CN107390167A - A kind of multichannel receiver signal imitation method - Google Patents
A kind of multichannel receiver signal imitation method Download PDFInfo
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- CN107390167A CN107390167A CN201710600064.9A CN201710600064A CN107390167A CN 107390167 A CN107390167 A CN 107390167A CN 201710600064 A CN201710600064 A CN 201710600064A CN 107390167 A CN107390167 A CN 107390167A
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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
- G01S3/00—Direction-finders for determining the direction from which infrasonic, sonic, ultrasonic, or electromagnetic waves, or particle emission, not having a directional significance, are being received
- G01S3/02—Direction-finders for determining the direction from which infrasonic, sonic, ultrasonic, or electromagnetic waves, or particle emission, not having a directional significance, are being received using radio waves
- G01S3/74—Multi-channel systems specially adapted for direction-finding, i.e. having a single antenna system capable of giving simultaneous indications of the directions of different signals
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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
- G01S3/00—Direction-finders for determining the direction from which infrasonic, sonic, ultrasonic, or electromagnetic waves, or particle emission, not having a directional significance, are being received
- G01S3/02—Direction-finders for determining the direction from which infrasonic, sonic, ultrasonic, or electromagnetic waves, or particle emission, not having a directional significance, are being received using radio waves
- G01S3/023—Monitoring or calibrating
- G01S3/026—Simulating means therefor
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Abstract
The present invention relates to electronic reconnaissance field.Purpose is to provide a kind of multichannel receiver signal imitation method, and the analogy method comprises the following steps：(1) multichannel array aerial signal model is established；(2) the delay inequality τ of each channel receiving signal of array antennakAnd Doppler frequency shift fdExtraction, while generate baseband modulation signal u (t)；(3) each array element delay inequality of array antenna and Doppler shift information loading and carrier phase compensation；(4) up-conversion is to radiofrequency signal；(5) radiofrequency signal of launching simulation.The present invention can be under analog crossover array or circular array or linear array direction-finding signal, simulating, verifying is carried out for direction-finding system, in the case of without outfield experiments, direction-finding system carries out related experiment checking, it is effectively convenient, not only shorten experimental period and also greatly save R＆D costs.
Description
Technical Field
The invention belongs to the field of electronic reconnaissance, and particularly relates to a signal simulation method of a multi-channel receiver.
Background
Electronic countermeasure can be generally classified into sonar countermeasure, radar countermeasure, communication countermeasure, photoelectric countermeasure, and the like, wherein radar countermeasure and communication countermeasure are important, and research of a direction-finding system, which is a key technology in radar reconnaissance and communication reconnaissance, has been the focus of electronic warfare technology.
There are many studies on signal simulation technology at home and abroad, and great achievement is achieved in the aspect of implementation technology. The human-computer environment research institute of the three military, such as the U.S. department of defense, mainly aims to research a signal simulator for training military weapons; the AN/PLM-4 signal simulator is a military simulator developed by EDO company, and is mainly suitable for radar alarm receiver detection of fighters and military aircrafts; the 1994 aviation sector 601 and Beijing aerospace university successfully develop a general Doppler radar signal simulator, wherein a computer can communicate with the simulator through a serial port to control the operation state of the simulator, and the relative time delay and Doppler relative frequency shift of a video pulse are changed to truly simulate the actual distance and relative movement speed between a radar and an unknown target.
However, signal generator products in the current market are more than high-precision single-tone signals, the signals are not suitable for being used as receiving signals of a direction-finding system, and the direction-finding system needs to be customized and can meet the requirement of high-precision time delay control among multiple channels to simulate an arrival angle. If under the condition of external field experiment, the direction-finding system carries out relevant experimental verification, not only the research and development cycle is long, but also the research and development cost is very high.
Disclosure of Invention
In view of this, the simulation method for the multi-channel receiver signal provided by the invention shortens the experimental period of the direction-finding system and reduces the research and development cost.
In order to achieve the purpose of the invention, the technical scheme adopted by the invention is as follows: a method of multi-channel receiver signal simulation, comprising the steps of:
(1) establishing a multi-channel array antenna signal model, and setting a target transmitting signal as s (t):
where u (t) is a baseband modulation signal, fcIs the signal center frequency;
(2) obtaining the time delay difference tau of the received signals of each channel of the array antenna according to the user setting parameterskAnd Doppler shift fdSimultaneously generating a baseband modulation signal u (t);
(3) loading delay difference of each array element of the array antenna and Doppler frequency shift information and compensating carrier frequency phase to obtain an analog signal Sbase(t)；
(4) Up-conversion to radio frequency signal, to analog signal Sbase(t) upconversionProcessing;
(5) transmitting an analog radio frequency signal, wherein the radio frequency signal received by an antenna receiving unit of a receiving platform is r (t):
wherein, taukIs the delay difference between channel k and channel 1, fdIn order to be the doppler shift frequency,is a phase compensation parameter for the carrier frequency.
Preferably, the baseband modulation signal u (t) is generated by a baseband modulation signal model.
Preferably, the baseband modulation signal u (t) is of the type radar signal or conventional communication signal.
Preferably, the delay difference τkAnd Doppler shift fdCalculated by an array antenna model.
Preferably, the step (3) is performed by a time delay information model.
Preferably, the step (4) is performed by an up-conversion model.
Preferably, the array antenna is a cross array antenna or a circular array antenna or a linear array antenna, and the number of the array antenna elements is 7.
Preferably, the step (2) specifically comprises:
firstly, a user sets the incoming wave direction of a target transmitting signal to be theta, the radial velocity to be v, the number of array elements of an array antenna to be N, and the length of a base line between the array elements to be l;
secondly, calculating the time delay difference tau between each array elementkWhen the array element k and the array element 1 are arranged in the same direction as the normal direction, the time delay difference between the array element k and the array element 1 is tauk1，
τk1＝(l1+...+lk-1)·sin(θ)/c；
When the array element k is perpendicular to the array element 1 in the arrangement direction and the normal direction, the time delay difference between the array element k and the array element 1 is tauk2，
τk2＝(l1+...+lk-1)·cos(θ)/c；
Where θ is the incoming wave direction of the target transmitting signal, l1Is the length of the base line between the array element 2 and the array element 1, lk-1Is the length of a base line between an array element k and an array element k-1;
third, calculating the Doppler shift fd：
fd＝(2v/c)·fc；
Where c is the speed of light, v is the radial velocity, fcIs the signal center frequency.
Preferably, the step (3) specifically comprises:
firstly, Doppler frequency shift loading is carried out to obtain a loaded signal
Secondly, carrying out time delay difference loading on the signals by using group delay to obtain
Thirdly, carrying out carrier phase compensation on the baseband modulation signal loaded by the time delay difference and the Doppler frequency shift to obtain an analog signal Sbase(t)，
The invention has the following beneficial effects: according to the technical scheme, the direction-finding system can simulate direction-finding signals under a cross array, a circular array or a linear array, can be used for simulation verification of the direction-finding system, can perform relevant experimental verification under the condition of not performing an external field experiment, is effective and convenient, shortens the experimental period, and greatly saves research and development cost. The signal simulation technology provided by the invention does not limit the signal type, has wide application range and provides self-adaptive simulation signals for the positioning system.
Drawings
FIG. 1 is a general block diagram of the present invention;
FIG. 2 is a general flow diagram of the present invention;
FIG. 3 is a schematic diagram of a cross array antenna of the present invention;
FIG. 4 is a simulation diagram of the delay of each channel of the radar signal according to the present invention;
fig. 5 is a simulation diagram of the delay of each channel of the communication CW signal according to the present invention.
Detailed Description
The technical solutions in the embodiments of the present invention will be clearly and completely described below with reference to the drawings in the embodiments of the present invention, and it is obvious that the described embodiments are only a part of the embodiments of the present invention, and not all of the embodiments. All other embodiments, which can be derived by a person skilled in the art from the embodiments given herein without making any creative effort, shall fall within the protection scope of the present invention.
Referring to fig. 1, a method for simulating a multi-channel receiver signal includes a baseband modulation signal model, an array antenna model, a delay information model, and an up-conversion model. The baseband modulation signal model generates baseband modulation signals required by each channel; the array antenna model obtains the time delay difference and the Doppler frequency shift of analog signals of each channel according to the direction of arrival angle, the radial speed and the antenna arrangement mode set by a user; the delay information module loads the delay difference and the Doppler frequency shift to corresponding baseband modulation signals according to the delay difference and the Doppler frequency shift of analog signals of each channel obtained by the array antenna model; and the up-conversion model up-converts the baseband modulation signal loaded with the time delay difference to radio frequency according to an up-conversion formula, and simulates the radio frequency signal of the corresponding direction angle under the current antenna model.
Referring to fig. 2, the method for simulating the receiving signal of the array antenna for direction finding in the invention comprises the following steps:
(1) establishing a multi-channel array antenna signal model;
(2) according to user parameter setting, obtaining time delay difference and Doppler frequency shift of received signals of each channel of the array antenna, and simultaneously generating baseband modulation signals;
(3) loading time delay difference and Doppler frequency shift information;
(4) up-converting to a radio frequency signal;
(5) a radio frequency analog signal is transmitted.
Further, the specific content of the step (1) is as follows: firstly, setting a target transmitting signal as s (t)
The signal received by the direction-finding antenna receiving unit is r (t)
Wherein, s (t) is a target emission signal set according to user parameters, the signal is a carrier of information, and the array signal model is expressed by complex signals. u (t) is a baseband modulation signal generated by a baseband modulation signal model according to a signal modulation type and a modulation parameter set by a user, fcIs the signal center frequency, fdIs the doppler shift. r (t) is the final output RF analog signal, τkIs the delay difference between channel k and channel 1,loading the delay difference and the Doppler frequency shift of the analog signal of each channel obtained by the array antenna model to the baseband modulation signal of the corresponding channel for the delay information model,the baseband signal u (t) is loaded with a doppler shifted signal,for time-delay difference loading of the signal loaded with Doppler frequency shiftThe phase compensation parameter of the carrier frequency is the phase variation of the carrier frequency and the delay difference tau when the radio frequency signal is delayedkProportional to the carrier frequency phase, so the carrier frequency phase needs to be compensated.Up-conversion information generated for the up-conversion model.
Further, as shown in fig. 3, the specific content of step (2) is: firstly, an included angle between an incoming wave direction of a target transmitting signal set by a user and a normal direction is theta, the normal direction is 0 DEG, and an angle change value of clockwise rotation of the included angle between the incoming wave direction of the target transmitting signal and the normal direction is 0-360 deg. The arrangement type of the array antenna set by the user is a cross array or a circular array or a linear array, and the invention prefers to crossAnd (4) array. The number of the array elements of the cross array antenna is set to be N, the length of a base line between each array element is set to be l, the number of corresponding channels is also set to be N, the channels refer to signal paths of transmitting signals reaching each array element, the number of the array elements of the cross array antenna is determined according to actual requirements, and the number of the array elements of the cross array antenna is 7. Then, the target transmitting the signal is regarded as a far-field radiation source, and the dotted line in fig. 3 refers to a cross section of each array element at the signal radiation distance, and the signal radiation distances on the cross section are the same. The radiation distance difference of the received signals among the array elements of the receiving antenna is d by taking the channel 1 as a referencek～1，τkIs the delay between channel k and channel 1, the delay difference τkAt the speed of light and the distance difference dk～1Is in direct proportion.
When the array element k and the array element 1 are in the same arrangement direction and the normal direction, the time delay difference between the array element k and the array element 1 is:
τk1＝(l1+...+lk-1)·sin(θ)/c；
wherein, theta is the angle between the incoming wave direction of the target emission signal and the normal direction, c is the speed of light, l1Is the length of the base line between the array element 2 and the array element 1, lk-1The length of a base line between an array element k and an array element k-1 is defined, and the signal of the current channel k lags behind the channel 1 when the delay is positive; a negative delay indicates that the signal for the current channel k leads channel 1.
When the array element k is perpendicular to the array element 1 in the arrangement direction and the normal direction, the time delay difference between the array element k and the array element 1 is:
τk2＝(l1+...+lk-1)·cos(θ)/c；
the arrangement directions of the array elements 5, 6 and 7 and the array elements 1 are the same as the normal direction, so that the time delay differences among the array elements 5, 6 and 7 and the array elements 1 are as follows:
τ5＝-l4·sin(θ)/c；
τ6＝l5·sin(θ)/c；
τ7＝(l5+l6)·sin(θ)/c；
the array elements 2, 3 and 4 are perpendicular to the array elements 1 in the normal direction, so that the time delay difference between the array elements 2, 3 and 4 and the array elements 1 is as follows:
τ2＝l1·cos(θ)/c；
τ3＝(l1+l2)·cos(θ)/c；
τ4＝(l1+l2+l3)·cos(θ)/c；
therefore, the arrival angle theta of the target transmitting signal is converted into the time delay difference tau of the signals among the array elements of the receiving antenna of the test systemk。
Setting the relative radial velocity v between the target and the platform where the receiving antenna is located, the doppler shift formula is as follows:
fd＝(2v/c)·fc；
thereby, the radial velocity v of the target transmission signal is converted into the frequency shift f of the signal at the receiving antenna of the test systemd。
Meanwhile, the required baseband modulation signal is obtained according to the modulation signal type and the modulation signal parameter set by the user. The modulation signal types include radar signals, conventional communication signals, and the like. The modulation signal parameters are not completely the same according to different loading signal parameter contents of modulation signal types, and when the modulation signal type is a radar signal, the modulation signal parameters comprise a central frequency fcPulse width τ, pulse repetition period PRI. When the modulation signal type is a conventional communication CW signal, the modulation signal parameter includes a center frequency fc. Before the time delay difference and the Doppler frequency shift are loaded, the baseband modulation signal of each channel is the same, the baseband modulation signal model can only generate the baseband modulation signal of one channel, and each subsequent channelWhen the time delay difference and the Doppler frequency shift are loaded, the baseband modulation signal is used, and the calculation amount and the algorithm complexity of a baseband modulation signal model are reduced.
Further, the specific content of the step (3) is as follows: first, Doppler frequency shift loading is carried out, and the Doppler frequency shift loading is multiplied by a baseband modulation signalObtaining the signal loaded by the Doppler frequency shift information
Then, the signal loaded with the Doppler frequency shift information is subjected to time delay difference loading to obtain When algorithm simulation is carried out, each channel signal is in a discrete form, and the sampling rate is fsTime delay difference tau of each channelkConvertible to number of delayed sampling points
Wherein,can be an integer or a decimal.
The invention utilizes the group delay characteristic of the linear phase filter to realize the delay of decimal or integer sampling points for signals.
The set signal x (n) is passed through a filter having the following frequency response:
wherein n is0Is the group delay of the filter and may not be an integer.
Setting the input signal of the filter as x (n) and the output signal as y (n), and obtaining frequency domain output by utilizing the time shift characteristic of Fourier transform:
and (3) time domain output:
y(n)＝x(n-n0)
the filter filters the input signal within the pass band such that the input signal produces n0The delay of (2). Is thus provided withTo obtain a group delay ofAccording to the delay difference tau of different channels and channel 1kAnd obtaining the group delay of the filters of different channels, and carrying out filtering processing on the baseband modulation signals corresponding to the channels by the filters to obtain the delayed signals of the different channels. In addition, another delay processing method of the present invention is that, after the frequency response of the filter is known, the signal after delay processing can be obtained by a frequency domain multiplication method instead of filtering.
Finally, after the time delay difference and the Doppler frequency shift are loaded to the signal, the radio frequency signal is delayed, and the carrier frequency phase variation and the time delay difference tau are carried outkProportional, so the carrier frequency phase needs to be compensated, and the signal is directly multiplied byObtaining an analog signal S containing information of arrival angle and radial velocitybase(t)：
Further, the specific content of the step (4) is as follows: the up-conversion model obtains the analog signal S subjected to delay difference and Doppler frequency shift loading and carrier frequency phase compensation according to the step (3)base(t) performing an up-conversion process on the analog signal Sbase(t) is:
the analog signal Sbase(t) multiplication byObtaining the radio frequency signal S after the up-conversion processingRF(t)，
SRF(t)＝real{Sbase(t)}·cos(2πfct)-imag{Sbase(t)}·sin(2πfct)
Wherein real refers to obtaining the analog signal Sbase(t) value of real part, imag means obtaining an analog signal SbaseThe imaginary value of (t).
Further, the step (5) is to obtain the radio frequency signal S processed in the step (4)RF(t) transmitting.
The other implementation mode of the invention is that the number of the array elements of the cross array antenna is 7, the arrangement direction of the array elements 2, 3, 4 and 1 is vertical to the normal direction, the arrangement direction of the array elements 5, 6, 7 and 1 is consistent with the normal direction, the array element 5 is at one side of the array element 1, and the array element 6 and 7 are at the other side of the array element 1. And array element 2 and array element 1, array element 3 and array element 2, array element 4 and array element 3, array element 5 and array element 1, array element 6The lengths of the base lines between the array element 1 and the array element 7 and the array element 6 are respectively set to be [0.1, 0.13, 0.12, 0.17, 0.11, 0.12%]m, the incoming wave direction theta is 40 degrees, and the radial speed is 300 m/s. Center frequency f of radar signalc500MHz, 2ms pulse width tau, 3ms pulse repetition period PRI, and center frequency f of conventional communication CW signalcIs 500 MHz.
The Doppler frequency shift is calculated to be 1KHz according to a Doppler frequency shift formula, and the time delay difference between each array element and the array element 1 is [0, 0.2143, 0.4928, 0.7499, -0.4341, 0.2809, 0.5873] ns according to an arrival angle rotation time delay difference algorithm. As shown in fig. 4-5, simulation graphs of the time delay between the conventional radar signal and the communication CW signal are obtained. As can be seen from fig. 4-5, the signals of the channel 3, the channel 4 and the channel 7 are delayed from the signal of the channel 1, and the signal of the channel 5 is advanced from the signal of the channel 1, and is consistent with the calculated delay difference information, so that the simulation method can accurately simulate the signals with different delays of the array antenna receiving unit, and perform simulation verification on the co-location direction-finding system.
The invention can simulate direction-finding signals under a cross array, a circular array or a linear array, the range of the arrival angle of the direction-finding signals is [0 DEG, 360 DEG ], and Doppler frequency shift information is added, so that the direction-finding signals in any direction can be simulated. The direction-finding system can provide required direction-finding signals for the direction-finding system, the direction-finding system is subjected to simulation verification, an outfield experiment is avoided, the direction-finding verification is effectively and conveniently carried out, the experiment period is shortened, and the development cost is saved. The signal simulation method provided by the invention is not limited in signal type, has wide application range and provides self-adaptive simulation signals for the positioning and direction finding system.
The above description is only for the purpose of illustrating the preferred embodiments of the present invention and is not to be construed as limiting the invention, and any modifications, equivalents, improvements and the like that fall within the spirit and principle of the present invention are intended to be included therein.
Claims (9)
1. A method for multi-channel receiver signal simulation, comprising: the method comprises the following steps:
(1) establishing a multi-channel array antenna signal model, and setting a target transmitting signal as s (t):
<mrow> <mi>s</mi> <mrow> <mo>(</mo> <mi>t</mi> <mo>)</mo> </mrow> <mo>=</mo> <mi>u</mi> <mrow> <mo>(</mo> <mi>t</mi> <mo>)</mo> </mrow> <mo>&CenterDot;</mo> <msup> <mi>e</mi> <mrow> <mi>j</mi> <mrow> <mo>(</mo> <mn>2</mn> <msub> <mi>&pi;f</mi> <mi>c</mi> </msub> <mi>t</mi> <mo>)</mo> </mrow> </mrow> </msup> <mo>;</mo> </mrow>
where u (t) is a baseband modulation signal, fcIs the signal center frequency;
(2) obtaining the time delay difference tau of the received signals of each channel of the array antenna according to the user setting parameterskAnd Doppler shift fdSimultaneously generating a baseband modulation signal u (t);
(3) loading delay difference of each array element of the array antenna and Doppler frequency shift information and compensating carrier frequency phase to obtain an analog signal Sbase(t)；
(4) Up-conversion to radio frequency signal, to analog signal Sbase(t) upconversionProcessing;
(5) transmitting an analog radio frequency signal, wherein the radio frequency signal received by an antenna receiving unit of a receiving platform is r (t):
<mrow> <mi>r</mi> <mrow> <mo>(</mo> <mi>t</mi> <mo>)</mo> </mrow> <mo>=</mo> <mo>{</mo> <mi>u</mi> <mrow> <mo>(</mo> <mi>t</mi> <mo>-</mo> <msub> <mi>&tau;</mi> <mi>k</mi> </msub> <mo>)</mo> </mrow> <mo>&CenterDot;</mo> <msup> <mi>e</mi> <mrow> <mi>j</mi> <mo>&lsqb;</mo> <mn>2</mn> <msub> <mi>&pi;f</mi> <mi>d</mi> </msub> <mrow> <mo>(</mo> <mi>t</mi> <mo>-</mo> <msub> <mi>&tau;</mi> <mi>k</mi> </msub> <mo>)</mo> </mrow> <mo>&rsqb;</mo> </mrow> </msup> <mo>}</mo> <mo>&CenterDot;</mo> <msup> <mi>e</mi> <mrow> <mi>j</mi> <mn>2</mn> <msub> <mi>&pi;f</mi> <mi>c</mi> </msub> <msub> <mi>&tau;</mi> <mi>k</mi> </msub> </mrow> </msup> <mo>&CenterDot;</mo> <msup> <mi>e</mi> <mrow> <mi>j</mi> <mn>2</mn> <msub> <mi>&pi;f</mi> <mi>e</mi> </msub> <mi>t</mi> </mrow> </msup> <mo>;</mo> </mrow>
wherein, taukIs the delay difference between channel k and channel 1, fdIn order to be the doppler shift frequency,is a phase compensation parameter for the carrier frequency.
2. A method for multi-channel receiver signal simulation according to claim 1, characterized by: the baseband modulation signal u (t) is generated by a baseband modulation signal model.
3. A method for multi-channel receiver signal simulation according to claim 2, characterized by: the baseband modulation signal u (t) is of the type radar signal or conventional communication signal.
4. A method for multi-channel receiver signal simulation according to claim 1, characterized by: said time delay difference τkAnd Doppler shift fdCalculated by an array antenna model.
5. A method for multi-channel receiver signal simulation according to claim 1, characterized by: and the step (3) is completed by a time delay information model.
6. A method for multi-channel receiver signal simulation according to claim 1, characterized by: and the step (4) is completed by an up-conversion model.
7. A method for multi-channel receiver signal simulation according to claim 1, characterized by: the array antenna is a cross array antenna or a circular array antenna or a linear array antenna, and the number of array elements of the array antenna is 7.
8. A method for multi-channel receiver signal simulation according to claim 1, characterized by: the step (2) specifically comprises:
firstly, a user sets the incoming wave direction of a target transmitting signal to be theta, the radial velocity to be v, the number of array elements of an array antenna to be N, and the length of a base line between the array elements to be l;
secondly, calculating the time delay difference tau between each array elementkWhen the array element k and the array element 1 are arranged in the same direction as the normal direction, the time delay difference between the array element k and the array element 1 is tauk1，
τk1＝(l1+...+lk-1)·sin(θ)/c；
When the array element k is perpendicular to the array element 1 in the arrangement direction and the normal direction, the time delay difference between the array element k and the array element 1 is tauk2，
τk2＝(l1+...+lk-1)·cos(θ)/c；
Where θ is the incoming wave direction of the target transmitting signal, l1Is the length of the base line between the array element 2 and the array element 1, lk-1Is the length of a base line between an array element k and an array element k-1;
third, calculating the Doppler shift fd：
fd＝(2v/c)·fc；
Where c is the speed of light, v is the radial velocity, fcIs the signal center frequency.
9. A method for multi-channel receiver signal simulation according to claim 1, characterized by: the step (3) specifically comprises:
firstly, Doppler frequency shift loading is carried out to obtain a loaded signal
Secondly, carrying out time delay difference loading on the signals by using group delay to obtain
Thirdly, carrying out carrier phase compensation on the baseband modulation signal loaded by the time delay difference and the Doppler frequency shift to obtain an analog signal Sbase(t)，
<mrow> <msub> <mi>S</mi> <mrow> <mi>b</mi> <mi>a</mi> <mi>s</mi> <mi>e</mi> </mrow> </msub> <mrow> <mo>(</mo> <mi>t</mi> <mo>)</mo> </mrow> <mo>=</mo> <mi>u</mi> <mrow> <mo>(</mo> <mi>t</mi> <mo>-</mo> <msub> <mi>&tau;</mi> <mi>k</mi> </msub> <mo>)</mo> </mrow> <mo>&CenterDot;</mo> <msup> <mi>e</mi> <mrow> <mi>j</mi> <mo>&lsqb;</mo> <mn>2</mn> <msub> <mi>&pi;f</mi> <mi>d</mi> </msub> <mrow> <mo>(</mo> <mi>t</mi> <mo>-</mo> <msub> <mi>&tau;</mi> <mi>k</mi> </msub> <mo>)</mo> </mrow> <mo>&rsqb;</mo> </mrow> </msup> <mo>&CenterDot;</mo> <msup> <mi>e</mi> <mrow> <mi>j</mi> <mn>2</mn> <msub> <mi>&pi;f</mi> <mi>c</mi> </msub> <msub> <mi>&tau;</mi> <mi>k</mi> </msub> </mrow> </msup> <mo>.</mo> </mrow>2
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| CN110109150A (en) * | 2019-04-22 | 2019-08-09 | 长沙翼盾电子科技有限公司 | A kind of high-precision array signal simulator and method |
| CN110716173A (en) * | 2018-07-12 | 2020-01-21 | 罗德施瓦兹两合股份有限公司 | Measuring device and measuring method for determining a test signal by simulating a departure angle |
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