CN112526458B - Broadband NLFM (non-line-of-sight) emission beam forming method based on parameter fraction time delay extraction - Google Patents

Broadband NLFM (non-line-of-sight) emission beam forming method based on parameter fraction time delay extraction Download PDF

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CN112526458B
CN112526458B CN202011355255.1A CN202011355255A CN112526458B CN 112526458 B CN112526458 B CN 112526458B CN 202011355255 A CN202011355255 A CN 202011355255A CN 112526458 B CN112526458 B CN 112526458B
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CN112526458A (en
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蒋德富
何翱宇
邓峣
李春生
丁晓伟
赫冉
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Hohai University HHU
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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
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Abstract

The invention discloses a broadband NLFM (non line frequency modulation) transmitting beam forming method based on extraction parameter fractional time delay, belonging to the technical field of array signal processing. Due to the problem of aperture transit, beam forming of broadband signals requires time delay processing, and a traditional time delay method uses a filter in a time domain and performs DFT in a frequency domain. Most studies on the generation of wideband transmit beams are directed to LFM signals, while few studies are directed to NLFM signals with more complex signal characteristics and excellent pulse pressure performance. The invention provides a broadband NLFM fractional beam forming method, which emphasizes the generation of a digital fractional time delay waveform: dividing the time delay into integer time delay and fractional time delay, obtaining a time domain expression of the broadband NLFM signal by utilizing exponential polynomial fitting processing, directly generating a fractional time delay waveform in a DDS (direct digital synthesizer) by a parameter extraction method, and finally forming a broadband NLFM transmitting beam through the integer time delay.

Description

Broadband NLFM (non-line-of-sight) emission beam forming method based on parameter fraction time delay extraction
Technical Field
The invention belongs to the technical field of array signal processing, and particularly relates to a broadband NLFM (non line of sight) transmitting beam forming method based on parameter extraction fractional time delay.
Background
The currently commonly used wideband radar signal is the LFM signal. In the pulse compression system radar, the side lobe of the LFM signal pulse compression result is higher. In order to reduce the side lobe, window function weighting is usually adopted, which causes problems such as loss of signal-to-noise ratio and main lobe broadening. And the distance sidelobe is lower after the NLFM signal pulse compression, and weighting is not needed, so that the loss of the signal-to-noise ratio caused by mismatch is avoided. The broadband radar system using the NLFM signals has the advantages of both the broadband signals and the NLFM signals: low interception and low pulse compression sidelobes. In wideband array signals, waveform generation of TTD is a fundamental requirement of transmit beamforming. The TTD line can divide the delay into an integer delay and a fractional delay, and two digital methods can be used to realize the fractional delay of the wideband waveform. One is the time domain method, digital Variable Fractional Delay (VFD) filters (e.g., farrow structure filters) and other filters using newton or spline interpolation have been extensively studied. Another method is a frequency domain method based on fourier transform time shift characteristics, which first transfers the original reference waveform to the frequency domain through Discrete Fourier Transform (DFT), then performs linear phase shift on each frequency domain component, and finally transfers the frequency domain components back to the time domain sequence using Inverse DFT (IDFT). However, in the time domain method, the VFD filter requires hundreds of taps, and the filter is required to have the characteristics of wide bandwidth, high amplitude flatness, high delay precision, and the like. For the frequency domain method, in order to meet the time delay precision, for a large time bandwidth product waveform, the number of DFT points should not be less than the number of sampling points, and the number of sampling points may exceed ten thousand. Although both methods can effectively implement arbitrary delay, the hardware and software for implementation are very complex and consume a lot of resources.
The TTD line can divide the delay into integer delay and fractional delay, and the fractional delay essentially changes the phase and envelope shift of the signal. The document proposes a method of compensating the phase of a signal in a DDS by varying the signal parameters, by analyzing the time domain representation of the signal, using the control parameters of a Direct Digital Synthesizer (DDS) to achieve the phase compensation. But this method requires obtaining a time domain phase representation of the signal. The commonly used NLFM signal is designed by a window function, and the time domain phase expression of the NLFM signal is obtained by inverting and then integrating the group delay function, which is implicit. The traditional method of NLFM signal generation is to design the waveform by phase-stationary principles using a window function. Currently, the research on NLFM signals is to improve a signal generation method, especially a fitting method, in a narrow-band background, and use a polynomial to fit a time domain expression of the NLFM signal or use fourier series expansion to obtain a signal phase expression. However, after Fourier series fitting, a trigonometric function appears in the expression, if a digital signal processing structure is used for generating fractional time delay signals, a large amount of precious multiplier resources are consumed, and if polynomial fitting is adopted, a phase accumulator can be used as much as possible, so that the resource consumption is low.
Disclosure of Invention
The technical problem to be solved by the invention is as follows: the system complexity is high and the resource consumption is large in the broadband beam forming, and the invention aims to perform the broadband beam forming in a mode of consuming less resources.
The invention adopts the following technical scheme for solving the technical problems: the method uses a least square method to carry out fitting approximation on the recessive expression to obtain an exponential polynomial expression of the approximate S-type NLFM signal time domain phase, and further adopts a parameter extraction method to directly generate a digital fractional time delay waveform. The theoretical derivation result indicates that the method can lead the forms of the fractional delay waveforms transmitted by each array element to be consistent, and the fractional delay waveforms of all the array elements can be directly generated only by changing the polynomial parameters. The broadband NLFM transmitting beam forming method based on the extraction parameter fractional time delay comprises the following steps:
step 1, selecting a Hamming window as a signal power spectrum to generate a nonlinear frequency modulation signal waveform, and obtaining a group delay function and a frequency spectrum of a signal and a phase function of the signal according to a phase stationary principle
Figure GDA0003668636640000021
And a wave function s (t);
step 2, carrying out transmission beam time delay division in a general uniform linear array transmission beam forming structure based on TTD and M identical omnidirectional antenna array element radiation delay waves into integer time delay and fractional time delay;
step 3, reference array element waveform s 0 (t) delaying corresponding integral multiple of sampling period, and delaying F according to fraction of m array elements m Generating a fractional delay waveform to realize signal delay of different array elements;
step 3-1, obtaining the phase of the reference array element signal through the phase polynomial function of the signal;
step 3-2, obtaining a delay waveform of the M +1 array element according to the waveform of the reference array element, wherein M is more than 0 and less than M-1;
3-3, calculating the envelope delay and the phase shift;
3-4, obtaining a fractional delay waveform of the m +1 array element according to the envelope delay and the phase shift;
step 4, calculating input parameters of a general digital signal processing structure based on a phase accumulator and a CORDIC RM module; and generating a broadband NLFM signal fractional time delay waveform according to the input parameters, and then performing integer time delay to form a complete broadband NLFM transmitting beam.
Further, the signal amplitude spectrum | S (f) | of the hamming window in step 1 satisfies:
Figure GDA0003668636640000022
wherein f is the signal frequency and B is the bandwidth of the frequency modulation; the group delay function T (f) and the spectrum f (T) of the signal are:
Figure GDA0003668636640000023
f(t)＝T -1 (f)
wherein K is 1 Is a constant coefficient; phase function of signal
Figure GDA0003668636640000024
And the waveform function s (t) is:
Figure GDA0003668636640000025
Figure GDA0003668636640000026
0≤t≤T
where T is the pulse width of the modulated waveform and a (T) is the envelope.
Further, the step 2 performs transmit beam time delay division under the uniform linear array model, and the specific process is as follows:
the first array element is taken as a reference array element, and the time difference tau is caused by the difference of the propagation paths of the m array elements compared with the reference array element tm ：
Figure GDA0003668636640000031
Wherein theta is t Is the angle of arrival, c is the speed of light, d is the array element spacing, and M is the number of array elements;
in far field, M array elements time delayed transmitting signal s m (t-τ tm ) Is combined into a composite signal x (t):
Figure GDA0003668636640000032
wherein s is m (t) is a transmitting signal before the M +1 array element is delayed, and M is more than 0 and less than M-1; delta (t-tau) tm ) Is s is m (t-τ tm ) An impulse function of the function; delta (t-tau) m -τ tm ) Is delta (t-tau) m ) And δ (t- τ) tm ) Of the convolution function, τ m The real time delay of the m +1 array element relative to the reference array element when the signal is transmitted is obtained;
according to the sampling period T s True time delay τ m Dividing into integer time delays T m And fractional delay F m Comprises the following steps:
Figure GDA0003668636640000033
wherein Int m Is the number of integer delays, round (·) denotes rounding to the nearest integer.
Further, in step 3, the generation of the digital fractional delay waveform of the extracted parameter specifically includes:
waveform s of reference array element 0 (t) is:
Figure GDA0003668636640000034
wherein a is 0 (t) is the envelope of the reference array element signal,
Figure GDA0003668636640000035
is the phase of the reference array element signal; setting the fitting as an exponential polynomial and the fitting order as n to obtain the phase of the reference array element signal
Figure GDA0003668636640000036
Comprises the following steps:
Figure GDA0003668636640000037
wherein P is i，0 Numerically integrating and fitting a curve according to the f (t) discrete values, i =0,1,2,. And n-1, n, wherein the subscript i represents a parameter corresponding to the index i; the delay waveform s of the m +1 th array element m (t) is:
Figure GDA0003668636640000038
wherein a is 0 (t-F m ) In order to envelope the time delay,
Figure GDA0003668636640000039
for phase shifting, δ (T-T) m ) Is an impulse function;
Figure GDA0003668636640000041
wherein the m +1 th array element transmits the phase parameter P of the fractional delay waveform i，m Comprises the following steps:
Figure GDA0003668636640000042
wherein
Figure GDA0003668636640000043
Is a permutation and combination; the fractional delay waveform of the m +1 array element is as follows:
Figure GDA0003668636640000044
wherein A is a constant envelope.
Further, in step 4, the input parameters of the general digital signal processing structure based on the phase accumulator and the CORDIC RM module are calculated, and the specific process is as follows:
a G-phase digital signal processing structure is adopted, and the digital sampling clock is as follows:
Figure GDA0003668636640000047
wherein T is CLK Is a clock pulse, and G is the phase number of the digital signal processing structure; clock T s The lower sample sequence number is n t ：
n t ＝G·i t +g
i t ＝0，1，2，...，N G -1，N G ＝i t /G，g＝0，1，2，...，G-1
Wherein i t For single-phase sampling sequences in multiphase structures, N G G is the length of a single-phase sampling sequence and is the number of each phase;
then for the reference array element, the g +1 th phase accumulator structure outputs the phase expression as:
Figure GDA0003668636640000045
Figure GDA0003668636640000046
the result of passing through n phase accumulators for the g +1 th phase;
wherein R is i，0，g For each coefficient of the formula, i =1,2, 3.., n-1, n, subscript i represents the number of accumulators passed, 0 represents the current corresponding 0 array element, which is a reference array element, and g represents the g +1 th term in the multiphase structure;
the expression of the m +1 th array element discrete phase function is as follows:
Figure GDA0003668636640000051
wherein the coefficient is R i，m，g ，i＝1，2，3，N-1, n, subscript i represents the number of accumulators passed, and m represents the number of the current array element; in the multi-phase digital signal processing structure, the g +1 th phase input parameters are as follows:
Figure GDA0003668636640000052
in which RW is m，g 、FW i，m，g 、PW m，g Are input parameters to the digital signal processing architecture.
Has the beneficial effects that: compared with the prior art, the technical scheme of the invention has the following beneficial technical effects:
the broadband NLFM transmitting wave beam forming method based on the extracted parameter fractional time delay is reliable in design principle and simple in structure, compared with the broadband LFM signal wave form generation, the broadband NLFM transmitting wave beam forming method can form the broadband NLFM transmitting wave form only by adding the phase accumulator, the consumption of multiplier resources is avoided, and meanwhile the performance of the transmitting signal is improved.
Drawings
FIG. 1 is a flow chart of a method of the present invention;
FIG. 2 is a diagram of a digital signal processing multi-phase architecture using phase accumulation;
FIG. 3 is a graph of pulse pressure results at different fitting orders;
FIG. 4 (a) is a diagram of a four-phase output waveform of a reference array element for FPGA simulation test;
FIG. 4 (b) is a diagram of a reference array element four-phase output waveform for MATLAB simulation test;
FIG. 5 (a) is a diagram of a second array element four-phase output waveform of FPGA simulation test;
FIG. 5 (b) is a diagram of the second array element four-phase output waveform of the MATLAB simulation test;
FIG. 6 is a diagram of the beam synthesis after synthesis at discrete time points in the time domain;
fig. 7 is a comparison graph of pulse pressures of LFM and NLFM echo signals under the same parameters.
Detailed Description
The technical scheme of the invention is further explained in detail by combining the attached drawings.
The invention provides a broadband NLFM (non line of sight) transmitting beam forming method based on extracted parameter fractional time delay, which comprises the following concrete implementation steps as shown in figure 1:
step 1, in order to reduce the distance side lobe pressure of an output waveform, a Hamming window is selected as a signal power spectrum to generate a nonlinear frequency modulation signal waveform, a group delay function and a frequency spectrum of a signal are obtained according to a phase stationary principle, and a phase function of the signal
Figure GDA0003668636640000054
And a wave function s (t). The signal amplitude spectrum | S (f) | of the Hamming window satisfies:
Figure GDA0003668636640000053
wherein f is the signal frequency, and B is the bandwidth of frequency modulation; the group delay function T (f) and the spectrum f (T) of the signal are:
Figure GDA0003668636640000061
f(t)＝T -1 (f)
wherein K is 1 Is a constant coefficient; phase function of signal
Figure GDA0003668636640000062
And the waveform function s (t) is:
Figure GDA0003668636640000063
Figure GDA0003668636640000064
0≤t≤T
where T is the pulse width of the modulated waveform and a (T) is the envelope.
Step 2, carrying out transmission beam time delay division in a general uniform linear array transmission beam forming structure based on TTD and M identical omnidirectional antenna array element radiation delay waves into integer time delay and fractional time delay;
the method comprises the following steps of carrying out time delay division on transmitted beams under a uniform linear array model, and specifically comprising the following steps:
the difference in propagation paths between the m array elements and the reference array element (the first array element, i.e. the 0 array element) results in a time difference τ tm ：
Figure GDA0003668636640000065
Wherein theta is t Is the angle of arrival, c is the speed of light, d is the array element spacing, and M is the number of array elements;
in far field, M array elements time delayed transmitting signal s m (t-τ tm ) Is combined into a composite signal x (t):
Figure GDA0003668636640000066
wherein s is m (t) is a transmitting signal before the M +1 array element is delayed, and M is more than 0 and less than M-1; delta (t-tau) tm ) Is as s m (t-τ tm ) An impulse function of the function; delta (t-tau) m -τ tm ) Is delta (t-tau) m ) And δ (t- τ) tm ) Convolution function of, τ m The real time delay of the m +1 array element relative to the reference array element when the signal is transmitted is obtained; if the maximum power of signal transmission points to the target angle theta t Then τ is m ＝-τ tm ；
According to the sampling period T s True time delay τ m Time delay T divided into integers m And fractional delay F m Comprises the following steps:
Figure GDA0003668636640000067
wherein Int m Is the number of integer delays, round (·) denotes rounding to the nearest integer.
Step 3, reference array element waveform s 0 (t) delaying corresponding integral multiple of sampling period, and delaying F according to fraction of m array elements m Generating a fractional delay waveform to realize signal delay of different array elements;
step 3-1, obtaining the phase of the reference array element signal through the phase polynomial function of the signal;
step 3-2, obtaining a delay waveform of the M +1 th array element according to the reference array element waveform, wherein M is more than 0 and less than M-1;
3-3, calculating the envelope delay and the phase shift;
and 3-4, obtaining the fractional delay waveform of the m +1 array element according to the envelope delay and the phase shift.
The generation of the digital fractional delay waveform of the extracted parameter comprises the following specific processes:
waveform s of reference array element 0 (t) is:
Figure GDA0003668636640000071
wherein a is 0 (t) is the envelope of the reference array element signal,
Figure GDA0003668636640000072
is the phase of the reference array element signal; setting the fitting order as n to obtain the phase of the reference array element signal
Figure GDA0003668636640000073
Comprises the following steps:
Figure GDA0003668636640000074
wherein P is i，0 Numerically integrating and fitting a curve according to the discrete values of f (t), wherein i =0,1,2,. Cndot., n-1, n, and subscript i represents a parameter corresponding to index i; the delay waveform s of the m +1 th array element m (t) is:
Figure GDA0003668636640000075
wherein a is 0 (t-F m ) In order to envelope the time delay,
Figure GDA0003668636640000076
for phase shifting, delta (T-T) m ) Is an impulse function;
if signal time delay of different array elements is to be realized, reference array element waveform s can be firstly compared 0 (t) delaying corresponding integral multiple of sampling period, and delaying according to fraction delay F m A fractional delay waveform is generated. The envelope delay a needs to be calculated for realizing the fractional delay 0 (t-F m ) And phase shift
Figure GDA0003668636640000077
In this embodiment, the envelope a (t) = a of the S-type NLFM signal, which is a constant modulus function.
Figure GDA0003668636640000078
If different array element signals are required to be at theta t The same phase synthesis is carried out in the direction, and then the phase parameter of the m +1 th array element transmitting fractional time delay waveform should be P i，m (i =0,1, 2.., n-1, n, subscript i represents the parameter correspondence index i, and m represents the array element number). According to the nature of the polynomial, P is known i，m The numerical values of (A) are:
Figure GDA0003668636640000079
wherein
Figure GDA00036686366400000710
If the phase fitting polynomial parameter of the reference array element is set for permutation and combination, the phase fitting polynomial parameter P of other M-1 array elements i，m The phases of all array elements are obtained through calculation.
The fractional delay waveform of the m +1 array element is as follows:
Figure GDA0003668636640000081
wherein A is a constant envelope.
Step 4, calculating input parameters of a general digital signal processing structure based on a phase accumulator and a CORDIC RM module; and generating a broadband NLFM signal fractional time delay waveform according to the input parameters, and then performing integer time delay to form a complete broadband NLFM transmitting beam. The specific process of calculating the input parameters comprises the following steps:
a G-phase digital signal processing structure is adopted, and the digital sampling clock is as follows:
Figure GDA0003668636640000082
wherein T is CLK Is a clock pulse, G is the phase number of the digital signal processing structure; clock T s The lower sample sequence number is n t ：
n t ＝G·i t +g
i t ＝0，1，2，...，N G -1，N G ＝i t /G，g＝0，1，2，...，G-1
Wherein i t For single-phase sampling sequences in multiphase structures, N G G is the length of a single-phase sampling sequence and is the number of each phase;
then for the reference array element, the g +1 th phase accumulator structure outputs the phase expression as:
Figure GDA0003668636640000083
Figure GDA0003668636640000084
the result of passing through n phase accumulators for the g +1 th phase;
wherein R is i，0，g For each coefficient of the equation, i =1,2,3The table corresponds to 0 array element at present, which is a reference array element, and g represents the g +1 th item in the multiphase structure;
the expression of the m +1 th array element discrete phase function is as follows:
Figure GDA0003668636640000085
wherein the coefficient is R i，m，g I =1,2, 3., n-1, n, the subscript i representing the number of accumulators passed, m representing the number of the current array element; in the multi-phase digital signal processing structure, the g +1 th phase input parameters are as follows:
Figure GDA0003668636640000091
in which RW m，g 、FW i，m，g 、PW m，g Are input parameters for the digital signal processing architecture, see fig. 2.
The algorithm and the processing method of the invention have passed verification, and have achieved satisfactory application effect:
1. conditions of the experiment
With bandwidth B =400MHz, pulse width T =10us, center frequency f c NLFM signal of =200MHz as input signal, sampling frequency f s =1600MHz, desired transmission direction θ t Is 30 degrees, the number M of the array elements is 64, the spacing d of the array elements is lambda c /2，λ c ＝c/f c 。
2. Emulation content
Simulation 1: and (5) adopting a signal pulse compression graph obtained after 5-order, 16-order and 50-order fitting. It can be seen that when 16-order fitting is taken, the side lobes after pulse compression have reached-40 dB or less, and as the order increases, the fitting accuracy has not improved significantly. Fig. 3 shows the pulse pressure results for different fitting orders.
Simulation 2: and inputting the calculation parameters into the system by using a 4-phase digital signal processing system (G = 4) to obtain a digital broadband fractional delay emission waveform of each array element, taking 0,1 array element as an example, and respectively referring to FIG. 4 and FIG. 5 to four-phase output waveforms of a reference array element and a second array element, wherein a is an FPGA simulation test result and b is an MATLAB simulation result.
Simulation 3: in the method for forming a fractional delay waveform by using the parameters extracted after the integer delay provided by the invention, fig. 6 is a beam synthesis diagram after the synthesis of each discrete time point in the time domain.
Simulation 4: and (3) comparing the compressed echo pulses of the broadband NLFM signal and the LFM signal under the condition of the same parameters. For convenience of comparison, the observation time does not cover the entire time width. Fig. 7 shows the pulse pressure contrast of LFM and NLFM echo signals under the same parameters.
3. Analysis of simulation results
As can be seen from fig. 3, when 16-order fitting is performed, the side lobes after pulse compression reach-40 dB or less, and as the order increases, the fitting accuracy is not improved significantly. As can be seen from fig. 4 and 5, the FPGA simulation result is identical to the MATLAB software simulation result, and the method generates an accurate fractional delay waveform. As can be seen from fig. 6, the beam is directed exactly at the predetermined 30 °, the synthetic direction of the transmitted beam is good, and there is no significant offset distortion. As can be seen from fig. 7, the NLFM signal slightly broadens the main lobe compared to the LFM signal, but the side lobe is significantly reduced, the reduction amplitude exceeds 20dB, and the improvement is significant.

Claims (5)

1. A broadband NLFM emission beam forming method based on parameter fraction time delay extraction is characterized by comprising the following specific steps:
step 1, selecting a Hamming window as a signal power spectrum to generate a nonlinear frequency modulation signal waveform, and obtaining a group delay function and a frequency spectrum of a signal and a phase function of the signal according to a phase stationary principle
Figure FDA0003668636630000011
And a waveform function s (t);
step 2, carrying out time delay division on the transmitting wave beams in a general uniform linear array transmitting wave beam forming structure based on TTD and M identical omnidirectional antenna array element radiation delay waves into integer time delay and fractional time delay;
step 3, reference array element waveform s 0 (t) delaying samples by respective integer multiplesPeriodically, and then according to the fractional delay F of m array elements m Generating a fractional time delay waveform to realize the signal time delay of different array elements;
step 3-1, obtaining the phase of the reference array element signal through the phase polynomial function of the signal;
step 3-2, obtaining a delay waveform of the M +1 array element according to the waveform of the reference array element, wherein M is more than 0 and less than M-1;
step 3-3, calculating envelope delay and phase shift;
3-4, obtaining a fractional delay waveform of the m +1 array element according to the envelope delay and the phase shift;
step 4, calculating input parameters of a general digital signal processing structure based on a phase accumulator and a CORDIC RM module; and generating a broadband NLFM signal fractional time delay waveform according to the input parameters, and then performing integer time delay to form a complete broadband NLFM transmitting beam.
2. The method for forming NLFM transmit beam based on fractional delay of extracted parameters as claimed in claim 1, wherein the signal magnitude spectrum | S (f) | of hamming window in step 1 satisfies:
Figure FDA0003668636630000012
wherein f is the signal frequency and B is the bandwidth of the frequency modulation; the group delay function T (f) and the spectrum f (T) of the signal are:
Figure FDA0003668636630000013
f(t)＝T -1 (f)
wherein K 1 Is a constant coefficient; phase function of signal
Figure FDA0003668636630000014
And the waveform function s (t) is:
Figure FDA0003668636630000015
Figure FDA0003668636630000016
0≤t≤T
where T is the pulse width of the modulated waveform and a (T) is the envelope.
3. The broadband NLFM transmission beam forming method based on extracted parameter fractional time delay as claimed in claim 2, wherein said step 2 performs transmission beam time delay division under a uniform linear array model, and the specific process is as follows:
setting the first array element as reference array element, the difference of propagation path between m array elements and reference array element results in time difference tau tm ：
Figure FDA0003668636630000017
Wherein theta is t Is the angle of arrival, c is the speed of light, d is the array element spacing, and M is the number of array elements;
in far field, M array elements time delayed transmitting signal s m (t-τ tm ) Is combined into a composite signal x (t):
Figure FDA0003668636630000021
wherein s is m (t) is a transmitting signal before the M +1 array element is delayed, and M is more than 0 and less than M-1; delta (t-tau) tm ) Is s is m (t-τ tm ) An impulse function of the function; v (t- τ) m -τ tm ) Is delta (t-tau) m ) And delta (t-tau) tm ) Of the convolution function, τ m The real time delay of the m +1 array element relative to the reference array element when the signal is transmitted is obtained;
according to the sampling period T s True time delay τ m Dividing into integer time delays T m And fractional delay F m Comprises the following steps:
Figure FDA0003668636630000022
wherein Int m Is the number of integer delays, round (·) denotes rounding to the nearest integer.
4. The wideband NLFM transmit beamforming method based on fractional delay of extracted parameters according to claim 3, wherein in step 3, the generation of the digital fractional delay waveform of the extracted parameters comprises the following specific processes:
waveform s of reference array element 0 (t) is:
Figure FDA0003668636630000023
wherein a is 0 (t) is the envelope of the reference array element signal,
Figure FDA0003668636630000024
is the phase of the reference array element signal; setting the fitting as an exponential polynomial and the fitting order as n to obtain the phase of the reference array element signal
Figure FDA0003668636630000025
Comprises the following steps:
Figure FDA0003668636630000026
wherein P is i，0 Numerically integrating and fitting a curve according to the f (t) discrete values, i =0,1,2,. And n-1, n, wherein the subscript i represents a parameter corresponding to the index i; the delay waveform s of the m +1 th array element m (t) is:
Figure FDA0003668636630000027
wherein a is 0 (t-F m ) In order to envelope the time delay,
Figure FDA0003668636630000028
for phase shifting, delta (T-T) m ) Is an impulse function;
Figure FDA0003668636630000029
wherein the m +1 th array element transmits the phase parameter P of the fractional time delay waveform i，m Comprises the following steps:
Figure FDA0003668636630000031
wherein
Figure FDA0003668636630000032
Is a permutation and combination; the fractional delay waveform of the m +1 array element is as follows:
Figure FDA0003668636630000033
wherein A is a constant envelope.
5. The wideband NLFM transmit beamforming method based on fractional time delay extraction of parameters as claimed in claim 4, wherein said step 4, calculating the input parameters of the generic digital signal processing architecture based on the phase accumulator and CORDIC RM module, comprises the following specific steps:
a G-phase digital signal processing structure is adopted, and the digital sampling clock is as follows:
Figure FDA0003668636630000034
wherein T is CLK Is a clock pulse, G is the phase number of the digital signal processing structure; clock T s The lower sample sequence number is n t ：
n t ＝G·i t +g
i t ＝0，1，2，...，N G -1，N G ＝i t /G，g＝0，1，2，...，G-1
Wherein i t Sequence of samples for a single phase in a multiphase structure, N G G is the length of a single-phase sampling sequence and is the number of each phase;
then for the reference array element, the g +1 th phase accumulator structure outputs the phase expression as:
Figure FDA0003668636630000035
Figure FDA0003668636630000036
the result of the g +1 th phase passing through n phase accumulators;
wherein R is i，0，g For each coefficient of the formula, i =1,2, 3.., n-1, n, subscript i represents the number of accumulators passed, 0 represents the current corresponding 0 array element, which is a reference array element, and g represents the g +1 th term in the multiphase structure;
the expression of the m +1 array element discrete phase function is as follows:
Figure FDA0003668636630000037
wherein the coefficient is R i，m，g I =1,2, 3., n-1, n, the subscript i representing the number of accumulators passed, m representing the number of the current array element; in the multi-phase digital signal processing structure, the g +1 th phase input parameters are as follows:
Figure FDA0003668636630000041
in which RW m，g 、FW i，m，g 、PW m，g Are input parameters of the digital signal processing architecture.
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