A Waveform Design and Signal Processing Method for Integrated OFDM Radar-Communication Based on ZC Sequences

Abstract

This invention discloses a waveform design and signal processing method for integrated OFDM radar communication based on ZC sequences, comprising the following steps: selecting ZC sequences as OFDM frequency domain coefficients for loading to obtain an OFDM radar transmission signal based on ZC sequences, and using a variable symbol interval phase mapping modulation algorithm to modulate the communication information to obtain an integrated OFDM radar communication waveform based on ZC sequences; then establishing a linear transmission and reception model based on the integrated radar communication system, and realizing zero-range sidelobe pulse compression and low bit error rate communication demodulation of the integrated OFDM radar communication signal based on ZC sequences according to the ZC-OFDM waveform pulse compression and variable symbol interval phase mapping demodulation algorithm.

Description

Technical Field

[0001] This invention belongs to the technical fields of wireless communication and radar target detection, and further relates to an integrated waveform design and signal processing method for OFDM radar communication based on ZC sequence. Background Technology

[0002] With the development of electronic warfare technology and the increasing complexity of modern warfare requirements, the military field has placed higher demands on integrated radar and communication systems. Balancing the performance of both radar and communication is currently a key focus. Traditional integrated systems employ separate designs for communication and detection functions. While both communication and detection may perform well under dedicated resource conditions, the lack of unified planning and design results in insufficient parallel coordination capabilities. Therefore, the design must not only consider the adaptability of waveforms to both radar and communication performance, but also develop corresponding radar pulse compression algorithms and communication modulation / demodulation algorithms, while also considering the ease of hardware implementation and power efficiency.

[0003] Xi'an University of Electronic Science and Technology disclosed a dual-function signal processing method in its patent application "A Method for Radar Detection and Communication Transmission Based on Linear Frequency Modulation Signal" (application date: January 16, 2017, publication number: CN106772350A, publication date: May 31, 2017). This technology constructs a multi-carrier linear frequency modulation signal system, where the main carrier maintains the traditional radar detection function, while the subcarrier modulates the communication data using frequency modulation parameters. Its innovation lies in utilizing the cross-correlation characteristics of signals with different frequency modulation slopes to map the serial communication data to the subcarrier frequency modulation parameters after group conversion, achieving multi-bit information transmission within a single pulse period and effectively reducing the data transmission error rate. However, this scheme has shortcomings at the signal design level: although functional multiplexing is achieved through the separation of the main and subcarriers, the inherent time-frequency coupling characteristics of linear frequency modulation signals do not fully address the impact on system performance. Especially in the range and velocity detection dimensions, the lack of sidelobe suppression measures exacerbates the sidelobe interference problem in the radar echo signal, thereby affecting the detection accuracy of the radar system and making it difficult to meet the performance requirements of modern radar systems in terms of target resolution.

[0004] The University of Electronic Science and Technology of China (UESTC) disclosed a method for designing an integrated radar and communication 5G signal in its patent application, "A Radar-Communication Integrated 5G Signal Design Method" (application date: December 27, 2021, publication number: CN114282369B, publication date: October 25, 2024). Its main feature is the use of an interval-based linear phase compression modulation algorithm to modulate communication information, thereby solving an optimization model with the frequency domain subcarrier coefficients of the designed integrated radar and communication signal as optimization variables, and signal detection performance and communication performance as objective functions. The advantage of using the interval-based linear phase compression modulation algorithm for communication information modulation is that it enhances communication noise immunity and allows for flexible modulation parameter configuration. However, this communication modulation method still has shortcomings. The compression interval of the interval-based linear phase compression modulation algorithm contradicts the communication bit error rate, with the bit error rate increasing as the compression interval increases. Furthermore, the hardware implementation of this algorithm is complex, requiring precise control of the phase compression and demodulation intervals.

[0005] The problems in the above research can be summarized in the following two aspects: 1) The pulse compression of the existing radar-communication integrated signal has the problem of radar echo signal sidelobe interference, which affects the detection performance of the integrated signal; 2) The modulation of communication information in the existing radar-communication integrated signal has the problems of high bit error rate and complex hardware implementation. Summary of the Invention

[0006] The purpose of this invention is to overcome the shortcomings of the prior art and provide an integrated waveform design and signal processing method for OFDM radar communication based on ZC sequence, which realizes radar detection and communication transmission functions by transmitting a single signal.

[0007] The objective of this invention is achieved through the following technical solution: an integrated waveform design and signal processing method for OFDM radar communication based on ZC sequences, which uses a variable symbol interval phase mapping modulation algorithm to modulate communication information and a ZC-OFDM waveform pulse compression algorithm to compress radar signal pulses; the specific steps of this method are as follows:

[0008] S1. Design an integrated OFDM radar-communication signal based on the ZC sequence; including the following sub-steps:

[0009] S11. Use the ZC sequence as OFDM frequency domain coefficients for loading; let the number of subcarriers be N and the frequency domain complex weighting coefficients be R. k The expression for the OFDM radar transmitted signal based on the ZC sequence is:

[0010]

[0011] Where k = 0, 1, ..., N-1; f k= kΔf, where Δf is the bandwidth of each subcarrier in OFDM; T is the time width of one period of an OFDM symbol; where R k It is a ZC sequence;

[0012] S12. Modulate communication information using a variable symbol interval phase mapping modulation algorithm; assuming the number of bits in a binary symbol is I, then the total number of modulation coefficients for the frequency domain subcarriers is D = 2. I The type, whose emitted bit combination is represented as {χ1,χ2,…,χ...} D Let the phase mapping function be P(·); when the communication symbol χ is transmitted... j When the phase mapping principle is:

[0013]

[0014] In the above formula, j = 1, 2, ..., D, e j Let σ be the lower boundary of the D intervals, and let D = 2πσ be the width of the compressed interval. When the input phase belongs to the sign mapping interval, its original phase information will be retained. When the input phase does not belong to the original sign mapping interval, the phase of the input will be adjusted through the phase mapping function.

[0015] Let the modulation function be G(·) and the modulation interval be μ. The frequency domain coefficients of the modulated OFDM signal are:

[0016]

[0017] ρ is a continuous sequence of non-negative integers not greater than (N-1) / μ;

[0018] S2. Establish a linear transmission and reception model based on an integrated radar-communication system; including the following sub-steps:

[0019] S21. Discretely sample the s′(t) signal to obtain the transmitted signal:

[0020]

[0021] S22. Suppose the radar detection area is divided into M range resolution cells. The final echo signal received by the radar is the superposition of the radar echo signals from each range resolution cell, resulting in the following radar echo signal:

[0022]

[0023] Where, d m This represents the scattering coefficient of each range-resolved cell. The time-domain sampling sequence is additive white Gaussian noise;

[0024] S23. There are W communication multipath channels, where the response of the w-th channel is h.w Then the expression for the communication received signal of the radar base station is:

[0025]

[0026] S3. ZC-OFDM waveform pulse compression and communication demodulation based on the ZC sequence-based OFDM radar-communication integrated signal; including the following sub-steps:

[0027] S31. Radar pulse compression is achieved using the ZC-OFDM waveform pulse compression algorithm;

[0028] S32, By calculating the demodulated data and modulation time The optimal demodulation case is determined by the Euclidean distance between the three cases based on the principle of minimum distance:

[0029]

[0030] in j = 1, 2, ..., D is the modulation phase. This is the demodulation phase of the variable symbol interval phase mapping modulation algorithm in step S12.

[0031] The beneficial effects of this invention are as follows: First, this invention modulates the transmitted signal of OFDM radar based on the ZC sequence using a variable symbol interval phase mapping modulation algorithm to obtain an integrated OFDM radar-communication signal based on the ZC sequence. Second, a linear signal transmission and reception model is established based on the integrated radar-communication system. Then, ZC-OFDM waveform pulse compression and a variable symbol interval phase mapping modulation algorithm are used to achieve radar signal pulse compression and communication signal demodulation. This invention modulates communication information using a variable symbol interval phase mapping modulation algorithm, which reduces the bit error rate and simplifies the hardware system complexity compared to traditional linear phase compression modulation algorithms. Furthermore, the ZC-OFDM waveform pulse compression method achieves range-sidelobe-free pulse compression. Therefore, the waveform design and signal processing method for integrated OFDM radar-communication based on the ZC sequence of this invention can effectively improve the overall performance of the integrated radar-communication signal. Attached Figure Description

[0032] Figure 1 This is a schematic diagram of an integrated radar and communication system according to an embodiment of the present invention;

[0033] Figure 2 This is a flowchart illustrating the steps of an embodiment of the present invention;

[0034] Figure 3 This is a diagram showing the amplitude-frequency response of the ZC sequence according to an embodiment of the present invention.

[0035] Figure 4This is a schematic diagram comparing the information modulation and demodulation performance of the variable symbol interval phase mapping modulation algorithm and the traditional interval linear phase compression modulation algorithm according to an embodiment of the present invention.

[0036] Figure 5 This is a performance analysis diagram of the ZC-OFDM waveform pulse compression algorithm according to an embodiment of the present invention;

[0037] Figure 6 This is a performance comparison chart of the ZC-OFDM waveform pulse compression algorithm and the traditional matched filter pulse compression in this embodiment of the invention;

[0038] Figure 7 This is a comparison chart of the pulse compression performance of the ZC-OFDM waveform pulse compression algorithm and the CP-OFDM-like inverse filter pulse compression algorithm in this embodiment of the invention. Detailed Implementation

[0039] This invention was verified through simulation experiments, and all related processes and conclusions were verified using the Matlab 2020b platform. The technical solution of this invention is further described below with reference to the accompanying drawings and specific embodiments.

[0040] A typical radar-communication integrated system, such as Figure 1 As shown, the integrated radar-communication system transmits integrated radar-communication signals and receives target echoes, and a communication link exists between the integrated radar-communication system and the communication base station.

[0041] This invention discloses an integrated waveform design and signal processing method for OFDM radar communication based on ZC sequences. It uses a variable symbol interval phase mapping modulation algorithm to modulate communication information and a ZC-OFDM waveform pulse compression algorithm to compress radar signal pulses. Figure 2 As shown, the specific steps of this method are as follows:

[0042] S1. Design an integrated OFDM radar-communication signal based on the ZC sequence; including the following sub-steps:

[0043] S11. Use the ZC sequence as OFDM frequency domain coefficients for loading; let the number of subcarriers be N and the frequency domain complex weighting coefficients be R. k The expression for the OFDM radar transmitted signal based on the ZC sequence is:

[0044]

[0045] Where k = 0, 1, ..., N-1; f k = kΔf, where Δf is the bandwidth of each subcarrier in OFDM; assuming the signal bandwidth is B, then Δf = B / N; T is the time width of one period of an OFDM symbol; where R kThis is a ZC sequence; ZC sequences exhibit good autocorrelation and cross-correlation properties, and their expression is:

[0046]

[0047] Where r is the root exponent, N zc Given the length of the ZC sequence, the amplitude-frequency response of the ZC sequence is shown in the figure. Figure 3 As shown, the ZC sequence remains a constant modulus sequence after FFT.

[0048] S12. The communication information is modulated using a variable symbol interval phase mapping modulation algorithm. Although the interval linear phase compression modulation algorithm has advantages such as relaxed waveform frequency domain constraints and high degree of freedom in phase design, it still has problems such as high bit error rate and high hardware implementation complexity. Therefore, this invention uses a variable symbol interval phase mapping modulation algorithm to expand the fault tolerance space, reduce complexity, and thus improve communication transmission performance.

[0049] In the explanation of the principle, assuming that the number of bits in the binary symbol is I, then the total number of modulation coefficients for the frequency domain subcarrier is D = 2. I The type, whose emitted bit combination can be represented as {χ1,χ2,…,χ...} D Let the phase mapping function be P(·). When the communication symbol χ is transmitted... j When the phase mapping principle is:

[0050]

[0051] In the above formula, j = 1, 2, ..., D, e j Let D be the lower boundary of the D intervals, and σ be the width of the compressed interval. It is easy to see that D = 2π / σ. From the above formula, it can be seen that when the input phase belongs to the symbol mapping interval, its original phase information will be retained. When the input phase does not belong to the original symbol mapping interval, the phase of the input will be adjusted through the phase mapping function.

[0052] In practical applications, the variable symbol interval phase mapping modulation algorithm first extracts the frequency domain coefficients containing the communication bits based on the designed sampling function. Since there are D possible combinations of transmitted bits, and D typically takes values ​​of 2, 4, or 8, further increasing this value would reduce the symbol spacing, causing the bit error rate to reach an unacceptable level. Therefore, the improvement made in this invention is actually a special simplified processing method considering the case where D = 2, 4, or 8. This method uses the real and imaginary symbols of the input data to replace the original phase rotation, thereby achieving the same effect.

[0053] Let the modulation function be G(·) and the modulation interval be μ. The frequency domain coefficients of the modulated OFDM signal are:

[0054]

[0055] ρ is a continuous sequence of non-negative integers not greater than (N-1) / μ;

[0056] The modulation function G(·) here and the phase mapping function P(·) mentioned above represent different manifestations of the same modulation algorithm in terms of complex signal data and signal phase. The modulation process of the modulation function G(·) is as follows: In the results It is still a complex number. The modulation function G(·) of the variable symbol interval phase mapping modulation algorithm is expressed as:

[0057]

[0058] in The frequency domain coefficients of the modulation signal are represented by the absolute value of their real parts. The absolute value of the imaginary part is The real part is s re The symbol for the imaginary part is s. im ;

[0059] The values ​​of the bit combination D represent different s re s im The following discussion will be divided into three scenarios: D takes the values ​​2, 4, and 8.

[0060] A. When D=2, the modulation information consists of only one bit b0, s im and Following the imaginary part of the input value, when b0 is 0, s re Add 1 to the result, otherwise subtract 1. Then it is determined based on the absolute value of the real part of the input data;

[0061] B. When D = 4, the modulation information has two bits b0b1, and its construction is as follows:

[0062]

[0063] C. When D = 8, the modulation information has three bits b0b1b2, and its construction is as follows:

[0064]

[0065] The final OFDM radar-communication integrated signal based on the ZC sequence is as follows:

[0066]

[0067] S2. Establish a linear transmission and reception model based on an integrated radar-communication system; including the following sub-steps:

[0068] S21. Discretely sample the s′(t) signal to obtain the transmitted signal:

[0069]

[0070] S22. Suppose the radar detection area is divided into M range resolution cells. The final echo signal received by the radar is the superposition of the radar echo signals from each range resolution cell, resulting in the following radar echo signal:

[0071]

[0072] in, G represents the scattering coefficient of each range-resolved unit. m Let f be the equivalent radar cross section corresponding to the scattering coefficients of all scattering points within the m-th range cell illuminated by radar at slow time η; 4πf c R m (η) / c represents the direction phase; The time-domain sampling sequence is additive white Gaussian noise with variance σ. 2 ;

[0073] S23. There are W communication multipath channels, where the response of the w-th channel is h. w Then the expression for the communication received signal of the radar base station is:

[0074]

[0075] S3. ZC-OFDM waveform pulse compression and communication demodulation based on the ZC sequence-based OFDM radar-communication integrated signal; including the following sub-steps:

[0076] S31. Radar pulse compression is achieved using the ZC-OFDM waveform pulse compression algorithm;

[0077] The transmission sequence s = [s1, s2, ..., s N-1 Add a zero-value sequence before and after as a protection unit, with a single-sided protection unit length of M-1, to obtain a new transmission sequence s′:

[0078]

[0079] When a radar base station transmits a radar-communication integrated signal s′, and the radar base station obtains a discrete echo sequence, since the first M-1 samples and the last M-1 samples do not contain the echo energy of all M different range resolution cells, removing the first M-1 samples and the last M-1 samples of the echo sequence (i.e., removing the cyclic prefix in communication technology, removing the first and last M-1 rows of the echo matrix) yields the following sequence:

[0080]

[0081] Furthermore, the received echo sequence vector It can be represented as:

[0082]

[0083] in, Representation matrix Perform a linear convolution with s′; H can be represented as:

[0084]

[0085] The noise vector v is a time-domain sampling sequence of additive white Gaussian noise, which can be represented as:

[0086] Since the first and last M-1 values ​​of the emission sequence s′ are all 0, the first and last M-1 values ​​of the emission sequence s′ can be removed to obtain s. t =[s0,s1,…,s N-1 ] T ; and the matrix After deleting the first M-1 columns and the last M-1 columns, we obtain matrix H:

[0087]

[0088] Therefore, the echo sequence u can be expressed as:

[0089]

[0090] in [·] T This is a transpose operation; The time-domain sampling sequence is additive white Gaussian noise;

[0091] Rewrite H using a circular matrix to obtain H′; perform folding on the received signal to obtain u′, and then obtain a new signal model:

[0092]

[0093] Rewriting matrix H as a cyclic matrix means concatenating matrix H from bottom to top M-1 layers to layers from top to bottom M-1 layers, resulting in an N×N cyclic matrix H′:

[0094]

[0095] Overlaying the received signal u means splicing u from bottom to top M-1 layers to obtain u′ from top to top 1 to M-1 layers, that is:

[0096]

[0097] right Taking the fast Fourier transform of both sides of the equation yields:

[0098] U k =D k S k +V k k = 0, 1, ..., N-1

[0099] Among them U k It is the result of the Fast Fourier Transform of the received echo u′; S k For time-domain emission sequence s t The result of the Fast Fourier Transform; V k Noise vector The results of the Fast Fourier Transform; The fast Fourier transform results of the scattering coefficients of each of the M range-resolved cells are obtained; D is then obtained. k The estimated value is:

[0100]

[0101] Due to S k with U k Given that, D can be obtained from the above formula. k The estimated value Again IFFT is performed to obtain the scattering coefficient vectors of M range-resolved cells, and then the equivalent RCS of each range cell is obtained to complete the radar pulse compression of the ZC-OFDM radar-communication integrated signal.

[0102] S33, By calculating the demodulated data and modulation time The Euclidean distances between the cases j = 1, 2, ..., D are used to determine the optimal demodulation case based on the minimum distance principle:

[0103]

[0104] in j = 1, 2, ..., D is the modulation phase. This refers to the demodulation phase of the variable symbol interval phase mapping modulation algorithm in step S12. By using the minimum absolute value of the phase angle difference in the above formula and determining the corresponding specific bit combination according to this criterion, the communication demodulation of the OFDM radar-communication integrated signal based on the ZC sequence can be completed.

[0105] To verify the integrated waveform design and signal processing method for OFDM radar and communication based on ZC sequence in this invention, and to test its radar detection and communication performance, the following experiments were conducted:

[0106] Simulation Experiment 1: Simulation Experiment 1 compares and analyzes the signal communication performance of QPSK modulation algorithm, Quadrature Phase Compression modulation algorithm, and VQPM (Variable Symbol Quadrature Phase Mapping) modulation algorithm used in this invention. The design uses a basic OFDM waveform with 1024 subcarriers and a modulation interval of 4. The Quadrature Phase Compression modulation algorithm is represented as QPC, and the VQPM as VQPM. The bit error rate (BER) curves of QPC, VQPM, and QPSK algorithms under different signal-to-noise ratio (SNR) conditions are compared. The BER range is set to -10dB to 10dB, with an increment step of 1dB. 3000 Monte Carlo simulations are run under each SNR condition, and the average value is taken as the BER value for that SNR condition. The final simulation results are as follows: Figure 4 As shown.

[0107] from Figure 4 As can be seen, the bit error rate curves of VQPM and QPSK algorithms almost coincide, proving that their modulation and demodulation performance in communication information is very similar. However, the bit error rate curve of QPC is significantly higher than that of the other two algorithms, proving that under the same conditions, the communication transmission performance using the QPC algorithm will be slightly reduced.

[0108] on the other hand, Figure 4 The results also show that the VQPM algorithm improves communication transmission performance from the original QPC curve to the QPSK curve. The QPSK bit error rate curve was chosen as the comparison because, under additive white Gaussian noise (AWGN) channel conditions, QPSK represents the theoretically optimal case for four-phase modulation in terms of bit error rate; the bit error rate curves of other four-phase modulation methods are generally not lower than that of QPSK. In other words, the VQPM algorithm has achieved the theoretically optimal bit error rate for four-phase modulation.

[0109] Simulation Experiment 2: Simulation Experiment 2 analyzes the pulse compression performance of the ZC-OFDM waveform pulse compression algorithm used in this invention. It is conducted under noise-free conditions, with 10 random targets within the detection range. The equivalent radar scattering coefficient of each target is designed to vary randomly between -20dB and 0dB. The final simulation results are as follows: Figure 5 As shown.

[0110] from Figure 5 (a) It can be seen that the ZC-OFDM waveform has good time-frequency domain properties, which in principle meets the equivalent conditions of low PAPR and high distance cell signal-to-noise ratio.

[0111] from Figure 5(b) It can be seen that the pulse compression noise floor can reach about -340dB, which is equivalent to zero noise. This means that the method can achieve pulse compression effect with zero distance sidelobes. That is, after using a clean waveform to perform the pulse compression algorithm, the noise floor will not be artificially high due to factors such as distance sidelobe interference, which is to say, a "false zero noise" situation will not occur.

[0112] Simulation Experiment 3: Simulation Experiment 3 compares the pulse compression performance of the ZC-OFDM waveform pulse compression algorithm used in this invention with that of traditional matched filtering under noise-free conditions. In the simulation experiment, the number of random targets within the detection range was set to 10, and the equivalent radar scattering coefficient varied randomly between -20dB and 0dB. The waveform used for matched filtering was a ZC-OFDM waveform with the same parameters. The final simulation results are as follows. Figure 6 As shown.

[0113] from Figure 6 As can be seen, the noise floor of matched filtering is approximately -50dB. This is because matched filtering, as a pulse compression algorithm, causes a certain degree of sidelobe interference around the correlation peak (detected target), thus exhibiting this "pseudo-zero noise" characteristic. In reality, signal transmission is certainly not in a zero-noise environment, and the sidelobe interference will be more obvious, to the point that it affects the radar's target detection to some extent. In contrast, the noise floor of the ZC-OFDM waveform pulse compression algorithm in this invention is significantly reduced to approximately -350dB, effectively avoiding sidelobe interference from other range cells. Therefore, the method used in this invention is far superior to matched filtering in reducing sidelobes.

[0114] Simulation Experiment 4: Simulation Experiment 4 compares the pulse compression performance of the ZC-OFDM waveform pulse compression algorithm used in this invention with that of the traditional CP-OFDM algorithm. The simulation experiment sets up 10 random targets and random scattering coefficients, but the waveform and noise signal-to-noise ratio are set to 3dB. The ZC-OFDM waveform with the same parameters is used as the radar's base waveform; only the signal processing method is changed. The final simulation results are as follows. Figure 7 As shown.

[0115] from Figure 7 (b) It can be seen that the traditional CP-OFDM algorithm does not have specific constraints on the frequency domain of the reference signal. Therefore, the frequency domain amplitude of the reference signal may have a minimum value at some point. Since the reference signal will eventually appear in the denominator, a denominator of 0 will have a great impact on the pulse compression algorithm. Therefore, the CP-OFDM algorithm considers using an algorithm similar to Clipping to optimize its frequency domain modulus constantness in waveform design.

[0116] from Figure 7(a) It can be seen that the ZC-OFDM waveform pulse compression algorithm used in this invention has good pulse compression performance and strong robustness to abnormal values ​​of the reference signal. This is because it takes into account the protection of the constant modulus of the reference signal in the frequency domain, thereby simplifying the waveform design and improving the pulse compression effect.

[0117] Those skilled in the art will recognize that the embodiments described herein are intended to help the reader understand the principles of the invention, and should be understood that the scope of protection of the invention is not limited to such specific statements and embodiments. Those skilled in the art can make various other specific modifications and combinations based on the technical teachings disclosed in this invention without departing from the spirit of the invention, and these modifications and combinations are still within the scope of protection of this invention.

Claims

1. A waveform design and signal processing method for integrated OFDM radar communication based on ZC sequence, characterized in that, The communication information is modulated using a variable symbol interval phase mapping modulation algorithm, and the radar signal pulse compression is achieved using a ZC-OFDM waveform pulse compression algorithm. The specific steps of this method are as follows: S1. Design an integrated OFDM radar-communication signal based on the ZC sequence; including the following sub-steps: S11. Use the ZC sequence as the OFDM frequency domain coefficients for loading; let the number of subcarriers be... The frequency domain complex weighting coefficients are The expression for the OFDM radar transmitted signal based on the ZC sequence is: ； in ; , It is the bandwidth of each subcarrier in OFDM; The time width within one period of an OFDM symbol; where It is a ZC sequence; S12. Modulate communication information using a variable symbol interval phase mapping modulation algorithm; assuming the number of bits in a binary symbol is I, then the total number of modulation coefficients for the frequency domain subcarriers is... The type, whose emitted bit combination is represented as Let the phase mapping function be When transmitting communication symbols When the phase mapping principle is: ； In the above formula, , for The lower boundary of the interval, To compress the width of the interval, ; When the input phase belongs to the sign mapping interval, its original phase information will be retained. When the input phase does not belong to the original sign mapping interval, the phase of the input will be adjusted by the phase mapping function. Let the modulation function be The modulation interval is The frequency domain coefficients of the modulated OFDM signal are obtained as follows: ； Not greater than A continuous sequence of non-negative integers; Modulation function The modulation process is In the results Still a complex number; modulation function of the variable symbol interval phase mapping modulation algorithm Represented as: ； in The frequency domain coefficients of the modulation signal are represented by the absolute value of their real parts. The absolute value of the imaginary part is The real part is symbolized as The symbol for the imaginary part is ; The values ​​of the bit combination D represent different , , , ; A. When D=2, the modulation information consists of only one bit. , and Following the imaginary part of the input value, when When it is 0, Add 1 to the result, otherwise subtract 1. Determined based on the absolute value of the real part of the input data; B. When D=4, the modulation information has two bits. Its structure is as follows: ； C. When At that time, the modulation information has three bits. Its structure is as follows: ； The final OFDM radar-communication integrated signal based on the ZC sequence is as follows: ； S2. Establish a linear transmission and reception model based on an integrated radar-communication system; including the following sub-steps: S21, to The signal is discretely sampled to obtain the transmitted signal: ； S22. Assume the radar detection area is divided into... The radar echo signal ultimately received by the radar is the superposition of the radar echo signals from each range resolution cell, resulting in the following radar echo signal: ； in, This represents the scattering coefficient of each range-resolved cell. The time-domain sampling sequence is additive white Gaussian noise; S23, with There are 10 communication multipath channels, of which the 10th The response of each channel is Then the expression for the communication received signal of the radar base station is: ； S3. ZC-OFDM waveform pulse compression and communication demodulation based on the ZC sequence-based OFDM radar-communication integrated signal; including the following sub-steps: S31. Radar pulse compression is achieved using the ZC-OFDM waveform pulse compression algorithm; S32, By calculating the demodulated data and modulation time The optimal demodulation case is determined by the Euclidean distance between the three cases based on the principle of minimum distance: ； in To modulate the phase, This is the demodulation phase of the variable symbol interval phase mapping modulation algorithm in step S12.

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