees of freedom of subcarrier allocation, which can significantly reduce the ISLR of the designed waveform and has good engineering application prospects.

[0021] (2) A subcarrier partitioning method (step 3) is proposed. This method innovatively utilizes the characteristics that the phase of the frequency-domain interpolation filter coefficients is linear and has cyclic shift. By rearranging and allocating the phases of the frequency-domain sequences, the waveform ISLR can be significantly reduced. At the same time, it also provides an initial waveform for sequence optimization, which is convenient for engineering implementation.

[0022] (3) A radar sequence optimization method under fixed communication symbols (step 4) is proposed. This method corrects the optimization of the waveform ISLR using all frequency-domain components in the CAN method to the optimization of the waveform ISLR using partial frequency-domain components, providing a suboptimal iterative solution for minimizing the waveform ISLR under the PAPR constraint condition, which can converge quickly and save the system operation cost.

[0023] In summary, the method of the present invention can obtain a communication-sensing integrated waveform design that can simultaneously be compatible with performance, cost, and feasibility. BRIEF DESCRIPTION OF THE DRAWINGS

[0024] Figure 1 It is a flowchart of a space-ground communication-sensing integrated waveform design method based on subcarrier optimization.

[0025] Figure 2 It is the spectrum resource allocation before and after subcarrier optimization. (a) Before subcarrier optimization. (b) After subcarrier optimization.

[0026] Figure 3 It is the normalized autocorrelation function under different methods. DETAILED DESCRIPTION OF THE EMBODIMENTS

[0027] The following is a further detailed description of the implementation of the present invention.

[0028] The usage scenario of the present invention is as follows:

[0029] The space-ground communication-sensing integrated waveform design method based on subcarrier optimization in the present invention can be applied to the field of communication-sensing integration. This method combines the degrees of freedom of subcarrier partitioning and sequence symbols, and completes the communication-sensing integrated waveform design by first performing subcarrier resource allocation and then optimizing the sequence symbols. Introducing the subcarrier degree of freedom can significantly reduce the ISLR, and has a very broad application prospect. The implementation steps are as follows:

[0030] Step 1, OFDM signal modeling.

[0031] Consider a Com-Rad system using OFDM signals under the 5G-NR standard for OFDM signal modeling. Under this standard, 1 basic frame can be divided into 10 subframes, and the subframes can be further divided into different numbers of time slots. The number of symbols in each time slot is the same, all being 14 OFDM symbols. In one OFDM symbol, the frequency-domain sequence is denoted as z = [z 1 , z 2,…,z N T , where \(N\) represents the number of subcarriers in a single OFDM symbol. According to the communication and sensing resource requirements, we further divide the frequency-domain subcarriers into communication subcarriers and radar subcarriers, denoted by \(z\) c and \(z\) r respectively, that is, \(z = \{z\) c ,z\) r \}, and the numbers of communication subcarriers and radar subcarriers are \(N\) c and \(N\) r respectively, and \(N = N\) c +N\) r . For the frequency-domain sequence of the OFDM signal, the corresponding time-domain sequence can be obtained by using the inverse Fourier transform and written as:

[0032]

[0033] where \(x\) n represents the \(n\)th element of the time-domain sequence of the OFDM signal, \(n = 1, 2,\cdots, L\),

[0034]

[0035] represents the Fourier transform matrix, and \(W\) N =e\) -j(2π / N) .

[0036] Step 2, Modeling and Constraining of Communication Subcarrier and Radar Subcarrier Sequences.

[0037] In the integrated communication and sensing waveform design dominated by communication, communication metrics are the primary guarantee, and on this basis, radar metrics are optimized. This type of design can be applied to the modified existing communication network, with high engineering practicability, and the communication rate will be affected to a certain extent. Communication metrics mainly include bit error rate and communication rate, radar metrics mainly refer to the integrated sidelobe level ratio (ISLR), and in addition, system metrics mainly refer to the peak-to-average power ratio (PAPR).

[0038] For communication subcarriers, the quadrature phase shift keying (QPSK) digital modulation method is adopted, and its bit error rate in the additive complex white Gaussian noise (AWGN) channel is:[[]]

[0039]

[0040] In the formula, \(\gamma = E\) b ​ / N 0 denotes the signal-to-noise ratio, where E b and N 0 are the signal power and the noise power (known data), respectively;

[0041]

[0042] denotes the right-tail function (Q-function) of the standard normal distribution;

[0043] The signal-to-noise ratio γ needs to satisfy:

[0044]

[0045] In the formula, denotes the bit error rate index (i.e., the bit error rate). Since we have allocated some subcarriers for radar detection, the communication rate will inevitably decrease within a certain range, and it is necessary to make a trade-off in the index design.

[0046] For radar subcarriers, target detection is the main task, while high signal sidelobes will cause sidelobe interference and main-lobe target competition, seriously affecting radar performance. To reduce signal sidelobes, the method of the present invention combines subcarrier allocation and OFDM frequency-domain sequence optimization for ISLR. The objective function of the optimization problem can be written as:

[0047]

[0048] In the formula, denotes the frequency set composed of the digital frequency points of radar subcarriers, is the number of radar frequency points after 2-fold interpolation, denotes the frequency set composed of the digital frequency points of communication subcarriers, is the number of communication frequency points after 2-fold interpolation, and constitutes the total digital frequency set U of frequency points,

[0049]

[0050] and

[0051]

[0052] denote the 2-fold interpolated Fourier matrices corresponding to communication subcarriers and radar subcarriers, respectively, where:

[0053] a(ω) = [1, e jω , …, e j2Nω T (9)

[0054] is the filter tap coefficient of frequency ω, ​Represents the phase of the Gerchberg - Saxton equivalent vector corresponding to the radar sub - carrier, Represents the phase of the Gerchberg - Saxton equivalent vector corresponding to the communication sub - carrier, then there is:

[0055]

[0056] and

[0057]

[0058] z(Μ) represents the rearranged sub - carrier set Μ.

[0059] The constraint conditions of the optimization problem include the total energy constraint and the PAPR constraint. Constraining the energy of a single communication sub - carrier to be unit energy, the total signal energy constraint can be expressed as:

[0060]

[0061] The PAPR constraint can avoid the signal having too large a peak - to - average power ratio and reduce the hardware burden. Constraining the PAPR of the signal not to exceed a certain threshold ρ, written as:

[0062] PAR(x)≤ρ (13)

[0063] Where:

[0064]

[0065] In the formula, x n represents the n - th element of the time - domain sequence of the OFDM signal, n = 1, 2, …, L.

[0066] Directly solving this constrained optimization problem involves a joint search of multi - dimensional variables. When the number of variable dimensions is large, this problem is a non - deterministic polynomial - time problem (NP - Hard). Therefore, we divide this problem into the following two steps, step 3 and step 4, for solution.

[0067] Step 3, communication sub - carrier and radar sub - carrier resource optimization.

[0068] Under the condition of initializing the frequency - domain sequence, perform communication sub - carrier and radar sub - carrier resource optimization. The communication symbols use QPSK modulation, and the radar sequence uses a constant - modulus random sequence with a uniform phase distribution. According to the interpolation formula: for a sequence that satisfies the Nyquist sampling theorem, for an unsampled signal, it can also be obtained from the sampled signal through the interpolation formula, then

[0069] A H y = B H z (15)

[0070] In the formula

[0071]

[0072] Extract the odd and even columns of matrix B to form matrix B o and B e then

[0073] B o ≈I N (17)

[0074] It means that the signal component at the current frequency point is only determined by the current frequency point.

[0075]

[0076] It means that the signal component at the interpolated frequency point will be obtained by weighting all frequency points, and the weights are determined by the coefficients calculated by the interpolation formula. B e is a circulant matrix, and the cyclic shift sequence b e has a symmetric amplitude sequence and a linear phase sequence. Minimizing the ISLR can be equivalent to:[[]]

[0077]

[0078] where b ej =B e (:,j). Equation (19) requires that the interpolated spectrum be uniform and the power be close to N. We construct the sequence as follows. Rearrange the frequency-domain sequence z in ascending order of phase, and split the sequence into 4 subsequences z 1 、z 2 、z 3 and z 4 , and extract 1 symbol from each subsequence in turn to form a new sequence, written as:[[]]

[0079]

[0080]

[0081] In this sequence, the internal phase difference of each subsequence remains constant, and there is only a common phase difference between subsequences, so as to obtain an approximately uniform power spectrum.

[0082] Step 4, optimization of the frequency-domain sequence.

[0083] Based on the communication subcarriers and radar subcarriers allocated in step 3, optimize the frequency-domain sequence. The problem of minimizing ISLR formulated by equations (6), (12) and (13) degenerates into

[0084]

[0085] where Different from optimizing the overall sequence in the Cyclic Algorithm New (CAN) algorithm, in problem (21), it is required that the communication symbols in the frequency-domain sequence are fixed, and only the remaining frequency-domain sequence can be optimized. We give an iterative solution under the condition of fixed communication symbols.

[0086] First, in the j-th iteration process, first fix x (j) , and the corresponding to the minimum objective function is written as:

[0087]

[0088] where arg(·) represents the phase-taking operation, and v can be determined by . Then fix v (j) , and obtain the transmitted waveform x (j) corresponding to the minimum objective function. Under the PAPR constraint, Tropp derived the solution of the transmitted waveform x (j) . Sort the transmitted waveform according to the energy magnitude. First, limit the modulus values of the first u elements to the maximum modulus value under the PAPR constraint, and then evenly distribute the remaining energy to the remaining (N - u) elements using the waveform energy constraint, which is expressed as: (j)

[0089]

[0090] In the formula, represents the maximum modulus value under the PAPR constraint, and

[0091]

[0092] represents the modulus value under the even distribution of the remaining energy. The above solution process needs to use a loop to traverse and optimize u from 1 to N to find the time-domain sequence waveform x o that satisfies the PAPR constraint.

[0093] Step 5, obtain the integrated communication and sensing waveform.

[0094] According to the resource optimization results of the communication subcarriers and radar subcarriers obtained in step 3 and the time-domain sequence optimization results in step 4, the frequency-domain representation of the designed integrated communication and sensing waveform can be obtained:

[0095] z o = [z o1 , z o2 , …, z oN T = F H x o (25).

[0096] ​The effects of the present invention are further illustrated below through simulation data.

[0097] Consider a communication-sensing integrated network with transmit-and-receive sharing. Assume that under the 5G-NR standard, an OFDM symbol contains N = 512 subcarriers. The subcarriers can be divided for the allocation of communication and radar frequency-domain resources, and the sequence length L = 512. For communication, the transmitted information is digitally modulated by QPSK and then modulated onto each communication subcarrier. The number of communication subcarriers is N c = 480; for radar, the initial sequence is selected as a constant-modulus random sequence. The number of radar subcarriers is N r = 32, and the PAPR constraint is limited to ρ = 2.5.

[0098] Table 1 presents the results before and after the optimization of the OFDM signal sequence. It can be seen that the PAPR before optimization is 6.88, and the large PAPR increases the hardware burden. After optimization, the PAPR is 2.5, which meets the design constraint conditions. We define the normalized ISLR as the ISLR calculated when r(0) = 1. It can be seen that the ISLR before optimization is -5.03 dB. After subcarrier division and frequency-domain sequence optimization, the ISLR drops to -8.66 dB, a decrease of approximately 3.6 dB. The proposed waveform design method can significantly reduce the sidelobes of the sequence under the agreed PAPR constraint.

[0099] Table 1

[0100]

[0101] Figure 2 The spectrum resource allocation results before and after subcarrier optimization are given. The red color represents the positions of radar subcarriers, and the blue color represents the positions of communication subcarriers. It can be seen that after optimization, the positions of communication subcarriers and radar subcarriers become more concentrated, and the radar subcarriers are near the digital zero frequency. The automatic clustering phenomenon of subcarriers can be explained by the fact that the constant-modulus degree of the interpolated spectrum determines the ISLR of the designed sequence. Although a lower ISLR can be obtained through subcarrier optimization, this sequence does not meet the PAPR constraint, but it can be used as the initial sequence for subsequent radar frequency-domain sequence optimization.

[0102] Figure 3The comparison of the normalized autocorrelation sidelobes of frequency-domain sequence optimization and joint subcarrier partitioning and frequency-domain sequence optimization is given, where the black dashed line represents the result of frequency-domain sequence optimization, and the red solid line represents the result of joint subcarrier partitioning and frequency-domain sequence optimization. It can be seen that due to having more degrees of freedom in subcarrier partitioning, joint subcarrier partitioning and frequency-domain sequence optimization can obtain a more uniform interpolated spectrum, and the autocorrelation sidelobes are significantly reduced. The latter is reduced by about 3.2 dB compared to the former. It should be noted that the main lobe of the autocorrelation after joint subcarrier partitioning and frequency-domain sequence optimization is slightly broadened, and the range resolution of radar detection will be slightly lost.

[0103] Simulation analysis and conclusion: The present invention aims at the integrated space-ground remote sensing and communication waveform design, and jointly optimizes the integrated waveform mainly for communication by subcarrier partitioning and sequence symbol degree of freedom optimization. It mainly includes three steps:

[0104] 1) Formulate the problem of minimizing the ISLR for joint subcarrier partitioning and frequency-domain sequence optimization under the PAPR constraint;

[0105] 2) Optimize the partitioning of communication subcarriers and radar subcarriers by means of sequence phase rearrangement and allocation;

[0106] 3) Optimize the sequence symbols corresponding to the radar subcarriers under the condition of fixed subcarrier partitioning to obtain the integrated remote sensing and communication waveform.

[0107] The method proposed in the present invention combines subcarrier partitioning and sequence symbol degree of freedom. Under the initial conditions of QPSK digital modulation for communication and random phase sequence for radar, after joint optimization, under the PAPR constraint condition, the ISLR can be reduced by about 3.6 dB, providing a good solution for the integrated remote sensing and communication waveform design.

Claims

1. A satellite-ground synaesthesia integrated waveform design method based on subcarrier optimization, characterized in that: The specific steps include: Step 1, OFDM signal modeling: For the frequency domain sequence of the OFDM signal, use inverse Fourier transform to obtain the corresponding time domain sequence; Step 2: Modeling of communication subcarrier and radar subcarrier sequences and constraints of optimization problems; communication indicators include bit error rate and communication rate, and radar indicators are integrated sidelobe ratio; constraints of optimization problems include total energy constraints and PAPR constraints; Step 3: Optimize communication subcarrier and radar subcarrier resources; Step 4: Based on the optimization of communication subcarrier and radar subcarrier resources, frequency domain sequence optimization is performed; Step 5, according to the resource optimization results of the communication subcarrier and the radar subcarrier obtained in step 3 and the time domain sequence optimization result in step 4, the synaesthesia integrated waveform is obtained.

2. The satellite-ground synaesthesia integrated waveform design method based on subcarrier optimization according to claim 1, characterized in that: In step 1, the OFDM signal modeling is performed using the Com-Rad system of OFDM signals. Under this standard, a basic frame can be divided into 10 subframes, and the subframes are further divided into different numbers of time slots. The number of symbols in each time slot is the same, which is 14 OFDM symbols. In an OFDM symbol, the frequency domain sequence is denoted as z = [z1, z2, …, z N ] T , where N represents the number of subcarriers in a single OFDM symbol; the frequency domain subcarriers are divided into communication subcarriers and radar subcarriers, respectively. c and z r It means that z={z c ,z r }, the number of communication subcarriers and radar subcarriers are N c 、N r , and N=N c +N r ; Use inverse Fourier transform on the frequency domain sequence of OFDM signal to obtain the corresponding time domain sequence, written as: Among them, x n The nth element of the time domain sequence of the OFDM signal, n = 1, 2, ..., L, represents the Fourier transform matrix, W N =e -j(2π / N) .

3. The satellite-ground synaesthesia integrated waveform design method based on subcarrier optimization as claimed in claim 2, characterized in that: In step 2, the communication index includes bit error rate and communication rate, and the radar index refers to the integrated sidelobe ratio ISLR; For the communication subcarrier, the orthogonal phase shift keying digital modulation method is adopted, and its bit error rate in the additive complex Gaussian white noise channel is: Where γ = E b / N0 represents the signal-to-noise ratio, where E b and N0 are signal power and noise power respectively; Represents the right tail function of the standard normal distribution; The signal-to-noise ratio γ must satisfy: In the formula, Indicates the bit error rate indicator; For radar subcarriers, joint subcarrier partitioning and OFDM frequency domain sequence optimization ISLR, the objective function of the optimization problem is written as: In the formula, Represents the frequency set composed of radar subcarrier digital frequency points, is the number of radar frequency points after 2 times interpolation, Represents the frequency set composed of the digital frequency points of the communication subcarriers, is the communication frequency point number after 2 times interpolation, and Constitute a total The digital frequency collection U of frequency points, and Represent the 2-fold interpolation Fourier matrices corresponding to the communication subcarrier and radar subcarrier, respectively, where: a(ω)=[1,e jω ,…,And j2Nω ] T (9) is the filter tap coefficient for frequency ω, represents the phase of the Gerchberg-Saxton equivalent vector corresponding to the radar subcarrier, Represents the phase of the Gerchberg-Saxton equivalent vector corresponding to the communication subcarrier, then: and z(Μ) represents the rearranged subcarrier set Μ; The constraints of the optimization problem include total energy constraint and PAPR constraint. If the energy of a single communication subcarrier is constrained to be unit energy, the total signal energy constraint is expressed as: PAPR constraint: constrain the signal PAPR not to exceed a certain threshold ρ, written as: PAR(x)≤ρ (13) in: In the formula, x n Represents the nth element of the time domain sequence of the OFDM signal, n = 1, 2, …, L.

4. The satellite-ground synaesthesia integrated waveform design method based on subcarrier optimization as claimed in claim 3 is characterized in that: In step 3: Under the condition of initializing the frequency domain sequence, the communication subcarrier and radar subcarrier resources are optimized; the communication symbol adopts QPSK modulation, and the radar sequence adopts a constant modulus random sequence with uniform phase distribution; according to the interpolation formula: for the sequence that satisfies the Nyquist sampling theorem, for the unsampled signal, the interpolation formula is obtained according to the sampled signal, then A H y=B H z (15) In the formula Extract the odd and even columns of matrix B to form matrix B o and B e ,but B o ≈I N (17) Indicates that the current frequency signal component is determined only by the current frequency; It means that the frequency signal component after interpolation will be obtained by weighting all the frequency points, and the weight is determined by the coefficient calculated by the interpolation formula; B e is a circulant matrix, and the cyclic shift sequence b e The amplitude is a symmetrical sequence and the phase is a linear phase sequence; minimizing ISLR is equivalent to: Where b ej =B e (:, j); Formula (19) requires that the interpolated spectrum is uniform and the power is close to N. We construct the sequence as follows: rearrange the frequency domain sequence z from small to large phase, and split the sequence into 4 subsequences z1, z2, z3 and z4. Extract one symbol from each subsequence in turn to form a new sequence, written as: In this sequence, the internal phase difference of each subsequence remains constant, and only a common phase difference exists between subsequences, thereby obtaining an approximately uniform power spectrum.

5. The satellite-ground synaesthesia integrated waveform design method based on subcarrier optimization as claimed in claim 4 is characterized in that: In step 4, the ISLR minimization problem planned by equations (6), (12) and (13) is reduced to: In the formula, Different from optimizing the whole sequence in the new periodic algorithm, problem (21) requires that the communication symbols in the frequency domain sequence be fixed, and only the remaining frequency domain sequence can be optimized. Here, an iterative solution under the condition of fixed communication symbols is given; First, in the jth iteration, x is fixed (j) , the minimum corresponding objective function Written as: Among them, arg(·) represents the phase operation, which is given by It can be determined that (j) ; Then fix v (j) , get the emission waveform x corresponding to the minimum objective function (j) ; Under the PAPR constraint, Tropp derived the transmit waveform x based on the KKT condition (j) The solution is to sort the transmitted waveforms according to the energy size, first limit the modulus of the first u elements to the maximum modulus under the PAPR constraint, and then use the waveform energy constraint to evenly distribute the remaining energy to the remaining (Nu) elements, expressed as: In the formula represents the maximum modulus value under PAPR constraint, represents the modulus value under the average distribution of the remaining energy; the above solution process needs to use a loop to traverse u from 1 to N to find the time domain sequence waveform x that meets the PAPR constraint o .

6. The satellite-ground synaesthesia integrated waveform design method based on subcarrier optimization as claimed in claim 5, characterized in that: In step 5, the frequency domain representation of the synaesthesia integration waveform is: z o =[z o1 ,z o2 ,…,z oN ] T =F H x o (25)。

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