Design method of integrated complementary waveform group for multi-carrier radar communication based on OTFS

Abstract

The present invention discloses a method for designing an integrated complementary waveform group for multi-carrier radar communication based on OTFS. The method relates to the field of waveform design technology and includes: constructing a multi-carrier radar communication integrated system model; processing the received echo signal of a single target by the multi-carrier radar communication integrated system; demodulating the received signal by a communication user; discretizing the transmitted waveform to obtain a radar data and communication data allocation scheme on the delay and Doppler plane that considers the communication bit error rate, and obtaining a radar data and communication data allocation scheme on the delay and Doppler plane that considers the waveform peak-to-average power ratio. The constructed optimization problem is solved using the ADMM algorithm to obtain an integrated complementary waveform group. The method analyzes the impact of data modulated at different positions on the delay-Doppler plane of the OTFS-CWG on the performance of the integrated waveform and proposes different data allocation schemes.

Description

Technical Field

[0001] The present invention belongs to the technical field of waveform design, and in particular relates to a method for designing an integrated complementary waveform group for multi-carrier radar communication based on OTFS. Background Art

[0002] In modern communication systems, multi-carrier waveforms are usually used to improve communication performance. Since multi-carrier waveforms have long been used in communication systems, radar communication integrated systems can be developed based on the original multi-carrier communication system, reducing changes to the hardware system. In addition, the demand for radar communication integration technology in the civilian field has gradually become clear. In 2021, the IMT-2030 (6G) Promotion Group released the "Communication Perception Integration Technology Report", which described the 6G system's requirements for integrated functions and clearly pointed out some key application scenarios, such as smart homes, vehicle networks, and drone networks. The use of multi-carrier integrated waveforms can better meet the application requirements in these scenarios. In summary, the use of multi-carrier waveforms to design integrated waveforms has strong practical significance.

[0003] Among multi-carrier integrated waveforms, OFDM (Orthogonal Frequency Division Multiplexing) (OFDM) integrated waveforms have garnered considerable attention. This is partly due to the maturing of OFDM radar waveform design technology and partly due to the excellent communication performance of OFDM waveforms, which have been widely adopted in 4G and 5G communication systems. However, OFDM waveforms still have several drawbacks, which present significant challenges to their practical application. For one thing, when there is relative motion between the transmitter and the user, OFDM waveforms are prone to inter-subcarrier crosstalk, resulting in degraded communication performance. Furthermore, OFDM waveforms typically exhibit high PAPR, which places high demands on the linearity of the integrated system's transmitter power amplifier. These issues have, to a certain extent, hindered the development of OFDM integrated waveforms. The excellent performance and application requirements of the OTFS (Over-the-Air (OTFS)) waveform have also stimulated research on the design of OTFS (Over-the-Air (OTFS)) radar and communication integrated waveforms. However, due to its relatively recent introduction, research on OTFS integrated waveform design is still limited. Currently, the industry primarily directly uses OTFS communication waveforms for radar detection to achieve radar and communication integration, while research on OTFS waveform design to optimize its radar and communication performance is relatively lacking. In addition, current research on the OTFS integrated waveform mainly focuses on its communication performance indicators, and pays less attention to radar performance indicators such as sidelobe level. At the same time, the autocorrelation sidelobes of a single OTFS waveform are high, which is not conducive to the detection of radar targets.

[0004] In view of this, there is an urgent need to improve the defect in the existing technology that the single OTFS waveform has high autocorrelation sidelobes, which is not conducive to the detection of radar targets. Summary of the Invention

[0005] To address the above-mentioned problems in the prior art, the present invention provides a method for designing an integrated complementary waveform group for multi-carrier radar communication based on OTFS. The technical problem to be solved by the present invention is achieved through the following technical solutions:

[0006] In a first aspect, the present invention provides a method for designing a multi-carrier radar communication integrated complementary waveform group based on OTFS, comprising:

[0007] Construct a multi-carrier radar communication integrated system model; wherein the multi-carrier radar communication integrated system is used to transmit waveforms to detect targets and communicate with communication users at the same time;

[0008] According to the transmission waveform, the multi-carrier radar communication integrated system processes the received echo signal of a single target to obtain a processing result; according to the transmission waveform, the communication user demodulates the received signal to obtain a demodulation result;

[0009] Discretize the transmit waveform, combine the processing results with the demodulation results, and, for the discretized transmit waveform, obtain a distribution scheme for radar data and communication data on the delay and Doppler plane that takes into account the communication bit error rate, and obtain a distribution scheme for radar data and communication data on the delay and Doppler plane that takes into account the waveform peak-to-average power ratio;

[0010] The constructed optimization problem is solved based on the ADMM algorithm to obtain an integrated complementary waveform group. The optimization problem is constructed based on the allocation scheme of radar data and communication data on the delay and Doppler plane considering the communication bit error rate, and the allocation scheme of radar data and communication data on the delay and Doppler plane considering the waveform peak-to-average power ratio.

[0011] Beneficial effects of the present invention:

[0012] (1) The present invention provides a method for designing an integrated complementary waveform group for OTFS radar communication. By analyzing the impact of data modulated at different positions in the delay-Doppler plane of the OTFS-CWG on the integrated waveform performance, different data allocation schemes are proposed.

[0013] (2) The present invention provides an OTFS radar communication integrated complementary waveform group design method. A constrained optimization problem is established for the OTFS-CWG design problem. The problem is transformed by introducing intermediate variables and solved by the ADMM algorithm. The original problem is decomposed into a series of constrained convex optimization problems, which are solved by the Active Set Method (ASM), ensuring the convergence of the algorithm.

[0014] The present invention will be further described in detail below with reference to the accompanying drawings and embodiments. BRIEF DESCRIPTION OF THE DRAWINGS

[0015] Figure 1 This is a flow chart of a method for designing a multi-carrier radar communication integrated complementary waveform group based on OTFS provided by an embodiment of the present invention;

[0016] Figure 2 This is a schematic diagram of a working scenario of a multi-carrier radar communication integrated system provided by an embodiment of the present invention;

[0017] Figure 3 Schematic diagram of the structure of the ZP-OTFS provided by an embodiment of the present invention;

[0018] Figure 4 This is a schematic diagram of a transmission waveform structure provided by an embodiment of the present invention;

[0019] Figure 5 This is a schematic diagram of the transmit waveform modulation principle in the OTFS-CWG provided by an embodiment of the present invention;

[0020] Figure 6 (a) is the sequence number n of different subcarriers in the delay-Doppler plane provided by the embodiment of the present invention c A schematic diagram of BER at ;

[0021] Figure 6 (b) is the sequence number n of different subcarriers in the delay-Doppler plane provided by the embodiment of the present invention. s A schematic diagram of BER at ;

[0022] Figure 7 1 is a schematic diagram of two OTFS-CWG data allocation schemes provided by an embodiment of the present invention;

[0023] Figure 8 The embodiment of the present invention provides A schematic diagram showing the performance comparison of integrated waveforms at different ratios;

[0024] Figure 9 1 is a schematic diagram of a relationship curve between the PSLR of the OTFS-CWG and the maximum PAPR of each group of waveforms provided by an embodiment of the present invention;

[0025] Figure 10 1 is a schematic diagram of a relationship curve between PSLR and v of OTFS-CWG provided by an embodiment of the present invention;

[0026] Figure 11 This is a schematic diagram of the relationship curves between BER and bit signal-to-noise ratio for different waveforms provided by an embodiment of the present invention;

[0027] Figure 12This is a schematic diagram of a PSLR and communication rate trade-off curve of OTFS-CWG provided by an embodiment of the present invention. DETAILED DESCRIPTION

[0028] The present invention will be further described in detail below with reference to specific examples, but the embodiments of the present invention are not limited thereto.

[0029] See Figure 1 , Figure 1 This is a flow chart of a method for designing a multi-carrier radar communication integrated complementary waveform group based on OTFS provided by an embodiment of the present invention. The method for designing a multi-carrier radar communication integrated complementary waveform group based on OTFS provided by the present invention includes:

[0030] S101. Construct a multi-carrier radar communication integrated system model; wherein the multi-carrier radar communication integrated system is used to transmit waveforms, detect targets, and communicate with communication users at the same time.

[0031] Specifically, in this embodiment, building a multi-carrier radar communication integrated system model includes:

[0032] Build work scenarios and signal models.

[0033] Specifically, the working scenario of the constructed multi-carrier radar communication integrated system is as follows: Figure 2 As shown, Figure 2 This is a schematic diagram of a working scenario of a multi-carrier radar communication integrated system provided by an embodiment of the present invention. A red vehicle is equipped with the multi-carrier radar communication integrated system and is traveling on the road. The vehicle detects targets while communicating with communication users through a transmitted waveform (OTFS-CWG). On the one hand, it is desired that the transmitted waveform has a low PAPR (peak-to-average power ratio) to meet the requirements of a linear power amplifier of the transmitter of the multi-carrier radar communication integrated system. On the other hand, since the detected targets include weak targets such as drones and strong targets such as other vehicles, it is desired that the transmitted waveform has a low sidelobe level to prevent the weak target echo from being overwhelmed by the sidelobes of the strong target echo.

[0034] The transmission waveform consists of multiple zero padding OTFS (ZP-OTFS) waveforms. The structures of ZP-OTFS and OTFS-CWG transmission waveform are as follows: Figure 3 and 4 As shown, Figure 3 is a schematic diagram of the structure of the ZP-OTFS provided by an embodiment of the present invention, Figure 4 This is a schematic diagram of the transmission waveform structure provided by an embodiment of the present invention. ZP-OTFS consists of two parts, one of which is the OTFS waveform part and the other is the zero-filling area, namely Figure 3In the ZP shown, the values ​​in this area are all 0. Figure 4 For the proposed transmission waveform structure, each group of OTFS-CWG contains M ZP-OTFS waveforms, and the mth transmission waveform is represented by s m The multi-carrier radar communication integrated system transmits these M waveforms with a transmission period of T to simultaneously realize the radar and communication functions.

[0035] Since the multi-carrier radar communication integrated system needs to realize functions such as road condition detection and vehicle collision avoidance, targets closer to the vehicle are often the detection targets that the multi-carrier radar communication integrated system is more interested in. This means that the multi-carrier radar communication integrated system needs to have independent transmitters and receivers to realize the detection of targets at relatively close distances. Figure 4 As shown, let the time width of a single ZP-OTFS waveform part in OTFS-CWG be T p , ZP time width is T g , T represents the transmission period, T = T p +T g . T g The choice of T needs to consider two factors. g It should be greater than the maximum multipath delay so that there is no inter-symbol interference in the signal received by the communication receiver; on the other hand, T g The selection of should ensure that the integrated system signal echo does not contain distance ambiguity signal. Considering that the transmission power of vehicle-mounted radar equipment is relatively low, the detection distance is usually not more than 1.5km. The power of the target echo signal farther than this distance will be lower than the minimum detectable power threshold of the radar receiver, which means that as long as T is met, g ≥10μs, there will be no range ambiguity signal in the radar echo of the multi-carrier radar communication integrated system.

[0036] The modulation principle of the transmission waveform in a single OTFS-CWG is as follows: Figure 5 As shown, Figure 5 This is a schematic diagram of the transmit waveform modulation principle in the OTFS-CWG provided by an embodiment of the present invention. The OTFS-CWG waveform modulates data into the delay-Doppler domain, and the delay-Doppler plane is recorded as:

[0037]

[0038] Among them, N c is the number of subcarriers, Δf is the subcarrier frequency interval, satisfying B=N c Δf, B is the transmission waveform bandwidth, N s is the number of sub-symbols, T r is the sub-symbol duration, and satisfies T p =N s T r , and Δf·Tr =1, it can be concluded that the total modulation N in the delay-Doppler domain c ×N s data, let:

[0039]

[0040] Among them, X m is the mth waveform s in OTFS-CWG m Delay-Doppler domain modulation data matrix. Figure 5 As shown in (a), each waveform in OTFS-CWG modulates N on P c N s The data are divided into two categories, including Communication data (indicated by red squares in the figure) and Radar data (represented by the blue squares in the figure), and Communication data uses communication modulation methods such as PSK modulation to transmit communication information. The value of communication data is only related to the communication information. It is assumed that the communication user knows the positions of the communication data and radar data on the delay-Doppler plane, and the communication data is extracted and demodulated based on this.

[0041] In the generated data symbol X m Then, the Inverse Symplec-tic FiniteFourier Transform (ISFFT) is used to transform X m Transform to frequency-time domain to obtain data symbols Among them, the matrix formed by the data symbols in the frequency-time domain is expressed as follows:

[0042]

[0043] in,

[0044]

[0045] Will Expressed as matrix multiplication, we can get:

[0046]

[0047] in, and N c and N s dimensional Fourier matrix, and then use the Heisenberg transform to convert the frequency-time domain data symbols Transformed into OTFS waveform, such as Figure 5 As shown in (c) in the figure, the expression of the OTFS waveform is:

[0048]

[0049] Among them, g tx represents the transmit pulse shaping function, and the notation is:

[0050]

[0051] It can be seen that the OTFS symbol is composed of N s It is composed of sub-symbols as shown in formula (1-7). Figure 5 The data in the red box in (b) points to Figure 5 The OTFS sub-symbol represented by (c) in the figure represents and By comparing Equation (7) with the expression of traditional OFDM symbols, it can be found that the expression for generating OTFS sub-symbols is similar to that of traditional OFDM symbols, which means that the OTFS-CWG radar communication integrated system can be developed based on the existing OFDM communication system.

[0052] S102. The multi-carrier radar communication integrated system processes the received echo signal of the single target according to the transmission waveform to obtain a processing result; and the communication user demodulates the received signal according to the transmission waveform to obtain a demodulation result.

[0053] Specifically, in this embodiment, the echo signal of a single target received by the radar receiver is preprocessed according to the transmission waveform of the multi-carrier radar communication integrated system.

[0054] Specifically, according to the transmission waveform s m (t), the echo signal of a single target received by the multi-carrier radar communication integrated system for:

[0055]

[0056] Among them, δ0 is the target complex scattering coefficient, n m (t) is the received Gaussian white noise signal, f d is the Doppler frequency shift of the echo signal, f d =2v / λ, v is the radial relative velocity between the multi-carrier radar communication integrated system and the target, λ is the wavelength of the transmitted signal, N s is the number of sub-symbols, N c The number of subcarriers, k is the kth subsymbol, i is the i-th subcarrier, is the data symbol in frequency and time domain, g tx is the transmit pulse shaping function, t is the time, T ris the sub-symbol duration, m is the mth transmitted waveform, r is the symbol, e is the natural base, j is the imaginary unit, and π is the circumference of a circle.

[0057] Preprocess the echo signal of a single target received by the radar receiver, including:

[0058] The radar function is realized by adding the matched filter output results of the echo signals received by the radar receiver within M transmission cycles. The process is expressed as:

[0059]

[0060]

[0061] Among them, y r (t) Add the echo signal matched filter output results, is the SACF when the target echo has Doppler, f m (t) is s m The autocorrelation function of (t), is the normalized Doppler frequency, T is the transmission period, is the noise signal output by the matched filter.

[0062] Specifically, in this embodiment, the signal received by the communication user is demodulated.

[0063] Specifically, demodulating the signal received by the communication user includes:

[0064] Assume that the channel between the multi-carrier radar communication integrated system and the communication user is a Gaussian white noise channel. When there is a radial relative velocity v between the multi-carrier radar communication integrated system and the communication user, the signal received by the communication user is The expression is:

[0065]

[0066] Among them, δ h is the communication channel coefficient, is the Doppler frequency shift of the signal received by the communication user, is the Gaussian white noise signal received by the communication user;

[0067] Use Wigner transform to process the signal received by the communication user to obtain discrete frequency and time domain data symbols Its expression is:

[0068]

[0069] Among them, g rx (t) corresponds to grx (t) communication reception pulse;

[0070] The discrete frequency and time domain data symbols are converted into the delay and Doppler domain using sigmoid Fourier transform to obtain the delay and Doppler domain data symbol Y m , whose expression is:

[0071]

[0072] make

[0073] Y m Expressed as matrix multiplication, we can get:

[0074]

[0075] in, N c -dimensional Fourier matrix, N s dimensional Fourier matrix, (·)H is the conjugate transpose;

[0076] Y m The communication data in the transmission waveform is extracted and decoded to obtain the communication information of the mth waveform.

[0077] S103. Discretize the transmit waveform, combine the processing results and the demodulation results, and obtain, for the discretized transmit waveform, a distribution scheme for radar data and communication data on the delay and Doppler plane that takes into account the communication bit error rate, and obtain a distribution scheme for radar data and communication data on the delay and Doppler plane that takes into account the waveform peak-to-average power ratio.

[0078] Specifically, in this embodiment, at the Nyquist sampling frequency, the sampling time is T s =T / N c , the discrete sampling result of the sub-symbol is:

[0079]

[0080] in, Then we have:

[0081]

[0082] The mth transmission waveform of the multi-carrier radar communication integrated system is Where L = N s N c For s m Length, G tx =diag{g tx}, according to the properties of Kronecker product, s mExpressed as:

[0083]

[0084] Introducing a vector, its expression is:

[0085]

[0086] in, is a column vector consisting of all communication data, For a column vector consisting of all radar data, there exists a transformation matrix Q such that:

[0087] x m =Q[vec(X m )] (19);

[0088] further:

[0089]

[0090] Define delay and Doppler data s m The mapping matrix is: but:

[0091]

[0092] By considering the communication bit error rate, the allocation scheme of radar data and communication data on the delay-Doppler plane is analyzed as follows:

[0093] Set the transmit pulse shaping function g tx (t) is a square wave function, ignoring the influence of noise, the communication receiver obtains the frequency and time domain data symbols through Wigner transform for:

[0094]

[0095]

[0096]

[0097] Where D is the diagonal matrix composed of the Doppler frequency shift within an OTFS sub-symbol, and B is the diagonal matrix composed of the Doppler frequency shift between OTFS sub-symbols;

[0098] According to formula (15), we can get:

[0099]

[0100] when When Y m =X m ;when When , we can get:

[0101]

[0102]

[0103]

[0104] Among them, the demodulated delay and Doppler domain result Y m [n c ,n s ] is the sum of two parts, where the first Contains the expected demodulation result X m [n c ,n s ]; the second item C m is the interference term; from the first term, we can see that a has the same effect on the data modulated at each point in the delay and Doppler domain. Since different rows on the delay and Doppler domain plane have different subcarrier numbers n c Therefore, the delay and Doppler domain data of the demodulation result are multiplied by different values ​​in different rows, that is, the subcarrier number is n c The line is multiplied by This causes different phase shifts in different row elements. Considering that Right now Therefore, as the subcarrier number n c As the delay and Doppler domain increase, the phase deflection of the modulated data will also increase, resulting in different error performance of the modulated data along the delay dimension. c The larger the position, the greater the phase shift, and thus the greater the BER.

[0105] The parameters shown in Table 1 are used to simulate the delay and Doppler planes for different subcarrier numbers n. c and sub-symbol number n s The bit error performance of the modulated data is as follows: Figure 6 As shown, Figure 6 This is a schematic diagram of a demodulation process of a received signal by a user provided by an embodiment of the present invention. Figure 6 From the result of (a), we can see that the sequence number n c The larger the position, the greater the bit error rate, for n c = 0, the bit error rate is 0.45%, for n c =63, the bit error rate is 0.69%, which is consistent with the previous analysis. Figure 6 From the result of (b), we can see that different sub-symbol numbers n s The bit error rates of the positions are not much different; Figure 6(a) is the sequence number n of different subcarriers in the delay-Doppler plane provided by the embodiment of the present invention c A schematic diagram of BER at Figure 6 (b) is the sequence number n of different subcarriers in the delay-Doppler plane provided by the embodiment of the present invention. s A schematic diagram of BER at .

[0106] According to this conclusion, the multi-carrier radar communication integrated system uses the first subcarrier number to modulate the communication data and the second subcarrier number to modulate the radar data; wherein the first subcarrier number is smaller than the second subcarrier number. c The second subcarrier number is n. s Position with a larger sequence number.

[0107] It is understandable that the integrated system can choose n as much as possible c The position with smaller sequence number modulates the communication data to ensure the communication performance, using n s Position modulated radar data with larger sequence numbers.

[0108] The allocation scheme of radar data and communication data on the delay-Doppler plane is analyzed by considering the waveform PAPR performance, specifically:

[0109] The nth OTFS-CWG transmission waveform s The nth sub-symbol c The sampling points can be expressed as:

[0110]

[0111] Table 1 PSLR and corresponding speed of the integrated waveform of multi-carrier radar communication

[0112]

[0113]

[0114] Among them, X m (n c ,:) is X m nth c OK, nth s elements, g tx (n c ) is a fixed value, so The value of X m nth c Try to modulate the communication symbols on n c The position with smaller sequence number is when the total number of communication symbols is When mThere are some rows that fully modulate communication symbols. According to the conclusion of formula (1-26), X m The rows that are all communication data correspond to It is only related to the communication data. Since the communication symbols of OTFS-CWG are not optimized, it is only related to the communication information, that is, X m The rows that are all communication data correspond to It will become a fixed value, and the sampling points of this part of the waveform cannot be optimized by optimizing the radar data. The PAPR of the mth waveform in OTFS-CWG can be expressed as:

[0115]

[0116] Among them, s m The PAPR is determined by the maximum |s m (l)| 2 If some sampling points are fixed, it will cause s m The PAPR is limited by the sampling points of this part, resulting in s m The PAPR is too high.

[0117] Based on the above conclusions, when the multi-carrier radar communication integrated system transmits a waveform with a PAPR greater than the first threshold, the communication symbol is modulated to a location where the delay and Doppler plane number are less than the set value; when the multi-carrier radar communication integrated system transmits a waveform with a PAPR less than the first threshold, data symbols are generated and radar data is set for each row. Among them, the first threshold is an artificially defined value. A value greater than the first threshold indicates a higher PAPR, and a value less than the first threshold indicates a lower PAPR. The set value indicates n c Smaller.

[0118] It is understandable that when the integrated system allows the waveform to have a higher PAPR, the communication symbols can be modulated to the delay-Doppler plane number n as much as possible. c In addition, when the integrated system requires the waveform to have a lower PAPR, it is necessary to ensure that X m Each row contains radar data, which provides enough degrees of freedom for PAPR optimization.

[0119] S104. Solve the constructed optimization problem based on the ADMM algorithm to obtain an integrated complementary waveform group; wherein the optimization problem is constructed based on the time delay considering the communication bit error rate and the allocation scheme of radar data and communication data on the Doppler plane, and the time delay considering the waveform peak-to-average power ratio and the allocation scheme of radar data and communication data on the Doppler plane.

[0120] Specifically, this embodiment first considers the sidelobe performance of the OTFS-CWG. Furthermore, given that the OTFS-CWG belongs to a complementary waveform group for integrated radar communications, and based on the aforementioned analysis, when there is relative motion between the integrated system and the target, the Doppler frequency of the echo will increase the sidelobes of the OTFS-CWG. Therefore, this section considers the sidelobe performance of the OTFS-CWG when the echo has Doppler and establishes corresponding optimization criteria. Furthermore, given that the waveform in the OTFS-CWG is non-constant modulus, inequality constraints are established to limit its PAPR, while equality constraints are established to limit its transmit power.

[0121] According to formula (10) and formula (20), the discrete autocorrelation function of the mth waveform of OTFS-CWG is set to:

[0122] f m =[f m (1-L),...,f m (-1),f m (0).f m (1),...,f m (L-1)] T (28);

[0123] in,

[0124] and, Among them, U l The expression is:

[0125]

[0126] Considering that the sidelobe of OTFS-CWG will increase when there is relative motion speed between the integrated system and the target, a weighted multi-objective optimization method is used to optimize the sidelobe performance of OTFS-CWG within the desired speed range. First, the desired optimized speed range is discretized to obtain the set:

[0127]

[0128] The normalized Doppler frequency is:

[0129]

[0130] The discrete SACF of OTFS-CWG is:

[0131]

[0132] Define the normalized Doppler frequency as The sidelobe level of the discrete SACF of OTFS-CWG is:

[0133]

[0134] According to the result of formula (20), combined with the properties of Fourier transform and VenaSchin’s theorem, formula (33) is equivalently transformed into:

[0135]

[0136] in, Π=√1F2L-1Vψ, and:

[0137]

[0138]

[0139] Among them, F 2L-1 is the 2L-1 order Fourier transform matrix;

[0140] Waveform m The PAPR of is given by equation (27), waveform s m The transmission power can be expressed as:

[0141]

[0142] It is expected that the OTFS-CWG sidelobe level will be minimized under the premise that the waveform transmit power is constrained to 1 and the PAPR of the transmit waveform is less than or equal to a constant η. The optimization problem can be written as:

[0143]

[0144] Among them, w p is a weight and satisfies:

[0145]

[0146] Solve the optimization problem based on the ADMM algorithm;

[0147] Specifically, in one embodiment of the present invention, analysis of the optimization problem (36) shows that the problem is a non-convex nonlinear optimization problem with nonlinear constraints, which needs to be transformed to make it easier to solve. First, the cost function is transformed and the constant term is discarded. When the constraint C2 of (36) is satisfied, the cost function can be simplified to:

[0148]

[0149] in,

[0150] When constraint C2 of (36) is satisfied, constraint C1 can be written as:

[0151] max{|sm (l)| 2 ,l=1,...,L}≤η,m=1,...,M (38);

[0152] Combined with formula (20), the M constraints in formula (8) can be equivalently replaced by LM constraints, that is:

[0153]

[0154] Among them, G l =ψ H E l ψ, and and is a matrix in which only the element with coordinate (1, 1) is 1 and the rest are 0. Similarly, according to formula 20, the constraint condition C2 can be transformed into:

[0155]

[0156] Where H = ψ H ψ, and According to equations (37) to (40), the optimization problem (36) can be transformed into:

[0157]

[0158] In order to solve the problem (41) using the ADMM algorithm, the intermediate variable And record it as:

[0159]

[0160] The optimization (41) can be equivalently transformed into:

[0161]

[0162] Problem (42) can be solved using the ADMM algorithm. To do this, we first need to write the augmented Lagrangian function of problem (42) and place the equality constraint in the augmented Lagrangian function, which yields:

[0163]

[0164] in, is a column vector of radar data of all OTFS-CWG transmitted waveforms, and:

[0165]

[0166] as well as μ and υ are dual vectors, ρ1 and ρ2 are penalty factors, For the front Matrix consisting of column elements After ∏ A matrix consisting of column elements.

[0167] As shown in Table 2, in the qth iteration, the ADMM algorithm includes the following steps:

[0168] Table 2 The qth iteration step of the ADMM algorithm to solve the problem (1-42)

[0169]

[0170] In Table 2, Λ x and Λ z are two sets consisting of the inequality constraints C1 in problem (42), namely:

[0171]

[0172]

[0173] in, G l Before The matrix of row elements, G l After A matrix consisting of row elements;

[0174] Implementing step 1 as shown in Table 2 is equivalent to solving the following sub-problems:

[0175]

[0176] in,

[0177] Obviously, subproblem (46) is a convex optimization problem with multiple inequality constraints. For this problem, the active set method (ASM) can be used to solve it. The active set method is an algorithm for iteratively solving optimization problems. The inequality constraint index set of the optimization problem (46) is defined as:

[0178]

[0179] The effective set of the optimization problem is defined as the set of constraint indices where the equal signs in the inequality constraints hold, that is:

[0180]

[0181] make for about The core idea of ​​the effective set method is to use the current effective set and cost function to calculate the iteration direction of the optimization variable, and according to Calculate the iteration step size, update the optimization variables, and then update the effective set based on the updated optimization variables Until the value of the optimized variable and No longer updated.

[0182] Using the active set method to solve problem (46), in the k0th iteration, we first need to solve the following sub-problems:

[0183]

[0184] in, represents the effective set at the k0th iteration. Problem (1-48) is a convex optimization problem with a first-order equality constraint, which can be solved using the Lagrange multiplier method. The Lagrange function of the optimization problem (1-48) is written as:

[0185]

[0186] Among them, γ m,l represents the Lagrange multiplier. The optimal solution of the optimization problem (48) satisfies:

[0187]

[0188] In order to facilitate the derivation of the formula, equation (49) is split into:

[0189]

[0190] in,

[0191]

[0192]

[0193]

[0194]

[0195] Solve the derivatives of equations (51) and (55) respectively, and according to the derivation rule, we can easily obtain:

[0196]

[0197] and:

[0198]

[0199] According to formula (57), we can get:

[0200]

[0201] in:

[0202]

[0203] According to (53), we can deduce:

[0204]

[0205] From (54), we can deduce:

[0206]

[0207] in, for The vector of column elements, we can get:

[0208]

[0209] in, Indicated by The block diagonal matrix composed of Indicated by A block diagonal matrix composed of After H The vector composed of column elements can be obtained from formula (55):

[0210]

[0211] According to formula (62), we can about The derivative of is expressed as:

[0212]

[0213] in, Representing a collection The momentum, that is The number of elements in , γ m By Lagrange multiplier The vector composed of Follow the steps shown in Table 3 to generate.

[0214] Table 3G Z Generation steps

[0215]

[0216] From formula (51) and formula (63), we can get:

[0217]

[0218] in,

[0219]

[0220] as well as

[0221] ω=ω1+G Z γ (66);

[0222] in,

[0223]

[0224] Note that Ω in (65) is reversible. Therefore, from equations (50) and (64), the optimal solution of (48) is:

[0225] x r =-Ω -1 ω (68);

[0226] At this time, the Lagrange multiplier It is still an unknown quantity, so we need to substitute equation (68) into the constraints of problem (48) to solve it. From (68), we can know that [Ω -1 ] m Ω - 1st Go to The matrix composed of row elements is:

[0227] x r m =-[Ω -1 ] m ω (69);

[0228] Combining formula (69) to transform the constraints of problem (48) we can obtain:

[0229]

[0230] From this we can get:

[0231] Aγ=ξ (71);

[0232] in, is The column vector composed of can be obtained according to formula (71):

[0233] γ=A -1 ξ (72);

[0234] Then substitute the result of formula (72) back into formula (68) to obtain: r ;

[0235] When using the ASM method to solve problem (46), let the result of k0 steps calculated through (68) be recorded as The initial feasible point of the k0th iteration is Note that when k0>1, It is also the iterative result of step k0-1, defining the direction vector:

[0236]

[0237] When using the ASM method to solve problem (1-46), the k0th iteration result is It can be expressed as:

[0238]

[0239] in, represents the iteration step, which aims to ensure that all constraints in the problem (1-46) are established, and we can get:

[0240]

[0241] in, express (m-1)Nth s M r +1 to mN s M r The vector is composed of elements. We can obtain After that, you need to update the valid set Its update expression is:

[0242]

[0243] in, Indicates from Remove elements from Indicates Adding elements (m, l) and using ASM to solve problem (46) is shown in Table 4.

[0244] Output from Table 4 This is the optimal solution to problem (46), which is the solution X of step 1 of the ADMM algorithm shown in Table 2. r(q+1) , according to the steps shown in Table 2, we can get x r(q+1) After that, you need to update z r(q+1) , that is, solve the following problem:

[0245]

[0246] Table 4 Process of solving problem (46) using ASM

[0247]

[0248] It can be seen that problem (77) is similar in form to problem (46), and is also solved using ASM. The solution process and results are similar to those of problem (46), so the specific derivation is not given.

[0249] The steps of using ADMM algorithm to solve problem (42) are shown in Table 5.

[0250] Table 5 Steps for solving problem (42) using the ADMM algorithm

[0251]

[0252] In seeking Then, according to equations (18) and (20), the final OTFS-CWG transmission waveform can be obtained:

[0253] Perform algorithm complexity analysis;

[0254] Specifically, in one embodiment of the present invention, the complexity of the ADMM algorithm shown in Table 5 is analyzed. In step 2, x is updated. r(q+1) In the process, calculate:

[0255] The main quantities are concentrated in Equation (68) and Equation (72), where the algorithm complexity of calculating Ω and the algorithm complexity of calculating ω are approximately as well as

[0256]

[0257] The number of iterations of the ASM algorithm. When the ASM algorithm is used for iteration, the number of iterations will not be greater than the total number of constraints, i.e.

[0258] The computational complexity of step 3 in Table 5 is the same as that of step 2, namely:

[0259]

[0260] The computational complexity of step 4 is:

[0261]

[0262] The computational complexity of step 5 is O(ML 3 ).

[0263] In summary, removing the low-order terms, the complexity of the ADMM algorithm shown in Table 5 can be expressed as:

[0264]

[0265] in, is the total number of iterations of the ADMM algorithm.

[0266] In summary, the present invention provides a method for designing an integrated complementary waveform group for OTFS radar communication. By analyzing the impact of data modulated at different positions on the OTFS-CWG delay-Doppler plane on the integrated waveform performance, different data allocation schemes are proposed.

[0267] The present invention provides an integrated complementary waveform group design method for OTFS radar communications. Aiming at the OTFS-CWG design problem, a constrained optimization problem is established. The problem is transformed by introducing intermediate variables and solved by the ADMM algorithm. This decomposes the original problem into a series of constrained convex optimization problems, which are solved by the Active Set Method (ASM), ensuring the convergence of the algorithm.

[0268] In an optional embodiment of the present invention, the beneficial effects of the present invention are further illustrated through simulation verification results.

[0269] The performance of the proposed OTFS-CWG is simulated and analyzed. The performance of the integrated waveform radar is measured using three performance parameters: PSLR, PAPR, and waveform power. First, PSLR is used to measure the sidelobe performance of the SACF of the OTFS-CWG, which is defined as:

[0270]

[0271] Among them, P ml is the peak value of the SACF main lobe, P sl Indicates the sidelobe peak value. The lower the PSLR, the better the sidelobe performance of the SACF of the OTFS-CWG.

[0272] Regarding PAPR performance, in addition to using the PAPR expression defined in Equation (27) to measure the PAPR of each waveform in OTFS-CWG, the PAPR of OTFS-CWG is also defined as:

[0273]

[0274] That is, the maximum PAPR of each waveform in OTFS-CWG. In addition, the transmit waveform power is defined by equation (35).

[0275] For communication performance, we use bit error rate (BER) and communication rate to measure. According to the integrated system model described in Example 1, the communication rate of OTFS-CWG can be expressed as:

[0276]

[0277] Among them, B0 represents the number of bits carried by each communication data. Considering that the designed waveform is based on the application scenario of integrated vehicle-mounted radar communication, this embodiment designs the corresponding simulation parameters based on the existing vehicle network protocol, namely the IEEE 802.11p protocol. The basic simulation parameters are shown in Table 6. All simulations in this embodiment use the parameters in Table 6. In this embodiment, the Ord-OTFS integrated waveform is used for comparison with the proposed OTFS-CWG. For Ord-OTFS, the parameters shown in Table 6 are also used for simulation. In addition, the sidelobe performance is measured by calculating the SACF of M different Ord-OTFS waveforms and calculating their PSLR.

[0278] Table 6 Basic simulation parameters

[0279]

[0280] Table 7 Integrated waveform performance parameters

[0281]

[0282] From the conclusion of Example 1, it can be seen that the different position allocation schemes of radar and communication data on the delay-Doppler plane will affect the final integrated waveform performance. Therefore, the simulation will adopt two modulation data position allocation schemes. The first one gives priority to modulating the communication data on the delay-Doppler plane. c The smaller position, the modulated waveform is recorded as OTFS-CWG-P1; the second scheme is to give priority to modulating the communication data in the delay-Doppler domain with sequence number n c The modulated waveform is recorded as OTFS-CWG-P2 at the smaller position. The two allocation schemes are shown in the following figure. Figure 7 As shown, Figure 7 It is a schematic diagram of two data allocation schemes of OTFS-CWG provided by an embodiment of the present invention. According to the parameters in Table 6, each waveform in OTFS-CWG modulates N on the delay-Doppler domain plane P. c =64 lines, N c = 4 columns of data, a total of 256 data, this embodiment will simulate 25% of the total modulation data volume (i.e. ).

[0283] First, let the expected optimization speed set considered in the OTFS-CWG design in formula (31) be Analysis of OTFS-CWG performance The change in the proportion of modulated data. Let the PAPR constraint η in problem (36) be 6.5dB, The performance of the integrated waveform when accounting for different proportions of the total modulation data is as follows: Figure 8 As shown, Figure 8The embodiment of the present invention provides A schematic diagram comparing the performance of the integrated waveform at different ratios. The specific performance parameters of the designed OTFS-CWG, including PSLR, waveform power, and PAPR, are shown in Table 7. Figure 8 The top three pictures show The SACF of the integrated waveform when the total modulation data volume accounts for different proportions, combined with Table 7, we can see that when When the proportion increases, the SACF sidelobe level of OTFS-CWG with the same data allocation scheme decreases. This is because when the radar data increases, problem (36) has more degrees of freedom to optimize the sidelobe performance of OTFS-CWG. When the ratios are the same, the sidelobe performance of OTFS-CWG-P1 is slightly inferior to that of OTFS-CWG-P2. Based on the conclusions of Example 1, the data allocation scheme of OTFS-CWG-P1 prevents the optimization of the waveform sampling points corresponding to all rows of modulated communication information on the delay-Doppler domain plane, resulting in poor sidelobe performance of OTFS-CWG. Finally, it can be seen that the designed OTFS-CWG consistently outperforms Ord-OTFS in sidelobe performance.

[0284] Figure 8 The three middle figures in (b) show the power of each waveform in the designed OTFS-CWG. It can be seen that the proposed OTFS-CWG design optimization problem can well achieve the power constraint. Figure 8 The bottom three figures in the figure show the PAPR of each waveform in OTFS-CWG. It can be seen that the proposed OTFS-CWG design optimization problem can achieve the PAPR constraint of OTFS-CWG. Figure 8 As can be seen from the last figure in , the PAPR of each waveform in OTFS-CWG-P2 does not reach the constrained 6.5dB, that is, the PAPR constraint in problem (36) is invalid at this time. When the PAPR constraint value η is too large, the PAPR of each waveform of the final designed OTFS-CWG will be less than η. Therefore, it is necessary to investigate and analyze the actual PAPR value range of OTFS-CWG.

[0285] The PSLR of OTFS-CWG and its actual PAPR, i.e. The relationship curve is as follows Figure 9 As shown, Figure 9 This is a schematic diagram of the relationship curve between the PSLR of the OTFS-CWG and the maximum PAPR of each group of waveforms provided by the embodiment of the present invention. First, when the OTFS-CWG adopts different radar and communication data allocation schemes, The value range is different. For OTFS-CWG-P1, The value range is 5.8dB-8.5dB; for OTFS-CWG-P2, The value range is 2.5dB-6.6dB. It can be seen that the use of different data allocation schemes has a greater impact on the PAPR performance of the integrated waveform. According to the above conclusions, the data allocation scheme of OTFS-CWG-P1 will cause some waveform sampling points to be unable to be optimized, and the final PAPR performance is poor. The modulation data allocation scheme adopted by OTFS-CWG-P2 can ensure that each sampling point of the waveform is optimized, so a waveform with a lower PAPR can be obtained. Secondly, it can be seen that when the value of OTFS-CWG increases, the PSLR of the integrated waveform decreases. When the values ​​are the same, the PSLR of OTFS-CWG-P1 is higher than that of OTFS-OTFS-CWG-P2, which is also due to the fact that some points of OTFS-CWG-P1 have not been optimized. According to the above results, the OTFS-CWG-P2 The minimum value is lower than that of OTFS-CWG-P1. When comparing performance, the sidelobe performance of OTFS-CWG-P2 is better. Figure 10 The relationship curve between PSLR and relative motion speed v of the designed OTFS-CWG is shown in Figure 10 is a schematic diagram of the relationship curve between PSLR and v of the OTFS-CWG provided by the embodiment of the present invention. Considering that the vehicle speed is usually not more than 40m / s, the expected optimized speed set considered in the OTFS-CWG design in formula (31) is and and The total modulated data volume accounts for 75%, and the PAPR constraint is η = 6.5dB. At the same time, the PSLR variation curves of Ord-OTFS and DR-JRC-CWG proposed in the above embodiment with v are simulated for comparison.

[0286] Depend on Figure 10 It can be seen that compared with OTFS-CWG-P1 has a higher PSLR when v < 9.8 m / s, and a lower PSLR when v ≥ 9.8 m / s. It has a higher PSLR when v < 6.3 m / s, and a lower PSLR when v ≥ 6.3 m / s. Since problem (36) is a weighted multi-objective optimization problem, when optimizing the sidelobe performance of the integrated waveform at different normalized Dopplers, the sidelobe performance of the integrated waveform near v = 0 m / s will deteriorate. Compared with Always has better sidelobe performance, which is consistent with Figure 10In addition, the designed OTFS-CWG always has lower PSLR than Ord-OTFS. For DR-JRC-CWG, when the target motion speed is low or zero, its sidelobe performance is better than the proposed As the target speed increases, its sidelobe performance will be worse than the proposed

[0287] In summary, when the integrated system and the target have a certain relative motion speed, the designed Sidelobe performance ratio The sidelobe performance is better.

[0288] Let OTFS-CWG Accounting for 50% of the total modulation data volume, Figure 11 1 is a schematic diagram of the relationship curves between BER and bit signal-to-noise ratio of different waveforms provided by an embodiment of the present invention. Figure 11 The BER and bit signal-to-noise ratio E of the integrated waveform are shown when the relative speed v between the integrated system and the communication user is different. b From the relationship curve of / N0, we can see that when v = 0, all integrated waveforms have the same BER; when v = 80m / s, OTFS-CWG-P2 and Ord-OTFS have the same BER, while OTFS-CWG-P1 has a lower BER. Specifically, when v = 80m / s, if the BER of the integrated waveform is required to not exceed 10-5, then for OTFS-CWG-P1, E b / N0≥15.77dB, for Ord-OTFS and OTFS-CWG-P2, E b / N0≥17.03dB. Figure 12 Conclusion Figure 12 This is a schematic diagram of the PSLR and communication rate trade-off curve of the OTFS-CWG provided by an embodiment of the present invention. OTFS-CWG-P1 uses the portion of the communication user received signal with a lower communication bit error rate when Doppler is present to modulate communication data, and the remaining portion to modulate radar data. Therefore, compared with Ord-OTFS and OTFS-CWG-P2, OTFS-CWG-P1 has a lower BER.

[0289] From formula (80), we can see that the communication data rate is related to the number of communication data per column modulated in the delay-Doppler plane. related, The larger the value, the higher the communication rate. However, due to That is, when L is fixed, The bigger, The smaller, according to Figure 8 The conclusion, when When decreases, the PSLR of OTFS-CWG increases, so there is a trade-off between the PSLR of OTFS-CWG and the communication rate. Figure 11 The trade-off curve between PSLR and communication rate of OTFS-CWG is shown in Figure 2. Figure 12 The PSLR curve of the DR-JRC-CWG designed in Example 1 is also plotted as a function of the communication rate. The transmit PRI of the DR-JRC-CWG is 40μs, the number of waveforms per group is M=6, and the length of each waveform is N=256, which is the same as that of the OTFS-CWG. It can be seen that the PSLR of the OTFS-CWG increases with the increase of the communication rate. At the same time, when the PAPR constraint η decreases, the PSLR of the OTFS-CWG also increases. For OTFS-CWG-P1, when the PAPR constraint is η=6dB and the communication rate is 0.6Mbps, its PSLR is -48.0dB. When the communication rate increases to 12Mbps, its PSLR increases to -25.0dB. When η=7dB and the communication rate is 0.8Mbps, the PSLR of OTFS-CWG-P1 is -50.2dB, and when the communication rate increases to 12Mbps, its PSLR increases to -28.0dB. For OTFS-CWG-P2, when η = 3dB and the communication rate is 2Mbps, the PSLR is -42.49dB. When the communication rate increases to 9.6Mbps, the PSLR increases to -25.1dB. When η = 4dB and the communication rate is 2Mbps, the PSLR is -48.29dB. When the communication rate increases to 9.6Mbps, its PSLR increases to -30.0dB.

[0290] In addition, by Figure 12 From (a) in the figure, we can see that the PSLR of DR-JRC-CWG is lower than that of OTFS-CWG-P1 when η=6dB, and higher than that of OTFS-CWG-P1 when η=7dB. Figure 11 As can be seen in (b), the PSLR of DR-JRC-CWG is lower than that of the designed OTFS-CWG-P2. This is mainly because the PSLR of OTFS-CWG decreases with the increase of PAPR constraint η. When η is small, the PSLR of OTFS-CWG may be worse than that of DR-JRC-CWG.

[0291] In practice, according to Figure 11The relationships shown here comprehensively consider the OTFS-CWG's sidelobe performance, PAPR performance, and communication rate to design the corresponding parameters. In summary, the designed OTFS-CWG exhibits better radar and communication performance than Ord-OTFS. On the other hand, OTFS-CWG-P1 exhibits inferior radar performance and a lower BER than OTFS-CWG-P2. However, in practice, a comprehensive consideration of radar and communication performance can be used to select an appropriate radar communication data modulation scheme.

[0292] It should be noted that, in this document, relational terms such as first and second are used solely to distinguish one entity or operation from another, and do not necessarily require or imply any actual relationship or order between these entities or operations. Furthermore, the terms "comprise," "include," or any other variations thereof are intended to encompass non-exclusive inclusion, such that an article or device comprising a list of elements includes not only those elements but also other elements not explicitly listed. Without further limitation, an element defined by the phrase "comprising a..." does not preclude the presence of additional identical elements in the article or device comprising the element. Terms such as "connected" or "connected" are not limited to physical or mechanical connections but may include electrical connections, whether direct or indirect. References to orientations or positional relationships, such as "upper," "lower," "left," and "right," are based on the orientations or positional relationships shown in the accompanying drawings and are intended solely to facilitate description and simplify the description of the present invention. They do not indicate or imply that the device or element referred to must have, be constructed, or operate in a specific orientation, and are therefore not to be construed as limiting the present invention.

[0293] In the description of this specification, the reference terms "one embodiment," "some embodiments," "example," "specific example," or "some examples" mean that the specific features or characteristics described in conjunction with the embodiment or example are included in at least one embodiment or example of the present invention. In this specification, the schematic representations of the above terms do not necessarily refer to the same embodiment or example. Moreover, the specific features or characteristics described can be combined in any suitable manner in one or more embodiments or examples. In addition, those skilled in the art can combine and combine different embodiments or examples described in this specification.

[0294] The above is a further detailed description of the present invention in conjunction with specific preferred embodiments, and the specific implementation of the present invention should not be considered to be limited to these descriptions. For those skilled in the art of the present invention, without departing from the concept of the present invention, several simple deductions or substitutions can be made, which should be considered to fall within the scope of protection of the present invention.

Claims

1. A method for designing an integrated complementary waveform group for multi-carrier radar communication based on OTFS, characterized in that: include: Construct a multi-carrier radar communication integrated system model; wherein the multi-carrier radar communication integrated system is used to transmit waveforms to detect targets and communicate with communication users at the same time; the transmitting waveform The expression is: ； in, is the number of subcarriers, is the number of sub-symbols, For the Sub-symbols, For the subcarriers, are data symbols in the frequency and time domains, For time, is the sub-symbol duration, is the transmit pulse shaping function, is the natural base, is the imaginary unit, is pi, is the subcarrier frequency spacing; According to the transmission waveform, the multi-carrier radar communication integrated system processes the received echo signal of a single target to obtain a processing result; according to the transmission waveform, the communication user demodulates the received signal to obtain a demodulation result; the echo signal of a single target received by the multi-carrier radar communication integrated system for: ； in, is the target complex scattering coefficient, is the received Gaussian white noise signal, is the Doppler shift of the echo signal, , is the radial relative velocity between the multi-carrier radar communication integrated system and the target, is the wavelength of the transmitted signal, is the number of sub-symbols, Number of subcarriers, For the Sub-symbols, For the subcarriers, are data symbols in the frequency and time domains, is the transmit pulse shaping function, For time, is the sub-symbol duration, For the A transmit waveform, is a symbol; The multi-carrier radar communication integrated system processes the received echo signal of a single target to obtain a processing result, including: Will In a transmission cycle, the output results of the matched filter of the echo signal of a single target are added to realize the radar function. The process is expressed as: ； ； in, is the sum of the echo signal matched filter output results, is the SACF when the target echo has Doppler, for The autocorrelation function of is the normalized Doppler frequency, , is the launch period, is the noise signal output by the matched filter; The transmit waveform is discretized, and in combination with the processing result and the demodulation result, a distribution scheme of radar data and communication data on a time delay and Doppler plane that takes into account a communication bit error rate is obtained for the discretized transmit waveform, as well as a distribution scheme of radar data and communication data on a time delay and Doppler plane that takes into account a waveform peak-to-average power ratio. The distribution scheme of radar data and communication data on a time delay and Doppler plane that takes into account a communication bit error rate includes: The multi-carrier radar communication integrated system uses a first subcarrier sequence number to modulate communication data and uses a second subcarrier sequence number to modulate radar data; wherein the first subcarrier sequence number is smaller than the second subcarrier sequence number; The distribution scheme of radar data and communication data on the Doppler plane and the time delay considering the peak-to-average power ratio of the waveform includes: When the multi-carrier radar communication integrated system transmits a waveform with a PAPR greater than a first threshold, the communication symbol is modulated to a location where the delay and Doppler plane sequence number are less than a set value; when the multi-carrier radar communication integrated system transmits a waveform with a PAPR less than the first threshold, data symbols are generated, and radar data is set for each row; The constructed optimization problem is solved based on the ADMM algorithm to obtain an integrated complementary waveform group; wherein the optimization problem is constructed based on the allocation scheme of radar data and communication data on the delay and Doppler plane considering the communication bit error rate, and the allocation scheme of radar data and communication data on the delay and Doppler plane considering the waveform peak-to-average power ratio; the expression of the constructed optimization problem is: ； in, is the weight, The normalized Doppler frequency is The sidelobe level of the discrete SACF of the transmitted waveform when is the normalized Doppler frequency, is the counting subscript, In order to discretize the desired optimized speed range, is a constant, The first The peak-to-average power ratio of the waveform, For waveform The transmission power.

2. The method for designing a multi-carrier radar communication integrated complementary waveform group based on OTFS according to claim 1, characterized in that: The communication user demodulates the received signal to obtain a demodulation result, including: The channel between the multi-carrier radar communication integrated system and the communication user is set to a Gaussian white noise channel. When there is a radial relative velocity between the multi-carrier radar communication integrated system and the communication user, When the communication user receives the signal The expression is: ； in, is the communication channel coefficient, is the Doppler frequency shift of the signal received by the communication user, is the Gaussian white noise signal received by the communication user; The signal received by the communication user is processed using Wigner transform to obtain discrete frequency and time domain data symbols , whose expression is: ； in, To correspond to Communication receiving pulse; The discrete frequency and time domain data symbols are converted into the delay and Doppler domain using a sigmoid Fourier transform to obtain the delay and Doppler domain data symbols. , whose expression is: ； make ; Will Expressed as matrix multiplication, we can get: ； in, for -dimensional Fourier matrix, for -dimensional Fourier matrix, is the conjugate transpose; Will The communication data is extracted and decoded to get the transmission waveform Communication information of a waveform.

3. The method for designing a multi-carrier radar communication integrated complementary waveform group based on OTFS according to claim 1, characterized in that: The discretizing the transmit waveform includes: At the Nyquist sampling frequency, the sampling time is , the discrete sampling result of the sub-symbol is: ； in, For counting, is the discrete sampling result of the sub-symbol, is a matrix, , then: ； in, To generate data symbols; Multi-carrier radar communication integrated system The transmission waveform is ,in, for length, , according to the properties of the Kronecker product Expressed as: ； Introducing vectors , whose expression is: ； in, is a column vector consisting of all communication data, is a column vector consisting of all radar data, and there is a transformation matrix , such that: ； further: ； Setting delay and Doppler data The mapping matrix is ,but: ； in, is the transpose, is the operator symbol, The field of real numbers.

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