CN107831471B - Radar waveform design method for restraining maximum distance straddling loss - Google Patents
Radar waveform design method for restraining maximum distance straddling loss Download PDFInfo
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Abstract
The invention discloses a radar waveform design method for restraining maximum distance straddling loss. And the distance straddling loss is incorporated into waveform optimization, so that the mismatching of the echo signal and the matched filter is reduced. The implementation process comprises the following steps: determining an initial value of a phase encoding vector of a phase modulation multi-phase code radar waveform; carrying out unconstrained optimization design on the phase encoding vector; determining a maximum distance straddling loss formula when no distortion exists; and carrying out constrained maximum distance ride loss optimization without distortion on the phase encoding vector. The maximum distance straddling loss formula without distortion is constructed, distance straddling loss is incorporated into waveform optimization, a distance straddling loss tolerance selection scheme is further provided, and waveform design efficiency is improved. The invention designs a waveform with good autocorrelation characteristic, high frequency spectrum convergence and good Doppler tolerance, and the waveform has lower distance straddle loss under the same condition. The method is applied to the waveform design of the phase modulation multi-phase code radar.
Description
Technical Field
The invention belongs to the technical field of radars, and mainly relates to a waveform design method, in particular to a radar waveform design method for restraining maximum distance ride loss, which is used for waveform design of a phase modulation multi-phase code radar.
Background
The transmitting waveform of the radar is basically constant modulus due to the maximum action distance of the radar. The polyphase code waveform is a commonly used radar waveform, and the common radar polyphase code waveform is composed of chips, the phase in each chip is unchanged, and the phase between adjacent chips is suddenly changed. Such waveforms are easy to analyze and optimize, and a large number of design algorithms are available at present, which can be used for designing multi-phase code waveforms with good autocorrelation characteristics, and some algorithms even incorporate factors such as Doppler tolerance and the like into the design of radar multi-phase code waveforms. The linear frequency modulation signal is also a common radar transmitting waveform, the frequency spectrum of the linear frequency modulation signal is a gate function, and the frequency spectrum convergence degree is excellent; and its Doppler tolerance is also very good, its fuzzy function is the famous "oblique cutting edge" shape; but the autocorrelation sidelobes of the chirp signal are too high, only-13.3 db.
Common polyphase code waveforms tend to have good autocorrelation properties. But its frequency spectrum tightness is very poor, and the bandwidth of the high-power transmitter is limited, which not only causes non-linear distortion, but also brings large transmission power loss; the doppler tolerance of the common polyphase code waveform is also poor, and although there are methods to incorporate doppler tolerance into the design of polyphase code waveforms, the effect is not comparable to the effect of the commonly used chirp signal.
The phase modulation multi-phase code radar is a radar with a new system, which is provided aiming at the defects of the multi-phase code waveform of the traditional radar and is based on a continuous phase modulation framework. The multiphase code waveform of the system radar has continuously-changed phase in each chip, the change rule is determined by a frequency window, the phase change range is determined by multiphase codes, and no phase mutation exists between adjacent chips. Common frequency windows are a raised cosine window and a rectangular window, and in particular, the phase of each chip in a rectangular window phase modulation polyphase code radar waveform is linearly changed, and a specific polyphase code vector is selected to approximate a chirp signal.
The distance straddling loss refers to the loss of the signal-to-noise ratio caused by mismatching of the actually sampled echo signal and a matched filter, and is caused by two factors, namely the distortion of the echo signal and the sampling deviation. The essence of the distance straddling loss caused by the sampling deviation is that the target echo delay is used as a continuous analog quantity, and the signal-to-noise ratio loss of the matched filtering is caused by the quantization loss caused by the sampling of a radar receiver into a digital quantity. This cost is unavoidable, but there is currently no method to incorporate distance-ride loss into the phase modulated polyphase code radar waveform design. If the distance straddling loss is not incorporated into the waveform design, a large matched filtering signal-to-noise ratio loss is caused under a lower sampling rate; if the loss of the signal-to-noise ratio of the matched filter is kept small, the sampling rate of the radar receiver is increased, and higher requirements are put on a hardware platform.
After a new system radar of a phase modulation multi-phase code radar is provided by Shannon D.Blunt et al, a waveform design method based on the phase modulation multi-phase code radar is also provided, and the method provides three optimization criteria of cyclic rotation peak side lobe level (PSL), integral side lobe level (ISL) and spectrum template error (FTE) and utilizes a greedy algorithm to carry out optimization design on a phase coding vector of a phase modulation multi-phase code radar waveform. The phase modulation multi-phase code radar waveform corresponding to the phase encoding vector designed by the method has good autocorrelation characteristic and spectrum tightness. In the simulation process, the waveforms designed by Shannon d. However, this method does not incorporate the distance straddling loss into the waveform design, resulting in a large mismatch between the echo signal and the matched filter, and thus a large signal-to-noise ratio loss in the matched filtering.
Disclosure of Invention
The invention aims to provide a radar waveform design method for restraining maximum distance straddle loss aiming at the defects of the prior art.
The invention relates to a radar waveform design method for restraining maximum distance straddle loss, which is characterized by comprising the following steps of:
1) determining initial values of phase-encoded vectors of phase-modulated polyphase-code radar waveforms by taking the polyphase-code length of the polyphase-code waveforms allowed to be transmitted by the phase-modulated polyphase-code radar system as N and the sampling rate of the receiver as K (number of samples/chip time width), using the phase-encoded vectors approximating chirp signals as the initial values α of the phase-encoded vectors of the phase-modulated polyphase-code radar waveforms0，
Namely:
wherein
Is the phase code of the nth chip, the physical meaning is the phase change range of the chip, the unit is rad, and the value range is
N is a subscript of the chip, N is 1, 2.
2) Carrying out unconstrained optimization design on phase encoding vectors of the phase modulation polyphase code radar waveform: circularly rotating three optimization criteria by using a sequence quadratic programming algorithm, wherein the three optimization criteria are respectively as follows: carrying out unconstrained minimization on peak side lobe level (PSL), integral side lobe level (ISL) and spectrum template error (FTE), wherein the optimization sequence of the three optimization criteria is adjustable; the spectrum template error (FTE) is a mean square error between a spectrum of a radar waveform and a spectrum template set by a user, and a mathematical expression of the spectrum template error (FTE) is as follows:
wherein, FTE is spectrum template error, | u (f) | is spectrum of radar waveform, | w (f) | is spectrum template set by user, fHIs the highest frequency, f, of the user-defined spectrum maskLIs the lowest frequency of the frequency spectrum template set by the user, f is an integral variable, and the value range is [ fL,fH]；
3) Determining a maximum distance ride loss formula under a distortion-free condition: according to a mathematical expression form of a frequency window of the phase modulation multi-phase code radar, a formula of maximum distance straddling loss under a distortion-free condition is constructed and obtained by utilizing a matched filtering formula;
4) carrying out optimization design of maximum distance straddling loss under a constrained distortion-free condition on the phase encoding vector: and (3) taking the phase coding vector of the phase modulation polyphase code radar waveform obtained in the step 2) as an initial point, constraining the maximum distance straddling loss under the distortion-free condition to be less than or equal to a distance straddling loss tolerance constant, minimizing a peak side lobe level (PSL) by using a sequence quadratic programming algorithm to obtain an optimized polyphase coding vector, and combining a mathematical expression of the waveform according to the polyphase coding vector to obtain the final phase modulation polyphase code radar waveform with smaller distance straddling loss. Wherein, the distance straddling loss tolerance constant is customized by a user, and is 0 < less than or equal to 1.
Compared with the prior art, the invention has the technical advantages that:
1. because the distance straddling loss of the waveform under the condition of no distortion is restrained in the design of the phase modulation polyphase code radar waveform, namely the loss of the matched filtering signal-to-noise ratio caused by sampling deviation is restrained, compared with the waveform designed by the previous phase modulation polyphase code radar waveform design method, the polyphase code waveform designed by the invention has smaller distance straddling loss under the same condition, so that the target detection is easier and the target parameter acquisition precision is improved in the subsequent signal processing;
2. the invention provides a method for quantitatively measuring the matched filtering loss of the radar transmitting waveform caused by sampling deviation due to the distance straddling loss calculation formula under the distortion-free condition. In the case of phase modulated polyphase code radar system determination, the formula is such that the maximum distance ride loss without distortion is determined only by the polyphase encoded vector, and the distance ride loss becomes a non-linear function of the polyphase encoded vector. This makes the idea of incorporating distance ride loss into waveform design, translating for a nonlinear function constraint added during waveform optimization, into a realizable measure.
3. The invention provides a method for selecting a distance straddling loss tolerance constant for a user, wherein 0 is less than or equal to 1, but under most conditions, a large part of values in the interval are values which cannot be obtained by the maximum distance straddling loss under the condition of no distortion, and values are closely related to radar system parameters and are relatively complex to adjust. An improper value may result in the parameter not being a significant constraint on the optimization process. If chosen empirically, it is clearly quite inefficient. The selection method provided by the invention is equivalent to filtering out an improper value range, so that a user can select a distance straddle loss tolerance constant meeting the design requirement in an appropriate range, and the efficiency of waveform design is greatly improved.
Drawings
FIG. 1 is a flow chart of the present invention;
FIG. 2 is an autocorrelation diagram of a rectangular window phase modulated polyphase code radar waveform designed at a sampling rate of 1 sample/chip duration;
FIG. 3 is a diagram of the spectral change before and after the transmission distortion of a rectangular window phase modulation multi-phase code radar waveform designed according to the present invention when the sampling rate is 1 sampling number/chip time width;
FIG. 4 is a graph of the ambiguity function of a rectangular window phase modulated polyphase code radar waveform designed according to the present invention at a sampling rate of 1 sample/chip duration;
figure 5 is a graph of the maximum distance ride-through loss and sampling rate of a design waveform, Shannon waveform and chirp signal after transmission distortion.
Detailed Description
The present invention will be described in detail below with reference to the accompanying drawings.
Example 1:
radar waveform design is a long-standing subject, and radar waveforms in different forms, such as chirp signals, common multi-phase code waveforms, non-chirp signals and the like, are often generated according to radars of different systems. The phase modulation multi-phase code radar is a new system radar which is provided aiming at the defects of common multi-phase code waveforms, and the designed waveforms have higher frequency spectrum tightness, so that smaller transmission distortion and transmission power loss can be realized. And the new system radar adopts a continuous phase modulation frame, so that the engineering realizability is good, and the future development prospect is promising. However, the method is not practical at present, and many engineering links need to be developed and innovated, and the waveform design method of the invention is directed at the radar of the new system. The invention provides a radar waveform design method for restraining maximum distance straddling loss, and referring to fig. 1, the radar waveform design process for restraining maximum distance straddling loss comprises the following steps:
1) determining initial values of phase-encoded vectors of phase-modulated polyphase-code radar waveforms by taking the polyphase-code length of the polyphase-code waveforms allowed to be transmitted by the phase-modulated polyphase-code radar system as N and the sampling rate of the receiver as K (number of samples/chip time width), using the phase-encoded vectors approximating chirp signals as the initial values α of the phase-encoded vectors of the phase-modulated polyphase-code radar waveforms0，
Namely:
wherein
Is the phase code of the nth chip, the physical meaning is the phase change range of the chip, the unit is rad, and the value range is
N is a subscript of the chip, and N is 1, 2.
The invention is based on a phase modulation multi-phase code radar, the waveform transmitted by the phase modulation multi-phase code radar is still a multi-phase code waveform, but the form is different from the common multi-phase code waveform, the waveform of the phase modulation multi-phase code radar is in one-to-one correspondence with a multi-phase coding vector, the common multi-phase code waveform is formed by closely arranging chips with constant modulus, the waveform of the phase modulation multi-phase code radar is also the same, but the phase change rule in each chip is different, and the phase coding vector α is [ α ]1,...,αN]Can uniquely correspond to the transmit waveform, αnIs the phase encoding of the nth chip, which is the range of phase variation within that chip. Due to the wide application of Direct Digital Synthesis (DDS) technology, continuous phase encoding is feasible in engineering. Similar to a common multi-phase code waveform, the number of chips of the phase modulation multi-phase code radar waveform is called as a multi-phase code length N; the sampling rate K means the number of samples per chip, and thus the unit is the number of samples/chip time width, and the sampling period T of the radar receiver in the general sense can be easily calculated according to Ks＝TpK, wherein TsIs the sampling period of the radar receiver, in seconds, TpIs chip time width in seconds. Both the polyphase code length N and the sampling rate K are important radar system parameters with respect to phase modulated polyphase code radar waveforms. Because the phase encoding vector approximating the linear frequency modulation signal is adopted, the phase modulation multi-phase code radar transmitting waveform designed by the invention has better autocorrelation and good Doppler tolerance.
2) Carrying out unconstrained optimization design on phase encoding vectors of the phase modulation polyphase code radar waveform: circularly rotating three optimization criteria by using a sequence quadratic programming algorithm, wherein the three optimization criteria are respectively as follows: carrying out unconstrained minimization on peak side lobe level (PSL), integral side lobe level (ISL) and spectrum template error (FTE), wherein the optimization sequence of the three optimization criteria is adjustable; the spectrum template error (FTE) is a mean square error between a spectrum of a radar waveform and a spectrum template set by a user, and a mathematical expression of the spectrum template error (FTE) is as follows:
wherein, FTE is spectrum template error, | u (f) | is spectrum of radar waveform, | w (f) | is spectrum template set by user, fHIs the highest frequency, f, of the user-defined spectrum maskLIs the lowest frequency of the frequency spectrum template set by the user, f is an integral variable, and the value range is [ fL,fH]。
The waveform of the phase modulation polyphase code radar corresponds to the polyphase code vector one by one, and according to the phase code vector alpha, the phase modulation polyphase code radar waveform corresponding to the phase code vector alpha one by one is obtained by the following formula:
where s (t; α) is a mathematical expression of a phase modulated polyphase code radar waveform with α as a parameter and a time variable t as an argument, j is an imaginary unit, and g (x) is a mathematical expression of a frequency window requiring its integration over a chip time width
Equal to 1, and is,
is the convolution sign, (t) is the impulse function, N is the summation variable, N is 1]，TpIs the chip time width in seconds, from waveform s (t; α), the peak side lobe level (PSL), the integrated side lobe level (ISL) are calculated using the following formula:
wherein PSL [ x (tau, omega) ]]Is the peak side lobe level (PSL) which is a function of the ambiguity function χ (τ, ω) which is a function of the waveform s (T; α) which is a function of the waveform s (T; α), s (T; α) is the waveform determined by the phase-encoding vector α, τ is the echo delay in seconds, ω is the Doppler angular velocity in rad/s, T is the time length of the waveform s (T; α), and T is NTpIn units of seconds, TpIs the chip time width, in seconds,t is an integral variable, representing the complex conjugate, τmIs the main lobe width, τ, of χ (τ, ω)m≈TpX is an integral variable and the value range is [0, T]It can be seen that the peak side lobe level (PSL), the integrated side lobe level (ISL) and the spectral template error (FTE) are non-linear functions of the phase encoded vector α, thus, the phase encoded vector is associated with three optimization criteria, a maximum number of rounds is set before the start of the round-robin, the round-robin is started again, after one round is completed, it is determined whether the maximum number of rounds is reached, if so, the round-robin is skipped into step 3), a maximum distance ride-over loss formula under distortion-free conditions is determined, otherwise, the round-robin is continued, and during the round-robin, the unconstrained minimization of the phase encoded vector is performed, which essentially minimizes the non-linear function of the phase encoded vector using a sequence quadratic programming algorithm.
3) Determining a maximum distance ride loss formula under a distortion-free condition: and according to the mathematical expression form of the frequency window of the phase modulation multi-phase code radar, constructing a formula for obtaining the maximum distance straddling loss under the distortion-free condition by using a matched filtering formula.
The distance straddling loss is a function of the sampling deviation tau, the maximum distance straddling loss is the maximum value of the distance straddling loss, and the method for obtaining the maximum distance straddling loss is to use a one-dimensional search method.
4) Carrying out optimization design of maximum distance straddling loss under a constrained distortion-free condition on the phase encoding vector: and (3) taking the phase coding vector of the phase modulation multi-phase code radar waveform obtained in the step 2) as an initial point, constraining the maximum distance straddling loss under the distortion-free condition to be less than or equal to a distance straddling loss tolerance constant, minimizing a peak side lobe level (PSL) by using a sequence quadratic programming algorithm to obtain an optimized multi-phase coding vector, obtaining a final phase modulation multi-phase code radar waveform with smaller distance straddling loss according to the multi-phase coding vector and combining a mathematical expression of the waveform, and transmitting the final phase modulation multi-phase code radar waveform by a radar transmitter to be used for detecting a target. Wherein, the distance straddling loss tolerance constant is customized by a user, and is 0 < less than or equal to 1.
The radar system parameters and the mathematical expression form of the frequency window are known, for a phase encoding vector alpha, according to the formula of the maximum distance straddling loss under the distortion-free condition, the phase encoding vector alpha is known to correspond to the maximum distance straddling loss, the maximum distance straddling loss is taken as a nonlinear function of the phase encoding vector alpha, thus, the waveform design for restraining the maximum distance straddling loss under the distortion-free condition is converted into a nonlinear minimization problem which takes the phase encoding vector alpha as an independent variable, restrains the nonlinear function describing the maximum distance straddling loss and takes a peak side lobe level (PSL) as an optimization criterion, a sequence quadratic programming algorithm is used for solving the minimization problem effectively to obtain a final phase encoding vector which uniquely corresponds to a phase modulation multiphase code radar waveform, namely the waveform finally designed by the method.
The invention provides a phase modulation multi-phase code radar waveform design method for restraining the maximum distance straddling loss on a platform of a phase modulation multi-phase code radar, which keeps the lower distance straddling loss, integrates the advantages of a common multi-phase code waveform and a linear frequency modulation waveform, and initiatively incorporates the distance straddling loss into the waveform design.
Example 2:
the radar waveform design method for constraining the maximum distance straddling loss is the same as the formula of the maximum distance straddling loss under the distortion-free condition, which is obtained by the construction in the step 2 of the embodiment 1, and the specific formula is as follows:
MaxRangeStraddlingLoss＝max[RangeStraddlingLoss(τ)]
namely: distance ride loss
The maximum distance straddling loss is the maximum value which can be obtained by the distance straddling loss (tau), the distance straddling loss (tau) is the distance straddling loss of the phase modulation multi-phase code radar waveform under the distortion-free condition and is a function of sampling deviation tau, the tau is the sampling deviation, namely the error that when target echo delay is sampled by a radar receiver, a continuous value is converted into a discrete value, and the value range is (-0.5T)s,0.5Ts)，TsIs the sampling period, T, of the radar receivers＝TpK, in seconds, TpIs the chip time width in seconds, K is the sampling rate in samples/chip, and represents the radar receiver at TpInner number of samples, αnIs the phase code of the nth chip, the physical meaning of which is the phase change range of the chip, the unit is rad, and the value range is-pi < αnN is a subscript of a chip, N is 1,2, N, j is an imaginary unit, t is an integral variable of tau, and the value range is [0, tau ]]U is a summation variable, u 1., K, g (t) is a mathematical representation of a frequency window, requiring its integration over the chip time width
Equal to 1.
The calculation formula of the maximum distance straddling loss under the distortion-free condition can quantitatively measure the matched filtering loss of the radar transmitting waveform caused by sampling deviation. No one in the prior art has incorporated the distance ride loss into the design of the waveform, but the invention does so that the designed waveform has lower distance ride loss than the waveforms designed by other methods under the same condition. In the case of phase modulated polyphase code radar system determination, the formula is such that the maximum distance ride loss without distortion is determined only by the polyphase encoded vector, and the distance ride loss becomes a non-linear function of the polyphase encoded vector. This makes the idea of incorporating distance ride loss into waveform design, translating for a nonlinear function constraint added during waveform optimization, into a realizable measure. Simulation results also prove that the waveform designed by the invention has lower distance ride loss than other waveforms under the same distortion condition. Although the distortion is not modeled by the invention, the waveform designed by the invention has lower distance ride loss than other waveforms under the same distortion, because the distance ride loss caused by sampling deviation is reduced, so that the overall distance ride loss is smaller than that of other waveforms.
Example 3:
the radar waveform design method for restraining the maximum distance straddling loss is the same as that of the embodiment 1-2, the user-defined distance straddling loss tolerance constant in the step 4) is more than or equal to 1 and the value range is defined as 1 according to the optimization requirement
The maximum distance ride loss is an average of the maximum distance ride loss of a phase modulated polyphase code radar waveform corresponding to a plurality of randomly generated phase code vectors without distortion.
The distance straddling loss tolerance constant is a user-defined distance straddling loss tolerance constant, 0 is less than or equal to 1, but under most conditions, a large part of values in the interval are values which cannot be obtained by the maximum distance straddling loss under the distortion-free condition, and values are closely related to radar system parameters and are relatively complex to adjust. An inappropriate value would result in the parameter not being a significant constraint to the optimization process, but being empirically chosen to be very inefficient. The invention provides a method for selecting a distance straddling loss tolerance constant, which defines the value range as
Of a plurality of randomly generated phase-coded corresponding phase-modulated polyphase-code radar waveformsAverage of maximum distance ride loss without distortion.
The waveform designed by the invention has lower maximum distance riding loss than other waveforms under the same condition. The invention takes the upper bound of
The maximum distance ride loss is an average of the maximum distance ride loss of a phase modulated polyphase code radar waveform corresponding to a plurality of randomly generated phase code vectors without distortion. The scheme is equivalent to filtering out improper value range, and in order to adjust parameters more conveniently, the value is equal to
k is a proportionality coefficient, and the value range of k is more than 0 and less than or equal to 1.
The invention provides the optimized value range of the distance straddle loss tolerance constant defined by the user through the combination of theoretical research and practice. Due to the adoption of the selection method provided by the invention, the improper value selection interval is filtered out, so that a user does not try one by one, and the efficiency of waveform design is greatly improved.
A more detailed example is given below to further illustrate the invention
Example 4:
the radar waveform design method for constraining the maximum distance straddling loss is the same as the embodiment 1-3, and referring to fig. 1, the specific implementation steps of the embodiment are as follows:
wherein
Is the phase code of the nth chip, the physical meaning is the phase change range of the chip, the unit is rad, and the value range is
N is a subscript of the chip, and N is 1, 2.
wherein PSL [ x (tau, omega) ]]Is the peak side lobe level (PSL), which is a function of the blur function χ (τ, ω), which is the waveform s (t; α)1) Is a waveform s (t; α)1) S (t; α)1) Is formed by a phase encoded vector α1The waveform determined, τ being the echo delay in seconds, ω being the Doppler angular velocity in rad/s, T being the waveform s (T; α)1) Time length of (1), T ═ NTpIn units of seconds, TpIs the chip time width in seconds, t is an integral variable representing the complex conjugate, τmIs the main lobe width, τ, of χ (τ, ω)m≈TpPerforming unconstrained minimization by using a sequential quadratic programming algorithm, setting the maximum iteration number of the sequential quadratic programming algorithm to be 5000 times, and obtaining an optimized phase encoding vector α2Order α1＝α2。
(2.2) at α1For the initial point, the Integrated Sidelobe Level (ISL) is the minimization criterion, and the calculation formula of the Integrated Sidelobe Level (ISL) is as follows:
wherein x is an integral variable and the value range is [0, T]Performing unconstrained minimization by using a sequential quadratic programming algorithm, setting the maximum iteration number of the sequential quadratic programming algorithm to be 5000 times, and obtaining an optimized phase encoding vector α2Order α1＝α2。
(2.3) at α1For the initial point, the spectrum template error (FTE) is the minimization criterion, and the calculation formula of the spectrum template error (FTE) is as follows:
wherein, FTE is spectrum template error, | u (f) | is spectrum of radar waveform, | w (f) | is spectrum template set by user, fHIs the highest frequency, f, of the user-defined spectrum maskLIs the lowest frequency of the frequency spectrum template set by the user, f is an integral variable, and the value range is [ fL,fH]Performing unconstrained minimization by using a sequential quadratic programming algorithm, setting the maximum iteration number of the sequential quadratic programming algorithm to be 5000 times, and obtaining an optimized phase encoding vector α2Order α1＝α2。
(2.4) if iter is less than or equal to the maximum number of rounds, iter +1 and jump back to step (2.1), otherwise jump out of the loop and go to current α1Phase code vector α obtained as an unconstrained optimized design of phase code vectors for phase modulated polyphase code radar waveforms1。
It should be noted that the order of the three optimization criteria of the loop round is adjustable, i.e. the order of step (2.1), step (2.2) and step (2.3) is adjustable.
distance ride loss
Maximum distance ride loss max [ distance ride loss (τ) ]
For any given phase encoding vector α, the distance ride loss is a function of the sampling offset τ, and the maximum distance ride loss is the maximum of the distance ride loss, which is obtained by a one-dimensional search method.
The invention brings the distance straddling loss of the radar waveform under the distortion-free condition into the design of the phase modulation polyphase code radar waveform, namely restricts the loss of the signal-to-noise ratio of matched filtering caused by sampling deviation, so that compared with the waveforms designed by other phase modulation polyphase code radar waveform design methods, the waveforms designed by the invention have smaller distance straddling loss under the same condition. Therefore, in subsequent signal processing, target detection is easier, and the accuracy of target parameter acquisition is improved.
The effect of the invention is further explained by the simulation comparison of the design result and the existing waveform:
example 5:
the radar waveform design method for constraining the maximum distance ride loss is the same as in examples 1-4,
simulation description:
set sampling rate KThe number of sampling times is 1,2, 3, 4, 5/chip time width, the maximum number of rounds is set to 3, and proper distance straddle loss tolerance constants are respectively selected according to the selection method of the distance straddle loss tolerance constant provided by the invention. Table 1 lists the average of the maximum distance ride-through loss without distortion for a phase modulated polyphase code radar waveform corresponding to 100 randomly generated phase encoding vectors for 5 sample rates
And a selected distance ride loss tolerance constant.
TABLE 1 mean value of maximum distance ride loss for different sampling rates and selected distance ride loss tolerance constant
For the case of transmit distortion, the modeling here is such that the transmit waveform passes through a first order Butterworth analog low pass filter with a bandwidth of 1/T to become a distorted echo signalpHz. A radar waveform is passed through this low pass filter and the resulting distorted signal is referred to as the waveform of the waveform through transmission distortion.
And (3) simulation result analysis:
the peak sidelobe levels of the rectangular window phase modulation multi-phase code radar waveform obtained by setting the sampling rate K to 1,2, 3, 4, 5 sampling values/chip time width design are shown in table 2:
table 2 different sampling rates K peak side lobe levels of waveforms designed to constrain maximum distance straddle loss in accordance with the present invention
| |
1 | 2 | 3 | 4 | 5 |
| Peak side lobe level (dB) | -27.67 | -26.72 | -23.81 | -22.44 | -20.14 |
By contrast, the peak sidelobe level of the chirp signal is-13.3 dB and the peak sidelobe level of the Shannon waveform is-40.2 dB.
Fig. 2 is an autocorrelation diagram of a rectangular window phase modulation polyphase code radar waveform designed when the sampling rate is 1 sampling number/chip duration, in the diagram, a thick solid line indicates the autocorrelation characteristic of the waveform designed by the present invention, a dotted line indicates the autocorrelation characteristic of a Shannon waveform, and a thin solid line indicates the autocorrelation characteristic of a chirp signal, and fig. 2 shows that the rectangular window phase modulation polyphase code radar waveform designed by the present invention has a lower peak sidelobe level, i.e., has a better autocorrelation characteristic, than the chirp signal, but because of the constraint of the present invention on the maximum distance ride loss, its peak sidelobe level is higher than that of the Shannon waveform.
Table 2 shows that the peak side lobe levels of the waveform designed with the maximum distance ride loss constrained by the present invention at different sampling rates K rapidly decrease the distance ride losses of all phase-modulated polyphase code radar waveforms as the sampling rate K increases, and the value selected by the method for selecting the distance ride loss tolerance constant provided by the present invention is more severe in constraining the maximum distance ride loss under the distortion-free condition, which results in deterioration of the autocorrelation characteristics of the waveform designed, so that the present invention is more suitable for waveform design at a low sampling rate, and the waveform designed at this time has not only a low distance ride loss but also good autocorrelation characteristics.
Example 6:
the radar waveform design method for restraining the maximum distance straddle loss is the same as that of the embodiments 1 to 4, and the simulation conditions and the simulation contents are the same as that of the embodiment 5.
Fig. 3 is a diagram of the spectral change before and after the transmission distortion of the rectangular window phase modulation polyphase code radar waveform designed when the sampling rate is 1 sampling number/chip time width. The solid line shows the spectrum of the waveform without transmission distortion, and the dotted line shows the spectrum of the waveform with transmission distortion. Comparing the two curves in fig. 3, it can be seen that the waveform designed by the present invention has good spectrum tightness, the influence of transmission distortion on the spectrum of the waveform is small, and the transmission power loss and waveform distortion of the waveform caused by the limited bandwidth of the transmitter are also small.
Example 7:
the radar waveform design method for restraining the maximum distance straddle loss is the same as that of the embodiments 1 to 4, and the simulation conditions and the simulation contents are the same as that of the embodiment 5.
Fig. 4 is a graph of the ambiguity function of a rectangular window phase modulated polyphase code radar waveform designed according to the present invention at a sampling rate of 1 sample/chip time width. It can be seen from fig. 4 that the ambiguity function of the waveform obtained by the maximum distance ride loss constrained design of the present invention is still "oblique blade" shaped, so its doppler tolerance is better. The peak sidelobe level of the chirp signal is-13.3 dB and the peak sidelobe level of the waveform is-27.67 dB, with much better autocorrelation characteristics than the chirp signal. It can be seen that the waveform obtained by the design of the invention can effectively integrate the advantages of the chirp waveform and the common multi-phase code waveform.
Example 8:
the radar waveform design method for restraining the maximum distance straddle loss is the same as that of the embodiments 1 to 4, and the simulation conditions and the simulation contents are the same as that of the embodiment 5.
Figure 5 is a graph of the maximum distance ride-through loss and sampling rate of a Shannon waveform and chirp signal after transmit distortion in accordance with the present invention. In the figure, the solid line is the maximum distance ride loss versus sampling rate of the waveform obtained by the design of the present invention for transmission distortion, the dotted line is the maximum distance ride loss versus sampling rate of the present Shannon waveform for transmission distortion, and the circled solid line is the maximum distance ride loss versus sampling rate of the chirp signal for transmission distortion. It can be seen from fig. 5 that the maximum distance ride loss of the resulting waveform is minimal for the inventive design. Although the present invention constrains the maximum distance ride loss under undistorted conditions, its maximum distance ride loss is still smaller after distortion than other waveforms, which is that it constrains the maximum distance ride loss under undistorted conditions, i.e., it reduces the distance ride loss caused by the sampling offset. And in the process of designing the waveform, the spectrum tightening degree of the waveform is optimized by using a spectrum template error (FTE), and the influence of transmission distortion on the waveform is small. The distance straddling loss is caused by two reasons, namely waveform distortion and sampling deviation, and the two reasons are considered in waveform design, so that the distance straddling loss of a waveform obtained by constraining the design of the maximum distance straddling loss is still better than that of other waveforms after transmission distortion.
From the above examples, at a lower sampling rate K, the waveform designed by the present invention has the characteristics of good autocorrelation property, high spectrum convergence and good doppler tolerance, and under the same distortion condition, the waveform designed by the present invention has lower distance ride loss than other waveforms. Because the waveform designed by the invention has good autocorrelation characteristics, the false alarm rate caused by the fact that the strong target echo side lobe submerges the weak target echo main lobe is reduced, and the false alarm rate caused by the target side lobe is also reduced; the waveform obtained by the design of the invention has high frequency spectrum convergence, and the nonlinear distortion and the transmission power loss caused by the limited bandwidth of the transmitter are also reduced; the Doppler tolerance of the waveform designed by the invention is good, and a high-speed target can be detected; compared with other waveforms, the waveform designed by the invention has lower distance straddling loss, so that the loss of the signal-to-noise ratio during matching filtering is reduced, and the precision of subsequent target parameters is improved.
In summary, the invention discloses a radar waveform design method for restraining the maximum distance straddling loss. The invention brings the distance straddling loss into waveform optimization, and reduces the mismatch of an echo signal and a matched filter. The realization process is to determine the initial value of the phase encoding vector of the phase modulation multi-phase code radar waveform; carrying out unconstrained optimization design on a phase encoding vector of a phase modulation multi-phase code radar waveform; determining a maximum distance straddling loss formula under a distortion-free condition; and carrying out optimization design on the maximum distance straddling loss under the constrained distortion-free condition on the phase encoding vector. The invention constructs the maximum distance straddling loss formula under the distortion-free condition, brings the distance straddling loss into the waveform optimization process, and also provides a distance straddling loss tolerance selection method. The waveform with good autocorrelation characteristic, high frequency spectrum convergence and good Doppler tolerance is designed, and under the same condition, the waveform designed by the method has lower distance straddling loss than other waveforms, and the waveform design efficiency is improved by the distance straddling loss tolerance selection method. The method is applied to the waveform design of the phase modulation multi-phase code radar.
Claims (3)
1. A radar waveform design method for restraining maximum distance straddle loss is characterized by comprising the following steps:
1) determining initial values of phase-encoded vectors of phase-modulated polyphase-code radar waveforms by setting the polyphase-code length of polyphase-code waveforms allowed to be transmitted by the phase-modulated polyphase-code radar system to N, the sampling rate of the receiver to K, and using the phase-encoded vectors approximating chirp signals as the initial values of the phase-encoded vectors of the phase-modulated polyphase-code radar waveforms α0，
Namely:
wherein
Is the phase code of the nth chip, the physical meaning is the phase change range of the chip, the unit is rad, and the value range is
N is a subscript of the chip, N is 1, 2.
2) Carrying out unconstrained optimization design on phase encoding vectors of the phase modulation polyphase code radar waveform: circularly rotating three optimization criteria by using a sequence quadratic programming algorithm, wherein the three optimization criteria are respectively as follows: carrying out unconstrained minimization on peak side lobe level, integral side lobe level and spectrum template error, wherein the optimization sequence of the three optimization criteria is adjustable; the spectrum template error is the mean square error between the spectrum of the radar waveform and the spectrum template set by the user, and the mathematical expression of the spectrum template error is as follows:
wherein, FTE is spectrum template error, | u (f) | is spectrum of radar waveform, | w (f) | is spectrum template set by user, fHIs the highest frequency, f, of the user-defined spectrum maskLIs the lowest frequency of the frequency spectrum template set by the user, f is an integral variable, and the value range is [ fL,fH]；
The waveform of the phase modulation polyphase code radar corresponds to the phase encoding vector one by one, and according to the phase encoding vector alpha, the phase modulation polyphase code radar waveform corresponding to the phase encoding vector alpha one by one is obtained by the following formula:
wherein s (t; α) is phase modulation with α as parameter and time variable t as independent variableMathematical expressions for producing polyphase code radar waveforms, j being units of imaginary numbers, g (x) being mathematical expressions for frequency windows requiring their integration over a chip time width
Equal to 1, and is,
is the convolution sign, (t) is the impulse function, N is the summation variable, N is 1]，TpIs chip time width in seconds, and calculates peak side lobe level PSL and integral side lobe level ISL according to waveform s (t; α) using the following equations:
wherein PSL [ x (tau, omega) ]]Is the peak side lobe level PSL which is a function of the ambiguity function χ (τ, ω) which is a function of the waveform s (T; α) which is a function of the waveform s (T; α), s (T; α) is the waveform determined by the phase encode vector α, τ is the echo delay in seconds, ω is the Doppler angular velocity in rad/s, T is the time length of the waveform s (T; α), T is NTpIn units of seconds, TpIs the chip time width in seconds, t is an integral variable representing the complex conjugate, τmIs the main lobe width, τ, of χ (τ, ω)m≈TpX is an integral variable and the value range is [0, T]The peak side lobe level PSL, the integral side lobe level ISL and the spectrum template error FTE are nonlinear functions of the phase code vector α, the maximum rotation times are set before the rotation starts, the rotation starts again, and when one rotation is completedAfter the rotation, judging whether the maximum rotation times are reached, if so, jumping out of the rotation, and entering the step 3) to determine a maximum distance straddle loss formula under a distortion-free condition; otherwise, continuing the cycle rotation; in the cyclic rotation process, the unconstrained minimization is carried out on the phase encoding vector, and the essence is that a sequence quadratic programming algorithm is utilized to carry out the minimization on the nonlinear function of the phase encoding vector;
3) determining a maximum distance ride loss formula under a distortion-free condition: according to a mathematical expression form of a frequency window of the phase modulation multi-phase code radar, a formula of maximum distance straddling loss under a distortion-free condition is constructed and obtained by utilizing a matched filtering formula;
4) carrying out optimization design of maximum distance straddling loss under a constrained distortion-free condition on the phase encoding vector: taking the phase coding vector of the phase modulation multi-phase code radar waveform obtained in the step 2) as an initial point, constraining the maximum distance straddling loss under a distortion-free condition to be less than or equal to a distance straddling loss tolerance constant, minimizing a peak side lobe level by using a sequence quadratic programming algorithm to obtain an optimized multi-phase coding vector, and obtaining a final phase modulation multi-phase code radar waveform with smaller distance straddling loss according to the multi-phase coding vector and by combining a mathematical expression of the waveform; wherein, the distance straddling loss tolerance constant is customized by a user, and is 0 < less than or equal to 1.
2. The method of claim 1, wherein the maximum distance ride loss constraint formula obtained in step 3 is a formula of maximum distance ride loss under distortion-free condition, specifically:
MaxRangeStraddlingLoss＝max[RangeStraddlingLoss(τ)]
namely:
the maximum distance straddling loss is the maximum value which can be obtained by the distance straddling loss (tau), the distance straddling loss (tau) is the distance straddling loss of the phase modulation multi-phase code radar waveform under the distortion-free condition and is a function of sampling deviation tau, the tau is the sampling deviation, namely the error that when target echo delay is sampled by a radar receiver, a continuous value is converted into a discrete value, and the value range is (-0.5T)s,0.5Ts)，TsIs the sampling period, T, of the radar receivers＝TpK, in seconds, TpIs the chip time width in seconds, K is the sampling rate in samples/chip, and represents the radar receiver at TpInner number of samples, αnIs the phase code of the nth chip, the physical meaning of which is the phase change range of the chip, the unit is rad, and the value range is-pi < αnN is a subscript of a chip, N is 1,2, N, j is an imaginary unit, t is an integral variable of tau, and the value range is [0, tau ]]U is a summation variable, u 1., K, g (t) is a mathematical representation of a frequency window, requiring its integration over the chip time width
Equal to 1.
3. The method as claimed in claim 1, wherein the user-defined distance ride loss tolerance constant in step 4) is 0 < 1, and the range is defined as the optimum range
Is a phase modulation corresponding to a plurality of randomly generated phase encoding vectorsAverage value of maximum distance ride loss without distortion for multi-phase code radar waveform.
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