MIMO radar waveform design method based on multi-dimensional joint coding

Abstract

The application discloses a MIMO radar waveform design method based on multi-dimensional joint coding, and mainly aims at solving the problems of low waveform design freedom, poor resolution performance and simple waveform form which is easily intercepted. The implementation steps are as follows: constructing a multi-dimensional joint coding MIMO radar waveform initial model; calculating the pulse synthesis result of each sampling point of each target sampling angle by using the echo signal of each target sampling angle of the generated radar array; constructing a cost function of a waveform optimization algorithm according to the sidelobe value of the pulse synthesis result; setting the constraint condition of the waveform optimization algorithm; and optimizing the MIMO radar waveform by using the cost function and the constraint condition. The MIMO radar waveform designed by the application increases the design freedom of the waveform, improves the resolution performance of the radar system on the target, and makes the waveform form complex, thereby improving the anti-interception performance of the waveform.

Description

Technical Field

[0001] This invention belongs to the field of radar technology, and further relates to a multi-input multiple output (MIMO) radar waveform design method based on multi-dimensional joint coding. This invention can be applied to designing the transmit waveform of a MIMO radar system, achieving excellent resolution performance while designing MIMO radar transmit waveforms with low intercept performance. Background Technology

[0002] With the development of radar countermeasures technology, the anti-interception and anti-jamming capabilities of radars have weakened. To ensure that radars function better and survive effectively, the most effective solution in waveform design is to design a waveform with good anti-interception performance. MIMO radars have extremely high waveform design freedom, allowing the transmitted energy to be concentrated in any area of ​​the airspace, and their performance in parameter discrimination and anti-interception is stronger than that of traditional phased array radars. Phase-coded signals have a high degree of design freedom and are easy to implement agility, therefore they are more widely used in anti-interception waveform design.

[0003] In his dissertation "MIMO Radar Waveform Design" (Xi'an University of Electronic Science and Technology, 2010 doctoral dissertation), Hu Liangbing proposed a phase-coded MIMO radar waveform design method. The method involves using the waveform covariance matrix of the ideal energy coverage range in the spatial domain as a constraint, calculating the pulse synthesis result from the array's waveform matrix, and using the sidelobe peak value of the obtained pulse synthesis result as a cost function to construct an optimization model. A sequential quadratic programming algorithm is used for optimization, with the phase of each symbol in the phase-coded signal as the parameter to be optimized. This algorithm simultaneously sets an optimization range for the parameter to be optimized, and the final transmitted waveform is obtained by optimizing the parameter. The method has shortcomings. Since the optimization degrees of freedom affect the algorithm's optimization effect, this method only has one parameter to be optimized, resulting in low degrees of freedom and thus high sidelobe peak values ​​in the pulse synthesis result. This affects the target resolution performance when processing the echo signal. Similarly, the limited number of waveform parameters to be optimized leads to an overly simple final transmitted waveform, making it vulnerable to interception by intercepting receivers in practical engineering applications.

[0004] The National University of Defense Technology disclosed a multi-dimensional joint coding radar waveform design method in its patent application, "A Multi-Dimensional Joint Coding Radar Waveform Design and Processing Method" (Patent Application No. CN 202210959947.X, Publication No. CN 115308706 A). The implementation steps of this waveform design method are as follows: The transmitted waveform is jointly modulated by amplitude, frequency, and phase. This can be viewed as amplitude coding modulation of an intra-pulse frequency agile-phase coded waveform. The pulse synthesis result is calculated using the modulated waveform matrix, and the final radar waveform is obtained by optimizing the sidelobe peaks of the pulse synthesis result. While this method increases the degree of freedom in waveform design and thus improves waveform complexity, it still has shortcomings. The amplitude coding modulation of the transmitted waveform leads to a non-constant mode waveform in the designed waveform. Non-constant mode waveforms have lower energy utilization than constant mode waveforms, resulting in significant energy waste when transmitting non-constant mode waveforms designed by this method. Summary of the Invention

[0005] The purpose of this invention is to address the shortcomings of existing technologies by proposing a multi-dimensional joint coding method for designing MIMO radar waveforms. This method solves the problems of low waveform design freedom leading to poor resolution, simple waveform forms making them easy to intercept, and waveforms with non-constant modulus wasting energy.

[0006] The specific approach to achieving the objective of this invention is as follows: This invention divides the waveform transmitted by each array element into sub-pulse intervals, using the sub-pulse duration as the interval. Each sub-pulse is then simultaneously subjected to multi-dimensional joint coding modulation, including modulation of the sub-pulse duration, phase, and frequency. This increases design freedom and waveform complexity, thereby solving the problems of poor waveform resolution and susceptibility to interception. No modulation is applied to the waveform amplitude during the design process, thus addressing the issue of wasted energy due to non-constant modulus waveforms. The pulse synthesis result of the echo signal is used as a cost function, and the transmitted energy coverage range is used as a constraint. Based on the cost function and constraints, the waveform is optimized to obtain the final MIMO radar waveform.

[0007] The specific steps of this invention include the following:

[0008] Step 1. Construct an initial model of the MIMO radar waveform using multi-dimensional joint coding:

[0009] The waveform transmitted by each array element is divided into sub-pulse intervals, and the time, phase and frequency of each sub-pulse are simultaneously coded and modulated to obtain the agile MIMO radar waveform.

[0010] Step 2. Using the echo signal from each target sampling angle of the generated radar array, calculate the pulse synthesis result for each sampling point of each target sampling angle;

[0011] Step 3. Construct the cost function of the waveform optimization algorithm based on the sidelobe values ​​of the pulse synthesis results;

[0012] Step 4. Set the constraints for the waveform optimization algorithm;

[0013] Step 5. Optimize the MIMO radar waveform using the cost function and constraints.

[0014] Compared with the prior art, the present invention has the following advantages:

[0015] First, this invention performs joint coding and modulation of phase, frequency, and time width on the sub-pulses of the transmitted waveforms of all array elements simultaneously, increasing the number of parameters to be optimized during optimization. This overcomes the shortcomings of low optimization freedom and overly simple waveform forms in the prior art, making the MIMO radar waveform designed in this invention less likely to be intercepted by the intercepting receiver during transmission. When processing the echo signal, it reduces the sidelobes of the pulse synthesis result and improves the anti-interception performance and resolution performance of the radar system.

[0016] Secondly, the present invention does not modulate the waveform amplitude in the entire MIMO radar waveform design process, which overcomes the shortcomings of the existing technology where the designed waveform is not constant due to amplitude modulation. This makes the MIMO radar waveform designed by the present invention constant in magnitude, which improves the energy utilization rate of the radar system when it is transmitted by the radar system. Attached Figure Description

[0017] Figure 1 This is a flowchart of the present invention;

[0018] Figure 2 The figure shows the simulation results of this invention. Detailed Implementation

[0019] The present invention will be further described below with reference to the accompanying drawings and embodiments.

[0020] Reference Figure 1 The specific steps for implementing the embodiments of the present invention will be further described below.

[0021] Step 1. Construct an initial model of the MIMO radar waveform with multidimensional joint coding.

[0022] The waveform transmitted by each array element is divided into sub-pulse intervals, and each sub-pulse is simultaneously encoded and modulated in terms of phase, frequency, and time width to obtain agile MIMO radar waveforms.

[0023] The duration of the above sub-pulse is obtained by the following formula:

[0024]

[0025] Where τ′(l) represents the duration of the l-th sub-pulse, τ(l) represents the random number selected from the l-th sub-pulse, l = 1, 2, ..., L, and L represents the total number of sub-pulses, T e This indicates the pulse width of the transmitted signal.

[0026] The modulation of phase, frequency, and time width is accomplished by the following formula:

[0027]

[0028] Among them, s m Let represent the agile waveform of the m-th element in the modulated MIMO radar waveform, where m = 1, 2, 3, ..., M, M represents the total number of radar array elements, rect[] represents a rectangular window, and t represents the time interval [0, T]. e Sampling time within the range, τ m (l) represents the modulation time of the l-th sub-pulse in the agile waveform of the m-th array element, exp[·] represents the exponential operation with the natural constant e as the base, j represents the imaginary unit sign, φ m (l) represents the modulation phase of the l-th sub-pulse in the agile waveform of the m-th array element, φ m (l) takes values ​​in the range [0, 2π), f m (l) represents the modulation frequency of the l-th sub-pulse in the transmitted waveform of the m-th array element, f m (l) takes values ​​in the range [0, f max ], f max The value is equal to the reciprocal of the narrowest sub-pulse width among all sub-pulses of the agile waveform.

[0029] Step 2. Using the echo signal of each target sampling angle of the generated radar array, calculate the pulse synthesis result of each sampling point of each target sampling angle.

[0030] The echo signals for each target sampling angle of the generated radar array are as follows:

[0031] S r =a(θ) p ) T S

[0032] Among them, S r Indicates the target sampling angle θ p The echo signal at point p = 1, 2, ..., P, where P represents the total number of target sampling angles within the transmission energy coverage area, and a(θ) p ) indicates that the MIMO radar array is pointing towards θ p The guiding vector at point a(θ) p )=[1,exp(j2πdsinθ p / λ),…,exp(j2πdsinθ p / λ)] T ,(·) T This indicates the transpose operation, and S represents the agile waveform matrix of the MIMO radar array.

[0033] The pulse synthesis result for each sampling point at each target sampling angle is obtained by the following formula:

[0034] y(θ p ,n)=xcorr(S r )

[0035] Where y(θ) p (n) represents the target sampling angle θ p The pulse synthesis result of the nth sampling point at point n, n = 1, 2, ..., 2N-1, where N represents the pulse synthesis result at point n in [0, T]. e The total number of sampling points within the range, xcorr(·) represents the autocorrelation function.

[0036] The radar antenna array can be of any configuration. In this embodiment of the invention, a uniform linear array is selected to receive radar target echo signals.

[0037] Step 3. Construct the cost function of the waveform optimization algorithm based on the sidelobe values ​​of the pulse synthesis results.

[0038] The cost function of the waveform optimization algorithm is as follows:

[0039]

[0040] Where J represents the cost function of the waveform optimization algorithm, Φ represents the set of all sub-pulse phases, and F represents the set of all sub-pulse frequencies. This indicates that at the target sampling angle [θ1, θ2]... P Within the range (0, N-1), min(·) represents the operation of taking the maximum value of the pulse synthesis result for sampling points in the range (0, N-1]. The operation that takes the minimum value obtained is called |·|, which represents the modulo operation.

[0041] Step 4. Set the constraints for the waveform optimization algorithm as follows:

[0042]

[0043] Among them, ||·|| F This indicates the F-norm operation, [·] H denoted by conjugate transpose operation, and R represents the waveform covariance matrix of the desired emission energy coverage area.

[0044] Step 5. Optimize the MIMO radar waveform using the cost function and constraints.

[0045] The steps for optimizing the MIMO radar waveform are as follows:

[0046] First, construct the first column vector, where all elements are 0, and the total number of elements is 2×K×G. Then, construct the second column vector, where the first K×G elements have a value of 2π, and the last K×G elements have a value of f. max The total number of elements is 2×K×G, where the value of K is equal to that of M, and the value of G is equal to that of L.

[0047] The second step is to use the cost function J as the function function of the optimization algorithm, the constraint condition as the constraint function of the optimization algorithm, and substitute the phase Φ and frequency F of all waveform sub-pulses into the fminimax optimization function. The minimum value vector of Φ and F optimized by the function is set as the first column vector mentioned in the first step, and the maximum value vector of Φ and F optimized by the function is set as the second column vector mentioned in the first step.

[0048] The third step is to perform iterative calculations on the function and select the phase and frequency corresponding to the minimum value in the iteration results as the phase and frequency of the optimized waveform sub-pulse.

[0049] The effects of this invention will be further illustrated below with simulation experiments:

[0050] 1. Simulation experimental conditions.

[0051] The software platform for the simulation experiment of this invention is: Windows 10 operating system and Matlab R2020b.

[0052] 2. Simulation content and result analysis.

[0053] The simulation experiments of this invention are three.

[0054] Simulation Experiment 1 simulates the time-domain waveform of the spatially synthesized signal of the MIMO radar waveform; Simulation Experiment 2 simulates the energy coverage map of the MIMO radar waveform; and Simulation Experiment 3 simulates the pulse synthesis results of the MIMO radar waveform at -5°, 0°, and 5°.

[0055] The existing technology refers to the method proposed by Hu Liangbing in his published paper "MIMO Radar Waveform Design" (Xi'an University of Electronic Science and Technology, 2010 doctoral dissertation).

[0056] Simulation Experiment 1 simulates the time-domain waveform of the spatially synthesized signal of the MIMO radar waveform.

[0057] The MIMO radar system used in simulation experiment 1 of this invention has a uniform linear array transmitting array with M = 8 elements, an element spacing of half a wavelength, and a signal duration T.e =25μs, number of sub-pulses L=50, control of the narrowest sub-pulse duration is 0.25µs, sub-pulse frequency modulation range is [0,4MHz], phase modulation range is (0,2π], transmit signal spatial domain synthesis bandwidth is B=8MHz, sampling frequency f s =8MHz, the desired transmit energy coverage beamwidth is 20°, and the beam center points to θ0 = 0°.

[0058] Simulation Experiment 1 of this invention uses the methods of this invention and existing technologies to obtain two curves for each method when pointing to 0°, representing the real and imaginary parts of the time-domain waveform of the spatially synthesized signal, respectively. The real and imaginary parts of the obtained time-domain waveforms are then plotted as follows: Figure 2 The four curves shown in (a) are shown in the middle.

[0059] Simulation Experiment 2 is a simulation of the energy coverage map of the MIMO radar waveform.

[0060] The parameters in simulation experiment 2 are the same as those in simulation experiment 1.

[0061] Simulation Experiment 2 of this invention uses the methods of this invention and existing technologies to obtain the energy distribution in the entire spatial domain, and then plots the obtained energy distribution as shown in the figure. Figure 2 The two curves shown in (b) are shown in the middle.

[0062] Simulation Experiment 3 simulates the pulse synthesis results of the MIMO radar waveform at -5°, 0° and 5° respectively.

[0063] The parameters in simulation experiment 3 are the same as those in simulation experiment 1.

[0064] Simulation Experiment 3 of this invention uses the method of this invention and a prior art to obtain pulse synthesis results at -5°, 0°, and 5°, respectively. The pulse synthesis results obtained at -5° are then plotted as shown below. Figure 2 The two curves shown in (c) are plotted as follows: The pulse synthesis results obtained at 0° are plotted as follows. Figure 2 The two curves shown in (d) are plotted as follows: The pulse synthesis results obtained at 5° are plotted as follows. Figure 2 The two curves shown in (e) are shown in the middle.

[0065] The following is combined with Figure 2 The simulation diagrams further illustrate the effects of the present invention.

[0066] Figure 2 In diagram (a), the horizontal axis represents the time delay of the transmitted waveform of the MIMO radar system, in μs, and the vertical axis represents the amplitude. The dashed line represents the time-domain waveform obtained using existing simulation techniques, while the solid line represents the time-domain waveform obtained using the method proposed in this invention.

[0067] from Figure 2 As can be seen from (a) in the present invention, the time-domain waveform of the spatially synthesized signal at 0° obtained by the method of the present invention has a faster amplitude change and a more complex waveform form compared with the prior art, thus improving the anti-interception performance of the waveform.

[0068] Figure 2 In (b), the horizontal axis represents the spatial coverage angle of the MIMO radar waveform in degrees, and the vertical axis represents the normalized amplitude in dB. The dotted line represents the ideal transmit energy coverage map, the dashed line represents the MIMO radar waveform transmit energy coverage map obtained using existing technology, and the solid line represents the MIMO radar waveform transmit energy coverage map obtained using the method proposed in this invention.

[0069] from Figure 2 As can be seen from (b) in the figure, the energy coverage map within the ideal range obtained by the method of the present invention has the same main lobe coverage as the prior art, the side lobes are slightly raised, and the overall difference is not significant.

[0070] Figure 2 In (c), (d), and (e), the horizontal axis represents the time delay of the MIMO radar waveform pulse synthesis result, in μs, and the vertical axis represents the amplitude, in dB. The dashed asterisk line represents the pulse synthesis result of the MIMO radar waveform obtained using existing techniques, while the solid line represents the pulse synthesis result of the MIMO radar waveform obtained using the method proposed in this invention.

[0071] from Figure 2 As can be seen from (c), (d) and (e), the method of the present invention has lower side lobes in the pulse synthesis results when pointing to -5°, 0° and 5° in the airspace than the methods of the prior art, and the pulse synthesis main lobe is also narrower, which improves the target resolution performance of the radar system.

Claims

1. A MIMO radar waveform design method based on multi-dimensional joint coding, characterized in that, The waveform transmitted by each array element is divided into sub-pulse intervals. Each sub-pulse is then simultaneously subjected to joint coding modulation of its time width, phase, and frequency. The MIMO radar waveform is optimized based on the pulse synthesis results of the modulated waveforms. The steps of this waveform design method include the following: Step 1. Construct the initial model of the MIMO radar waveform with multi-dimensional joint coding: The waveform transmitted by each array element is divided into sub-pulse intervals, and the time, phase and frequency of each sub-pulse are simultaneously coded and modulated to obtain the agile MIMO radar waveform. The duration of the sub-pulse is obtained by the following formula: ； in, Indicates the first The duration of each sub-pulse Indicates from the first Random numbers selected from each sub-pulse , This indicates the total number of sub-pulses. Indicates the pulse width of the transmitted signal; The modulation of phase, frequency, and time width is accomplished by the following formula: ； in, Indicates the first digit of the modulated MIMO radar waveform. The agile waveform of each array element , This indicates the total number of elements in the radar array. This represents a rectangular window. Indicates in Sampling time within the range, Indicates the first In the agile waveform of each array element, the first... The modulation duration of each sub-pulse This indicates an exponential operation with the natural constant e as the base. The symbol representing the imaginary unit. Indicates the first In the agile waveform of each array element, the first... The modulation phase of each sub-pulse The range of values ​​is , Indicates the first In the waveform emitted by the array element, the first The modulation frequency of each sub-pulse The range of values ​​is , The value is equal to the reciprocal of the narrowest sub-pulse width among all sub-pulses of the agile waveform; Step 2. Using the echo signal from each target sampling angle of the generated radar array, calculate the pulse synthesis result for each sampling point of each target sampling angle; The echo signal of each target sampling angle of the radar array is obtained by the following formula: ； in, Indicates the target sampling angle echo signal at that location, , This represents the total number of target sampling angles within the range of the emitted energy. Indicates the direction of the MIMO radar array The guide vector at that location, This indicates the transpose operation. Represents the agile waveform matrix of a MIMO radar array; The pulse synthesis result of each sampling point at each target sampling angle is obtained by the following formula: ； in, Indicates the target sampling angle The first The pulse synthesis result of each sampling point , Indicates in The total number of sampling points within the range, Represents the autocorrelation function; Step 3. Construct the cost function for the waveform optimization algorithm based on the sidelobe values ​​of the pulse synthesis results: ； in, This represents the cost function of the waveform optimization algorithm. Represents the set of all sub-pulse phases. This represents the set of all sub-pulse frequencies. Indicates the target sampling angle Within the range, for sampling points The operation of taking the maximum value of the pulse synthesis result within the range. Indicates to The operation of taking the minimum value from the maximum value. Indicates a modulo operation; Step 4. Set the constraints for the waveform optimization algorithm as follows: ； in, This indicates the F-norm operation. This indicates the conjugate transpose operation. The waveform covariance matrix represents the expected range of emitted energy coverage. Step 5. Optimize the MIMO radar waveform using the cost function and constraints.

2. The MIMO radar waveform design method based on multi-dimensional joint coding according to claim 1, characterized in that, The steps for optimizing the MIMO radar waveform described in step 5 are as follows: The first step is to construct the first column vector, in which all elements are 0, and the total number of elements is 0. Construct a second column vector, in which the first... The value of each element is ,back The value of each element is The total number of elements is , The value of and equal, The value of and equal; The second step is to apply the aforementioned cost function. As the function of the optimization algorithm, the aforementioned constraints are used as the constraint function of the optimization algorithm, and the phase of all waveform sub-pulses is determined. and frequency Substituting into the fminimax optimization function, the function is optimized... and Let the minimum value vector be the first column vector mentioned in the first step, and optimize the function. and The maximum value vector is set as the second column vector mentioned in the first step; The third step is to perform iterative calculations on the function and select the phase and frequency corresponding to the minimum value in the iteration results as the phase and frequency of the optimized waveform sub-pulse.

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