CN113238212A - Space-time coding-based frequency diversity array radar range resolution enhancement method - Google Patents
Space-time coding-based frequency diversity array radar range resolution enhancement method Download PDFInfo
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- CN113238212A CN113238212A CN202110404613.1A CN202110404613A CN113238212A CN 113238212 A CN113238212 A CN 113238212A CN 202110404613 A CN202110404613 A CN 202110404613A CN 113238212 A CN113238212 A CN 113238212A
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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
- G01S13/00—Systems using the reflection or reradiation of radio waves, e.g. radar systems; Analogous systems using reflection or reradiation of waves whose nature or wavelength is irrelevant or unspecified
- G01S13/02—Systems using reflection of radio waves, e.g. primary radar systems; Analogous systems
- G01S13/06—Systems determining position data of a target
- G01S13/08—Systems for measuring distance only
- G01S13/10—Systems for measuring distance only using transmission of interrupted, pulse modulated waves
- G01S13/106—Systems for measuring distance only using transmission of interrupted, pulse modulated waves using transmission of pulses having some particular characteristics
Abstract
The invention belongs to the technical field of radar signal processing, and particularly discloses a method for enhancing the range resolution of a frequency diversity array radar based on space-time coding.
Description
Technical Field
The invention relates to the technical field of radar signal processing, in particular to a frequency diversity array transmitting diversity technology, and specifically relates to a method for enhancing the range resolution of a frequency diversity array radar based on space-time coding, which can be used for enhancing the range resolution of the radar.
Background
The concept of frequency diversity array radar was proposed by Antonik and Wick et al in the IEEE international radar conference. Compared with the fixed transmitting frequency and the single-angle directional transmitting wave beam of the traditional phased array radar, the carrier frequency of the transmitting signal between the adjacent channels of the frequency diversity array radar has a tiny frequency shift, and a distance-angle two-dimensional coupling transmitting directional diagram can be formed. Compared with the traditional transmission mode of the orthogonal waveform group of the MIMO radar, each array element of the frequency diversity array transmits a single waveform, so that the automatic scanning of a single-pulse inner full airspace can be realized, and the airspace is fully covered.
The frequency diversity array utilizes the characteristics of wide transmission and narrow reception, realizes full-airspace detection under the transmission condition of a single waveform, can be widely applied to wide-area early warning radars, effectively solves the problem that an ideal orthogonal waveform group of the MIMO radar is difficult to apply in practical engineering, and in addition, when linear frequency modulation signals LFMs are transmitted, the range sidelobe of a high-resolution range profile at the receiving end of the frequency diversity array can be lower than-45 dB under the condition of no window function weighting. The ultralow sidelobe characteristic of the frequency diversity array radar greatly improves the weak and small target detection capability of the radar system in a strong clutter environment.
The wide angle coverage advantage of frequency diversity arrays comes at the expense of range resolution. The frequency diversity array emission signal is processed by the receiving end matching filter, so that an equivalent emission beam can be formed, the equivalent emission bandwidth corresponding to the beam main lobe is reduced compared with the emission signal bandwidth, and the distance resolution is directly reduced. The reduction of the distance resolution is not favorable for high-precision parameter estimation of the target, and also causes difficulty in subsequent target detection, positioning and identification.
Disclosure of Invention
Aiming at the problems in the prior art, the invention aims to provide a method for enhancing the range resolution of a frequency diversity array radar based on space-time coding, which realizes the enhancement of the range resolution of a high-resolution range profile of the frequency diversity array radar by designing two-dimensional space-time coding.
The technical idea of the invention is as follows: the linear frequency modulation signal is transmitted through a frequency diversity array, the angle-frequency two-dimensional frequency spectrum of a transmission directional diagram is obtained through a stationary phase principle, effective frequency bands corresponding to all pulses are shifted through analyzing the linear relation between the angle and the frequency and designing two-dimensional space-time coding, and the distance resolution is improved through coherent pulse accumulation and synthesis bandwidth.
In order to achieve the purpose, the invention is realized by adopting the following technical scheme.
A frequency diversity array radar range resolution enhancement method based on space-time coding comprises the following steps:
Compared with the prior art, the invention has the beneficial effects that:
(1) the invention realizes the time-frequency transformation of a transmitting directional diagram by adopting a transmitting mode of linear frequency modulation signals and utilizing a stationary phase principle, obtains the linear relation of one-to-one correspondence between the frequency and the angle by researching the analytic expressions of the transmitting frequency and the space angle in the two-dimensional frequency spectrum of the frequency diversity array, and lays a theoretical foundation for the subsequent two-dimensional space-time coding design.
(2) The invention makes the transmitted pulse generate offset in the frequency domain by designing two-dimensional space-time coding. Under the condition of same angle pointing, the frequency ranges of the sub-bands corresponding to the transmitted pulses are not the same. The bandwidths of the sub-bands corresponding to the adjacent pulses are the same and are 1/M of the total transmission bandwidth, the central frequency points of the sub-bands corresponding to the adjacent pulses are uniformly spaced, and the spacing amount is equal to 1/M of the total transmission bandwidth.
(3) The invention designs the number of the pulse trains in the coherent accumulation time, so that the total synthesis bandwidth of the transmitted pulse trains is equal to the total transmission bandwidth. Under the design scheme that the number of the pulse trains is equal to the number of the transmitting array elements, the distance resolution is improved along with the increase of the equivalent transmitting bandwidth. The distance resolution is the same as that of the traditional phased array with the same array configuration, and is improved by M times of that of the traditional frequency diversity array.
Drawings
The invention is described in further detail below with reference to the figures and specific embodiments.
FIG. 1 is a flow chart of an implementation of the present invention;
FIG. 2 is a frequency-angle spectrum of a first transmit pulse simulated with the present invention;
FIG. 3 is a frequency-angle spectrum of a transmit burst simulated with the present invention;
FIG. 4 is a matched filtered one-dimensional range profile simulated using the present invention.
Detailed Description
Embodiments of the present invention will be described in detail below with reference to examples, but it will be understood by those skilled in the art that the following examples are only illustrative of the present invention and should not be construed as limiting the scope of the present invention.
Referring to fig. 1, a method for enhancing range resolution of a frequency diversity array radar based on space-time coding provided by the present invention includes the following steps:
the frequency diversity array radar system can be equivalent to a one-dimensional co-location equidistant linear array, the receiving and transmitting antennas are not shared, and all transmitting channels transmit signals simultaneously.
1a) Introducing a relative frequency shift delta f between adjacent transmitting array elements of the co-located uniform linear array, wherein the transmitting frequency of the mth transmitting array element is as follows:
fm＝f0+(m-1)Δf，m＝1，2，...，M
wherein f is0For the signal carrier frequency, Δ f is the amount of frequency shift.
1b) If the frequency diversity array transmits the chirp signal, the baseband signal form is:
where rect (-) represents rectangular envelope, T is time, E is total energy of transmitting signal, M is number of transmitting array elements, j is imaginary unit, mu is B/TpFor chirp rate, B for transmit signal bandwidth, TpFor transmitting the signal pulse width.
The transmission signal of the mth transmission array element is:
1c) carrying out coherent accumulation on the transmitting signals of all transmitting array elements to obtain transmitting combined signals of the frequency diversity array at time t and an angle theta:
wherein d is the array element spacing, lambda0Is the emission wavelength.
in order to explore the space-frequency spectrum characteristic of a space-time coding array, a linear relation between the angle and the frequency of the frequency diversity array needs to be obtained, and the method specifically comprises the following steps:
2a) transforming the transmitting composite signal from the time domain to the frequency domain according to a stationary phase principle (POSP) to obtain a frequency domain representation s (f, theta) of the transmitting composite signal, wherein the expression is as follows:
wherein f represents the transmission frequency, | · | represents the absolute value;
2b) the quadratic phase term associated with the number of array elements can be ignored when the amount of frequency shift is much smaller than the carrier frequency and transmission bandwidth. According to the theory, the frequency domain expression of the transmitting combined signal is expanded and approximated, and a simplified frequency domain expression is obtained:
wherein the content of the first and second substances,
aT(theta) is a space domain steering vector, and superscript H represents the conjugate transpose of the matrix;
in the form of a frequency-domain steering vector,
is a frequency domain baseband waveform; the expressions are respectively:
wherein, superscript T represents the transpose of the matrix;
under the weighting effect of the space-domain steering vector and the frequency-domain steering vector, different frequency bands of the transmitted signal point to different space angles.
2c) When the phase terms of the space-domain steering vector and the frequency-domain steering vector are completely cancelled, the following conditions are satisfied:
dsinθ/λ0+Δf(f-f0)/μ＝0
the frequency band corresponding to the main lobe of the beam space domain transmitted by the frequency diversity array can be obtained:
f＝f0-μdsinθ/λ0Δf
therefore, the linear relation of one-to-one correspondence between the angles and the frequencies of the frequency diversity array can be obtained. When the difference between the transmission frequency and the frequency band corresponding to the main lobe is large, a large energy loss exists at the spatial angle corresponding to the transmission frequency.
3a) the frequency domain main lobe bandwidth (3dB) corresponding to any airspace angle of the frequency diversity array, namely the effective transmission bandwidth, is reduced to 1/M of the total transmission bandwidth. Therefore, a coherent pulse train consisting of M pulses is designed, i.e. the number of pulses is equal to the number of array elements.
3b) And performing two-dimensional space-time coding design on the transmitted signal to enable the frequency point value of the k-th sub-pulse frequency domain main lobe center to be equal to (k-1) B/M. Meanwhile, the main lobe bandwidth (3dB) of each sub-pulse frequency domain is 1/M of the total bandwidth of the transmitted signal. In addition, the central frequency points of the main lobes of the adjacent sub-pulse frequency domains are different by B/M. Through coherent accumulation of M sub-pulses, the total bandwidth of the frequency domain of the burst synthesis is equal to the transmission bandwidth B.
According to this design concept, the space-time coding on the kth pulse of the mth array element can be expressed as:
αk，m＝e-j2π(m-1)(k-1)ΔfB/μ/M
wherein M is 1, 2, …, M, k is 1, 2, …, M;
3c) at 1/TpWith respect to the m-th array element, the space-time coding on the k-th pulse can be simply expressed as:
αk，m＝e-j2π(m-1)(k-1)/M。
4a) The array transmission composite signal of the kth sub-pulse after space-time coding is as follows:
4b) the transmission combined signal of the frequency diversity array after space-time coding at time t and angle theta, namely the transmission combined signal of the coherent pulse train after space-time coding, is as follows:
the transmission signal of the mth array element can be expressed as:
the transmit waveform can be expressed as:
wherein T is a pulse repetition interval;
according to radar signal processing principles, the range resolution Δ R can be expressed as:
where B is the transmitted signal bandwidth and c is the speed of light.
The frequency diversity array of the invention is subjected to two-dimensional space-time coding at a transmitting end, and the total bandwidth of the synthesis of M sub-pulses after coherent accumulation is the bandwidth B of a transmitting signal. Compared with the traditional frequency diversity array, after space-time coding, the equivalent transmission bandwidth of any spatial directional angle is improved by M times. Therefore, the distance resolution of the frequency diversity array can be improved by M times by the two-dimensional space-time coding technology at the transmitting end.
In order to further verify the rationality of the two-dimensional space-time coding design, the following derivation verification is carried out:
first, a frequency domain representation of the array transmit composite signal is obtained.
a) Transforming the array transmission composite signal of the k sub-pulse from the time domain to the frequency domain by Fourier transform:
wherein f iskIs the center frequency of the k-th pulse.
b) Ignoring secondary phase terms associated with transmit beamforming, obtaining a frequency domain representation of the array transmit composite signal:
then, an expression of the k-th sub-pulse center frequency is obtained.
Similar to step 2c), when the phase terms of the space-domain steering vector and the frequency-domain steering vector completely cancel, that is, the following conditions are satisfied:
through mathematical transformation, an analytical expression between the center frequency point of the kth sub-pulse transmitting frequency band and the main lobe direction of the transmitting beam can be obtained:
the above formula is analyzed, and the frequency diversity array does not destroy the one-to-one linear relation between the beam space pointing angle sin theta and the center frequency of the transmitted pulse through the two-dimensional space-time coding of the transmitting end. The frequency difference value of the central frequency point of the adjacent pulse transmission frequency band is fixed and is B/M. The maximum and minimum central frequency points in the M pulses, namely the central frequency points of the first pulse and the Mth pulse transmitting frequency band, and the frequency deviation value is equal to B-B/M. Further, the frequency bands of adjacent sub-pulses do not overlap each other. Therefore, after the M sub-pulses are coherently accumulated, the total bandwidth of the resultant is equal to the bandwidth B of the transmitted signal.
Simulation experiment
1. Simulation parameters:
the transmitting end of the frequency diversity array adopts a half-wavelength equidistant linear array, the number M of array elements is 13, the spacing d of the array elements is 0.15M, and the number K of the transmitted pulses is 13. Transmission signal bandwidth BW100MHz, pulse width T of transmitted signalP5us, carrier frequency f0At 1GHz, the pulse repetition frequency PRF is 20kHz and the frequency increment Δ f is 200 kHz.
The simulation parameters are shown in table 1:
TABLE 1 System simulation parameters
2. Simulation content:
As can be seen from fig. 2, different spatial angles correspond to different frequency domain main lobes, and the equivalent transmission bandwidth at any spatial angle is smaller than the total transmission bandwidth of the array. Furthermore, the side lobe levels for most of the frequency domain are less than 20 dB.
And 2, simulating the frequency-angle spectrum of the frequency diversity array transmitting pulse train by using the method for enhancing the range resolution of the frequency diversity array radar based on the space-time coding design under the simulation parameters, wherein the result is shown in figure 3.
As can be seen from fig. 3, after coherent accumulation of M pulses in the transmitted burst, the gain along the frequency axis is approximately constant, only in the order of magnitude of about 10-7Micro undulations of the surface. The space-time coding at the transmitting end proves that the frequency-angle spectral distribution is independent of the angle, and the equivalent transmission bandwidth in any direction is increased and is equal to the transmission bandwidth of the original reference signal. Thus, the distance resolution is enhanced.
And 3, comparing one-dimensional distance images output after matched filtering of array emission composite signals by a receiving end in three modes of a basic Frequency Diversity Array (FDA), a frequency diversity array (Barker-FDA) based on a Barker code and a frequency diversity array (STC-FDA) based on the space-time coding design by using the method for enhancing the radar distance resolution of the frequency diversity array based on the space-time coding design under the simulation parameters, wherein the result is shown in FIG. 4.
As can be seen from fig. 4, the one-dimensional range profile of the frequency diversity array designed based on the barker code and based on the space-time code is smaller than that of the basic frequency diversity array by 3dB from the main lobe, which proves that the range resolution can be improved by both of the two coding schemes. In addition, the peak side lobes of the frequency diversity array designed based on the Barker code and the space-time code are respectively about-20 dB and-35 dB, and the frequency diversity array designed based on the space-time code has the advantage of low side lobes in distance while improving the distance resolution.
In conclusion, the simulation verifies the correctness, the effectiveness and the reliability of the method.
Although the present invention has been described in detail in this specification with reference to specific embodiments and illustrative embodiments, it will be apparent to those skilled in the art that modifications and improvements can be made thereto based on the present invention. Accordingly, such modifications and improvements are intended to be within the scope of the invention as claimed.
Claims (7)
1. A frequency diversity array radar range resolution enhancement method based on space-time coding is characterized by comprising the following steps:
step 1, setting a transmitting end of a frequency diversity array radar to be composed of M transmitting array elements, wherein the array elements are equidistantly distributed by taking half wavelength as an interval; all the transmitting array elements transmit signals simultaneously, and the carrier frequency of the transmitting signals of all the transmitting array elements has fixed frequency offset; acquiring a transmitting signal of each transmitting array element so as to obtain a transmitting combined signal of the frequency diversity array at time t and an angle theta;
step 2, according to the stationary phase principle, converting the transmitting composite signal s (t, theta) from the time domain to the frequency domain to obtain the frequency domain representation s (f, theta) of the transmitting composite signal, and accordingly obtaining the linear relation between the angle and the frequency of the frequency diversity array;
step 3, designing two-dimensional space-time coding of array elements and pulse dimensions according to the linear relation between the angle and the frequency of the frequency diversity array;
step 4, performing phase weighting on each sub-pulse transmitting signal by adopting the two-dimensional space-time code to obtain an array transmitting combined signal of each sub-pulse after space-time coding; and carrying out coherent accumulation on the array transmitting combined signals of the M space-time coded sub-pulses to obtain a transmitting combined signal of the space-time coded coherent pulse train, namely the transmitting signal with enhanced range resolution.
2. The space-time coding based frequency diversity array radar range resolution enhancement method according to claim 1, wherein the specific process of obtaining the transmission signal of each transmission array element is as follows:
1a) introducing a relative frequency shift delta f between adjacent transmitting array elements of the co-located uniform linear array, wherein the transmitting frequency of the mth transmitting array element is as follows:
fm＝f0+(m-1)Δf，m＝1，2，...，M
wherein f is0Is the signal carrier frequency, and is the frequency shift amount;
1b) if the frequency diversity array transmits the chirp signal, the baseband signal form is:
where rect (-) represents rectangular envelope, T is time, E is total energy of transmitting signal, M is number of transmitting array elements, j is imaginary unit, mu is B/TpFor chirp rate, B for transmit signal bandwidth, TpPulse width for transmitting signal;
the transmission signal of the mth transmission array element is:
3. a method for enhancing radar range resolution based on a space-time coding frequency diversity array according to claim 2, wherein the expression of the transmitted combined signal of the frequency diversity array at time t and angle θ is:
wherein d is the array element spacing, lambda0Is the emission wavelength.
4. A space-time coding based frequency diversity array radar range resolution enhancement method according to claim 3, wherein the frequency domain representation of the transmit composite signal is:
where f represents the transmit frequency, |, represents the absolute value.
5. The space-time coding based frequency diversity array radar range resolution enhancement method according to claim 1, wherein the obtaining of the linear relationship between the angle and the frequency of the frequency diversity array comprises the following specific steps:
first, when the frequency shift is far smaller than the carrier frequency and the transmission bandwidth, the quadratic phase term related to the array element number is ignored, and accordingly, the frequency domain representation of the transmission composite signal is expanded and approximated, and a simplified frequency domain expression is obtained:
wherein the content of the first and second substances,
f represents the transmission frequency, and theta is an angle; f. of0Is the signal carrier frequency, and is the frequency shift amount; | represents absolute value, rect (·) represents rectangular envelope, T is time, E is total energy of transmitted signal, M is number of transmitting array elements, j is imaginary unit, mu is B/TpFor chirp rate, B for transmit signal bandwidth, TpFor transmitting the pulse width of the signal, d is the spacing between the array elements, λ0Is the emission wavelength;
aT(theta) is a space domain steering vector, and superscript H represents the conjugate transpose of the matrix;
in the form of a frequency-domain steering vector,
is a frequency domain baseband waveform; the expressions are respectively:
wherein, superscript T represents the transpose of the matrix;
under the weighting effect of the space domain guide vector and the frequency domain guide vector, different frequency bands of the transmitted signal point to different space angles;
then, when the phase terms of the space-domain steering vector and the frequency-domain steering vector completely cancel, that is, the following conditions are satisfied:
dsinθ/λ0+Δf(f-f0)/μ＝0
obtaining a frequency band corresponding to a main lobe of a beam space domain transmitted by the frequency diversity array:
f＝f0-μdsinθ/λ0Δf；
the above equation is a linear relationship between the angle and the frequency of the frequency diversity array.
6. A method for enhancing the range resolution of a space-time coding based frequency diversity array radar according to claim 1, wherein the two-dimensional space-time coding of array elements and pulse dimensions is designed according to the linear relationship between the angle and the frequency of the frequency diversity array, and the method comprises the following specific steps:
3a) the frequency domain main lobe bandwidth corresponding to any airspace angle of the frequency diversity array, namely the effective transmission bandwidth, is reduced to 1/M of the total transmission bandwidth; therefore, a coherent pulse train consisting of M pulses is designed, namely the pulse number is equal to the array element number;
3b) performing two-dimensional space-time coding design on a transmitting signal to enable a frequency point value of a main lobe center of a kth sub-pulse frequency domain to be equal to (k-1) B/M; simultaneously, the main lobe bandwidth of each sub-pulse frequency domain is 1/M of the total bandwidth of the transmitted signal; and the difference of the central frequency points of the main lobes of the adjacent sub-pulse frequency domains is B/M; through coherent accumulation of M sub-pulses, the frequency domain total bandwidth of the pulse train synthesis is equal to the transmission bandwidth B;
the space-time coding on the kth pulse of the mth array element is designed as follows:
αk，m＝e-j2π(m-1)(k-1)ΔfB/μ/M
wherein M is 1, 2, …, M, k is 1, 2, …, M; Δ f is the amount of frequency shift; j is an imaginary unit, mu is B/TpIs the chirp rate, B isThe bandwidth of the transmitted signal is,
3c) at 1/TpUnder the condition of (3), the space-time coding reduction on the kth pulse of the mth array element is expressed as:
αk，m＝e-j2π(m-1)(k-1)/M。
7. a method for enhancing range resolution of a frequency diversity array radar based on space-time coding according to claim 2, wherein in step 4, the array transmission composite signal of the kth sub-pulse after space-time coding is:
wherein alpha isk，mRepresenting space-time coding on the kth pulse of the mth array element;
the transmission combined signal of the frequency diversity array at time t and angle θ after space-time coding, that is, the transmission combined signal of the coherent pulse train after space-time coding, is:
where T is the pulse repetition interval.
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