CN117411794A - Beyond-view-range time reversal focusing simulation method based on Watterson channel model - Google Patents
Beyond-view-range time reversal focusing simulation method based on Watterson channel model Download PDFInfo
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Abstract
The invention relates to a beyond visual range time reversal focusing simulation method based on a Watterson channel model, belongs to the field of electromagnetic wave regulation and control, and solves the problem that the existing free space channel model is not suitable for a short wave time reversal focusing simulation process. The simulation process comprises the following steps: the target point emits a low-frequency electromagnetic wave signal; transmitting the low-frequency electromagnetic wave signal to a time reversal mirror through an ionosphere channel; the ionosphere channel adopts a Watterson channel model; the time reversal mirror receives the low-frequency electromagnetic wave signal, performs time reversal operation on the low-frequency electromagnetic wave signal, and then transmits the low-frequency electromagnetic wave signal to the direction of the target point, and transmits the low-frequency electromagnetic wave signal through the ionosphere channel; and acquiring the distribution of the electric field intensity of the time reversal signals received by the target point and the neighborhood thereof in space, and acquiring the focusing point of the time reversal signals according to the distribution of the electric field intensity in space. The method realizes a feasible beyond-view-range time reversal focusing simulation method, and the simulation result obtained by the method is closer to reality, so that guidance can be provided for the fields of beyond-view-range communication, detection and the like.
Description
Technical Field
The invention relates to a beyond-view-range time reversal focusing simulation method based on a Watterson channel model.
Background
The time reversal wave has the characteristic of space-time synchronous focusing, and has great application potential in the fields of communication, electronic interference, detection and the like. The beyond-view-range time reversal focusing can be used for realizing beyond-view-range electronic reconnaissance, electronic interference, radar detection, communication and the like, and has wide application prospect. Before the time reversal focusing technology is applied to the fields of beyond-view-range electronic reconnaissance, electronic interference, radar detection and communication, it is necessary to perform beyond-view-range time reversal focusing simulation in advance, and in the simulation process, a proper channel model needs to be selected according to the channel environment of an actual application scene so that a simulation result is more in line with the actual situation, and the application of the time reversal focusing to the actual implementation is effectively guided.
Currently, free space time-reversal focusing has progressed in theoretical and simulation simulations. Typically, when performing time-reversal focusing simulation in free space or simple environments, the channel response is characterized by a green function.
When the time reversal mirror is far away from the target focusing point, the sight distance signal cannot reach the focusing point, and the signal of a lower frequency band in the short wave and the ultrashort wave is required to be adopted to realize the propagation of the beyond sight distance, so that the electromagnetic wave of the frequency band can be utilized to realize the time reversal focusing of the beyond sight distance. Considering that the environment of electromagnetic wave propagation is not ideal free space environment in practical application scenes, when performing beyond-view-range time reversal focusing simulation, a channel model directly adopting free space electromagnetic wave propagation is not suitable, and an ionosphere is used as a main transmission medium of short waves, noise and interference in a reflection channel of the ionosphere continuously change along with time and place changes, so that a mathematical model capable of comprehensively describing the channel is difficult to accurately establish like free space, a Watterson channel model is a common short wave channel model, and factors such as fading, multipath propagation and noise of signals are considered by the model, so that the transmission characteristic of the short wave channel can be accurately simulated. Therefore, when performing beyond-view-range time reversal focusing simulation, a Watterson channel model is required to simulate the transmission environment of short waves and electromagnetic waves with lower frequency bands in the ultrashort waves so as to meet the complex environment in practical application.
Disclosure of Invention
In view of the above analysis, the embodiment of the invention aims to provide a beyond-view-range time reversal focusing simulation method based on a Watterson channel model, which is used for solving the problem that the existing free space channel model cannot be used for beyond-view-range time reversal focusing simulation.
In one aspect, an embodiment of the present invention provides a beyond-view-range time-reversal focusing simulation method based on a Watterson channel model, where the simulation process includes: the target point emits a low-frequency electromagnetic wave signal; transmitting the low-frequency electromagnetic wave signal to a time reversal mirror through an ionosphere channel; the ionosphere channel adopts a Watterson channel model; the time reversal mirror receives the low-frequency electromagnetic wave signal, performs time reversal operation on the low-frequency electromagnetic wave signal, and then transmits the low-frequency electromagnetic wave signal to the direction of the target point, and transmits the low-frequency electromagnetic wave signal through the ionosphere channel; and acquiring the distribution of the electric field intensity of the time reversal signals received by the target point and the neighborhood thereof in space, and acquiring the focusing point of the time reversal signals according to the distribution of the electric field intensity in space.
Specifically, the low-frequency electromagnetic wave signal emitted by the target point is a low-frequency single-frequency signal or a Gaussian pulse signal.
Specifically, the low-frequency electromagnetic wave signal emitted by the target point is a low-frequency single-frequency signal or a Gaussian pulse signal.
Specifically, the low-frequency electromagnetic wave signal is transmitted to the time reversal mirror through the Watterson channel in a simulation mode, which comprises the following steps of: multipath simulation for simulating multipath propagation of low-frequency electromagnetic waves in an ionosphere channel; the fading simulation is used for simulating the fading of the ionosphere on the absorption characteristic of the low-frequency electromagnetic wave signal and the signal fading caused by multipath effect; and the noise simulation is used for simulating the influence of noise in the ionosphere channel on the low-frequency electromagnetic wave signal.
Specifically, the multipath simulation includes:
designing an FIR low-pass filter, and constructing a Hilbert filter by using a conversion formula of coefficients of the low-pass filter and the Hilbert filter; the original low-frequency electromagnetic wave signals are respectively input into a band-pass filter and a Hilbert filter, and an original complex signal S (t) =I (t) +jQ (t) of the original signals is generated;
setting a plurality of different time delays tau for the initial complex signal i (i=1, 2,., l) is the number of paths, resulting in a multiplexed signal S i (t i ) Wherein t is i ＝t-τ i 。
Specifically, the fading simulation includes a doppler frequency spread simulation and a doppler frequency shift simulation.
Further, the simulation process of the Doppler frequency expansion is as follows:
the Gaussian noise generator generates two paths of independent Gaussian noise I 1 And Q 1 The two Gaussian signals II and QQ are output through a Gaussian FIR low-pass filter and an interpolation FIR filter respectively, and the formed complex signal is G (t) =II+ jQQ;
the input signal before Doppler frequency expansion is S i (t i )＝I i (t i )+jQ i (t i ) Complex multiplication is performed with complex signal G (t) to obtain complex output signal S' i (t i )＝I′ i +jQ′ i The real part and the imaginary part are respectively:
wherein,θ is the phase of the initial complex signal S (t) =i (t) +jq (t), a is the amplitude of the initial complex signal; f (f) 0 A center frequency that is the passband of the low pass filter; the Doppler frequency spread signal is S' i (t i )＝I′ i +jQ′ i ，(i＝1，2，...，l)。
Further, the simulation process of the Doppler frequency shift is as follows:
generating two paths of frequencies f d Is respectively:
I d ＝cos(f d t)，Q d ＝sin(f d t)
wherein f d Is Doppler shift; two orthogonal signals form complex signal s d (t)＝I d +jQ d ；
Spread Doppler spread signal s i ′(t i ) And complex signal s d (t) multiplying to obtain Doppler frequency shifted signal
Specifically, the noise simulation process is as follows:
each path of signal after Doppler frequency shift simulationAdding to obtain a summation signal;
generating Gaussian white noise, and inputting the Gaussian white noise into a band-pass filter to obtain noise required to be added into a signal;
multiplying the sum signal and noise with root mean square of the signal and noise respectively to obtain gain or attenuated sum signal and noise; adding the added signal after gain or attenuation with noise to obtain an output signal, and completing noise simulation;
the output signal is the electromagnetic wave signal output by the Watterson channel.
Specifically, the conversion formula of the low-pass filter and the hilbert filter coefficients is:
wherein h is IBP (n) and h QBP (n) is the coefficients of the I and Q paths of the Hilbert filter, h LP (n) is the coefficient of the n-order finite impulse response low-pass filter, f 0 The center frequency of the passband of the filter is T is the sampling period and N is the order of the Hilbert filter.
Specifically, root mean square of the signal and noise are calculated by the following formula:
wherein x is j Values representing all the samples of the signal or noise, N representing the number of samples of the signal or noise.
Compared with the prior art, the invention has at least the following beneficial effects: by applying the Watterson channel model to the beyond-line-of-sight time reversal focusing simulation process, compared with a free space channel model, the method is more in line with the actual transmission environment, and the simulation result is more reliable.
In the invention, the technical schemes can be mutually combined to realize more preferable combination schemes. Additional features and advantages of the invention will be set forth in the description which follows, and in part will be obvious from the description, or may be learned by practice of the invention. The objectives and other advantages of the invention may be realized and attained by the structure particularly pointed out in the written description and drawings.
Drawings
The drawings are only for purposes of illustrating particular embodiments and are not to be construed as limiting the invention, like reference numerals being used to designate like parts throughout the drawings;
FIG. 1 is a schematic diagram of a time reversal signal focusing process based on a Watterson channel;
FIG. 2 is a flow chart of a time-reversal focus simulation;
FIG. 3 is a simulated overall block diagram of the Watterson channel model;
FIG. 4 is a schematic diagram of a simulation of Doppler frequency spread;
FIG. 5 is a schematic diagram of a simulation of Doppler shift;
FIG. 6 (a) is a schematic diagram showing the relative positions of the target point and the time reversal mirror in simulation examples 1 and 3; FIG. 6 (b) is a schematic diagram showing the relative positions of the target point and the time reversal mirror in simulation examples 2 and 4;
fig. 7 (a), (b), (c) and (d) are the signal emitted from the target point, the signal received by the time reversal mirror, the signal emitted from the time reversal mirror and the signal received by the target point in the simulation example 1 and the simulation example 2, respectively;
fig. 8 (a), (b), (c) and (d) are respectively the instantaneous value of the target point transmission signal, the instantaneous value of the time reversal mirror reception signal, the instantaneous value of the time reversal mirror transmission signal and the instantaneous value of the target point reception signal in simulation example 3 and simulation example 4;
fig. 8 (e), (f), (g) and (h) are the spectrograms of the target point emission signal, the spectrograms of the time-reversal mirror reception signal and the spectrograms of the target point reception signal in the simulation example 3 and the simulation example 4, respectively;
fig. 9 (a), (b), (c) and (d) show the spatial distribution of the electric field intensity of the time-reversal signals in the vicinity of the target point in simulation examples 1,2, 3 and 4, respectively.
Detailed Description
Preferred embodiments of the present invention will now be described in detail with reference to the accompanying drawings, which form a part hereof, and together with the description serve to explain the principles of the invention, and are not intended to limit the scope of the invention.
In one embodiment of the present invention, a beyond-view-range time reversal focusing simulation method based on a Watterson channel model is disclosed, as shown in FIG. 1 and FIG. 2, the simulation process includes: the target point emits a low-frequency electromagnetic wave signal; transmitting the low-frequency electromagnetic wave signal to a time reversal mirror through an ionosphere channel; the ionosphere channel adopts a Watterson channel model; the time reversal mirror receives the low-frequency electromagnetic wave signal, performs time reversal operation on the low-frequency electromagnetic wave signal, and then transmits the low-frequency electromagnetic wave signal to the direction of the target point, and transmits the low-frequency electromagnetic wave signal through the ionosphere channel; and acquiring the distribution of the electric field intensity of the time reversal signals received by the target point and the neighborhood thereof in space, and acquiring the focusing point of the time reversal signals according to the distribution of the electric field intensity in space.
In general terms, the target point is where the time-reversal signal is focused; in the field of beyond-view communication, the target point is a signal receiving system in a communication system, and in the fields of beyond-view radar detection and beyond-view electronic reconnaissance, the target point is an enemy radar; the frequency of the low-frequency electromagnetic wave signal is 3-30 MHz.
The beyond-view-range time reversal focusing simulation method based on the Watterson channel model can simulate the short-wave time reversal focusing process; compared with a simulation method using a green function suitable for free space as a channel, the simulation result obtained by the simulation method is more practical, and can effectively guide the successful application of the subsequent electromagnetic wave time reversal focusing phenomenon to the scenes such as beyond-line-of-sight communication, radar detection, electronic interference and the like.
The time reversal focusing theory is described as follows:
at r F The signal emitted by the target point F of (a) is:
wherein A is F Representing the signal amplitude, omega as angular frequency,Is the initial phase.
Is positioned at r after being transmitted through an ionosphere channel i The signals received by the time reversal mirror unit i are:
wherein,is the channel response function that the signal emitted by the target point is transmitted to the time reversal mirror.
The time inversion mirror performs time inversion on the signals, and the retransmitted signals are as follows:
wherein A is i Is the gain of the retransmission.
The signal is transmitted through an ionosphere channel, and the electric field in the neighborhood of the target point is:
wherein,is the channel response function experienced by the time-reversed signal transmitted to the target point.
In free space or simple environments, the channel response is green's function, and the corresponding channel in the time domain is impulse function. The noise and interference in the ionospheric reflection channel are changed continuously along with the change of time and place, and it is difficult to accurately establish a mathematical model capable of comprehensively reflecting the characteristics of the channel as free space.
The invention adopts a Watterson channel model to simulate the ionosphere channel.
Specifically, the Watterson channel model is a model for simulating a channel by using a Gaussian scattering tap gain delay line model, and the simulation of the channel model mainly comprises multipath simulation, fading simulation and noise simulation; wherein, the multipath simulation is used for simulating the multipath propagation of the low-frequency electromagnetic wave in the ionosphere channel; the fading simulation is used for simulating the fading of the ionosphere on the absorption characteristic of the low-frequency electromagnetic wave signal and the signal fading caused by multipath effect; and the noise simulation is used for simulating the influence of noise in the ionosphere channel on the low-frequency electromagnetic wave signal.
The overall simulation flow block diagram of the Watterson channel model is shown in FIG. 3, and the multipath simulation includes steps S1 and S2, as described below; the fading simulation comprises steps S3 and S4; the noise simulation comprises steps S5 and S6; in general, the simulation flow of the transmitted low-frequency electromagnetic wave signal through the Watterson channel is as follows:
s1, designing an FIR low-pass filter, constructing the Hilbert filter by using a conversion formula of coefficients of the low-pass filter and the Hilbert filter, and completing simulation of the Hilbert filter;
the conversion formula of the low-pass filter and the Hilbert filter coefficients is as follows:
wherein h is IBP (n) and h QBP (n) is the coefficients of the I and Q paths of the Hilbert filter, h LP (n) is the coefficient of the n-order finite impulse response low-pass filter, f 0 The center frequency of the passband of the filter is T is the sampling period, and N is the order of the Hilbert filter;
step S2, the original low-frequency electromagnetic wave signal is respectively input to a band-pass filter and a hilbert filter, and an original complex signal S (t) =i (t) +jq (t) of the original signal is generated; setting a plurality of different time delays tau for the initial complex signal i (i=1, 2,., l) is the number of paths, resulting in a multiplexed signal S i (t i ) Wherein t is i ＝t-τ i The simulation of multipath effect is completed;
step S3, doppler frequency expansion simulation is carried out on each path of signal respectively to obtain S i ′(t i ) (i=1, 2,., l); specifically, the flow of the doppler frequency spread simulation is shown in fig. 4:
the Gaussian noise generator generates two paths of independent Gaussian noise I 1 And Q 1 Respectively via GaussianThe output of the FIR low-pass filter and the interpolation FIR filter is still two Gaussian signals II and QQ, and the formed complex signal is G (t) =II+ jQQ;
the input signal before Doppler frequency expansion is S i (t i )＝I i (t i )+jQ i (t i ) Complex multiplication is performed with complex signal G (t) to obtain complex output signal S' i (t i )＝I′ i +jQ′ i The real part and the imaginary part are respectively:
wherein,θ is the phase of the initial complex signal S (t) =i (t) +jq (t), a is the amplitude of the initial complex signal; the Doppler frequency spread signal is S' i (t i )＝I′ i +jQ′ i ，(i＝1，2，...，l)；
Step S4, pair S i ′(t i ) Performing Doppler frequency shift simulation, adding each path of signals after Doppler frequency shift simulation, and outputting added signals; specifically, the simulation of doppler shift is shown in fig. 5:
generating two paths of frequency omega d Is respectively:
I d ＝cos(ω d t)，Q d ＝sin(ω d t)
wherein omega d Is Doppler shift; two orthogonal signals form complex signal s d (t)＝I d +jQ d ；
Spread Doppler spread signal S i ′(t i ) And complex signal s d (t) multiplying to obtain Doppler frequency shifted signal
S5, generating Gaussian white noise by a Gaussian noise generator, and inputting the Gaussian white noise into a band-pass filter to obtain output noise required to be added into a signal;
s6, multiplying the summation signal and the output noise with root mean square of the signal and the noise respectively to obtain gain or attenuated summation signal and noise, and adding the summation signal and the noise to perform noise simulation to obtain an output signal; the output signal is the electromagnetic wave signal output by the Watterson channel.
Specifically, root mean square of the signal and noise are calculated by the following formula:
wherein x is j Values representing all sample points of a signal or noise, N representing signal or noise samples
The number of points;representing the total energy of the signal or noise; />Representing the average power of the signal or noise; the definition of signal to noise ratio is:
wherein RMS s And RMS N Root mean square of signal and noise, respectively; after the SNR is typically set, by adjusting the RMS N The purpose of increasing or reducing noise can be achieved.
Acquiring the distribution of the electric field intensity of the time reversal signals received by the target point and the neighborhood thereof in space, and acquiring the focusing point of the time reversal signals according to the distribution of the electric field intensity in space; comprising the following steps:
acquiring a time-dependent change image of the instantaneous amplitude of the time-reversal signal received by the target point, observing the moment when the instantaneous amplitude has a peak value, wherein the moment is the focusing moment of the time-reversal signal and is marked as t p ；
Plotting the focus time of the time-reversal signal, i.e. t p The distribution of the instantaneous amplitude of the time reversal signal in the vicinity of the target point is the distribution diagram of the electric field intensity of the time reversal signal in space;
and observing the electric field intensity values of each point in the neighborhood of the target point to obtain the focusing point of the time reversal signal.
When the beyond-view-range time reversal focusing simulation method based on the Watterson channel model is implemented, the time reversal mirror is set to be an omni-directional antenna, the gain is 3dBi, and the time reversal mirror comprises 100 array elements and is uniformly distributed around a target point in a ring shape.
In simulation example 1, the emitted low-frequency electromagnetic wave signal was set to a single-frequency signal of 20MHz, as shown in (a) of fig. 7; the target point is located at r F = (0, 0) m, 100 array elements of the time reversal mirror are uniformly distributed around the target point, are in the same horizontal plane with the target point, and are 1000Km away from the target point, as shown in (a) of fig. 6; the signals received by the time reversal mirror, the time reversal signals transmitted by the time reversal mirror and the instantaneous values of the target point receiving signals in the simulation process are respectively shown in (b) of fig. 7, (c) of fig. 7 and (d) of fig. 7; as a result of the simulation, that is, the spatial distribution of the electric field intensity of the received signal at the target point and its vicinity is shown in fig. 9 (a), it can be seen that the signal is focused at the target emission point at this time.
In simulation example 2, the emitted low-frequency electromagnetic wave signal was set to a single-frequency signal of 20MHz, as shown in (a) of fig. 7; the target point is located at r F ＝(0，0，6×10 5 ) m, 100 array elements of the time reversal mirror are positioned on a plane z=0, and the distance (0, 0) points are 800Km, as shown in fig. 6 (b); the signals received by the time reversal mirror, the time reversal signals transmitted by the time reversal mirror and the instantaneous values of the target point receiving signals in the simulation process are respectively shown in (b) of fig. 7, (c) of fig. 7 and (d) of fig. 7; simulation results, i.e. spatial separation of the electric field strength of the received signals at the target point and its neighboursThe arrangement is shown in fig. 9 (b), where the signal is seen to be focused at the target emission point.
In simulation example 3, a gaussian signal with a center frequency of 20MHz and a bandwidth of 3MHz was set as the transmitted low-frequency electromagnetic wave signal, and the instantaneous amplitude and frequency spectrum thereof are shown in fig. 8 (a) and 8 (e); the relative positions of the target point and the time reversal mirror are the same as in example 1, as shown in fig. 6 (a); in the simulation process, the instantaneous amplitude and the frequency spectrum of a received signal of the time reversal mirror are shown in (b) in fig. 8 and (f) in fig. 8, the instantaneous amplitude and the frequency spectrum of a time reversal signal transmitted by the time reversal mirror are shown in (c) and (g) in fig. 8, and the instantaneous amplitude and the frequency spectrum of a received signal of a target point are shown in (d) and (h) in fig. 8; as can be seen from fig. 8 (f) and 8 (g), the signal frequency through the Watterson channel model is broadened; as a result of the simulation, that is, the spatial distribution of the electric field intensities of the received signals at the target point and its vicinity is shown in fig. 9 (c), it can be seen that the widened signal is still focused at the target emission point.
In simulation example 4, a gaussian signal having a center frequency of 20MHz and a bandwidth of 3MHz was set as the transmitted low-frequency electromagnetic wave signal, and the instantaneous amplitude and frequency spectrum thereof are shown in fig. 8 (a) and 8 (e); the relative positions of the target point and the time reversal mirror are the same as in example 2, as shown in fig. 6 (b); in the simulation process, the instantaneous amplitude and the frequency spectrum of a time reversal mirror received signal are shown in (b) and (8) in fig. 8, the instantaneous amplitude and the frequency spectrum of a time reversal signal transmitted by the time reversal mirror are shown in (c) and (8) in fig. 8, and the instantaneous amplitude and the frequency spectrum of a target point received signal are shown in (d) and (h) in fig. 8; as can be seen from fig. 8 (f) and 8 (g), the signal frequency through the Watterson channel model is broadened; as a result of the simulation, that is, the spatial distribution of the electric field intensities of the received signals at the target point and its vicinity is shown in fig. 9 (d), it can be seen that the widened signal is still focused at the target emission point.
In general, by adopting the beyond-view-range time reversal focusing simulation method based on the Watterson channel model, the short-wave time reversal focusing process can be simulated; compared with the simulation method using the green function suitable for free space as the channel, the simulation method provided by the invention adopts the Watterson channel model to simulate the transmission medium of short waves, namely the ionosphere channel, so that the simulation result is more practical, and therefore, the simulation result obtained by the method provided by the invention can be used for effectively guiding the implementation and application of electromagnetic wave time reversal focusing in the scenes such as beyond-the-horizon communication, radar detection, electronic interference and the like.
Those skilled in the art will appreciate that all or part of the flow of the methods of the embodiments described above may be accomplished by way of a computer program to instruct associated hardware, where the program may be stored on a computer readable storage medium. Wherein the computer readable storage medium is a magnetic disk, an optical disk, a read-only memory or a random access memory, etc.
The present invention is not limited to the above-mentioned embodiments, and any changes or substitutions that can be easily understood by those skilled in the art within the technical scope of the present invention are intended to be included in the scope of the present invention.
Claims (10)
1. A beyond-view-range time reversal focusing simulation method based on a Watterson channel model is characterized in that the simulation process comprises the following steps:
the target point emits a low-frequency electromagnetic wave signal;
transmitting the low-frequency electromagnetic wave signal to a time reversal mirror through an ionosphere channel; the ionosphere channel adopts a Watterson channel model;
the time reversal mirror receives the low-frequency electromagnetic wave signal, performs time reversal operation on the low-frequency electromagnetic wave signal, and then transmits the low-frequency electromagnetic wave signal to the direction of the target point, and transmits the low-frequency electromagnetic wave signal through the ionosphere channel;
and acquiring the distribution of the electric field intensity of the time reversal signals received by the target point and the neighborhood thereof in space, and acquiring the focusing point of the time reversal signals according to the distribution of the electric field intensity in space.
2. The beyond-view-range time reversal focusing simulation method based on a Watterson channel model according to claim 1, wherein the low-frequency electromagnetic wave signal emitted by the target point is a low-frequency single-frequency signal or a Gaussian pulse signal.
3. The beyond-sight time reversal focusing simulation method based on the Watterson channel model as claimed in claim 2, wherein the transmission of the low-frequency electromagnetic wave signal to the time reversal mirror through the Watterson channel by simulation comprises the following steps:
multipath simulation for simulating multipath propagation of low-frequency electromagnetic waves in an ionosphere channel;
the fading simulation is used for simulating the fading of the ionosphere on the absorption characteristic of the low-frequency electromagnetic wave signal and the signal fading caused by multipath effect; the method comprises the steps of,
and the noise simulation is used for simulating the influence of noise in the ionosphere channel on the low-frequency electromagnetic wave signal.
4. The beyond-view time reversal focusing simulation method based on the Watterson channel model as set forth in claim 3, wherein the multipath simulation includes:
designing an FIR low-pass filter, and constructing a Hilbert filter by using a conversion formula of coefficients of the low-pass filter and the Hilbert filter; the original low-frequency electromagnetic wave signals are respectively input into a band-pass filter and a Hilbert filter, and an original complex signal S (t) =I (t) +jQ (t) of the original signals is generated;
setting a plurality of different time delays tau for the initial complex signal i (i=1, 2, …, l), i being the number of paths, a multipath signal S is obtained i (t i ) Wherein t is i ＝t-τ i 。
5. The method for beyond-view time reversal focusing simulation based on the Watterson channel model according to claim 4, wherein the fading simulation comprises a Doppler frequency spread simulation and a Doppler frequency shift simulation.
6. The beyond-view time reversal focusing simulation method based on the Watterson channel model as set forth in claim 5, wherein the simulation process of Doppler frequency expansion is as follows:
gaussian noise generator generationTwo paths of mutually independent Gaussian noise I 1 And Q 1 The two Gaussian signals II and QQ are output through a Gaussian FIR low-pass filter and an interpolation FIR filter respectively, and the formed complex signal is G (t) =II+ jQQ;
the input signal before Doppler frequency expansion is S i (t i )＝I i (t i )+jQ i (t i ) Complex multiplication is performed with complex signal G (t) to obtain complex output signal S' i (t i )＝I′ i +jQ′ i The real part and the imaginary part are respectively:
wherein,θ is the phase of the initial complex signal S (t) =i (t) +jq (t), a is the amplitude of the initial complex signal; f (f) 0 A center frequency that is the passband of the low pass filter; the Doppler frequency spread signal is S' i (t i )＝I′ i +jQ′ i ，(i＝1,2,…,l)。
7. The method for simulating beyond-view time reversal focusing based on Watterson channel model as set forth in claim 6, wherein the Doppler shift simulation process is as follows:
generating two paths of frequencies f d Is respectively:
I d ＝cos(f d t),Q d ＝sin(f d t)
wherein f d Is Doppler shift; two orthogonal signals form complex signal s d (t)＝I d +jQ d ；
Doppler will beSpread signal S i ′(t i ) And complex signal s d (t) multiplying to obtain Doppler frequency shifted signal
8. The beyond-view time reversal focusing simulation method based on the Watterson channel model as set forth in claim 7, wherein the noise simulation process is as follows:
each path of signal after Doppler frequency shift simulationi=1, 2, …, l to obtain the addition signal;
generating Gaussian white noise, and inputting the Gaussian white noise into a band-pass filter to obtain noise required to be added into a signal;
multiplying the sum signal and noise with root mean square of the signal and noise respectively to obtain gain or attenuated sum signal and noise; adding the added signal after gain or attenuation with noise to obtain an output signal, and completing noise simulation;
the output signal is the electromagnetic wave signal output by the Watterson channel.
9. The beyond-view time reversal focusing simulation method based on the Watterson channel model as set forth in claim 4, wherein the conversion formula of the low-pass filter and the Hilbert filter coefficients is:
wherein h is IBP (n) and h QBP (n) are respectively Hilbert filter I-path sumsCoefficient of Q path, h LP (n) is the coefficient of the n-order finite impulse response low-pass filter, f 0 The center frequency of the passband of the filter is T is the sampling period and N is the order of the Hilbert filter.
10. The Watterson channel model-based beyond-view time reversal focusing simulation method of claim 8, wherein root mean square of the signal and noise are both calculated by:
wherein x is j Values representing all the samples of the signal or noise, N representing the number of samples of the signal or noise.
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