A Method for Generating and Optimizing a Composite Modulation Signal with Non-Uniform Frequency and Phase

Abstract

The present invention discloses a method for generating and optimizing a composite modulation signal with non-uniform frequency and phase, which can make up for the drawbacks of single modulation signals and conventional composite modulation signals. Frequency modulation is performed between signal sub-pulses, and arbitrary phase coding modulation is performed within sub-pulses. Moreover, the number of chips and widths of each sub-pulse can also be different, dynamically allocating the time domain and frequency domain information of the signal, increasing the design freedom and signal complexity, improving the radar anti-jamming and low intercept performance. Even if the radar signal is intercepted, it is difficult to extract the important features of the signal. And based on the coordinate descent method and the cost function diversity method, the signal parameters are searched and optimized to improve the pseudo-randomness of the signal and the target detection ability under clutter background.

Description

Technical Field

[0001] The present invention relates to the technical field of radar waveform design, and particularly relates to a method for generating and optimizing a composite modulation signal with non-uniform frequencies and phases. Background Art

[0002] With the increasingly complex electromagnetic environment, the survival space of radars faces huge challenges. Radar systems must give full play to the degrees of freedom at the transmitting end, and increase the uncertainty of signals through frequency modulation or phase modulation to improve the anti-reconnaissance and anti-jamming capabilities of radars in electronic countermeasures. To further improve the survival ability of radars, frequency-phase two-dimensional composite modulation waveforms have emerged, improving the complexity and randomness of signals.

[0003] However, with the rapid development of technologies such as electronic reconnaissance, interference, and anti-radiation, the survival of radars faces more severe challenges. In the existing solutions, the bandwidth of phase-coded signals is limited by the width of sub-pulse chips, and the carrier frequency is single; frequency-coded signals have a large equivalent bandwidth, but their spectrum modulation is relatively simple. The above two types of signals are easily intercepted by the enemy and then jammed. For conventional frequency-phase composite modulation signals, the sub-pulse widths are equal, and the widths of each chip and the number of bits of sub-pulse phase encoding are the same. Although two-dimensional modulation is achieved, compared with one-dimensional modulation signals, the form is more complex, and the anti-jamming and low-intercept performance are enhanced. However, due to the fixed equal width of sub-pulses and the fixed carrier frequency interval, a rectangular broadband spectrum is formed in the frequency domain, and its autocorrelation result performance is poor, the sidelobes in the range dimension are too high, and the detection performance is poor, which can no longer meet the anti-jamming and low-intercept performance requirements of modern radars.

[0004] Radar low-intercept waveforms should be as complex as possible so that it is difficult to extract radar signal characteristics even if intercepted by reconnaissance equipment. Therefore, a method for generating and optimizing a composite modulation signal with non-uniform frequencies and phases is proposed. The composite modulation signal generated by this method has frequency modulation between sub-pulses of the signal, arbitrary phase encoding within sub-pulses, and the number and width of chips of each sub-pulse can also be different. By changing the time-width distribution of each sub-pulse in the time domain, the energy distribution at different frequency points is changed, which is equivalent to windowing in the frequency domain, improving its autocorrelation performance in the time domain. By flexibly adjusting the number and width of chips, the design freedom and complexity of the signal are improved, thereby enhancing the radar low-intercept performance and improving its own target detection ability. Summary of the Invention

[0005] In view of this, the present invention provides a method for generating and optimizing a composite modulation signal with non-uniform frequencies and phases, which can make up for the drawbacks of single modulation signals and conventional composite modulation signals.

[0006] In order to solve the above technical problems, the present invention is implemented as follows.

[0007] A method for generating a composite modulation signal with non-uniform frequency and phase, comprising:

[0008] The method includes:

[0009] Through multi-subpulse modulation, each pulse is divided into N subpulses, frequency modulation is performed between the subpulses, and the sequence numbers of the subpulses are marked as [0, N-1]; the pulse width is T p , and the widths of the N subpulses are respectively T s0 , T s1 … T s(N-1) , the carrier frequency of the nth subpulse is f n = f 0 + Δf n , and it randomly jumps within the agile bandwidth, where n = 1, 2, … N-1; f 0 is the initial carrier frequency of the subpulse, and Δf n is the frequency interval between the carrier frequency of the nth subpulse and the initial carrier frequency. The subpulse carrier frequency sequence is f 0 , f 1 , … f N - 1 , the number of chips of the nth subpulse is M n , and the phase coding sequence is The chip width is T cn , then its modulation bandwidth is B n = 1 / T cn .

[0010] One of the influencing factors for the value of the carrier frequency f n of the nth subpulse is Δf n , and Δf n satisfies a limiting condition with the bandwidth of the nth subpulse. The limiting condition is:

[0011] If frequency stepped modulation is adopted, the bandwidths of the N subpulses are respectively B 0 , B 1 , … B N-1 , then the setting formula for Δf n is as follows:

[0012]

[0013] Preferably, the total bandwidth of the signal spectrum is:

[0014]

[0015] The composite modulation radar waveform is expressed as:

[0016]

[0017] In the formula, s n(t) is the nth sub-pulse signal, and its expression is:

[0018]

[0019] In the formula is the frequency modulation term of the nth sub-pulse, and T sn is the width of the nth sub-pulse, and rect(t / T sn ) is a time rectangular window with a width of T sn .

[0020] u n (t) is the in-pulse phase modulation signal of the nth sub-pulse, and its expression is:

[0021]

[0022] In the formula, T cn is the chip width of the nth sub-pulse, is the total time width of the first n sub-pulses, and M n is the number of chips of the nth sub-pulse, is the mth phase encoding within the nth sub-pulse, and φ n (m) is the phase modulation function, which takes any value in [0, 2π);

[0023] Then the mathematical expression of the radar waveform is:

[0024]

[0025] Preferably, each sub-pulse can adopt different widths and numbers of phase encodings, and can further adopt frequency modulation between pulses.

[0026] An optimization method for a composite modulation signal with non-uniform frequency and phase provided by the present invention is based on the signal described above, and the optimization method includes the following steps:

[0027] Step S1: Input the number of sub-pulses N and the number of phase encodings M, and initialize and generate a frequency-phase composite signal with equal chip width and equal number of chips; initialize the outer iteration number num0 to 1;

[0028] Step S2: Obtain the chip width vector and the outer iteration number num0, search and optimize the chip width vector, and update the chip width vector;

[0029] Step S3: Obtain the updated chip width vector, search and optimize the chip number vector, and update the chip number vector;

[0030] Step S4: If the outer iteration number num0 reaches the preset maximum value L or the cost function satisfies the first threshold, enter step S5; otherwise, enter step S6;

[0031] Step S5: Stop the search iteration. Based on the explored and optimized parameters, substitute the searched and optimized parameters into the formula to construct a composite modulation signal with non-uniform frequency and phase. The formula is:

[0032]

[0033] The method ends;

[0034] Step S6: Assign the outer iteration number num0 as num0 + 1, and use the updated chip number vector as the chip width vector, then enter Step S2.

[0035] Preferably, in Step S2: Obtain the chip width vector and the outer iteration number num0, search and optimize the chip width vector, and update the chip width vector, including:

[0036] Step S21: Set the initial chip width vector:

[0037]

[0038] is the initial chip width of the nth sub-pulse, where 0 ≤ n ≤ N - 1;

[0039] Initialize the current first inner iteration number num1 as 1;

[0040] If the outer iteration number num0 = 1, use the initial chip number vector as the chip number vector corresponding to the current first inner iteration number num1;

[0041] If the outer iteration number num0 > 1, use the updated chip number vector as the chip number vector corresponding to the current first inner iteration number num1;

[0042] Step S22: Obtain the chip number vector corresponding to the outer iteration number num0, fix the chip number vector corresponding to the current first inner iteration number num1, and search and optimize the chip width vector corresponding to the current first inner iteration number num1 based on the coordinate descent method, including:

[0043] Step S221: Select an unoptimized chip width T cn as the current chip width T ccur and keep the remaining N - 1 chip width parameters unchanged;

[0044] Step S222: Search and optimize the current chip width T ccur among the Q possible chip width values in the chip width set : If the current chip width parameter T ccurWhen it is the q-th chip width value, the cost function is calculated to determine that the maximum performance improvement can be provided at this time, and then the q-th chip width value is used to replace the current chip width parameter T ccur with its previous value;

[0045] Step S223: If the current number of the first inner iterations num1 reaches the preset maximum value L1 or the cost function error satisfies the second threshold, obtain the final chip width vector search result and enter Step S23; otherwise, assign num1 + 1 to the current number of inner iterations num1 and enter Step S221;

[0046] Step S23: Search for the optimized chip width vector T c(end) as the updated chip width vector; since the chip width changes, the sub-pulse bandwidth also changes accordingly, and the sub-pulse carrier frequency f n is updated according to the following formula:

[0047] Preferably, the Step S3: Obtain the updated chip width vector, search and optimize the chip number vector, and update the chip number vector, includes:

[0048] Step S31: Obtain the updated chip width vector. Based on the updated chip width vector, the initial chip number vector is expressed as:

[0049]

[0050] is the initial chip number of the n-th sub-pulse, 0 ≤ n ≤ N - 1;

[0051] Initialize the current number of the second inner iterations num2 to 1;

[0052] Take the updated chip width vector T c (end) as the chip width vector corresponding to the current number of the second inner iterations num2;

[0053] Step S32: Obtain the chip width vector corresponding to the current number of the second inner iterations num2, and fix the chip width vector corresponding to the current number of the second inner iterations num2. Based on the coordinate descent method, search and optimize the chip number vector, including:

[0054] Step S321: Except for the sub-pulse of the center frequency, set the corresponding chip number set Ω for different sub-pulses Mn , to ensure that the total number of chips is fixed. Therefore, it is necessary to delete and supplement the chips to be optimized and the chips of the sub-pulse of the center frequency, and select an unoptimized chip number Mn As the current chip number M cur , the remaining N - 2 parameters of the chip number vector M remain unchanged;

[0055] Step S322: For the current chip number M cur Search and optimize among the P possible chip number values in the chip number set ; if the chip number parameter M cur is the p-th chip number value, determine the maximum performance improvement at this time by calculating the cost function, and then replace the previous value of the current chip number parameter M with the p-th chip number value. At the same time, the chip number of the center frequency sub-pulse is changed accordingly to ensure that the total number of chips remains unchanged; cur

[0056] Step S323: If the current second inner-layer iteration number num2 reaches the preset maximum value L2 or the cost function error satisfies the third threshold, obtain the final chip number vector search result and enter step S33; otherwise, assign the current second inner-layer iteration number num2 to num2 + 1 and enter step S321;

[0057] S33: The searched and optimized chip number vector M (end) is used as the updated chip number vector.

[0058] Beneficial effects:

[0059] (1) The present invention provides a method for generating a composite modulation signal with non-uniform frequency and phase. It increases the design freedom and signal complexity, dynamically modulates the radar signal spectrum distribution by allocating the time-domain and frequency-domain information of the signal, and improves the radar anti-jamming and low intercept performance. Even if the radar signal is intercepted, it is difficult to extract the important features of the signal.

[0060] (2) The present invention provides a method for optimizing a composite modulation signal with non-uniform frequency and phase. Based on the idea of coordinate descent method and cost function diversity, it searches and optimizes the signal parameters, thus greatly reducing the probability of local minimum solutions, reasonably setting the signal parameters, improving the pseudo-randomness of the signal, and enhancing the anti-jamming and low intercept performance of the signal while improving the target detection ability under clutter background. Description of the drawings

[0061] Figure 1 is a time-domain schematic diagram of a composite modulation signal with non-uniform frequency and phase proposed by the present invention;

[0062] Figure 2 is a frequency-domain schematic diagram of a composite modulation signal with non-uniform frequency and phase proposed by the present invention;

[0063] ​Figure 3 Schematic diagram of the signal optimization method proposed by the present invention;

[0064] Figure 4 Schematic diagram of the chip width vector search optimization based on the coordinate descent method and cost function diversity;

[0065] Figure 5 Schematic diagram of the chip number vector search optimization based on the coordinate descent method and cost function diversity;

[0066] Figure 6 Search optimization result diagram of the peak sidelobe level of the signal proposed by the present invention;

[0067] Figure 7 Spectrum comparison result between the conventional frequency-phase composite modulation signal and the non-uniform frequency and phase composite modulation signal after search optimization;

[0068] Figure 8 Range ambiguity function comparison result between the conventional frequency-phase composite modulation signal and the non-uniform frequency and phase composite modulation signal after search optimization. Detailed implementation manners

[0069] The present invention will be described in detail below with reference to the accompanying drawings and embodiments.

[0070] A method for generating a non-uniform frequency and phase composite modulation signal according to the present invention, as Figure 1 - Figure 2 shown, the method includes:

[0071] The signal time-domain structure is as Figure 1 shown. Through multi-subpulse modulation, each pulse is divided into N subpulses, frequency modulation is performed between the subpulses, and the serial numbers of the subpulses are marked as [0, N-1]; its pulse width is T p , and the widths of the N subpulses are T s0 , T s1 … T s(N-1) , the carrier frequency of the nth subpulse is f n = f 0 + Δf n , and randomly jumps within the agile bandwidth, where n = 1, 2, … N-1; f 0 is the initial carrier frequency of the subpulse, Δf n is the frequency interval between the carrier frequency of the nth subpulse and the initial carrier frequency, and the subpulse carrier frequency sequence is f 0 , f 1 , … f N-1 , the number of chips of the nth subpulse is M n , and the phase coding sequence is The chip width is T cn , then its modulation bandwidth is B n= 1 / T cn 。

[0072] The carrier frequency f of the nth sub-pulse n One of the influencing factors of the value is Δf n , Δf n and the bandwidth of the nth sub-pulse satisfy the limiting condition, and the limiting condition is:

[0073] If frequency stepped modulation is adopted, the bandwidths of N sub-pulses are B 0 , B 1 , … B N-1 , then the setting formula of Δf n is as follows:

[0074]

[0075] The signal spectrum structure is as Figure 2 shown, and the total bandwidth is:

[0076]

[0077] The composite modulation radar waveform can be expressed as:

[0078]

[0079] where s n (t) is the nth sub-pulse signal, and the expression is:

[0080]

[0081] where is the frequency modulation term of the nth sub-pulse, T sn is the width of the nth sub-pulse, rect(t / T sn ) is a time rectangular window with a width of T sn .

[0082] u n (t) is the in-pulse phase modulation signal of the nth sub-pulse, and the expression is:

[0083]

[0084] where T cn is the chip width of the nth sub-pulse, is the total time width of the first n sub-pulses, M n is the number of chips of the nth sub-pulse, is the mth phase encoding within the nth sub-pulse, φ n (m) is the phase modulation function, which takes any value in [0, 2π);

[0085] Then the mathematical expression of the radar waveform is as follows:

[0086]

[0087] To ensure coherent wideband synthesis processing of the signal and avoid notches or overlaps in the synthesized spectrum, which would affect the imaging performance, it is necessary to control the carrier frequency \(f\) of the sub-pulses. n of the \(n\)th sub-pulse. Furthermore, since one of the influencing factors for the value of the carrier frequency \(f\) n of the \(n\)th sub-pulse is \(\Delta f\) n , \(\Delta f\) n and the bandwidth of the \(n\)th sub-pulse should satisfy the limiting condition, i.e., Equation 1.

[0088] In this embodiment, each sub-pulse can adopt different widths and numbers of phase encodings, and frequency stepping modulation can be used between pulses; the frequency encoding and phase encoding patterns between each pulse are variable, further synthesizing a larger bandwidth signal, with flexible signal design and strong randomness. The sub-pulses in this embodiment adopt non-uniform frequency agility, non-uniform phase agility, non-uniform chip width agility, and non-uniform chip number agility. This waveform is of great significance in the fields of radar anti-jamming and low intercept technology.

[0089] The radar waveform generated in this embodiment, that is, the composite modulation signal, has a large degree of design freedom. Therefore, the waveform design is flexible and has strong randomness. By using intra-pulse frequency-phase composite coding for secondary spread spectrum, a large time-bandwidth product signal can be obtained, improving the range and velocity resolution capabilities of the signal waveform. At the same time, it can improve the pseudo-randomness of the signal, thereby greatly reducing the probability of the signal being intercepted.

[0090] To improve the pseudo-randomness and detection ability of the signal, in this embodiment, the parameters of the sub-pulse chip width and chip number are jointly optimized.

[0091] As Figure 3 shown, the present invention provides an optimization method for a composite modulation signal with non-uniform frequency and phase, including the following steps:

[0092] Step S1: Input the number of sub-pulses \(N\) and the number of phase encodings \(M\), and initialize and generate a frequency-phase composite signal with equal chip width and equal chip number; initialize the outer iteration number \(num0\) to 1;

[0093] Step S2: Obtain the chip width vector and the outer iteration number \(num0\), search and optimize the chip width vector, and update the chip width vector;

[0094] Step S3: Obtain the updated chip width vector, search and optimize the chip number vector, and update the chip number vector;

[0095] Step S4: If the number of outer iterations num0 reaches the pre-set maximum value L or the cost function satisfies the first threshold, proceed to Step S5; otherwise, proceed to Step S6;

[0096] Step S5: Stop the search iteration. Based on the explored and optimized parameters, substitute the searched and optimized parameters into the formula to construct a composite modulation signal with non-uniform frequency and phase. The formula is:

[0097]

[0098] The method ends;

[0099] Step S6: Assign num0 + 1 to the number of outer iterations num0, and use the updated chip number vector as the chip width vector, then proceed to Step S2.

[0100] The optimization idea of this embodiment is as follows: First, determine the number of sub-pulses and phase encoding. Each sub-pulse signal is initialized with equal chip width and equal number of chips. From the method for generating a composite modulation signal with non-uniform frequency and phase, it can be seen that the chip width and number of the signal are variable. Therefore, the chip width and number can be jointly optimized. The search strategy used here is the coordinate descent method, and the chip width vector T c and the chip number vector M are changed according to an appropriate optimization metric criterion. When the number of iterations reaches the pre-set maximum value or the cost function error satisfies the threshold, the parameter update is stopped, and the optimized composite modulation signal with non-uniform frequency and phase is output.

[0101] In this embodiment, the cost function changes with the number of iterations. If only performance parameters such as the Peak Sidelobe Level (PSL), Integrated Sidelobe Level (ISL), and Frequency Template Error (FTE) of the signal are used as the cost function, it is easy to reach the local optimality condition. By changing different cost functions to solve the local minimum solution problem, this method is called cost diversity because the probability of different cost functions reaching the same local optimality condition in the search space is very small. For example, use the cost function set {PSL, ISL, FTE} to repeat the search process, where the local minimum solution of each cost function is used as the initialization of the next cost function, and cost function diversity is used to avoid obtaining a local minimum by searching a single cost function.

[0102] The said Step S2: Obtain the chip width vector and the number of outer iterations num0, search and optimize the chip width vector, and update the chip width vector, including:

[0103] Step S21: Set the initial chip width vector:

[0104]

[0105] is the initial chip width of the nth sub-pulse, where 0 ≤ n ≤ N - 1;

[0106] Initialize the current first inner iteration number num1 to 1;

[0107] If the outer iteration number num0 = 1, use the initial chip number vector as the chip number vector corresponding to the current first inner iteration number num1;

[0108] If the outer iteration number num0 > 1, use the updated chip number vector as the chip number vector corresponding to the current first inner iteration number num1;

[0109] Step S22: Obtain the chip number vector corresponding to the outer iteration number num0, fix the chip number vector corresponding to the current first inner iteration number num1, and perform search optimization on the chip width vector corresponding to the current first inner iteration number num1 based on the coordinate descent method, including:

[0110] Step S221: Select an unoptimized chip width T cn as the current chip width T ccur , and keep the remaining N - 1 chip width parameters unchanged;

[0111] Step S222: Search and optimize the current chip width T ccur among the Q possible chip width values in the chip width set : If the current chip width parameter T ccur is the qth chip width value, determine the maximum performance improvement at this time by calculating the cost function, and replace the previous value of the current chip width parameter T ccur with the qth chip width value;

[0112] Step S223: If the current first inner iteration number num1 reaches the preset maximum value L1 or the cost function error satisfies the second threshold, obtain the final chip width vector search result and enter step S23; otherwise, assign the current inner iteration number num1 to num1 + 1 and enter step S221;

[0113] Step S23: The search-optimized chip width vector T c (end) is used as the updated chip width vector; Since the chip width changes, the sub-pulse bandwidth also changes accordingly, and the sub-pulse carrier frequency f n is updated according to the following formula:

[0114] Step S2 determines the optimal solution through independent parallel search, constructs a set of cost functions Φ with different measurement criteria, and this search process can be expressed as:

[0115]

[0116] where are the values of the independent variables n and l when the function reaches the minimum.

[0117] The said step S3: Obtain the updated chip width vector, search and optimize the chip number vector, and update the chip number vector, including:

[0118] Step S31: Obtain the updated chip width vector. Based on the updated chip width vector, the initial chip number vector is expressed as:

[0119]

[0120] is the initial chip number of the nth sub-pulse, 0 ≤ n ≤ N - 1;

[0121] Initialize the current second inner iteration number num2 to 1;

[0122] Take the updated chip width vector T c (end) as the chip width vector corresponding to the current second inner iteration number num2;

[0123] Step S32: Obtain the chip width vector corresponding to the current second inner iteration number num2, and fix the chip width vector corresponding to the current second inner iteration number num2. Search and optimize the chip number vector based on the coordinate descent method, including:

[0124] Step S321: Except for the center frequency sub-pulse, set corresponding chip number sets for different sub-pulses To ensure that the total number of chips is fixed, it is necessary to delete and supplement the chips to be optimized and the chips of the center frequency sub-pulse. Select an unoptimized chip number M n as the current chip number M cur , and keep the remaining N - 2 parameters of the chip number vector M unchanged;

[0125] Step S322: Search and optimize the current chip number M cur among the P possible chip number values in the chip number set ; if the chip number parameter M curWhen it is the p-th chip quantity value, calculate the cost function to determine that the maximum performance improvement can be provided at this time, and then replace the current chip quantity parameter M with the p-th chip quantity value cur At the same time, the chip quantity of the center frequency sub-pulse is changed accordingly to ensure that the total chip quantity remains unchanged;

[0126] Step S323: If the current second inner-layer iteration number num2 reaches the preset maximum value L2 or the cost function error meets the third threshold, obtain the final chip quantity vector search result Enter step S33; otherwise, assign the current second inner-layer iteration number num2 to num2 + 1 and enter step S321;

[0127] S33: Search for the optimized chip quantity vector M (end) As the updated chip quantity vector.

[0128] Step S3 determines the optimal solution through independent parallel search, and this search process can be described as:

[0129]

[0130] In this embodiment, the chip quantity vector search optimization based on the coordinate descent method and cost function diversity is used. While increasing the signal complexity, improving the anti-jamming performance and low intercept performance, it ensures the excellent detection performance of the signal itself.

[0131] The following gives a simulation example applying the present invention and analyzes and explains its implementation process.

[0132] As Figure 1 shown, assume that the number of sub-pulses N = 5 and the total chip quantity M = 450.

[0133] Step 1. Initialize the signal: The chip width and the chip quantity of the sub-pulse are equal, and the initialized conventional frequency-phase composite modulation signal is generated according to the parameters in Table 1 below;

[0134] Table 1 Simulation parameters of the initialized signal

[0135]

[0136] Step 2. Update the chip width parameter: As Figure 4 shown, construct a composite modulation signal with non-uniform frequency and phase, search and optimize the chip width vector based on the coordinate descent method, fix the chip quantity vector, and the chip width set is Use {PSL, ISL, PSL} as the cost function diversity Φ, and output the optimized chip width vector as the initialization parameter for the next step;

[0137] Step 3. Update the chip quantity parameter: AsFigure 5 As shown, based on the coordinate descent method, the chip number vector is searched and optimized. The chip width vector is fixed, and sub-pulse 3 is set as the center frequency pulse. The search range is set for the chip numbers of the remaining sub-pulses. The chip number set of sub-pulse 1 is The chip number set of sub-pulse 2 is The chip number set of sub-pulse 4 is The chip number set of sub-pulse 5 is The cost function diversity is the same as in step 2, and the optimized chip number vector is output as the initialization parameter for the next step;

[0138] Step 4: Convergence judgment: If the pre-set maximum value is reached or the cost function meets the threshold, the search is terminated; otherwise, the iteration count is incremented by 1, and it returns to step 2.

[0139] According to the above steps and set conditions, the iterative optimization results are as Figure 6 shown. The final non-uniform frequency and phase composite modulation signal is obtained by searching and optimizing the signal parameters according to Table 2 below.

[0140] Table 2 Signal simulation parameters after search and optimization

[0141]

[0142] Performing simulation and comparative analysis on the above two signals, the results are as Figure 7 , Figure 8 shown.

[0143] The conventional frequency-phase composite modulation signal forms a rectangular spectrum in the frequency domain, and the time-domain autocorrelation result is the inverse Fourier transform result of its power spectrum. It can be seen that its autocorrelation result has poor performance, and the PSL is -15.02 dB;

[0144] The non-uniform frequency and phase composite modulation signal forms a window-shaped spectrum in the frequency domain, with a PSL of -25.33 dB. Compared with the above signal, the PSL performance is improved, and the signal has higher complexity, stronger pseudo-randomness, and more flexible and diverse modulation methods. Even when the enemy passive detection system intercepts this signal, it is difficult to obtain useful information. Therefore, this signal has good anti-jamming performance, low intercept performance, radio frequency stealth performance, and detection performance, and has good application prospects in modern electronic warfare.

[0145] The above specific embodiments only describe the design principle of the present invention. The shapes and names of the components in this description can be different and are not limited. Therefore, those skilled in the art of the present invention can modify or equivalently replace the technical solutions recorded in the foregoing embodiments; and these modifications and replacements do not depart from the gist and technical solutions of the present invention, and shall all fall within the protection scope of the present invention.

Claims

1. An optimization method for a composite modulation signal with non-uniform frequency and phase, characterized in that, the optimization method comprises the following steps: Step S1: Input the number of sub-pulses N and the number of phase encodings M, and initialize and generate a frequency-phase composite signal with equal chip widths and equal chip numbers; initialize the number of outer iterations num0 to 1; Step S2: Obtain the chip width vector and the number of outer iterations num0, search and optimize the chip width vector, and update the chip width vector; Step S3: Obtain the updated chip width vector, search and optimize the chip number vector, and update the chip number vector; Step S4: If the number of outer iterations num0 reaches a preset maximum value L or the cost function satisfies the first threshold, enter Step S5; otherwise, enter Step S6; Step S5: Stop the search iteration, and based on the explored and optimized parameters, substitute the searched and optimized parameters into the formula to construct a composite modulation signal with non-uniform frequency and phase. The formula is: The method ends; Step S6: Assign num0 + 1 to the number of outer iterations num0, and use the updated chip number vector as the chip width vector, then enter Step S2; The generation method of the composite modulation signal with non-uniform frequency and phase includes: Through multi-sub-pulse modulation, each pulse is divided into N sub-pulses, frequency modulation is performed between the sub-pulses, and the serial numbers of the sub-pulses are marked as [0, N-1]; the pulse width is T p , the widths of the N sub-pulses are respectively T s0 , T s1 … T s(N-1) , the carrier frequency of the nth sub-pulse is f n = f 0 + Δf n , and it randomly jumps within the agile bandwidth, where n = 1, 2, … N-1; f 0 is the initial carrier frequency of the sub-pulse, and Δf n is the frequency interval between the carrier frequency of the nth sub-pulse and the initial carrier frequency. The sub-pulse carrier frequency sequence is f 0 , f 1 , … f N-1 , the number of chips of the nth sub-pulse is M n , and the phase coding sequence is The chip width is T cn , then its modulation bandwidth is B n = 1 / T cn ; The carrier frequency f of the nth sub-pulse n One of the influencing factors of the value of n is Δf n Δf satisfies a limiting condition with the bandwidth of the nth sub-pulse, and the limiting condition is: If frequency-stepped modulation is adopted, the bandwidths of N sub-pulses are B 0 , B 1 , … B N-1 , then the setting formula of Δf n is as follows:

2. The method according to claim 1, characterized in that, Step S2 in the above: Obtain the chip width vector and the number of outer iterations num0, search and optimize the chip width vector, and update the chip width vector, includes: Step S21: Set the initial chip width vector: is the initial chip width of the nth sub-pulse, where 0 ≤ n ≤ N - 1; Initialize the current first inner iteration number num1 to 1; If the number of outer iterations num0 = 1, use the initial chip number vector as the chip number vector corresponding to the current first inner iteration number num1; If the number of outer iterations num0 > 1, use the updated chip number vector as the chip number vector corresponding to the current first inner iteration number num1; Step S22: Obtain the chip number vector corresponding to the number of outer iterations num0, fix the chip number vector corresponding to the current first inner iteration number num1, and search and optimize the chip width vector corresponding to the current first inner iteration number num1 based on the coordinate descent method, including: Step S221: Select an unoptimized chip width T cn as the current chip width T ccur , and keep the remaining N-1 chip width parameters unchanged; Step S222: For the current chip width T ccur Perform a search optimization among the Q possible chip width values in the chip width set : If the current chip width parameter T ccur is the q-th chip width value, determine that the maximum performance improvement can be provided at this time by calculating the cost function, and then replace the previous value of the current chip width parameter T ccur with the q-th chip width value; Step S223: When the current number of first inner-layer iterations num1 reaches a preset maximum value L1 or the cost function error meets the second threshold, obtain the final search result of the chip width vector Proceed to step S23; otherwise, assign num1 + 1 to the current number of inner-layer iterations num1 and proceed to step S221; Step S23: Search for the optimized chip width vector T c(end) as the updated chip width vector; since the chip width changes, the sub-pulse bandwidth also changes accordingly, and the sub-pulse carrier frequency f n is updated according to the following formula:

3. The method according to claim 2, characterized in that, Step S3 in the above: Obtain the updated chip width vector, search and optimize the chip number vector, and update the chip number vector, includes: Step S31: Obtain the updated chip width vector. Based on the updated chip width vector, the initial chip number vector is expressed as: is the initial chip number of the n-th sub-pulse, where 0 ≤ n ≤ N - 1; Initialize the current second inner iteration number num2 to 1; Take the updated chip width vector T c (end) as the chip width vector corresponding to the current second inner iteration number num2; Step S32: Obtain the chip width vector corresponding to the current second inner iteration number num2, and fix the chip width vector corresponding to the current second inner iteration number num2, and search and optimize the chip number vector based on the coordinate descent method, including: Step S321: Except for the central frequency sub-pulse, set corresponding chip number sets for different sub-pulses To ensure that the total number of chips is fixed, it is necessary to delete and supplement the chip numbers to be optimized and the chip numbers of the central frequency sub-pulse, and select an unoptimized chip number M n as the current chip number M cur , and the remaining N - 2 parameters of the chip number vector M remain unchanged; Step S322: For the current chip number M cur Search and optimize among the P possible chip number values in the chip number set ; if the chip number parameter M cur is the p-th chip number value, determine that the maximum performance improvement can be provided at this time by calculating the cost function, and then replace the previous value of the current chip number parameter M with the p-th chip number value. At the same time, the chip number of the center frequency sub-pulse is changed accordingly to ensure that the total number of chips remains unchanged; cur ​ Step S323: If the current number of second inner-layer iterations num2 reaches the pre-set maximum value L2 or the cost function error meets the third threshold, obtain the final search result of the chip number vector Proceed to step S33; otherwise, assign the current number of second inner-layer iterations num2 the value of num2 + 1, and proceed to step S321; S33: Search for the optimized chip number vector M (end) as the updated chip number vector.

4. The method according to claim 1, characterized in that: The total bandwidth of the signal spectrum is: The composite modulation radar waveform is expressed as: where s n (t) is the nth sub-pulse signal, and its expression is: In the formula is the frequency modulation term of the nth sub-pulse, and T sn is the width of the nth sub-pulse, and rect(t / T sn ) is a time rectangular window with a width of T sn ; u n (t) is the in-pulse phase modulation signal of the nth sub-pulse, and its expression is: where T cn is the chip width of the nth sub-pulse, is the total time width of the first n sub-pulses, M n is the number of chips of the nth sub-pulse, is the mth phase encoding within the nth sub-pulse, φ n (m) is the phase modulation function, taking any value in [0, 2π); Then the mathematical expression of the radar waveform is:

5. The method according to claim 1, characterized in that, Each sub-pulse can adopt phase encoding with different widths and numbers, and can further adopt frequency modulation between pulses.

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