CN111965611B - Construction method of phase jitter DDMA waveform - Google Patents
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- G—PHYSICS
- G01—MEASURING; TESTING
- G01S—RADIO DIRECTION-FINDING; RADIO NAVIGATION; DETERMINING DISTANCE OR VELOCITY BY USE OF RADIO WAVES; LOCATING OR PRESENCE-DETECTING BY USE OF THE REFLECTION OR RERADIATION OF RADIO WAVES; ANALOGOUS ARRANGEMENTS USING OTHER WAVES
- G01S7/00—Details of systems according to groups G01S13/00, G01S15/00, G01S17/00
- G01S7/02—Details of systems according to groups G01S13/00, G01S15/00, G01S17/00 of systems according to group G01S13/00
- G01S7/41—Details of systems according to groups G01S13/00, G01S15/00, G01S17/00 of systems according to group G01S13/00 using analysis of echo signal for target characterisation; Target signature; Target cross-section
- G01S7/418—Theoretical aspects
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- G—PHYSICS
- G01—MEASURING; TESTING
- G01S—RADIO DIRECTION-FINDING; RADIO NAVIGATION; DETERMINING DISTANCE OR VELOCITY BY USE OF RADIO WAVES; LOCATING OR PRESENCE-DETECTING BY USE OF THE REFLECTION OR RERADIATION OF RADIO WAVES; ANALOGOUS ARRANGEMENTS USING OTHER WAVES
- G01S7/00—Details of systems according to groups G01S13/00, G01S15/00, G01S17/00
- G01S7/02—Details of systems according to groups G01S13/00, G01S15/00, G01S17/00 of systems according to group G01S13/00
- G01S7/41—Details of systems according to groups G01S13/00, G01S15/00, G01S17/00 of systems according to group G01S13/00 using analysis of echo signal for target characterisation; Target signature; Target cross-section
- G01S7/414—Discriminating targets with respect to background clutter
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- G01—MEASURING; TESTING
- G01S—RADIO DIRECTION-FINDING; RADIO NAVIGATION; DETERMINING DISTANCE OR VELOCITY BY USE OF RADIO WAVES; LOCATING OR PRESENCE-DETECTING BY USE OF THE REFLECTION OR RERADIATION OF RADIO WAVES; ANALOGOUS ARRANGEMENTS USING OTHER WAVES
- G01S7/00—Details of systems according to groups G01S13/00, G01S15/00, G01S17/00
- G01S7/02—Details of systems according to groups G01S13/00, G01S15/00, G01S17/00 of systems according to group G01S13/00
- G01S7/41—Details of systems according to groups G01S13/00, G01S15/00, G01S17/00 of systems according to group G01S13/00 using analysis of echo signal for target characterisation; Target signature; Target cross-section
- G01S7/415—Identification of targets based on measurements of movement associated with the target
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Abstract
The invention discloses a construction method of a phase jitter DDMA waveform, which comprises the following steps: calculating Doppler frequency of the phase jitter DDMA waveform of the transmitting array element according to the transmitting array element number and the pulse repetition frequency; according to signals received by any receiving array element and the calculated Doppler frequency, calculating Doppler domain signal components of a phase jitter DDMA waveform of the receiving array element by utilizing a target aliasing formula; the Doppler domain signal component at least comprises the frequency and the phase of clutter signals on each orthogonal slow time channel on a transmitting array element; constructing an intensity accumulation expression of clutter signals according to the calculated frequency and phase; and searching the intensity accumulation expression in an angle interval of [0,2 pi ] to obtain an optimal initial phase set corresponding to the clutter with the minimum intensity. The invention can make DDMA signal suitable for airborne slow time MIMO radar, thereby reducing blind speed problem of target detection caused by Doppler blurring easily caused by DDMA signal.
Description
Technical Field
The invention belongs to the technical field of radar signal processing, and particularly relates to a construction method of a phase jitter DDMA waveform.
Background
MIMO (Multiple Input Multiple Output ) radar is a new system of interest, and the concept of MIMO radar was proposed in 2004 by fisher in the lincoln laboratory of the university of american bureau of technology, which successfully references the multiple input multiple output technology in the modern communication field, and is a further development of the conventional phased array radar. Theoretical studies have shown that: compared with the traditional phased array radar, the airborne MIMO radar can improve the performances of clutter suppression, low-speed target detection, weak target detection in a strong clutter background and the like.
Slow time MIMO is a special mechanism that implements waveform orthogonality after doppler processing at the receiving end by pulse-to-pulse phase encoding, under which waveforms of different array elements are orthogonal throughout the coherent accumulation time, and single pulses are coherent. The DDMA (Doppler Division Multiple Access, doppler frequency division multiple access) signal maintains a certain correlation among the transmitted signals, has high bandwidth efficiency, and can utilize clutter correlation among channels to perform clutter cancellation, thereby improving the performances of minimum detectable speed and the like, and being very suitable for being applied to slow-time MIMO radars. Furthermore, in terms of hardware, each transmitter need only generate a DDMA waveform by one phase shifter, and the receiver hardware prior to pulse compression need not be modified at reception. Therefore, the DDMA waveform is used on the onboard MIMO radar, so that the detection performance, the resolution capability and the parameter estimation capability of a low-speed target of the onboard radar are greatly possibly improved.
However, on the premise that the pulse repetition frequency for determining the non-blurring distance is unchanged, the Doppler non-blurring interval of the DDMA signal is smaller; if the target speed is too high, the target echo of one transmitting array element may be mistaken for the low-speed target echo of another transmitting array element, and the blind speed problem that the target cannot be detected may be caused by the fact that the target echo has the same Doppler frequency as the main lobe clutter of the other transmitting array element. Therefore, there is no better solution in the prior art how to adapt the DDMA signal to the onboard slow-time MIMO radar, so as to reduce the blind speed problem of target detection caused by doppler ambiguity that is easily caused by the DDMA signal.
Disclosure of Invention
In order to enable the DDMA signal to be suitable for an onboard slow-time MIMO radar, thereby reducing the problem of blind speed of target detection caused by Doppler blurring which is easy to be caused by the DDMA signal, the invention provides a construction method of a phase jitter DDMA waveform.
The technical problems to be solved by the invention are realized by the following technical scheme:
a construction method of a phase jitter DDMA waveform comprises the following steps:
acquiring the number M of transmitting array elements of the airborne MIMO radar and the pulse repetition frequency f r And according to the number M of the transmitting array elements and the pulse repetition frequency f r Calculating Doppler frequency alpha of phase jitter DDMA waveform of each transmitting array element m ，m∈[1，M]，M≥2；
Doppler frequency alpha of DDMA waveform according to signal received by any receiving array element and phase jitter of M transmitting array elements m Calculating Doppler domain signal components of the phase jitter DDMA waveform of the receiving array element by utilizing a target aliasing formula of a preset phase jitter DDMA waveformAn amount of; the Doppler domain signal component includes at least: the frequency and phase of clutter signals on each transmitting array element on each orthogonal slow time channel;
constructing an intensity accumulation expression of clutter signals on M transmitting array elements according to the calculated frequency and phase;
searching the intensity accumulation expression in an angle interval of [0,2 pi ] to obtain an optimal initial phase set corresponding to clutter with minimum intensity, wherein the optimal initial phase set comprises M optimal initial phases;
and constructing a phase jitter DDMA waveform in the airborne MIMO radar based on the optimal initial phase set.
Preferably, the target aliasing formula of the phase jitter DDMA waveform is:
wherein { X t } nk,i Represents the output result of the received nth signal after the kth pulse is subjected to down-conversion and matched filtering processing and phase compensation of the ith Doppler filter, { X } t } nk,i-q Representing the output result of the phase compensation of the ith-q Doppler filter after the down-conversion and matched filtering treatment of the kth pulse received by the nth receiving array element, wherein i is more than or equal to 0 and less than or equal to M-1, n is more than or equal to [1, N ]]，k∈[1，K]N is the total number of the received signals, K is the pulse number in one coherent processing time;indicating the initial phase of the ith transmit element,/->Representing the initial phase of the i-q th transmitting array element; f (f) t Satisfy f r /2＞|f t I > Δf/2, representing the Doppler frequency of the high-speed target signal, f t -q.DELTA.f satisfies |f t -q.DELTA.f|is less than or equal to DELTA.f/2, representing the Doppler frequency of the low-speed target signalRate of->Represents a frequency interval, q is an integer and satisfies alpha i ＝α i-q +q.Δf, where α i And alpha i-q The Doppler frequencies of the phase jitter DDMA waveforms of the ith and the ith-q transmitting array elements are respectively represented;the upper horizontal line represents pair->Performing fast Fourier transform, ">The upper horizontal line represents pair->A fast fourier transform is performed.
Preferably, the intensity cumulative expression is:
wherein Y represents the intensity accumulation result,is a random initial phase set; />Is a target sequence constructed according to the calculated distribution of the frequency and the phase over the orthogonal slow time channels, the target sequence representing the phase ratio phi dither (M) cyclically moving the conjugated complex sequence of length M after item i; y (i) is phi dither The M points of (M) cycle the single point output of the autocorrelation function.
Preferably, said transmitting array element number M and said pulse repetition frequency f r Calculating Doppler frequency alpha of phase jitter DDMA waveform of each transmitting array element m Comprising:
according to the number M of the transmitting array elements and the pulse repetition frequency f r Calculating the Doppler frequency alpha of the phase jitter DDMA waveform of each transmitting array element by using a preset Doppler frequency calculation formula m ；
The Doppler frequency calculation formula is as follows: alpha m ＝Δf·(m-1)。
Preferably, m=4, the optimal initial phase set is {0, pi }.
In the construction method of the phase jitter DDMA waveform, the optimal initial phase set corresponding to the clutter with the minimum intensity is obtained by means of angle search, so that the intensity of the fuzzy clutter is almost zero, the problem of blind speed of target detection caused by Doppler blurring easily caused by DDMA signals is reduced, and the problem of high noise level of the frequency jitter DDMA waveform in a non-main clutter region is solved.
Compared with the frequency jitter DDMA waveform Doppler frequency non-fuzzy interval less than 1/M, the phase jitter DDMA waveform provided by the invention is the same as the Doppler frequency non-fuzzy interval of the traditional DDMA waveform, and is 1/M, so that the problem that the frequency jitter DDMA waveform Doppler frequency non-fuzzy interval is less than 1/M is solved.
In the invention, only one random initial phase is added on each transmitting array element, so that the hardware structure of the DDMA waveform of the transmitting phase jitter of the transmitter is simple.
In addition, in the invention, the random initial phase is added on the transmitting array element and is linearly transformed in slow time, and compared with the target aliasing formula of the frequency jitter DDMA waveform, the target aliasing formula of the phase jitter DDMA waveform provided by the invention is simple, and the problems of difficult deduction and more situations can not occur.
The present invention will be described in further detail with reference to the accompanying drawings.
Drawings
Fig. 1 is a schematic flow chart of a method for constructing a phase jitter DDMA waveform according to an embodiment of the present invention;
figure 2 is a schematic diagram of an exemplary doppler domain signal component;
FIG. 3 is a schematic diagram of a simulation of the Doppler domain signal component of FIG. 2;
FIG. 4 (a) is an original clutter range-Doppler plot of a conventional DDMA waveform;
FIG. 4 (b) is a clutter range-Doppler plot after clutter suppression of the original clutter range-Doppler plot of FIG. 4 (a) using a space-time-code adaptive processing technique;
FIG. 4 (c) is an original clutter distance-Doppler plot obtained from a phase jitter DDMA waveform obtained using the method provided by embodiments of the present invention;
fig. 4 (d) is a clutter range-doppler plot after clutter suppression of the original range-doppler plot of fig. 4 (c) using space-time-code adaptive processing techniques.
Detailed Description
The present invention will be described in further detail with reference to specific examples, but embodiments of the present invention are not limited thereto.
In order to enable a DDMA signal to be suitable for an onboard slow-time MIMO radar, so that the problem of blind speed of target detection caused by Doppler blurring which is easily caused by the DDMA signal is solved. As shown in fig. 1, the method may include the steps of:
s10: and acquiring the number of transmitting array elements and the pulse repetition frequency of the airborne MIMO radar, and calculating the Doppler frequency of the phase jitter DDMA waveform of each transmitting array element according to the number of transmitting array elements and the pulse repetition frequency.
In particular, the number M of the transmitting array elements and the pulse repetition frequency f can be used r Calculating the Doppler frequency alpha of the phase jitter DDMA waveform of each transmitting array element by using a preset Doppler frequency calculation formula m ；
The Doppler frequency calculation formula is as follows: alpha m =Δf· (m-1). Wherein,representing the frequency interval. m is E [1, M]，M≥2。
S20: according to the signal received by any receiving array element and the Doppler frequency of the phase jitter DDMA waveform of each transmitting array element, calculating the Doppler domain signal component of the phase jitter DDMA waveform of the receiving array element by using a target aliasing formula of the preset phase jitter DDMA waveform; the Doppler domain signal component includes at least: the phase and frequency of the clutter signal on each of the transmit array elements on the respective quadrature slow time channels.
The target aliasing formula of the phase jitter DDMA waveform is derived according to a phase compensation formula, wherein the phase compensation formula is a formula for compensating the additional frequency and the additional phase of the DDMA signal to be zero; the derived target aliasing formula is:
in the target aliasing formula of the phase jitter DDMA waveform, { X t } nk,i Represents the output result of the received nth signal after the kth pulse is subjected to down-conversion and matched filtering processing and phase compensation of the ith Doppler filter, { X } t } nk,i-q Representing the output result of the phase compensation of the ith-q Doppler filter after the down-conversion and matched filtering treatment of the kth pulse received by the nth receiving array element, wherein i is more than or equal to 0 and less than or equal to M-1, n is more than or equal to [1, N ]]，k∈[1，K]N is the total number of received signals, K is the number of pulses in a coherent processing time, and the subscript K in the target aliasing formula is changed from the pulse sequence number to the Doppler channel sequence number.
Indicating the initial phase of the ith transmit element,/->Representing the initial phase of the i-q th transmitting array element; f (f) t Satisfy f r /2＞|f t I > Δf/2, representing the Doppler frequency of the high-speed target signal, f t -q.DELTA.f satisfies |f t -q.DELTA.f|.ltoreq.DELTA.f/2, representing the Doppler frequency of the low-speed target signal,/o>Represents a frequency interval, q is an integer and satisfies alpha i ＝α i-q +q.Δf, where α i And alpha i-q The Doppler frequencies of the phase-dithered DDMA waveforms for the ith and ith-q transmit elements, respectively. In practical applications, the Doppler frequency of the target may be based on the radial velocity v of the target t Flying speed v of carrier a Space cone angle of target t Carrier wavelength lambda 0 The calculation formula is as follows: f (f) t ＝2v t /λ 0 +2v a cosψ t /λ 0 。
The upper horizontal line represents pair->Performing fast Fourier transform, ">The upper horizontal line represents pair->A fast fourier transform is performed.
It will be appreciated that the target aliasing formula for the phase-dithered DDMA waveform is: output result of high-speed target signal after passing through ith Doppler filterIs equal to the product of the output result of the low-speed target signal after passing through the ith Doppler filter and +.>Is a product of (a) and (b).
In practical application, a Doppler domain signal component diagram of the phase jitter DDMA waveform of the receiving array element can be drawn according to a target aliasing formula of the phase jitter DDMA waveform, and the Doppler domain signal component diagram not only comprises the phase of the clutter signal on each transmitting array element on each orthogonal slow time channel, but also comprises the frequency of the clutter signal on each transmitting array element on each orthogonal slow time channel, and the phase and the frequency of the target signal on each transmitting array element on each orthogonal slow time channel. Figure 2 schematically illustrates a doppler domain signal component diagram; in fig. 2, m=4, and the patterns filled with black, light gray, white, and dark gray correspond to the transmitting element 1, the transmitting element 2, the transmitting element 3, and the transmitting element 4, respectively; the rectangle represents the clutter signal; the circle represents a low-speed target echo with Doppler frequency ofThe triangle represents a high-speed target echo whose Doppler frequency is +.>The difference phi between the two angles marked on the top of the rectangle i -φ m Is the phase of the clutter echo signal, wherein +.>And->Corresponding to the same orthogonal slow time channel, the rest 0,And corresponding to the other 3 orthogonal slow time channels.
It can be understood that by drawing a schematic diagram of the doppler domain signal components, the distribution of the clutter signals on each transmitting array element on each orthogonal slow time channel can be intuitively known.
S30: and constructing an intensity accumulation expression of clutter signals on each transmitting array element according to the calculated phases and frequencies.
Specifically, according to the calculated distribution of the frequency and the phase on each orthogonal slow time channel, the single-point output of the M-point cyclic autocorrelation function of each clutter signal or the cumulative vector of the intensity of the fuzzy clutter is obtained. Thus, the constructed intensity cumulative expression may be:
wherein Y represents the intensity accumulation result,is a random initial phase set; />Is a target sequence constructed according to the calculated distribution of the frequency and the phase over the orthogonal slow time channels, the target sequence representing the frequency and the phase of the signal dither (M) cyclically moving the conjugated complex sequence of length M after item i; y (i) is phi dither The M points of (M) cycle the single point output of the autocorrelation function.
Taking fig. 2 as an example, when i=m, for each transmitting element, the phase values of the clutter signals on the transmitting element are all 0, and the clutter gain multiples thereof are:
when i.noteq.m, the phase values of the clutter signals are different from each other, which corresponds to the sum of a plurality of vectors, and the clutter gain multiple is not more than 4.
Specifically, the phase of the clutter signal corresponds toWhen (1):
alternatively, the phase of the clutter signal corresponds toWhen (1):
alternatively, the phase of the clutter signal corresponds toWhen (1):
it is understood that the clutter gain multiple is the accumulated result of the clutter signal intensity.
Based on equations (1) - (4), the vector sum of each clutter signal can be regarded as Φ dither The single point output y (i) of the M-point cyclic autocorrelation function of the sequence, which can be expressed as:
as can be seen from the equation (5), only when i=0, that is, only y (0) represents the gain of the real target without ambiguity, the maximum value M is obtained at this time, and the outputs of the cyclic autocorrelation functions of the remaining M-1 points y (i) (1.ltoreq.i.ltoreq.M-1) are all equal to or less than M.
S40: and searching the intensity accumulation expression in an angle interval of [0,2 pi ] to obtain an optimal initial phase set corresponding to clutter with minimum intensity.
The optimal initial phase set includes M optimal initial phases.
It can be appreciated that the M optimal initial phases correspond to a computational complexity equal to 360 M 。
In addition, it should be noted that there is not only one optimal initial phase set corresponding to the clutter with the minimum intensity, that is, the optimal initial phase obtained in the embodiment of the present invention is not unique, so that the phase jitter value of the DDMA waveform can be selected more freely.
Taking fig. 2 as an example, assume a first term phi of the random initial phase set 1 The simulation results of the minimum clutter intensity simulation are shown in fig. 3. In FIG. 3, angle 2 of the x-axis represents φ 1 Angle 3 of the y-axis represents phi 2 Different colors within the coordinate system represent different clutter intensities. The calibrated coordinate position in FIG. 3 is [180180 ]]The point of (2) is a minimum clutter intensity, and as can be seen from fig. 3, the point of minimum clutter intensity is not the only point.
Optionally, in an airborne MIMO radar, the number of transmitting array elements m=4, and at this time, the optimal phase jitter set of the phase jitter DDMA waveform obtained by using the construction method provided by the embodiment of the present invention is {0, pi }.
S50: and constructing a phase jitter DDMA waveform in the airborne MIMO radar based on the optimal initial phase set.
Specifically, after the optimal initial phase set is obtained in step S40, the optimal initial phase set may be applied to the transmitter of the airborne MIMO radar, so that the transmitter generates and transmits the radar signal in the phase jitter DDMA waveform format by using the optimal initial phase set. Thus, the intensity of the fuzzy clutter is made to be almost zero, and the problem of blind speed of target detection caused by Doppler fuzzy which is easy to be caused by DDMA signals is reduced.
Compared with the frequency jitter DDMA waveform Doppler frequency non-blurring interval which is smaller than 1/M, the phase jitter DDMA waveform provided by the embodiment of the invention is the same as the Doppler frequency non-blurring interval of the traditional DDMA waveform, and is 1/M, so that the problem that the frequency jitter DDMA waveform Doppler frequency non-blurring interval is smaller than 1/M is solved.
In the embodiment of the invention, only one random initial phase is added on each transmitting array element, so that the hardware structure of the transmitter transmitting phase jitter DDMA waveform is simple.
In addition, in the embodiment of the invention, the random initial phase is added on the transmitting array element and is linearly transformed in slow time, and compared with the target aliasing formula of the frequency jitter DDMA waveform, the target aliasing formula of the phase jitter DDMA waveform provided by the embodiment of the invention is simple, and the problems of difficult deduction and more conditions can not occur.
The beneficial effects of the embodiment of the invention are further described below in connection with simulation experiments. The simulation experiment was implemented on a software platform of MATLAB R2017a, with simulation parameter settings see table 1.
TABLE 1 on-board DDMA-MIMO radar simulation parameters
Based on the simulation setting, the traditional DDMA waveform and the phase jitter DDMA waveform generated by the construction method provided by the embodiment of the invention are respectively simulated. FIG. 4 (a) shows an original clutter range-Doppler plot of a conventional DDMA waveform; FIG. 4 (b) is a clutter range-Doppler plot after clutter suppression of the original clutter range-Doppler plot of FIG. 4 (a) using a space-time-code adaptive processing technique; FIG. 4 (c) shows an original clutter distance-Doppler plot obtained from a phase jitter DDMA waveform obtained using the method provided by embodiments of the present invention; fig. 4 (d) is a clutter range-doppler plot after clutter suppression of the original range-doppler plot of fig. 4 (c) using space-time-code adaptive processing techniques. In fig. 4 (a) -4 (b), the different color shades represent the intensity of the radar echo, and the right color bar indicates the specific gravity of the radar echo intensity.
As can be seen by comparing fig. 4 (a) and fig. 4 (c), the clutter echoes of the phase jitter DDMA waveform and the conventional DDMA waveform provided by the embodiment of the present invention are uniformly distributed in the doppler domain, so that clutter corresponding to four transmitting array elements and a target signal can be extracted and separated by the DDMA.
As can be seen from fig. 4 (b), the conventional DDMA waveform causes the corresponding main clutter centers to appear on the four orthogonal doppler channels, resulting in multiple blind speeds for the DDMA-MIMO radar. As can be seen by comparing fig. 4 (b) with fig. 4 (d), the blind speed of the target is substantially suppressed, the blind speed problem is substantially solved, and there is a smaller minimum detectable speed compared to fig. 4 (b). Therefore, the method for constructing the optimum phase jitter DDMA can avoid the problem of blind speed.
In the description of the present specification, a description referring to terms "one embodiment," "some embodiments," "examples," "specific examples," or "some examples," etc., means that a particular feature or characteristic described in connection with the embodiment or example is included in at least one embodiment or example of the present invention. In this specification, schematic representations of the above terms are not necessarily directed to the same embodiment or example. Furthermore, the particular features or characteristics described may be combined in any suitable manner in any one or more embodiments or examples. Further, one skilled in the art can engage and combine the different embodiments or examples described in this specification.
Although the present application has been described herein in connection with various embodiments, other variations to the disclosed embodiments can be understood and effected by those skilled in the art in practicing the claimed application, from a review of the figures, the disclosure, and the appended claims.
The foregoing is a further detailed description of the invention in connection with the preferred embodiments, and it is not intended that the invention be limited to the specific embodiments described. It will be apparent to those skilled in the art that several simple deductions or substitutions may be made without departing from the spirit of the invention, and these should be considered to be within the scope of the invention.
Claims (3)
1. The construction method of the phase jitter DDMA waveform is characterized by comprising the following steps:
acquiring the number M of transmitting array elements of the airborne MIMO radar and the pulse repetition frequency f r And according to the number M of the transmitting array elements and the pulse repetition frequency f r Calculating Doppler frequency alpha of phase jitter DDMA waveform of each transmitting array element m ，m∈[1，M]，M≥2；
Doppler frequency alpha of DDMA waveform according to signal received by any receiving array element and phase jitter of M transmitting array elements m Calculating Doppler domain signal components of the phase jitter DDMA waveform of the receiving array element by using a target aliasing formula of a preset phase jitter DDMA waveform; the Doppler domain signal component includes at least: the frequency and phase of clutter signals on each transmitting array element on each orthogonal slow time channel;
constructing an intensity accumulation expression of clutter signals on M transmitting array elements according to the calculated frequency and phase;
searching the intensity accumulation expression in an angle interval of [0,2 pi ] to obtain an optimal initial phase set corresponding to clutter with minimum intensity, wherein the optimal initial phase set comprises M optimal initial phases;
constructing a phase jitter DDMA waveform in the airborne MIMO radar based on the optimal initial phase set;
the target aliasing formula of the phase jitter DDMA waveform is as follows:
wherein { X t } nk,i Represents the output result of the received nth signal after the kth pulse is subjected to down-conversion and matched filtering processing and phase compensation of the ith Doppler filter, { X } t } nk,i-q Representing the output result of the phase compensation of the ith-q Doppler filter after the down-conversion and matched filtering treatment of the kth pulse received by the nth receiving array element, wherein i is more than or equal to 0 and less than or equal to M-1, n is more than or equal to [1, N ]]，k∈[1，K]N isThe total number of the received signals, K, is the pulse number in one coherent processing time;indicating the initial phase of the ith transmit element,/->Representing the initial phase of the i-q th transmitting array element; f (f) t Satisfy f r /2>|f t |>Δf/2, representing the Doppler frequency of the high-speed target signal, f t -q.DELTA.f satisfies |f t -q.DELTA.f|.ltoreq.DELTA.f/2, representing the Doppler frequency of the low-speed target signal,/o>Represents a frequency interval, q is an integer and satisfies alpha i ＝α i-q +q.Δf, where α i And alpha i-q The Doppler frequencies of the phase jitter DDMA waveforms of the ith and the ith-q transmitting array elements are respectively represented; />The upper horizontal line represents pair->Performing fast Fourier transform, ">The upper horizontal line represents pair->Performing fast Fourier transform;
the intensity cumulative expression is:
wherein the method comprises the steps ofY represents the intensity accumulation result,is a random initial phase set; />Is a target sequence constructed according to the calculated distribution of the frequency and the phase over the orthogonal slow time channels, the target sequence representing the phase ratio phi dither (M) cyclically moving the conjugated complex sequence of length M after item i; y (i) is phi dither The M points of (M) cycle the single point output of the autocorrelation function.
2. The method of claim 1, wherein said transmitting element number M and said pulse repetition frequency f are based on r Calculating Doppler frequency alpha of phase jitter DDMA waveform of each transmitting array element m Comprising:
according to the number M of the transmitting array elements and the pulse repetition frequency f r Calculating the Doppler frequency alpha of the phase jitter DDMA waveform of each transmitting array element by using a preset Doppler frequency calculation formula m ；
The Doppler frequency calculation formula is as follows: alpha m ＝Δf·(m-1)。
3. The method of claim 1, wherein the optimal initial phase set is {0, pi }, when M = 4.
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