CN113030882B - Method for constructing carrier-free ultra-wideband emission signal waveform library - Google Patents
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Abstract
The invention provides a method for constructing a carrier-free ultra-wideband emission signal waveform library, which constructs a carrier-free ultra-wideband single pulse waveform according to selected single pulse waveform parameters including pulse forming factors, pulse orders, wavelet forming factors and translation factors; carrying out Fourier transform on the carrier-free ultra-wideband monopulse waveform to construct a carrier-free ultra-wideband monopulse frequency domain signal; according to the constructed carrier-free ultra-wideband single pulse waveform, combining the selected code pattern and modulation mode, carrying out pulse position, amplitude, polarity and waveform modulation under different code patterns, realizing multiple composite modulation of pulse polarity-position, pulse amplitude-position and the like, and constructing a modulated carrier-free ultra-wideband pulse sequence; and constructing fuzzy domain waveforms of the carrier-free ultra-wideband pulse trains in different modulation modes according to the carrier-free ultra-wideband pulse sequences in different modulation modes. The invention solves the problems of single waveform form and modulation mode, insufficient fuzzy domain analysis and the like of the existing carrier-free ultra-wideband signal transmission.
Description
Technical Field
The invention relates to a carrier-free ultra-wideband transmitting technology, in particular to a method and a system for constructing a carrier-free ultra-wideband transmitting signal waveform library.
Background
The carrier-free ultra-wideband radar realizes detection, identification, imaging and the like of targets by transmitting carrier-free narrow pulse signals. On one hand, the nanosecond or sub-nanosecond carrier-free ultra-wideband signal has very wide electromagnetic spectrum distribution, so that the ultra-wideband signal has very high resolution and has strong electromagnetic interference resistance and anti-stealth capability; on the other hand, the low-frequency component in the ultra-wideband enables the impulse radar system to have stronger penetrating power, and is suitable for developing through-wall, ground penetrating or jungle radars. Therefore, the carrierless ultra-wideband signal has very important research significance.
The single pulse form of the pulse ultra-wideband signal can influence the power spectrum density of the transmission signal, and the selection of the single pulse form is in accordance with the principles of high spectrum utilization rate, flexible interference suppression, easy pulse generation and the like. However, the existing carrier-free ultra-wideband transmitting waveforms mainly comprise Gaussian pulses, the transmitting waveform form and the modulating mode are single, and the spectrum utilization rate is low. The carrier-free ultra-wideband signal does not contain carrier frequency, and the fuzzy function analysis is different from the fuzzy function analysis of the traditional narrowband signal, so that the existing carrier-free ultra-wideband signal has less fuzzy domain analysis data and single content.
Disclosure of Invention
The invention aims to provide a method and a system for constructing a carrier-free ultra-wideband emission signal waveform library, which are used for solving the problems of single modulation mode, insufficient fuzzy domain analysis and the like of the existing carrier-free ultra-wideband signal emission waveform form.
The technical solution for realizing the purpose of the invention is as follows: a method for constructing a carrier-free ultra-wideband emission signal waveform library comprises the following steps:
step 1, constructing a carrier-free ultra-wideband monopulse waveform according to selected monopulse waveform parameters including a pulse forming factor, a pulse order, a wavelet forming factor and a translation factor;
step 2, carrying out Fourier transform on the carrier-free ultra-wideband monopulse waveform to construct a carrier-free ultra-wideband monopulse frequency domain signal;
step 3, according to the constructed carrier-free ultra-wideband single pulse waveform, combining the selected code pattern and modulation mode, carrying out pulse position, amplitude, polarity and waveform modulation under different code patterns, realizing various composite modulation of pulse polarity-position, pulse amplitude-position and the like, and constructing a modulated carrier-free ultra-wideband pulse sequence;
and 4, constructing fuzzy domain waveforms of the carrier-free ultra-wideband pulse trains in different modulation modes according to the carrier-free ultra-wideband pulse trains in different modulation modes.
Further, in step 1, a carrierless ultra-wideband monopulse waveform is constructed according to selected monopulse waveform parameters including pulse shaping factors, pulse orders, wavelet shaping factors and translation factors, including Gaussian pulse waveforms and their derivatives,
The modified Hermite pulse waveform and the wavelet pulse waveform are specifically:
(1) Gaussian pulse and its derivatives
The gaussian pulse signal s (t) has the expression:
the first derivative s' (t) and the second derivative s "(t) of the gaussian pulse are expressed as follows:
where t is a time factor, A is a signal amplitude, and τ is a shaping factor of the pulse waveform.
(2) Hermite pulses and their respective derivatives
Hermite pulse h en The polynomial form of (t) is as follows:
the Hermite pulse is non-orthogonal and the modified orthogonal Hermite pulse h n The expression of (t) is as follows:
where n is the order of the Hermite pulse.
(3) Wavelet pulse
The expression of Moelet mother wavelet ψ (t) is defined as:
the generated wavelet function ψ a,b The expression of (t) is:
wherein a is a scaling factor of the wavelet function, b is a translation factor, f 0 Is the carrier frequency.
Further, step 2, performing fourier transform on the carrierless ultra-wideband monopulse waveform to construct a carrierless ultra-wideband monopulse frequency domain signal, which specifically includes:
(1) Gaussian pulse and its derivatives
The fourier transform P (ω) of the gaussian pulse signal is:
fourier transform P of first-order Gaussian pulse signal (1) (ω) is:
fourier transform P of second-order Gaussian pulse signal (2) (ω) is:
where ω is an angular frequency factor.
(2) Hermite pulse
The fourier transform expression for the modified orthogonal Hermite pulse is:
where f is a frequency factor.
Further, step 3, according to the constructed carrierless ultra-wideband single pulse waveform, combining the selected code pattern and modulation mode, modulating pulse positions, amplitudes, polarities and waveforms under different code patterns, realizing multiple composite modulations such as pulse polarity-positions, pulse amplitude-positions and the like, and constructing a modulated carrierless ultra-wideband pulse sequence, which specifically comprises:
(1) Random pulse position modulation, i.e. pulse position
Ultra wideband pulse train signal u under random pulse position modulation 1 Mathematical expression of (t):
wherein p (T) is a carrierless ultra-wideband monopulse signal, T is a time factor, T is a pulse repetition period, N is the number of pulses, X i Is [0, T 0 ]Is a random variable uniformly distributed above, and X when i not equal to j is satisfied i And X is j Independently of each other, the pulse width of p (T) is defined as DeltaT, and the condition T should be satisfied in order to avoid pulse overlap 0 ≤T-ΔT。
(2) Pulse polarity modulation
When pulse polarity modulation is carried out on the carrierless ultra-wideband signal, a chaotic code or a pseudo code is selected as a modulation signal so as to realize the polarity modulation of the carrierless ultra-wideband pulse sequence, and an ultra-wideband pulse train signal u under the pulse polarity modulation 2 The mathematical expression of (t) is:
wherein s is i Representing a bipolar chaotic sequence or a pseudo-code sequence.
(3) Pulse amplitude modulation
Pulse amplitude modulation is a way of modulating information on the pulse amplitude, under pulse amplitude modulationUltra wideband pulse train signal u 3 The expression (t) is as follows:
wherein a is i Is [0,1 ]]And random variables subject to uniform distribution.
(4) Pulse waveform modulation
The pulse waveform can also be used for ultra-wideband modulation, and the pulse waveform modulation is generally realized by using different orthogonal pulses, and for binary modulation, the ultra-wideband pulse train signal u under the pulse waveform modulation 4 The expression (t) is:
wherein b is i E {0,1} is the modulated signal, p 0 (t) and p 1 (t) are respectively orthogonal pulse sequences of different shapes.
(5) Pulse complex modulation
Combining pulse amplitude modulation and pulse position modulation to obtain a pulse amplitude-position composite modulation signal u 5 (t) expression:
combining pulse polarity modulation with pulse position modulation to obtain pulse polarity-position composite modulation signal u 6 The expression (t) is:
further, step 4, constructing a fuzzy domain waveform, i.e. a fuzzy function, of the no-carrier ultra-wideband pulse train in different modulation modes according to the no-carrier ultra-wideband pulse train in different modulation modes, specifically:
random pulse position modulationFuzzy function X of down-loading no-carrier ultra-wideband pulse train 1 (τ,v)：
Fuzzy function X of carrier-free ultra-wideband pulse train under pulse polar modulation 2 (τ,T d )：
Fuzzy function X of carrier-free ultra-wideband pulse train under pulse amplitude modulation 3 (τ,T d )：
Fuzzy function X of carrier-free ultra-wideband pulse train under pulse waveform modulation 4 (τ,T d )：
Fuzzy function X of pulse polarity-position composite modulation carrier-free ultra-wideband pulse train 5 (τ,v)：
Fuzzy function X of carrier-free ultra-wideband pulse train under pulse amplitude-position modulation 6 (τ,v)：
Wherein τ and T d Delay and Doppler shift, v, representing the ideal point target "2" relative to target "1", respectively 1 Velocity of motion, v, for target "1 2 The approach speed of the object '2' relative to the object 1, c is the speed of light;
further, the implementation is based on a GUI platform.
The system for constructing the carrierless ultra-wideband emission waveform library is characterized by constructing the carrierless ultra-wideband emission waveform library based on the method.
A computer device comprising a memory, a processor and a computer program stored on the memory and executable on the processor, the processor implementing the method to construct a carrierless ultra-wideband transmit waveform library when the computer program is executed.
A computer readable storage medium having stored thereon a computer program which, when executed by a processor, implements the method to construct a carrierless ultra wideband transmit waveform library.
The carrier-free ultra-wideband emission waveform library is characterized by being constructed based on the method.
Compared with the prior art, the invention has the remarkable advantages that: the invention constructs the fuzzy functions of the no-carrier ultra-wideband pulse trains under different pulse waveforms and different modulation modes, and is different from the functions of signal delay and Doppler frequency shift of the traditional signal.
Drawings
FIG. 1 is a flow chart of a method for constructing a carrier-free ultra wideband transmission signal waveform library according to the present invention.
Fig. 2 is a schematic diagram of a main interface of a carrierless ultra-wideband transmit waveform library on a GUI platform.
FIG. 3 is a schematic diagram of a time domain waveform display interface with a zero order Gaussian pulse in single pulse form and a pulse shaping factor of 0.5 ns.
Fig. 4 is a schematic diagram showing the interface of the frequency domain waveform of the zero-order gaussian pulse signal with a pulse shaping factor of 0.5 ns.
Fig. 5 is a schematic diagram of a fuzzy function of a second-order gaussian pulse train with a pseudo-random code in symbol form and polar modulation in modulation mode.
Detailed Description
In order to make the objects, technical solutions and advantages of the present application more apparent, the present application will be further described in detail with reference to the accompanying drawings and examples. It should be understood that the specific embodiments described herein are for purposes of illustration only and are not intended to limit the present application.
A method for constructing a carrier-free ultra-wideband emission waveform library comprises the following steps:
step 1, constructing a carrierless ultra-wideband monopulse waveform according to selected monopulse waveform parameters including pulse shaping factors, pulse orders, wavelet shaping factors and translation factors, wherein the carrierless ultra-wideband monopulse waveform comprises Gaussian pulses and derivatives of Gaussian pulses, modified Hermite pulse waveforms of different orders and wavelet pulses. The construction of the carrier-free ultra-wideband single pulse waveform enriches the waveform form of the carrier-free ultra-wideband pulse, and can better exert the advantages of the carrier-free ultra-wideband signal in different forms in time domain and frequency domain when facing different application scenes and environments.
(1) Gaussian pulse and its derivatives
The gaussian pulse signal has the expression:
the first and second derivatives of the gaussian pulse are expressed as follows:
where t is the time factor, A is the signal amplitude, τ is the shaping factor of the pulse waveform, its magnitude affects the width and amplitude of the pulse, and as τ increases, the pulse amplitude decreases and the pulse width widens.
(2) Hermite pulses and their respective derivatives
The polynomial form of the Hermite pulse is as follows:
the above-mentioned Hermite pulses are non-orthogonal, and the modified orthogonal Hermite pulses are expressed as follows:
where n is the order of the Hermite pulse. Like gaussian pulses, as τ increases, the pulse amplitude decreases and the pulse width widens.
(3) Wavelet pulse
Let function ψ (t) ∈L 2 (R) satisfies the conditionThen ψ (t) is called the mother wavelet function, the generated wavelet function is denoted +.>Where b is a translation factor and a is a telescoping factor.
The expression of the Moelet mother wavelet is defined as:
the expression of the wavelet function generated by the method is as follows:
wherein a is a scaling factor of the wavelet function, b is a translation factor, f 0 Is the carrier frequency.
And 2, constructing a frequency spectrum signal corresponding to the carrierless ultra-wideband time domain signal through Fourier transformation according to the carrierless ultra-wideband single pulse waveform constructed in the previous step. The construction of the carrier-free ultra-wideband pulse frequency domain waveform realizes the spectrum analysis of the selected carrier-free ultra-wideband single pulse, and the corresponding time domain waveform can be obtained by reversely adjusting the parameters according to the spectrum requirement.
(1) Gaussian pulse and its derivatives
The fourier transform of the gaussian pulse signal is:
the fourier transform of the first order gaussian pulse signal is:
the fourier transform of the first order gaussian pulse signal is:
where ω is an angular frequency factor.
When the pulse order is fixed, as the pulse shaping factor tau increases, the time domain width of the Gaussian pulse increases, but the corresponding frequency spectrum width decreases correspondingly; when the pulse shaping factor tau is fixed, differentiating the Gaussian pulse inevitably affects the energy spectrum density, and the peak frequency of the pulse and the bandwidth of the pulse are affected, and observing the Fourier transform f of the k-order derivative (k) (ω) satisfies the following formula:
further deriving the above results in terms of peak frequency f peak The relation among the order k and the pulse shaping factor tau is expressed as follows:
the above equation shows that as the order of the gaussian function increases, the peak frequency increases, indicating that the differentiation moves the signal energy to higher frequencies, and it can be seen that as the pulse shaping factor increases, the peak frequency and bandwidth of the pulse decreases.
(2) Hermite pulse
The fourier transform expression for the modified orthogonal Hermite pulse is:
the influence of the pulse shaping factor tau and the pulse order n of the Hermite pulse on the pulse waveform and the energy spectrum density is similar to the case of Gaussian pulse, when the pulse order is fixed, the pulse width is increased along with the increase of the pulse factor tau, and the peak frequency of the pulse bandwidth and the energy spectrum density is reduced; when τ is fixed, the peak frequency increases with increasing order.
And 3, modulating pulse positions, amplitudes, polarities and waveforms under different code types according to the constructed carrier-free ultra-wideband single pulse waveform and combining the selected code types and modulation modes, realizing various composite modulations such as pulse polarity-positions, pulse amplitude-positions and the like, and constructing a modulated carrier-free ultra-wideband pulse sequence.
When the ultra-wideband signal is subjected to target detection, available information only comprises pulse amplitude, pulse position, pulse polarity and pulse waveform, so that pulse amplitude, pulse position, pulse polarity, pulse waveform modulation and various complex modulations are mainly integrated in a carrier-free ultra-wideband pulse waveform library, and various modulations under different code types are realized by combining pseudo-random codes and chaotic codes.
(1) Random pulse position modulation, i.e. pulse position modulation
Mathematical expression of ultra wideband pulse train signal under random pulse position modulation:
wherein p (T) is a carrierless ultra-wideband monopulse signal, T is a time factor, T is a pulse repetition period, N is the number of pulses, X i Is [0, T 0 ]Is a random variable uniformly distributed above, and X when i not equal to j is satisfied i And X is j Independent of each other. Defining the pulse width of p (T) as DeltaT, the condition T should be satisfied in order to avoid pulse overlap 0 ≤T-ΔT。
(2) Pulse polarity modulation
When the non-carrier ultra-wideband signal is subjected to pulse polarity modulation, a chaotic code or a pseudo code is selected as a modulation signal so as to realize the polarity modulation of the non-carrier ultra-wideband pulse sequence. The mathematical expression of the ultra-wideband pulse train signal under pulse polarity modulation is:
wherein s is i Representing a bipolar chaotic or pseudo code sequence, T is a time factor and T is a pulse repetition period. The chaotic code has noise-like statistical properties, and the detection system transmitting signal which is taken as a modulation signal has the characteristics of a 'thumbtack type' fuzzy function, and has high distance and speed resolution and strong anti-interference capability. There are many typical chaotic system models, such as Logistic maps, bernoulli mapsA Tent map, a Henon map, and a hyper-chaotic map. Pseudo-random code is also a signal with statistical properties similar to white noise, which has periodicity and whose fuzzy function diagram also approximately exhibits a pin shape. Typical pseudo-random codes are m-sequences, gold sequences, barker codes, L-sequences, etc.
(3) Pulse amplitude modulation
Pulse amplitude modulation is a way to modulate information on the pulse amplitude, expressed as follows:
wherein a is i Is [0,1 ]]And random variables subject to uniform distribution.
(4) Pulse waveform modulation
The pulse waveform can also be used for ultra-wideband modulation, and the pulse waveform modulation is generally realized by using different orthogonal pulses, and for binary modulation, the expression of a modulation signal is as follows:
in which the signal b is modulated i ∈{0,1}，p 0 (t) and p 1 And (t) respectively orthogonal pulse sequences with different shapes, wherein the orthogonal waveforms adopted in the invention are modified Hermite orthogonal pulse waveforms constructed in a waveform library.
(5) Pulse complex modulation
Two complex modulation modes, pulse amplitude-position complex modulation and pulse polarity-position complex modulation are also constructed in the waveform library. The pulse amplitude modulation and the pulse position modulation are combined to obtain a pulse amplitude-position composite modulation signal expression:
combining pulse polarity modulation with pulse position modulation can yield a signal expression of pulse polarity-position complex modulation:
and 4, constructing a fuzzy domain waveform, namely a fuzzy function, of the no-carrier ultra-wideband pulse train in different modulation modes according to the no-carrier ultra-wideband pulse train in different modulation modes, so as to analyze the detection performance of the no-carrier ultra-wideband radar from the angle of the fuzzy function.
Specific analysis is performed by taking the fuzzy function of pulse amplitude modulation and polarity-random pulse position modulation ultra-wideband pulse trains as an example.
The mathematical expression of the pulse amplitude modulation ultra-wideband pulse train is:
for an ideal point target "1", the target echo signal expression is:
where x represents the time delay and y is the Doppler shift.
For an ideal point target "2", there is a delay τ and a Doppler shift T relative to target "1 d The echo signal of target "2" is:
the mean square error criterion is used here as the best resolution criterion to derive the blurring function of the pulse amplitude modulated ultra wideband signal:
the echo signal energy in which the first term is the ideal point target "1" is denoted as E 1 The method comprises the steps of carrying out a first treatment on the surface of the The echo signal energy in which the second term is the ideal point target '2' is marked as E 2 The method comprises the steps of carrying out a first treatment on the surface of the Irrespective of attenuation during signal transmission, E 1 ＝E 2 =e. Let t- (x+τ) =t', y=0, and perform variable substitution on the above equation to obtain a fuzzy function of the pulse amplitude modulation ultra wideband pulse train:
it can be seen from the above equation that, unlike the conventional signal ambiguity function, the carrierless ultra-wideband pulse train ambiguity function constructed in the present invention converts the conventional doppler shift resolution problem into a doppler shift resolution problem with minimum mean square error as the optimal decision criterion.
According to the pulse polarity-position composite modulation expression, an ideal point target '1' with unchanged motion speed can be obtained, and the echo signal expression for simultaneously carrying out polarity modulation and position modulation is as follows:
in the formula, v 1 Is the rate of approach of the transmitter to the target "1", c represents the speed of light.
For an ideal point target "2", there is a delay τ and approach velocity v relative to a reference target "1 2 The echo signal expression for target "2" is:
the mean square error criterion is used here as the best resolution criterion to derive the blurring function of the random pulse-modulated ultra-wideband signal. Is obtained by the above method
Wherein the first term is the echo signal energy of the ideal point target '1', denoted as E 1 The method comprises the steps of carrying out a first treatment on the surface of the The echo signal energy in which the second term is the ideal point target '2' is marked as E 2 The method comprises the steps of carrying out a first treatment on the surface of the Irrespective of attenuation during signal transmission, E 1 ＝E 2 =e. Let t- (x+τ) =t', perform variable substitution on the above equation to obtain a fuzzy function of the polar-random pulse-modulated ultra-wideband pulse train:
for pulse polarity-position complex modulated ultra-wideband pulse trains, the Doppler shift is varied at different pulse repetition periods, so the present invention writes its blurring function as a function of delay and velocity.
Similarly, a blurring function of ultra-wideband pulses under other modulation modes can be constructed:
blur function of carrier-free ultra-wideband pulse train under pulse polar modulation:
fuzzy function of carrier-free ultra-wideband pulse train under random pulse position modulation:
the fuzzy function of the carrier-free ultra-wideband pulse train under pulse waveform modulation:
fuzzy function of no-carrier ultra-wideband pulse train under pulse amplitude-position modulation:
and step 5, realizing a carrier-free ultra-wideband single pulse waveform selection interface, a waveform parameter input interface, a modulation mode setting interface and a time domain, frequency domain and fuzzy domain signal display interface based on the GUI platform.
The invention also provides a system for constructing the carrierless ultra-wideband emission waveform library, which is characterized in that the carrierless ultra-wideband emission waveform library is constructed based on the method.
A computer device comprising a memory, a processor and a computer program stored on the memory and executable on the processor, the processor implementing the method to construct a carrierless ultra-wideband transmit waveform library when the computer program is executed.
A computer readable storage medium having stored thereon a computer program which, when executed by a processor, implements the method to construct a carrierless ultra wideband transmit waveform library.
The carrier-free ultra-wideband emission waveform library is characterized by being constructed based on the method.
Examples
In order to verify the effectiveness of the scheme of the invention, the following simulation experiment is carried out, and the system parameters are as follows: the carrier-free ultra-wideband single pulse waveform is zero-order Gaussian pulse, the pulse forming factor is 0.5ns, the modulation mode is polar modulation, the code element is the application scene of pseudo random code, and the carrier-free ultra-wideband signal time domain waveform, the carrier-free ultra-wideband time domain signal spectrum waveform and the carrier-free ultra-wideband signal fuzzy domain waveform are constructed.
FIG. 2 is a main interface of a carrierless ultra-wideband transmit waveform library on a GUI platform, with alternative display interfaces including a time domain waveform display interface, a frequency domain waveform display interface, and a fuzzy function display interface. Fig. 3 shows a time domain waveform display interface when the single pulse is zero order gaussian pulse and the pulse shaping factor is 0.5 ns. Fig. 4 is a frequency domain waveform display interface of a zero-order gaussian pulse signal with a pulse shaping factor of 0.5 ns. Fig. 5 shows a pseudo-random code in symbol form and a fuzzy function of a second-order gaussian pulse train under polar modulation in a modulation mode, and it is obvious that the fuzzy function of the second-order gaussian pulse train under the modulation mode is in a thumbtack shape.
The technical features of the above embodiments may be arbitrarily combined, and all possible combinations of the technical features in the above embodiments are not described for brevity of description, however, as long as there is no contradiction between the combinations of the technical features, they should be considered as the scope of the description.
The above examples merely represent a few embodiments of the present application, which are described in more detail and are not to be construed as limiting the scope of the invention. It should be noted that it would be apparent to those skilled in the art that various modifications and improvements could be made without departing from the spirit of the present application, which would be within the scope of the present application. Accordingly, the scope of protection of the present application is to be determined by the claims appended hereto.
Claims (10)
1. The method for constructing the carrier-free ultra-wideband emission signal waveform library is characterized by comprising the following steps of:
step 1, constructing a carrier-free ultra-wideband monopulse waveform according to selected monopulse waveform parameters including a pulse forming factor, a pulse order, a wavelet forming factor and a translation factor;
step 2, carrying out Fourier transform on the carrier-free ultra-wideband monopulse waveform to construct a carrier-free ultra-wideband monopulse frequency domain signal;
step 3, according to the constructed carrier-free ultra-wideband single pulse waveform, combining the selected code pattern and modulation mode, carrying out pulse position, amplitude, polarity and waveform modulation under different code patterns, realizing multiple composite modulation of pulse polarity-position and pulse amplitude-position, and constructing a modulated carrier-free ultra-wideband pulse sequence;
and 4, constructing fuzzy domain waveforms of the carrier-free ultra-wideband pulse trains in different modulation modes according to the carrier-free ultra-wideband pulse trains in different modulation modes.
2. The method for constructing a carrierless ultra wideband transmit signal waveform library according to claim 1, wherein in step 1, a carrierless ultra wideband single pulse waveform is constructed according to selected single pulse waveform parameters including pulse shaping factors, pulse orders, wavelet shaping factors, and translation factors, including gaussian pulse waveforms and their derivatives, modified Hermite pulse waveforms, and wavelet pulse waveforms, specifically:
(1) Gaussian pulse and its derivatives
The gaussian pulse signal s (t) has the expression:
the first derivative s' (t) and the second derivative s "(t) of the gaussian pulse are expressed as follows:
wherein t is a time factor, A is a signal amplitude, and τ is a shaping factor of a pulse waveform;
(2) Hermite pulses and their respective derivatives
Hermite pulse h en The polynomial form of (t) is as follows:
the Hermite pulse is non-orthogonal and the modified orthogonal Hermite pulse h n The expression of (t) is as follows:
where n is the order of the Hermite pulse;
(3) Wavelet pulse
The expression of Moelet mother wavelet ψ (t) is defined as:
the generated wavelet function ψ a,b The expression of (t) is:
wherein a is a scaling factor of the wavelet function, b is a translation factor, f 0 Is the carrier frequency.
3. The method for constructing a carrier-free ultra-wideband transmission signal waveform library according to claim 2, wherein step 2, fourier transform is performed on a carrier-free ultra-wideband single pulse waveform to construct a carrier-free ultra-wideband single pulse frequency domain signal, specifically:
(1) Gaussian pulse and its derivatives
The fourier transform P (ω) of the gaussian pulse signal is:
fourier transform P of first-order Gaussian pulse signal (1) (ω) is:
fourier transform P of second-order Gaussian pulse signal (2) (ω) is:
wherein ω is an angular frequency factor;
(2) Hermite pulse
The fourier transform expression for the modified orthogonal Hermite pulse is:
where f is a frequency factor.
4. The method for constructing a carrierless ultra-wideband transmission signal waveform library according to claim 1, wherein step 3, according to the constructed carrierless ultra-wideband single pulse waveform, pulse position, amplitude, polarity and waveform modulation under different code types are performed in combination with the selected code type and modulation mode, so as to realize multiple complex modulations of pulse polarity-position and pulse amplitude-position, and a modulated carrierless ultra-wideband pulse sequence is constructed, specifically:
(1) Random pulse position modulation, i.e. pulse position
Ultra wideband pulse train signal u under random pulse position modulation 1 Mathematical expression of (t):
wherein p (T) is a carrierless ultra-wideband monopulse signal, T is a time factor, T is a pulse repetition period, N is the number of pulses, X i Is [0, T 0 ]Is a random variable uniformly distributed above, and X when i not equal to j is satisfied i And X is j Independently of each other, the pulse width of p (T) is defined as deltat, which, in order to avoid pulse overlap,should satisfy the condition T 0 ≤T-ΔT；
(2) Pulse polarity modulation
When pulse polarity modulation is carried out on the carrierless ultra-wideband signal, a chaotic code or a pseudo code is selected as a modulation signal so as to realize the polarity modulation of the carrierless ultra-wideband pulse sequence, and an ultra-wideband pulse train signal u under the pulse polarity modulation 2 The mathematical expression of (t) is:
wherein s is i Representing a bipolar chaotic sequence or a pseudo code sequence;
(3) Pulse amplitude modulation
Pulse amplitude modulation is a way of modulating information on the pulse amplitude, ultra wideband pulse train signal u under pulse amplitude modulation 3 The expression of (t) is as follows:
wherein a is i Is [0,1 ]]Random variables obeying uniform distribution;
(4) Pulse waveform modulation
Pulse waveform is used for ultra-wideband modulation, different orthogonal pulses are used for realizing pulse waveform modulation, and for binary modulation, ultra-wideband pulse train signal u under pulse waveform modulation 4 The expression of (t) is:
wherein b is i E {0,1} is the modulated signal, p 0 (t) and p 1 (t) respectively orthogonal pulse sequences of different shapes;
(5) Pulse complex modulation
Combines pulse amplitude modulation with pulse position modulation,obtaining a pulse amplitude-position composite modulation signal u 5 (t) expression:
combining pulse polarity modulation with pulse position modulation to obtain pulse polarity-position composite modulation signal u 6 The expression (t) is:
5. the method for constructing a carrier-free ultra-wideband transmission signal waveform library according to claim 4, wherein step 4, according to the carrier-free ultra-wideband pulse sequences under different modulation modes, a fuzzy domain waveform, i.e. a fuzzy function, of the carrier-free ultra-wideband pulse trains under different modulation modes is constructed, specifically:
fuzzy function X of carrier-free ultra-wideband pulse train under random pulse position modulation 1 (τ,v)：
Fuzzy function X of carrier-free ultra-wideband pulse train under pulse polar modulation 2 (τ,T d )：
Fuzzy function X of carrier-free ultra-wideband pulse train under pulse amplitude modulation 3 (τ,T d )：
PulseFuzzy function X of carrier-free ultra-wideband pulse train under waveform modulation 4 (τ,T d )：
Fuzzy function X of pulse polarity-position composite modulation carrier-free ultra-wideband pulse train 5 (τ,v)：
Fuzzy function x of carrier-free ultra-wideband pulse train under pulse amplitude-position modulation 6 (τ,v)：
Wherein τ and T d Delay and Doppler shift, v, representing the ideal point target "2" relative to target "1", respectively 1 Velocity of motion, v, for target "1 2 The approach speed of the target "2" to the target 1 is given, and c is the speed of light.
6. The method for constructing a carrierless ultra-wideband transmit signal waveform library of claim 1, wherein the method is implemented based on a GUI platform.
7. A system for constructing a carrierless ultra wideband transmit waveform library, wherein the carrierless ultra wideband transmit waveform library is constructed based on the method of any one of claims 1-6.
8. A computer device comprising a memory, a processor and a computer program stored on the memory and executable on the processor, the processor implementing the method of any one of claims 1-6 to construct a carrierless ultra-wideband transmit waveform library when the computer program is executed.
9. A computer readable storage medium having stored thereon a computer program which, when executed by a processor, implements the method of any of claims 1-6 to construct a carrierless ultra wideband transmit waveform library.
10. A carrierless ultra-wideband transmit waveform library constructed based on the method of any one of claims 1-6.
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