Intra-pulse frequency encoding method combined with multiple mismatch filter optimization design

Abstract

The application discloses an intra-pulse frequency coding method combined with multiple mismatch filter optimization design, comprising the following steps: obtaining an optimized frequency set according to an optimization cost function, and designing an intra-pulse sparse frequency coding waveform with low distance grating lobes; dividing a signal into three segments according to prior information of interference, and making the frequency band sets of the three signal segments orthogonal to each other through secondary optimization; obtaining an echo signal of a disturbed agile frequency waveform according to a model based on a pulse echo signal and an interference signal; performing down-conversion processing on the echo signal of the agile waveform to obtain a down-converted disturbed baseband echo signal; taking the pulse echo signal, a signal segment of an interference sampling part and a signal segment of a first retransmission of the intermittent sampling interference as a matching function of pulse compression, and obtaining an interference-free target echo signal through cancellation means. The application eliminates the intermittent sampling interference based on the mismatch filter, thereby effectively reducing the influence of residual interference in the interference transition band.

Description

TECHNICAL FIELD

[0001] The present application belongs to the technical field of radar, and particularly relates to an intra-pulse frequency coding method with optimized design of a multiple mismatched filter. BACKGROUND

[0002] With the increasing types of active deception jamming generated by the jammer based on digital radio frequency memory storage and forwarding equipment, the jamming performance is getting better and better, and thus the problem that the radar cannot work normally due to jamming is increasingly prominent. The active deception jamming is generated by modulating and forwarding the intercepted radar signal through the digital radio frequency memory, attacks and destroys the working system of the radar. The jamming signal is very similar to the transmitted signal, and the jamming signal can also obtain the coherent gain of processing after being received by the radar, which makes the radar unable to identify the information of the real target. With the shortening of the signal interception time of the digital radio frequency memory storage and forwarding equipment, it can generate intermittent sampling jamming with intra-pulse modulation, and the waveform with inter-pulse modulation is no longer effective in countering intermittent sampling jamming. The intra-pulse frequency coding waveform can well counter intermittent sampling jamming, and in recent years, many intra-pulse frequency coding waveforms have been proposed for intermittent sampling jamming, such as intra-pulse random step frequency coding waveform and intra-pulse Costas frequency coding waveform. The intra-pulse sparse frequency coding waveform is widely used in electronic countermeasures because it can cover the same signal bandwidth with fewer sampling points, thereby greatly reducing the data volume, shortening the pulse width time, and reducing the information dependency on each frequency point.

[0003] The existing intra-pulse frequency agile waveform adopts waveforms such as intra-pulse random step frequency coding and intra-pulse Costas frequency coding, and the frequency variation law is relatively fixed, and the waveform agile strategy is not complex, so it is very likely to be intercepted and cracked by the jammer. The existing intra-pulse sparse random frequency coding waveform has a complex agile strategy, but the sparsity of its spectrum causes some empty frequency bands in the frequency domain, which will cause high sidelobes after range pulse compression, thereby affecting the pulse compression performance.

[0004] If the interference energy of the intra-pulse frequency coding waveform for intermittent sampling and forwarding jamming is too large, the residual interference energy will still be very strong, and the expected suppression effect cannot be achieved. SUMMARY

[0005] In order to solve the above problems existing in the prior art, the present application provides an intra-pulse frequency coding method with optimized design of a multiple mismatched filter.

[0006] The technical problem to be solved by the present application is solved by the following technical scheme:

[0007] The present application provides an intra-pulse frequency coding method with optimized design of a multiple mismatched filter, comprising:

[0008] An autocorrelation function of a waveform range ambiguity function of the pulse echo signal is obtained;

[0009] A peak-to-sidelobe ratio is obtained according to the autocorrelation function of the waveform range ambiguity function of the pulse echo signal, and an optimized frequency set is obtained according to an optimization cost function of waveform construction based on the peak-to-sidelobe ratio;

[0010] The optimized frequency set sorted in a preset manner is divided based on the number of sub-pulses of the three signal segments of the pulse echo signal, so that the frequency band sets of the three signal segments are mutually orthogonal, wherein the three signal segments include a signal segment of an interference sampling part, a signal segment of intermittent sampling interference first forwarding, and a remaining signal segment not sampled;

[0011] Under the condition that the frequency band sets of the three signal segments are mutually orthogonal and the intermittent sampling interference environment, an echo signal of a frequency agile waveform disturbed by interference is obtained based on the pulse echo signal and the interference signal;

[0012] The echo signal of the frequency agile waveform is down-converted to obtain a down-converted baseband echo signal disturbed by interference;

[0013] The pulse echo signal, the signal segment of the interference sampling part, and the signal segment of the intermittent sampling interference first forwarding are taken as a matched function of pulse compression, so that a first pulse compression result, a second pulse compression result, and a third pulse compression result corresponding to the down-converted baseband echo signal disturbed by interference are obtained, and an interference-free target echo signal is obtained by cancellation.

[0014] Optionally, the autocorrelation function of the waveform range ambiguity function of the pulse echo signal includes:

[0015] The pulse echo signal is obtained, and the mth pulse echo signal is represented as:

[0016]

[0017] Wherein, s m The mth pulse echo signal is represented as: s m (t) = rect (Nt / T 1 ) exp (j2πf 0 t+1 / 2γt 2 ), t ∈ [0, T], m = 0, 1, 2, …, M-1, where s m (t) is the mth pulse echo signal, N is the number of sub-pulses, n = 0, 1, …, N-1, rect(·) is a rectangular window function, exp(·) is an exponential factor, j is an imaginary factor, t is a fast time, T 1 is a sub-pulse width, γ is a frequency modulation slope, f 0 is a carrier frequency, and T is a pulse repetition interval (PRI). n The nth sub-pulse carrier frequency is f n = f 0 + nγT 1 / N.

[0018] Based on the ambiguity function, an autocorrelation function of a waveform range ambiguity function of the pulse echo signal is obtained, and the autocorrelation function of the waveform range ambiguity function is represented as:

[0019]

[0020] wherein h (α, 0) is an autocorrelation of a waveform range profile, α is a range delay, and sinc (·) is a sinc function.

[0021] Optionally, a peak-to-sidelobe ratio is obtained according to an autocorrelation function of a waveform range profile of the pulse echo signal, and an optimized frequency set is obtained according to an optimization cost function of a waveform constructed based on the peak-to-sidelobe ratio, comprising:

[0022] The peak-to-sidelobe ratio is obtained according to an autocorrelation function of a waveform range profile of the pulse echo signal, and the peak-to-sidelobe ratio is expressed as:

[0023]

[0024] wherein P (α) is a peak-to-sidelobe ratio, h (α, 0) is an autocorrelation of a waveform range profile, h (0, 0) is an autocorrelation function of the waveform range profile when α is 0, and α is a range delay.

[0025] The optimization cost function of the waveform is obtained according to the peak-to-sidelobe ratio, and the optimization cost function of the waveform is expressed as:

[0026]

[0027] s.t.B=[max(f n )-min(f n ]+B1]

[0028] B1<δf,f n <B

[0029] wherein max (·) is a maximum value operation, min (·) is a minimum value operation, Z is a set of carrier frequencies of all sub-pulses, Z={f0, f1, …, f n , …, f N-1}, f n is a carrier frequency of an nth sub-pulse, N is a number of sub-pulses, n=0, 1, …, N-1, α1 is a main lobe width, s.t. is a constraint condition, B is a pulse bandwidth, B1 is a bandwidth of a sub-pulse, and δf is a minimum frequency hopping interval between adjacent sub-pulses.

[0030] The optimized frequency set is obtained according to the optimization cost function of the waveform.

[0031] Optionally, the optimized frequency set sorted in a preset manner is divided based on a number of sub-pulses of three signal segments of the pulse echo signal, so that frequency bands of the three signal segments are orthogonal to each other, comprising:

[0032] The optimized frequency set is sorted according to the preset method to obtain a reordered frequency set, wherein the preset method includes ascending order;

[0033] Based on the number of sub-pulses in the three signal segments of the pulse echo signal, the reordered frequency set is divided into a first subset of signal segments in the interference sampling portion, a second subset of signal segments in the intermittent sampling interference first relay, and a third subset of the remaining unsampled signal segments. The first subset, the second subset, and the third subset are respectively represented as follows:

[0034] Z 11 ={f′0,…,f′ p·(Q+1) ,…,f′ (P-1)(Q+1)}

[0035] Z 12 ={f′1,…,f′ p·(Q+1)+1 ,…,f′ (P-1)(Q+1)+1}

[0036] Z 13 ={f′2,…,f′ p·(Q+1)+Q ,. . . ,f′ P·(Q+1)-1}

[0037] Among them, Z 11 Z is the first subset of the signal segments in the interference sampling section. 12 Z represents the second subset of the signal segments that intermittently sample and interfere with the first relay of the signal segment. 13 The third subset of the remaining unsampled signal segments is N = (Q+1)·P, where N is the number of sub-pulses, P is the number of interference samples, and Q is the number of interference repeaters. T is the total length of a pulse. For the floor operation, T c The sampling period is the intermittent sampling interference period, T1 is the sub-pulse width, and T... e f′ is the length of the signal segment of a pulse that is not sampled during an interference sampling period. p·(Q+1) Let f′ be the carrier frequency of the p-th (Q+1)th sub-pulse in the first subset. (P-1)(Q+1) Let f′ be the carrier frequency of the (P-1)(Q+1)th sub-pulse in the first subset. p·(Q+1)+1 f′ is the carrier frequency of the p·(Q+1)+1th sub-pulse in the second subset. (P-1)(Q+1)+1 f′ is the carrier frequency of the (P-1)(Q+1)+1th sub-pulse in the second subset. p·(Q+1)+Q Let f′ be the carrier frequency of the p·(Q+1)+Q-th sub-pulse in the third subset. P·(Q+1)-1 Let P be the carrier frequency of the P·(Q+1)-1th sub-pulse in the third subset;

[0038] The first subset, the second subset and the third subset are made to be pairwise orthogonal based on a preset constraint satisfied by the first subset, the second subset and the third subset, and the preset constraint is represented as:

[0039] max(Z 11 )<min(Z 12 )

[0040] max(Z 12 )<min(Z 13 )

[0041] Wherein, max(·) is a maximum value operation, and min(·) is a minimum value operation.

[0042] Optionally, the echo signal of the agile frequency waveform is represented as:

[0043] y(t,τ)=s m (t,τ)+J(t,τ)

[0044] s m (t,τ)=s m (t-k(τ))exp[j2πf c (t+τ-k(τ))]

[0045] s m (t-k(τ))=x1(t-k(τ))+x2(t-k(τ))+x3(t-k(τ))

[0046] Wherein, y(t,τ) is the echo signal of the agile frequency waveform, exp(·) is an exponential factor, j is an imaginary factor, f c is an initial carrier frequency of a pulse, t is a fast time, τ is a slow time, k(τ) is a target delay, x1(·) is a signal segment of an interference sampling part, x2(·) is a signal segment of a first retransmission of the intermittent sampling interference, x3(·) is a remaining signal segment that is not sampled, and J(t,τ) is an interference signal.

[0047] Optionally, the down-converted baseband echo signal interfered by the interference is represented as:

[0048]

[0049] Wherein, y1(t,τ) is the down-converted baseband echo signal interfered by the interference, k J (τ) is a time delay of the intermittent sampling interference signal, is a convolution operator, δ(·) is an impulse function, and Q is a retransmission number of the interference.

[0050] Optionally, the pulse echo signal, the signal segment of the interference sampling part and the signal segment of the first retransmission of the intermittent sampling interference are taken as a matching function of pulse compression, and a first pulse compression result, a second pulse compression result and a third pulse compression result corresponding to the down-converted interfered baseband echo signal are obtained by cancellation to obtain an interference-free target echo signal, comprising:

[0051] The pulse echo signal is taken as a matching function of pulse compression, and the pulse echo signal is convolved with the down-converted interfered baseband echo signal in the time domain to obtain the first pulse compression result, which is expressed as:

[0052]

[0053] Wherein, y2(t,τ) is the first pulse compression result, y1(t,τ) is the down-converted interfered baseband echo signal, t is the fast time, τ is the slow time, T1 is the sub-pulse width, is a convolution operation, s * m is the conjugate of s m is the conjugate of s m is the mth pulse echo signal, x1(·) is the signal segment of the interference sampling part, k J (τ) is the time delay of the intermittent sampling interference signal, k(τ) is the target delay, is the conjugate of x1(·), δ(·) is the impulse function, Q is the number of interference retransmissions, j is the imaginary factor, f c is the initial carrier frequency of the pulse;

[0054] The signal segment of the interference sampling part is taken as a matching function of pulse compression, and the signal segment of the interference sampling part is convolved with the down-converted interfered baseband echo signal to obtain the second pulse compression result, which is expressed as:

[0055]

[0056] Wherein, y3(t,τ) is the second pulse compression result;

[0057] The signal segment of the interference sampling part is taken as a matching function of pulse compression, and the signal segment of the interference sampling part is convolved with the down-converted interfered baseband echo signal to obtain the third pulse compression result, which is expressed as:

[0058]

[0059] Wherein, y4(t,τ) is the third pulse compression result, x2(·) is the signal segment of the first retransmission of the intermittent sampling interference, is a conjugate of x2(·);

[0060] According to the first pulse pressure result, the second pulse pressure result and the third pulse pressure result, the interference-free target echo signal is obtained by cancellation.

[0061] Optionally, according to the first pulse pressure result, the second pulse pressure result and the third pulse pressure result, the interference-free target echo signal is obtained by cancellation, comprising:

[0062] According to the second pulse pressure result and the third pulse pressure result, the interference signal to be eliminated is obtained, and the interference signal to be eliminated is expressed as:

[0063]

[0064] Wherein, y5(t,τ) is the interference signal to be eliminated;

[0065] According to the first pulse pressure result and the interference signal to be eliminated, the interference-free target echo signal is obtained.

[0066] Optionally, the interference-free target echo signal is expressed as:

[0067]

[0068] Wherein, y6(t,τ) is the interference-free target echo signal.

[0069] The application also provides an intra-pulse frequency encoding system combined with a multiple mismatch filter optimization design, comprising:

[0070] An autocorrelation module is configured to obtain an autocorrelation function of a waveform range ambiguity function of a pulse echo signal.

[0071] A sparse frequency set generation module of a low range grating lobe is configured to obtain a peak-to-sidelobe ratio based on the autocorrelation function of the waveform range ambiguity function of the pulse echo signal, and obtain an optimized frequency set based on an optimization cost function of the waveform constructed based on the peak-to-sidelobe ratio.

[0072] An orthogonal module is configured to divide the optimized frequency set sorted in a preset manner based on the number of sub-pulses of three signal segments of the pulse echo signal, so that the frequency band sets of the three signal segments are orthogonal to each other, wherein the three signal segments include a signal segment of an interference sampling part, a signal segment of intermittent sampling interference first forwarding and a remaining signal segment not sampled.

[0073] The modeling module of the agile waveform echo interfered by the echo is used for obtaining the echo signal of the agile frequency waveform interfered by the pulse echo signal and the interference signal under the condition that the frequency band set of the three signal segments is orthogonal to each other and the intermittent sampling interference environment;

[0074] The down-conversion processing module is used for performing down-conversion processing on the echo signal of the agile frequency waveform to obtain a down-converted interfered baseband echo signal;

[0075] The target echo signal generation module is used for taking the pulse echo signal, the signal segment of the interference sampling part and the signal segment of the first time forwarding of the intermittent sampling interference as a pulse compression matching function to obtain a first pulse compression result, a second pulse compression result and a third pulse compression result based on the down-converted interfered baseband echo signal, and obtain an interference-free target echo signal through cancellation.

[0076] Compared with the prior art, the beneficial effects of the present application are that:

[0077] The intra-pulse frequency encoding method of the joint multiple mismatch filter optimization design provided by the present application increases the complexity of the agile waveform strategy, reduces the distance grating caused by the frequency sparsity of the waveform, further optimizes the performance of the waveform pulse compression, and effectively reduces the influence of the residual interference in the interference transition zone.

[0078] The present application will be further described in detail below with reference to the accompanying drawings and the present application. BRIEF DESCRIPTION OF DRAWINGS

[0079] Figure 1 is a flowchart of the intra-pulse frequency encoding method of the joint multiple mismatch filter optimization design provided by the embodiment of the present application;

[0080] Figure 2 is a pulse segmentation and division schematic diagram provided by the embodiment of the present application;

[0081] Figure 3 is a comparison diagram of the autocorrelation and cross-correlation of the optimized intra-pulse frequency provided by the embodiment of the present application;

[0082] Figure 4 is a comparison diagram of the suppression effects of different waveforms on the intermittent sampling interference provided by the embodiment of the present application;

[0083] Figure 5 is a schematic diagram of the intra-pulse frequency encoding system of the joint multiple mismatch filter optimization design provided by the embodiment of the present application. DETAILED DESCRIPTION

[0084] The application will be described in further detail below with reference to specific embodiments, but the embodiments of the application are not limited thereto.

[0085] Embodiment one

[0086] See Figure 1 , Figure 1 is a flowchart of a method of intra-pulse frequency encoding provided by an embodiment of the application, the method of intra-pulse frequency encoding provided by an embodiment of the application is a method of intra-pulse frequency encoding combined with optimal design of multiple mismatch filters, and the method comprises the following steps:

[0087] Step 1: obtaining an autocorrelation function of a waveform range ambiguity function of a pulse echo signal.

[0088] Specifically, because the carrier frequencies of the sub-pulses of the intra-pulse sparse frequency encoding waveform are random, non-uniform and rapidly varying sparse, due to the existence of empty frequency bands in the intra-pulse, high grating lobes will appear in the range direction after pulse compression, resulting in false targets in radar detection. Therefore, the frequency encoding can be optimized to reduce the grating lobes through analysis of the ambiguity function of the intra-pulse frequency encoding waveform. In this embodiment, the pulse echo signal is first obtained, and then the autocorrelation of the waveform range ambiguity function is determined based on the obtained pulse echo signal.

[0089] In an optional embodiment, step 1 can specifically comprise:

[0090] Step 1.1: obtaining a pulse echo signal, and the mth pulse echo signal is represented as:

[0091]

[0092] wherein s m (t) is the mth pulse echo signal, N is the number of sub-pulses (i.e. there are N sub-pulses in the mth pulse echo signal), n=0, 1,..., N-1, rect(·) is a rectangular window function, exp(·) is an exponential factor, j is an imaginary factor, t is fast time, T1 is the sub-pulse width, γ is the frequency modulation slope, f n is the carrier frequency of the nth sub-pulse.

[0093] In this embodiment, the sub-pulse width of the proposed waveform needs to be set according to the sampling width of the intermittent sampling interference, so that it can better resist intermittent sampling retransmission interference. The sampling period and sampling width of the intermittent sampling interference can be determined according to some existing signal processing methods, which will not be described here. Therefore, the specific form of the mth pulse echo signal described above is determined under the condition that the sampling width of the intermittent sampling interference is known.

[0094] Step 1.2, obtaining the autocorrelation function of the waveform range ambiguity function according to the pulse echo signal based on the ambiguity function.

[0095] Specifically, the sampling width of the intermittent sampling interference is The sub-pulse time width is set to The definition of the ambiguity function is:

[0096]

[0097] Wherein, a is the range delay, β is the Doppler delay, s * m The conjugate of s m The conjugate of s m The mth pulse echo signal is s

[0098] Then, formula (1) is substituted into formula (2) to obtain the two-dimensional ambiguity function of the waveform. Since the range and Doppler correlation of the ambiguity function is low, the influence of the grating lobe can be ignored. Therefore, only the influence of the autocorrelation of the ambiguity function needs to be considered. Let β = 0 to obtain the autocorrelation of the waveform range ambiguity function. Therefore, the autocorrelation function of the waveform range ambiguity function is represented as:

[0099]

[0100] Wherein, h(a, 0) is the autocorrelation function of the waveform range ambiguity function, and sinc(·) is the sinc function.

[0101] Step 2, obtaining the peak sidelobe ratio according to the autocorrelation function of the waveform range ambiguity function of the pulse echo signal, and constructing an optimization cost function of the waveform based on the peak sidelobe ratio to obtain an optimized frequency set to design a low-range grating lobe intra-pulse sparse frequency coded waveform.

[0102] Specifically, the peak sidelobe ratio can be used as an index to measure the grating lobe level of the waveform. Therefore, in this embodiment, the peak sidelobe ratio is obtained according to the autocorrelation of the waveform range ambiguity function of the pulse echo signal, and then the peak sidelobe ratio is used to construct an optimization cost function of the waveform to obtain an optimized frequency set. The optimized frequency set is the frequency set of the low-grating lobe sub-pulse sparse frequency optimized coding sequence.

[0103] In an optional embodiment, step 2 can specifically include:

[0104] Step 2.1, obtaining the peak sidelobe ratio according to the autocorrelation function of the waveform range ambiguity function of the pulse echo signal.

[0105] In this embodiment, the peak sidelobe ratio is represented as:

[0106]

[0107] Where P(α) is the peak-to-sidelobe ratio, and h(0,0) is the autocorrelation function of the waveform distance ambiguity function when α is 0.

[0108] Step 2.2: Obtain the optimized cost function of the waveform based on the peak-to-sidelobe ratio.

[0109] Specifically, this embodiment also needs to ensure that the main lobe's energy is not lost. Since the bandwidth of a pulse in a waveform is fixed, and the bandwidth of a sub-pulse within a pulse is less than the frequency interval between adjacent sub-pulses, in order to limit the grating lobes of the waveform to a certain range, waveform optimization only reduces the amplitude of the distance from the grating lobe to below a threshold. Therefore, the waveform optimization cost function can be obtained as follows:

[0110]

[0111] Where max(·) is the maximum value operation, min(·) is the minimum value operation, and Z is the set of carrier frequencies of all sub-pulses, Z={f0,f1,…,f n ,…,f N-1}, f n Let α1 be the carrier frequency of the nth sub-pulse, N be the number of sub-pulses, n = 0, 1, ..., N-1, α1 be the main lobe width, st be the constraint condition, B be the pulse bandwidth, B1 be the bandwidth of the sub-pulse, and δf be the minimum frequency hopping interval between adjacent sub-pulses.

[0112] Step 2.3: Obtain the optimized frequency set based on the waveform optimization cost function.

[0113] Specifically, the sequential quadratic programming algorithm is an effective tool for handling constrained optimization problems. By solving formula (5), the frequency set of the low-grid-lobe sub-pulse sparse frequency optimized coding sequence can be obtained, that is, the optimized frequency set. Assume that the optimized frequency set is Z1={f′0,f′1,…,f′ n ,…,f′ N-1}, f′ n It is the carrier frequency of the nth sub-pulse in the optimized frequency set.

[0114] Step 3: Based on the number of sub-pulses of the three signal segments of the pulse echo signal, divide the optimized frequency set after sorting according to a preset method so that the frequency band sets of the three signal segments are mutually orthogonal. The three signal segments include the signal segment of the interference sampling part, the signal segment of the first relay of the intermittent sampling interference, and the remaining signal segment that has not been sampled.

[0115] Specifically, because the pulse echo signal is composed of three signal segments, a signal segment of interference sampling part, a signal segment of intermittent sampling interference first retransmission and a remaining signal segment not sampled, the optimized frequency set can be sorted in a preset manner first, and then the sorted optimized frequency set is divided according to the number of sub-pulses of the three signal segments of the pulse echo signal, so that the frequency band sets of the three signal segments are orthogonal to each other, thereby facilitating the use of the subsequent optimal mismatch filter to suppress the intermittent sampling interference.

[0116] In an optional embodiment, step 3 can specifically include:

[0117] Step 3.1, sorting the optimized frequency set in a preset manner to obtain a reordered frequency set, and the preset manner includes from small to large.

[0118] Specifically, in order to facilitate the use of the subsequent optimal mismatch filter to suppress the intermittent sampling interference, the optimized intra-pulse frequency order is designed to make the frequency bands of the above-mentioned three signal segments orthogonal to each other. The elements in the optimized frequency set Z1 are arranged in order from small to large to obtain a reordered frequency set.

[0119] Step 3.2, dividing the reordered frequency set into a first subset of the signal segment of the interference sampling part, a second subset of the signal segment of the intermittent sampling interference first retransmission and a third subset of the remaining signal segment not sampled based on the number of sub-pulses of the three signal segments of the pulse echo signal.

[0120] Specifically, by optimizing the frequency encoding method, the range grating lobes of the intra-pulse sparse frequency encoding waveform can be reduced, but the waveform anti-intermittent sampling interference performance is not considered in detail. In the embodiment, the intra-pulse frequency encoding waveform is optimized again by combining multiple interference mismatch filters to achieve the best interference suppression effect.

[0121] Since the ambiguity function has frequency shift invariance, the low lobe property of the intra-pulse frequency waveform optimized in the above will not change with the change of the frequency order. Therefore, the agile strategy of the optimized waveform is optimized again by multiple interference mismatch filters. Due to the characteristics of intermittent sampling interference sampling discontinuity, the pulse signal can be divided according to the intermittent sampling interference sampling and retransmission segment in the pulse signal. Figure 2

[0122] In the embodiment, it is assumed that the length of the signal segment of the pulse not sampled by the interference in one interference sampling period is T e , it can be known that T is the total length of a pulse, is a down rounding operation, T c ​The interference sampling period is intermittent sampling. Thus, the echo signal can be transformed into the following form:

[0123] s m (t)=x1(t)+x2(t)+x3(t) (6)

[0124] Wherein, x1(·) is the signal segment of the interference sampling part, x2(·) is the signal segment of the first retransmission of the intermittent sampling interference, and x3(·) is the remaining signal segment which is not sampled. x1(·), x2(·) and x3(·) are respectively represented as:

[0125]

[0126] Wherein, P is the number of interference samples, Q is the number of interference retransmissions, The relationship between the number of sub-pulses, the number of interference samples and the number of interference retransmissions is: N=(Q+1)·P.

[0127] After arranging the elements in the optimized frequency set Z1 in order from small to large, according to the number of sub-pulses of each signal segment, the set is divided into three parts, i.e. the first sub-set of the signal segment of the interference sampling part, the second sub-set of the signal segment of the first retransmission of the intermittent sampling interference and the third sub-set of the remaining signal segment which is not sampled, and the second sub-set and the third sub-set are respectively represented as:

[0128]

[0129] Wherein, Z 11 is the first sub-set of the signal segment of the interference sampling part, Z 12 is the second sub-set of the signal segment of the first retransmission of the intermittent sampling interference, and Z 13 is the third sub-set of the remaining signal segment which is not sampled, f′ p·(Q+1) is the carrier frequency of the p·(Q+1)th sub-pulse in the first sub-set, f′ (P-1)(Q+1) is the carrier frequency of the (P-1)(Q+1)th sub-pulse in the first sub-set, f′ p·(Q+1)+1 is the carrier frequency of the p·(Q+1)+1th sub-pulse in the second sub-set, f′ (P-1)(Q+1)+1 is the carrier frequency of the (P-1)(Q+1)+1th sub-pulse in the second sub-set, f′ p·(Q+1)+Q is the carrier frequency of the p·(Q+1)+Qth sub-pulse in the third sub-set, f′ P·(Q+1)-1 is the carrier frequency of the P·(Q+1)-1th sub-pulse in the third sub-set.

[0130] Step 3.3, based on the first sub-set, the second sub-set and the third sub-set satisfying the preset constraint, making the first sub-set, the second sub-set and the third sub-set orthogonal to each other, and the preset constraint is represented as:

[0131]

[0132] Therefore, the carrier frequency sequences in the three sets are respectively taken as the carrier frequencies of the three signal segments. The three signal segments are orthogonal to each other, that is, they are weakly correlated. Since the ambiguity function has time shift invariance, the low sidelobe of the optimized intra-pulse frequency waveform does not change with the change of the frequency sequence. The random agility of the sub-pulse frequency of each signal segment increases the unpredictability of the transmitted signal, and the orthogonality between the signal segments does not change.

[0133] Step 4, under the condition that the frequency band sets of the three signal segments are orthogonal to each other and in the intermittent sampling interference environment, obtaining the echo signal of the disturbed agile frequency waveform based on the pulse echo signal and the interference signal.

[0134] Specifically, in the intermittent sampling interference environment, the echo signal of the agile frequency waveform is represented as:

[0135] y(t,τ)=s m (t,τ)+J(t,τ) (12)

[0136] s m (t,τ)=s m (t-k(τ))exp[j2πf c (t+τ-k(τ))] (13)

[0137] s m (t-k(τ))=x1(t-k(τ))+x2(t-k(τ))+x3(t-k(τ)) (14)

[0138] Wherein, y(t,τ) is the echo signal of the agile frequency waveform, k(τ) is the target delay, and J(t,τ) is the interference signal.

[0139] Step 5, performing down-conversion processing on the echo signal of the agile frequency waveform to obtain a down-converted interference baseband echo signal.

[0140] In this embodiment, the down-converted interference baseband echo signal is represented as:

[0141]

[0142] Wherein, y1(t,τ) is the down-converted interference baseband echo signal, k J (τ) is the time delay of the intermittent sampling interference signal, is a convolution operation.

[0143] Step 6, taking the pulsed echo signal, the signal segment of the interference sampling part and the signal segment of the first retransmission of the intermittent sampling interference as a matched function of pulse compression, to obtain the first, second and third pulse compression results corresponding to the down-converted interfered baseband echo signal, and to obtain the target echo signal without interference by cancellation.

[0144] Specifically, after obtaining the down-converted interfered baseband echo signal, the pulsed echo signal, the signal segment of the interference sampling part and the signal segment of the first retransmission of the intermittent sampling interference are taken as a filter function (i.e. a matched function of pulse compression) to process y1(t,τ) so as to suppress the intermittent sampling interference. Because the pulsed echo signal and the signal segment of the interference sampling part can be matched with the target signal and the interference signal, both can obtain coherent integration gain. However, the signal segment of the first retransmission of the intermittent sampling interference is only matched with the target signal, and because the number of sub-pulses of the signal segment of the first retransmission of the intermittent sampling interference is the same as that of the signal segment of the interference sampling part, the gain of the part matched with the target is the same as that of the signal segment of the interference sampling part. The target signal can obtain full coherent processing gain through the pulsed echo signal, and based on the above analysis, the intermittent sampling interference can be eliminated by cancellation processing through multiple filters to reduce the energy loss of the target. Because of the previously designed frequency orthogonality, the cross-correlation of the three signals x1(·), x2(·) and x3(·) can be ignored.

[0145] Therefore, by taking the pulsed echo signal, the signal segment of the interference sampling part and the signal segment of the first retransmission of the intermittent sampling interference as a matched function of pulse compression, the down-converted interfered baseband echo signal is processed in turn to obtain the first, second and third pulse compression results, and the target echo signal without interference can be obtained by cancellation through the first, second and third pulse compression results.

[0146] In an optional embodiment, step 6 can specifically include:

[0147] Step 6.1, taking the pulsed echo signal as a matched function of pulse compression, convolving the pulsed echo signal with the down-converted interfered baseband echo signal in the time domain to obtain the first pulse compression result.

[0148] In this embodiment, the first pulse compression result is represented as:

[0149]

[0150] Wherein, y2(t,τ) is the first pulse compression result.

[0151] Step 6.2, taking the signal segment of the interference sampling part as a matched function of pulse compression, convolving the signal segment of the interference sampling part with the down-converted baseband echo signal interfered to obtain a second pulse compression result.

[0152] In this embodiment, the second pulse compression result is represented as:

[0153]

[0154] wherein y3(t, τ) is the second pulse compression result.

[0155] Step 6.3, taking the signal segment of the interference sampling part as a matched function of pulse compression, convolving the signal segment of the interference sampling part with the down-converted baseband echo signal interfered to obtain a third pulse compression result.

[0156] In this embodiment, the third pulse compression result is represented as:

[0157]

[0158] wherein y4(t, τ) is the third pulse compression result, is the conjugate of x2(·).

[0159] Step 6.4, obtaining the target echo signal without interference by cancellation according to the first pulse compression result, the second pulse compression result and the third pulse compression result.

[0160] Step 6.41, obtaining the interference signal to be eliminated according to the second pulse compression result and the third pulse compression result.

[0161] Specifically, the third pulse compression result is subtracted from the second pulse compression result, that is, the energy of the target is eliminated and the energy of the intermittent sampling interference is retained, so that the interference signal to be eliminated is obtained, and the interference signal to be eliminated is represented as:

[0162]

[0163] wherein y5(t, τ) is the interference signal to be eliminated.

[0164] Step 6.42, obtaining the target echo signal without interference according to the first pulse compression result and the interference signal to be eliminated.

[0165] Specifically, the first pulse compression result is subtracted from the interference signal to be eliminated, that is, formula (16) is subtracted from formula (19), so that the target echo signal without interference is obtained, and the target echo signal without interference is represented as:

[0166]

[0167] wherein y6(t, τ) is the target echo signal without interference.

[0168] In order to reflect the orthogonality of each sub-pulse segment of the optimized waveform in the pulse-in-frequency encoding method of the joint multiple mismatch filter optimization design, Figure 3 The cross-correlation functions of the three sub-pulse segments are compared. Figure 3 It can be seen that the cross-correlation levels of them are much lower than the highest distance sidelobe, so they are considered to be orthogonal, and the influence of their cross-correlation can be ignored in signal processing.

[0169] Figure 4 The anti-intermittent sampling interference of different waveforms is simulated, Figure 4 Fig. (a) is a linear frequency modulation waveform, Fig. (b) is a Costas frequency encoding waveform, Fig. (c) is a non-optimized pulse-in-frequency encoding waveform, and Fig. (d) is an optimized pulse-in-frequency encoding waveform, and it can be seen that the waveform has better anti-interference effect than other waveforms.

[0170] The pulse-in-frequency encoding waveforms used in the existing technology, such as pulse-in-random step frequency encoding and pulse-in-Costas frequency encoding, have relatively fixed frequency variation rules, and the agile strategy is not complex, and it is possible to be intercepted and cracked by the interference party. Although the existing pulse-in-sparse frequency agile waveform has a relatively complex agile strategy, the problem of high distance sidelobe caused by its frequency domain sparsity has not been well solved. Moreover, when the energy of the intermittent sampling interference is too large, the residual interference energy after using the existing pulse-in-agile waveform is still strong, and the expected suppression effect cannot be achieved. Therefore, the pulse-in-sparse frequency encoding waveform used in the present application not only has a complex agile strategy, but also reduces the distance sidelobe through optimization, and optimizes its pulse compression performance. In addition, for the intermittent sampling interference, the agile strategy of the optimized waveform is optimized again through multiple interference mismatch filters, and finally the interference is eliminated through the interference cancellation method. Experiments prove that the waveform used in the present application has better anti-interference effect than the existing waveforms.

[0171] Embodiment two

[0172] Please refer to Figure 5 , Figure 5 is a schematic diagram of a pulse-in-frequency encoding system of a joint multiple mismatch filter optimization design provided by an embodiment of the present application. The embodiment of the present application provides a pulse-in-frequency encoding system of a joint multiple mismatch filter optimization design on the basis of the embodiment one, and the system comprises:

[0173] The autocorrelation module is configured to obtain the autocorrelation function of the waveform range ambiguity function of the pulse echo signal.

[0174] The sparse frequency set generation module of low range grating lobe is used for obtaining a peak sidelobe ratio according to an autocorrelation function of a waveform range ambiguity function of the pulse echo signal, and obtaining an optimized frequency set according to an optimization cost function of the waveform based on the peak sidelobe ratio.

[0175] The orthogonal module is used for dividing the optimized frequency set sorted in a preset mode based on the number of sub-pulses of the three signal segments of the pulse echo signal, so that the frequency band sets of the three signal segments are orthogonal to each other, wherein the three signal segments include a signal segment of an interference sampling part, a signal segment of intermittent sampling interference first forwarding and a remaining signal segment not sampled.

[0176] The modeling module of the agile waveform echo interfered by the interference is used for obtaining an echo signal of the agile frequency waveform interfered by the interference according to the pulse echo signal and the interference signal under the condition that the frequency band sets of the three signal segments are orthogonal to each other and the intermittent sampling interference environment.

[0177] The down-conversion processing module is used for performing down-conversion processing on the echo signal of the agile frequency waveform to obtain a down-converted interference baseband echo signal.

[0178] The target echo signal generation module is used for taking the pulse echo signal, the signal segment of the interference sampling part and the signal segment of the intermittent sampling interference first forwarding as a matching function of pulse compression, so as to obtain a first pulse compression result, a second pulse compression result and a third pulse compression result corresponding to the down-converted interference baseband echo signal, and obtain a target echo signal without interference through cancellation.

[0179] The present application aims at the problems of high range grating lobe of intra-pulse sparse frequency encoding waveform and poor anti-interference effect of the waveform when the intermittent sampling interference energy is too large. The present application proposes an optimization method of intra-pulse sparse frequency encoding waveform with low range grating lobe through derivation of the ambiguity function of the intra-pulse sparse frequency encoding waveform, and further optimizes the performance of pulse compression of the waveform. Then, for the intermittent sampling interference, the frequency encoding is optimized twice through multiple interference mismatch filters, and finally an interference cancellation method is proposed to suppress the interference, which effectively reduces the influence of residual interference in the interference transition band.

[0180] It should be noted that the terms "first", "second" are only used for description purposes, and cannot be understood as indicating or implying relative importance or implicitly indicating the number of indicated technical features. Therefore, the features defined with "first", "second" can explicitly or implicitly include one or more features. In the description of the present application, the meaning of "multiple" is two or more, unless otherwise specifically limited.

[0181] In the description of the specification, the description of the terms "one embodiment", "some embodiments", "an example", "a specific example", or "some examples" and the like means that the specific features or characteristics described in connection with the embodiment or example are included in at least one embodiment or example of the present application. In the specification, the illustrative description of the above terms does 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 integrate different embodiments or examples described in the specification.

[0182] Although the present application is described herein in conjunction with various embodiments, it is understood that other variations of the disclosed embodiments can be understood and realized by those skilled in the art upon review of the drawings and the disclosure. In the specification, the word "comprise" does not exclude other components or steps, and "a" or "one" does not exclude a plurality. Certain measures are described in mutually different embodiments, but this does not mean that these measures cannot be combined to produce good results.

[0183] The above is a further detailed description of the present application in conjunction with specific preferred embodiments, and the specific implementation of the present application cannot be limited to these descriptions. For those skilled in the art to which the present application belongs, without departing from the concept of the present application, a number of simple deductions or substitutions can be made, which should be considered as falling within the scope of protection of the present application.

Claims

1. A method for intra-pulse frequency coding with joint multiple mismatched filter optimization design, characterized in that, The method comprises the following steps: obtaining an autocorrelation function of a waveform range ambiguity function of a pulse echo signal; obtaining a peak-to-sidelobe ratio according to the autocorrelation function of the waveform range ambiguity function of the pulse echo signal, and obtaining an optimized frequency set according to an optimization cost function of a waveform constructed based on the peak-to-sidelobe ratio; dividing the optimized frequency set sorted in a preset mode based on the number of sub-pulses of three signal segments of the pulse echo signal, so that the frequency band sets of the three signal segments are orthogonal to each other, wherein the three signal segments include a signal segment of an interference sampling part, a signal segment of intermittent sampling interference first retransmission, and a remaining signal segment not sampled; under the condition that the frequency band sets of the three signal segments are orthogonal to each other and the intermittent sampling interference environment, obtaining an echo signal of a disturbed agile frequency waveform based on the pulse echo signal and the interference signal; performing down-conversion processing on the echo signal of the agile frequency waveform to obtain a down-converted disturbed baseband echo signal; taking the pulse echo signal, the signal segment of the interference sampling part, and the signal segment of the intermittent sampling interference first retransmission as a matching function of pulse compression, so as to obtain a first pulse compression result, a second pulse compression result, and a third pulse compression result corresponding to the down-converted disturbed baseband echo signal, and obtain an interference-free target echo signal through cancellation; specifically comprising: taking the pulse echo signal as a matching function of pulse compression, convolving the pulse echo signal with the down-converted disturbed baseband echo signal in the time domain to obtain the first pulse compression result, which is expressed as: wherein is a first pulse pressure result, is a down-converted interfered baseband echo signal, is a fast time, is a slow time, is a sub-pulse width, is a convolution operation, is a conjugate of is a first m pulse echo signal, is a signal segment of an interfered sampling portion, is a time delay of an intermittently sampled interfered signal, is a target delay, is a conjugate of is an impulse function, is a number of interference retransmissions, is an imaginary factor, is an initial carrier frequency of a pulse, is a sub-pulse width; taking the signal segment of the interference sampling part as a matching function of pulse compression, convolving the signal segment of the interference sampling part with the down-converted disturbed baseband echo signal to obtain the second pulse compression result, which is expressed as: wherein, is the second pulse pressure result; taking the signal segment of the interference sampling part as a matching function of pulse compression, convolving the signal segment of the interference sampling part with the down-converted disturbed baseband echo signal to obtain the third pulse compression result, which is expressed as: wherein is a third pulse pressure result, is an intermittent sampling interference first retransmitted signal segment, is a conjugate of obtaining the interference-free target echo signal through cancellation according to the first pulse compression result, the second pulse compression result, and the third pulse compression result.

2. The method of claim 1, wherein the joint multiple mismatched filter optimization design is performed in the frequency domain. The method comprises the following steps: acquiring the pulse echo signals, the first m of the pulse echo signals is represented as: wherein is the number of the pulse echo signal, m is the number of the sub-pulse, is the number of sub-pulses, , is a rectangular window function, is an exponential factor, is an imaginary factor, is a fast time, is a sub-pulse width, is a frequency modulation slope, is the number of the pulse echo signal, is a carrier frequency of the sub-pulse; obtaining an autocorrelation function of a waveform range ambiguity function of a pulse echo signal; wherein, is the autocorrelation of the wave shape distance ambiguity function, is the distance time delay, is the sinc function.

3. The method of claim 1, wherein the joint multiple mismatched filter optimization design is performed in the frequency domain. obtaining a peak-to-sidelobe ratio according to the autocorrelation function of the waveform range ambiguity function of the pulse echo signal, and obtaining an optimized frequency set according to an optimization cost function of a waveform constructed based on the peak-to-sidelobe ratio; obtaining the peak-to-sidelobe ratio according to the autocorrelation function of the waveform range ambiguity function of the pulse echo signal, the peak-to-sidelobe ratio being expressed as: wherein is a peak-to-sidelobe ratio, is an autocorrelation of the range profile ambiguity function, is is an autocorrelation function of the range profile ambiguity function for 0, is a range delay; obtaining the optimization cost function of the waveform according to the peak-to-sidelobe ratio, the optimization cost function of the waveform being expressed as: wherein, is a maximum value operation, is a minimum value operation, is a set of carrier frequencies of all sub-pulses, , is a carrier frequency of the th sub-pulse, is a number of sub-pulses, , is a main lobe width, is a restriction condition, is a pulse bandwidth, is a bandwidth of a sub-pulse, is a minimum frequency hopping interval between adjacent sub-pulses; obtaining the optimized frequency set according to the optimization cost function of the waveform.

4. The method of claim 1, wherein the joint multiple mismatched filter optimization design is performed in the frequency domain. The optimized frequency set is sorted according to a preset mode, and the frequency bands of the three signal segments are mutually orthogonal based on the number of sub-pulses of the three signal segments of the pulse echo signal, including: The optimized frequency set is sorted according to a preset mode, and the frequency bands of the three signal segments are mutually orthogonal based on the number of sub-pulses of the three signal segments of the pulse echo signal, including: The optimized frequency set is sorted according to a preset mode, and the frequency bands of the three signal segments are mutually orthogonal based on the number of sub-pulses of the three signal segments of the pulse echo signal, including: in, The first subset of signal segments in the interference sampling section. This is the second subset of the signal segments that intermittently sample and interfere with the first relay. The third subset of the remaining unsampled signal segments. , The number of sub-pulses, To reduce the number of interference samples, To interfere with the number of forwards, , , The total length of a pulse. This is a round-down operation. For intermittent sampling interference sampling period, The width of the sub-pulse. The length of the signal segment of a pulse that is not sampled during an interference sampling period. For the first subset of the The carrier frequency of each sub-pulse For the first subset of the The carrier frequency of each sub-pulse For the second subset The carrier frequency of each sub-pulse For the second subset The carrier frequency of each sub-pulse For the third subset The carrier frequency of each sub-pulse For the third subset The carrier frequency of each sub-pulse; The optimized frequency set is sorted according to a preset mode, and the frequency bands of the three signal segments are mutually orthogonal based on the number of sub-pulses of the three signal segments of the pulse echo signal, including: wherein is a maximum operation, is a minimum operation.

5. The method of claim 1, wherein the joint multiple mismatched filter optimization design is performed in the frequency domain. The echo signal of the agile frequency waveform is represented as: wherein is the echo signal of the chirp waveform, is an exponential factor, is an imaginary factor, is the initial carrier frequency of the pulse, is the fast time, is the slow time, is the target delay, is the signal segment of the jammer sample portion, is the signal segment of the first retransmission of the intermittent sample jammer, is the remaining signal segment not sampled, is the jammer signal.

6. The method of claim 5, wherein the joint multiple mismatched filter optimization design is performed by using a genetic algorithm. The down-converted interfered baseband echo signal is represented as: wherein is a down-converted interfered baseband echo signal, is a time delay of the intermittently sampled interference signal, is a convolution operator, is an impulse function, is a number of interference retransmissions.

7. The method of claim 1, wherein the joint multiple mismatched filter optimization design is performed in the frequency domain. According to the first pulse pressure result, the second pulse pressure result and the third pulse pressure result, the interference-free target echo signal is obtained by cancellation, including: According to the second pulse pressure result and the third pulse pressure result, the interference signal to be eliminated is obtained, and the interference signal to be eliminated is represented as: wherein is the interference signal to be cancelled; According to the first pulse pressure result and the interference signal to be eliminated, the interference-free target echo signal is obtained.

8. The intra-pulse frequency coding method for joint multiple mismatch filter optimization design according to claim 7, characterized in that, The interference-free target echo signal is represented as: wherein is the target echo signal without interference.

9. An intra-pulse frequency coding system with joint multiple mismatch filter optimization design, characterized in that, including: The autocorrelation module is configured to obtain an autocorrelation function of a waveform range ambiguity function of a pulse echo signal. The sparse frequency set generation module is configured to obtain a peak-to-sidelobe ratio based on the autocorrelation function of the waveform range ambiguity function of the pulse echo signal, and obtain an optimized frequency set based on an optimization cost function of a waveform constructed based on the peak-to-sidelobe ratio. The orthogonal module is configured to divide the optimized frequency set sorted according to a preset mode based on the number of sub-pulses of the three signal segments of the pulse echo signal, so that the frequency band sets of the three signal segments are mutually orthogonal, wherein the three signal segments include a signal segment of an interference sampling part, a signal segment of a first-time retransmission of intermittent sampling interference, and a remaining signal segment not sampled. The modeling module of the agile waveform interfered echo is configured to obtain an echo signal of an interfered agile frequency waveform based on a pulse echo signal and an interference signal under the condition that the frequency band sets of the three signal segments are mutually orthogonal and in an intermittent sampling interference environment. The down-conversion processing module is configured to perform down-conversion processing on the echo signal of the agile frequency waveform to obtain a down-converted interfered baseband echo signal. The target echo signal generation module is configured to take the pulse echo signal, the signal segment of the interference sampling part and the signal segment of the first-time retransmission of the intermittent sampling interference as a matching function of pulse compression, to obtain an interference-free target echo signal by cancellation based on first, second and third pulse compression results corresponding to the down-converted interfered baseband echo signal; specifically comprising: The pulse echo signal is taken as a matching function of pulse compression, and the pulse echo signal is convolved with the down-converted interfered baseband echo signal in the time domain to obtain the first pulse compression result, which is expressed as: in, This is the result of the first pulse pressure. This is the baseband echo signal affected by interference during down-conversion. To save time, For slow time, The width of the sub-pulse. For convolution operations, for conjugate, For the first m One pulse echo signal, For the signal segment of the interference sampling section, The time delay for intermittent sampling of interference signals, Delay for target, for conjugate, Let be the impulse function. To interfere with the number of forwards, Imaginary factor The initial carrier frequency of the pulse. The width of the sub-pulse; The signal segment of the interference sampling part is taken as a matching function of pulse compression, and the signal segment of the interference sampling part is convolved with the down-converted interfered baseband echo signal to obtain the second pulse compression result, which is expressed as: wherein, is the second pulse pressure result; The signal segment of the interference sampling part is taken as a matching function of pulse compression, and the signal segment of the interference sampling part is convolved with the down-converted interfered baseband echo signal to obtain the third pulse compression result, which is expressed as: wherein is the third pulse pressure result, is the intermittent sampling interference first retransmitted signal segment, is the conjugate of The interference-free target echo signal is obtained by cancellation based on the first, second and third pulse compression results.

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