RU2518443C2 - Composite optimum filtering method for detection of weak signals - Google Patents

Abstract

FIELD: radio engineering, communication.

SUBSTANCE: disclosed method of processing information based on a method for composite optimum filtration of a weak signal of a space radar system relates to radio engineering. In the first version of the disclosed method, a reference signal used for the convolution process in an optimum filter includes an additive which compensates for Doppler distortion of the frequency of the space radio link, wherein the compensating additive is a nonlinear function of time. The second version of the disclosed method involves filtering an input signal with noise in a matched filter with coherent signal accumulation with subsequent conversion in a detector with non-coherent additive accumulation of correlation responses, wherein during the process of matched filtering with coherent signal accumulation, a time-nonlinear frequency additive which compensates for frequency distortion of the signal is introduced; the output correlation response of the matched filter is subjected to nonlinear conversion of the nonlinear weighting type with limitation; the signal after nonlinear weighting is converted through synchronous detection with non-coherent multiplicative accumulation of correlation responses.

EFFECT: interference suppression when detecting weak signals.

2 cl, 20 dwg, 1 tbl

Description

            Technical field

            The claimed method of processing information on the basis of the method of complex optimal filtering of a weak signal of the space radar complex (RRC) relates to the field of radio engineering.

                                             State of the art

Optimal filtering methods have long been used in radar for the selection of moving targets by speed (SDC) against a background of interference [1]. The target speed V creates a Doppler shift f _D = 2 · V / λ, where λ is the carrier wavelength in monostatic (single-position) radar and f _D = V / λ in bistatic (two-position) radar. As a prototype, the SDS system was described, described in [2].

             It is known that in space radio lines: broadcasting (Express series satellites), radio communications (Lightning, Meridian, etc.) radio navigation (GLONASS, GPS), radars (Dnepr-3U, Darial, Volga "and others), complexes of distant sounding of the ionosphere [3] there are strong frequency distortions due to changes in the electron density of the ionosphere in space and time. These frequency distortions alter the information signal generated by the transmitter or due to the scattering of the electromagnetic wave of a moving radar target. To compensate for these distortions, various types of frequency correctors are used.

             As the first analogue of the method of complex composite optimal filtering to compensate for the distortion of the Doppler signal due to the influence of the ionosphere, we selected a digital system for calculating the time-linear addition to the Doppler frequency of the satellite transmitter based on the results of measuring the total change in the frequency of the satellite transmitter in GLONASS [4].

              Received signals reflected from space targets (in radar) or emitted from satellites (in radio communications and broadcasting) have a low power level on the Earth (less than -160 dBW), which is 20 dB ÷ 60 dB lower than the input noise level of the receiver. The reception of such weak signals is usually carried out by the optimal filtering method, in which the reference (model) ground signal in the optimal receiver is known. However, simple methods of optimal (consistent) filtering for a number of reasons do not provide a high degree of interference suppression, for example, for the aforementioned reason for signal distortion in the ionosphere, a high level of unsteady and non-Gaussian noise of a satellite transmitter, undetermined movements of a satellite and a space target, and many other reasons natural and artificial origin.

However, there are complex optimal filters consisting of a series-matched matched filter with coherent signal accumulation and a filter with incoherent accumulation.

As a second analogue of the claimed method, the principle of filtering is applied using a complex filter used in GLONASS or GPS [4].

                                         SUMMARY OF THE INVENTION

                                                    Introduction

      Accurate knowledge of the frequency of the Doppler signal of a satellite transmitter in space radio communication systems is necessary for the correction of signal codes, which are however sensitive to phase and frequency distortion of the signal. In space radar systems, knowledge of the Doppler frequency of the target allows for stable tracking of the target in speed and, in addition, the transfer of reliable information about the speed of the target to the missile defense or missile defense system. In space navigation systems, accurate knowledge of the Doppler frequency of a satellite transmitter implements highly accurate calculation of the location of a GLONASS or GPS information consumer.

      Since a signal in the form of an electromagnetic wave from a satellite or from a space target moves part of the time in the ionosphere, which is an ionized and magnetized plasma that is unstable and is disturbed by solar radiation, the electromagnetic wave in this medium disperses and shifts in time, and the frequency and phase of the wave. This leads to distortion of information. As a result of theoretical and experimental studies on the remote sensing of the ionosphere from satellites and from the Earth by signals of various shapes and, in particular, by the LFM signal of a satellite transmitter, a multiple dispersion-time spreading of pulses of the probing LFM signal was detected, as well as a time delay of several microseconds during the period Microwave carrier frequency 0.1 ns ÷ 1 ns [5]. There are various ways to account for this signal distortion. One of these methods is proposed in the claimed invention.

         In order to isolate a weak signal against a background of noise, optimal convolution filters are used. In the simplest case, the AFC of the filter is a complex conjugate function of the detected signal (code). Such filters with a base of the LFM signal of the order of 30 dB theoretically provide noise suppression by 30 ÷ 40 dB. They also use more sophisticated anti-interference coding, for example, elementary Barker binary codes with a code base of about 60 dB or multi-element Costas codes with a base of about 100 dB, which provide interference suppression of up to 100 dB and higher. However, the output signal of such a filter (optimal filter response) in the form of a correlation function of the received noisy code and model code is sensitive to the obviously unknown Doppler frequency shift of the carrier signal, which is also distorted by the influence of the ionosphere. So, for example, the distortion of the parameters of the emitted signal in frequency (or the uncertainty of the model signal) reduces by 1% the degree of suppression by 10 dB, by 2% reduces the degree of suppression by 20 dB, etc., which is not acceptable in real space radio communication systems and radar. Therefore, accurate knowledge of the Doppler frequency shift and the distortion of this Doppler shift, which is used to correct codes in the decoder-discriminator in the receiver on Earth, is required. There are also methods that are insensitive to Doppler shift noise-protective coding, for example complementary codes (dual-parallel), but they have their drawbacks that are not related to the subject of this invention for the invention.

              There are nonlinear optimal filters that are less sensitive to variations in filter parameters (or distortion of the model signal), however, they have a significantly lower degree of interference suppression and are not universal, that is, their calculated parameters (according to the accepted optimality criterion) are valid only for specific signal codes in the calculated a narrow range of amplitudes, phases, and frequencies, which is not always possible in practice.

  Optimal filtering systems for space radio links widely use complex optimal filters that use a coded signal, for example, a pseudo-random sequence (PSP) of binary pulses as in the GLONASS system [4].

First, this signal code is detected in the form of a correlation response in a matched correlation filter with coherent accumulation of the convolution type with noise suppression of 35 dB. Then, many correlation responses from many bursts of SRP pulses (512 binary pulses in a packet for GLONASS or 1028 for GPS) are filtered by incoherent accumulation of responses in the additive adder with an additional suppression of another 10 dB; in total, the interference suppression is 45 dB or more.

Nonlinear detectors with signal limitation are known [6], in which the noise is greater than the signal is attenuated, and a weak signal is amplified on the contrary. An important property of these detectors is a 2-fold increase in the signal-to-noise ratio (SS _OUT ) at the detector output relative to the signal-to-noise ratio (SS _OUT ) at its input. In this case, the noise factor of the detector BF = (NW _IN ) / (NW _OUT ) decreases. That is, a large amplitude noise does not suppress a weak signal, as occurs in linear or quadratic detectors. This property of non-linear detectors with restriction is used in the claimed invention.

             In addition, synchronous detectors are known which are the cosine channel of complex signal quadrature detectors.

These synchronous detectors are a multiplier of the voltage of the signal channel (the cosine component of the complex input signal) and the voltage of the reference channel. These detectors are also non-linear detectors with a restriction with their inherent property described above. These synchronous detectors are also used in the claimed invention.

                              The first independent claim.

         A method of compensating for the distortion of the Doppler signal by introducing a nonlinear time-compensating additive in the reference signal of the optimal filter.

         It was experimentally found that in a space radio line created for radar targets at ranges up to 1000 km, a strong dispersion in time of the signal scattered by a space target is observed, while the Doppler frequency of a moving target is distorted due to the influence of the ionosphere. When creating the optimal filter, the Doppler frequency of the model signal is selected from the matrix of a priori specified frequencies. This model signal is used for the convolution algorithm in a matched filter. The magnitude of the Doppler frequency distortion is not known in advance due to the uncertainty of the ionosphere parameters. The determination of these parameters is an independent complex task (such as the GLONASS system) and is not considered in this application for an invention.

                       A negative effect was experimentally detected: convolution in the optimal (matched) filter of the received signal and the model signal in the form of LFM, when the Doppler frequency of the model signal is f_D =  k · t / 2, where k is the rate of linear change of the Doppler frequency due to the motion of a space object (satellite), does not give a response to the correlation function in the observed noise. Therefore, for the convolution in the optimal filter in the form of an additive (a · t²) a non-linear in time change in the frequency of the model (reference) signal f_D almost repeating the form of distortion of the Doppler signal of the space target in the form:

f_D =  k t / 2 + a t²,

where k is the rate of linear change of the Doppler chirp signal (selected for each space object in the programming process until the maximum response of a correlation function of the convolution type is obtained),

a is the coefficient of the quadratic additive in time due to the nonlinear distortion of the Doppler signal in the ionosphere (it was selected during programming to obtain the maximum response of a convolution type correlation function),

t is the current time.

A qualitative view of the frequency relationship of the Doppler chirp signal, the quadratic time additive, and the model total distorted signal is shown in the diagram of FIG. one.

In the diagram of FIG. Figure 1 shows the specific experimental result obtained in the space bistatic radar complex, where the Doppler LFM signal of a space target in the form of a satellite had a value of 1400 Hz, the time the space target moves in the detection barrier is 3 seconds. A more detailed description of the recorded data and the result of their processing are given below in the paragraph of evidence of the feasibility of this method. For the created optimal filter, the coefficient of the quadratic additive a = 30 was selected, which was selected during the programming of the optimal filter to achieve the maximum correlation response at the output of the digital optimal filter.

        In connection with the foregoing, the first independent feature of the invention on the method has the following wording.

        A method of complex optimal filtering that implements compensation for the distortion of the Doppler frequency of a space radio line, consisting in the fact that the reference signal used for the convolution process in the optimal filter contains an additive that compensates for the Doppler frequency distortion of the space radio line, characterized in that the compensating additive is a nonlinear function of time.

                                The second independent claim.

          A method of complex optimal filtering by sequential signal processing, first matched by a filter with coherent signal accumulation, and then by a filter with incoherent multiplicative signal accumulation in the form of a synchronous detector.

Due to the fact that in space radio links the signal level in the receiver on Earth is small and the increase in power of satellite transmitters is limited by the mass-dimensional parameters of the satellites, it is relevant to create optimal filtering methods with noise suppression of more than 60 dB and an error probability level of no worse than 10 ^-10 . As indicated in the introduction, the simple application of noise-protective coding of information does not give the desired result, since this coding requires accurate knowledge of the Doppler frequency shift of the satellite transmitter or the frequency of the scattered signal of a space target in radar. A vicious circle is formed: the detection and measurement of the amplitude of a weak signal on Earth in an optimal filter requires accurate knowledge of the Doppler frequency shift and distortion of this signal, for example by the ionosphere, but accurate frequency measurement requires accurate measurement of the amplitude of a weak signal, which is only possible by strongly suppressing noise, which is much higher signal amplitude. Here the uncertainty principle known in the theory of information is fulfilled, similar to the Heisenberg uncertainty principle in quantum mechanics. As is known, in order to circumvent this contradiction, the principle of multichannel optimal reception is applied [7], and synchronous and in-phase channels parallel in space and time can be created by multi-frequency channel separation or by multi-code channel separation (as in GLONASS or GPS), or both way together, i.e. multifrequency and multicode (as in high-definition space television at 3,000 or 6,000 subcarrier frequencies with two-layer anti-interference coding by orthogonal Reed-Solomon codes on each subcarrier). These methods have their advantages and disadvantages and their consideration is not included in the task of describing the invention of the method in this application.

           This application proposes an alternative method for effectively suppressing interference, based on the above-described property of non-linear detectors with the restriction of increasing the signal-to-noise ratio. The principle of operation of a complex optimal filter with this type of detector is described in detail below in the paragraph "Description of the principle of operation". The essence of the second independent paragraph on the method is as follows.

           The method of complex optimal filtering of a weak signal, which consists in the fact that the input signal with noise is filtered in a matched filter with coherent signal accumulation with subsequent conversion in a detector with incoherent additive accumulation of correlation responses, characterized in that, firstly, in the process of matched filtering with coherent signal accumulation introduces a frequency addition nonlinear in time, compensating for the frequency distortion of the signal as in the first independent claim of the invention, secondly secondly, the output correlation response of the matched filter is subjected to nonlinear transformation such as nonlinear weighting with restriction and, thirdly, the signal after nonlinear weighting is converted by the method of synchronous detection with incoherent multiplicative accumulation of correlation responses.

          Description of the method of complex optimal filtering.

          The method of complex composite optimal filtering of a weak signal is described on a specific experimentally tested example of the operation of a space bistatic complex in which this method of filtering a signal was used. This complex was a ground-space-based radar system in which a transmitter with a radiating antenna was mounted on a satellite moving in a highly elliptical orbit (HEO) or geostationary orbit (GSO), and a highly sensitive receiver with a receiving antenna was on Earth. The organization diagram of the bistatic radio link is shown in FIG. 2. The task of a space bistatic radar is to detect a diffraction (luminal) signal from a flying KO in the bistatic radar detection zone. The transillumination signal in the common 3-decibel zone of the bottom beam and the 3-decibel zone of the bottom beam forms the detection zone of the beam along its transparent beam (scattered radiation forward along the direction of propagation of the incident electromagnetic wave from the transmitter).

In FIG. 2 is designated: 1 - ground receiving antenna, 2 - space object detected in the ASC, 3 - transmitting antenna of a spacecraft (satellite on a VEO or GSO), spacecraft DN - beam pattern of the transmitting antenna of the spacecraft, NAM NA - scanning beam pattern of the receiving ground antenna Nam CO - directivity pattern diffraction scattering space object electromagnetic radiation antenna 3, CO is a passive repeater antenna radiation spacecraft, R ₁ - slant range from a terrestrial antenna 1 to CO, R ₂ - Naklo Naya distance from the CO to the antenna 3 of the spacecraft, "bistatic line" - axis in the space connecting the spacecraft antenna phase centers and the terrestrial antenna, and an ellipsoidal region about this axis defines a detection area DA space bistatic radar.

In the experiment, we used a terrestrial parabolic receiving antenna with a wavelength of the order of λ ~ 0.1 m and a diameter of D = 25 m with a radiation pattern width (BH ON) of the order of θ _pr ~ 0.3 deg and directional coefficient (Knd _pr )

KND _pr ≈ (π · D / λ) ² = 360000 = 55dB. (one)

The satellite’s space transmitting antenna in the form of a headlamp has a beam width equal to θ _lane ≈6 deg, and its corresponding directivity gain

KND _per ≈ 890 = 29 dB. (2)

The lumen width of the lumen of the light beam of the detected space object has a maximum value of θ _ka = 3 deg and a minimum value of Δθ _ka = 1 deg, then the corresponding bistatic BKND _{to the} bistatic effective scattering surface (BEPR) of the shadow diameter of this KO is

BKND _ko = 3560 ÷ 32000 = 36 dB ÷ 45 dB,

and the corresponding shadow area of KO is equal to

S _co = BKND _co · λ ² / 4π = (3560 ÷ 32000) 0.13 ² / 4π = (4.8 ÷ 43) m ² ≈ 5 m ² (the minimum detectable area of the shadow contour of the CO),

therefore BEPR (bistatic EPR) of this KO is equal to:

BEPR _co = BKND _co · S _ko , i.e.

BEPR _co = (3560 ÷ 32000) · (4.8 ÷ 43) ≈ (17100 ÷ 1380000) m ² .

          The power of the microwave radiation of the transmitting antenna is 10 watts.

          Inclined range from the ground receiver to the CO

R ₁ = 10 ⁶ m, (3)

slant range from CO to satellite satellite transmitter

R ₂ = 39 · 10 ⁶ m. (4)

According to the formula for the power minimum the display of radar received signal P _ave (when BEPR _to minimal) takes the form: S _ka ≈ 5 m ^2, P = 1 W. _Lane,

P _pr = P _per · KND _per · S _ko ² · KND _pr / [(4π) ² · R ₁ ² · R ₂ ² ] =

= 365000 · 5 ² · 890 / [4 ² · π ² · 10 ¹² · 39 ² · 10 ¹² ] ≈

≈ 3.65 · 10 ⁵ · 5 ² · 9 · 10 ² / (16 · 9.86 · 10 ¹² · 1.5 · 10 ³ · 10 ¹² ) = 0.38 · 10 ^-19 W = -194 dBW. (5)

The intrinsic thermal noise of the digital receiving path at the input of the optimal filter after the low-noise antenna amplifier (LNA) with an effective temperature T _E = 40K is

P _W = k · T _E · F = -188 dBW, (6)

where k = 1.38 · 10 ^-23 W / Hz is the Boltzmann constant,

F ~ 3000 Hz is the effective frequency band of the optimal filter tuned to pass the Doppler frequency band of the translucent chirp signal when a space object passes through the detection area of a space bistatic radar. Comparing P _GW and P _ol , it is clear that the minimum signal is 6 dB lower than the thermal noise of the digital receiving path, but when experimenting with a specific satellite transmitter, it turned out that at the input of the LNA the microwave transmitter noise is another 24 dB more than the above thermal noise, so that the total noise exceeded the transparency signal from the CO by 30 dB, that is, the signal-to-noise ratio = -30 dB. Therefore, to ensure the signal-to-noise ratio = +20 dB with an error probability of no worse than 10 ^-11, it is necessary to suppress noise by 50 dB, which is solved by the method of complex optimal filtering. A diagram of a general optimal filtering method is shown in FIG. 3.

According to the theory of optimal signal processing [7], the probability of correct detection is determined by the value of the signal-to-noise ratio at the output of the optimal receiver or the optimal filter as applied to the created system for measuring the transmission signal. This ratio is calculated by the formula:

NW _OUT = NW _IN · T / t _CORR ,

where indicated

NW _OUTPUT = P ^OUTPUT / P _W ^OUTPUT - the ratio of the power P ^{OUT of the} output signal of the optimal filter to the power P _W ^{OUT of the} output noise of the optimal filter,

NW _IN = P ^IN / P _W ^IN - the ratio of the power P ^IN input signal at the input of the optimal filter to the power P _W ^IN input noise of the optimal filter,

T is the accumulation time of the input signal or the pulse duration of the Doppler translucent chirp LFM signal equal to the time of flight of the QoS of the bistatic detection zone,

t _CORR - correlation time of the output filter noise,

or the ratio indicated is

NW _OUT = NW _IN · T · Δf _D , (7)

Where

T · Δf _D - compression ratio or base signal of the optimal filter,

Δf _D = 2 · f _D = 1 / t _CORR is the band of change of the Doppler frequency f _{D of the} translucent chirp signal

Schematically, the action of the optimal filter by signal is shown in FIG. 3. The diagram shows the fact that, according to the formula of the radar range of bistatic radar, the maximum range R _{1 is} achieved with a minimum (threshold) input power P ^BX _{MIN of the} optimal receiver or optimal filter. This formula has the form

(R ₁ · R ₂ ) ² = P _PER · K _PER · S _KO ² · K _PR / (16π ² · P ^IN _MIN )

or taking into account (7) P ^IN _MIN = NW _OUT · P _W ^IN / (T · f _D ) this range formula takes the standard form:

     (R_oneR₂)²= P_PER·TO_PERS_KO ²·TO_ETC(T_D) / (16π²· USA_OUT· P_W ^VX),

where the values specified in the experiment are denoted as

R ₁ - slant range along the line "antenna KP-KO",

R ₂ - the slant range along the line "KO-antenna KA"

P _PER - transmitter power of the spacecraft,

K _PER is the gain of the transmitting antenna of the spacecraft,

S _KO - the area of the shadow contour KO,

To _PR - gain of the receiving antenna of the KP.

The objective of the optimal filter is twofold: to ensure the reception of a small input threshold power P ^IN _MIN to achieve long range and to provide the required high output signal-to-noise ratio NW _OUT to obtain a high probability of detection or a minimum probability of a reception error. This problem is solved by setting the accumulation time T of the input LFM signal and the Doppler frequency band Δf _{D of the} compressed filter output signal, and the value 1 / Δf _D determines the correlation time of the filter output noise. Since the energy of the signal at the input and output of the filter is the same (by the definition of the optimal filter) and the noise power also does not change, a high level of output power is provided by the redistribution of the energy of the signal at the output to a short pulse of the order of t _CORR ~ 1 / Δf _D in a wide frequency band Δf _D with a compression coefficient K _SJ = T · Δf _D , which is included in the numerator of the radar range formula of the above standard form.

Under the conditions of the described experiments, the values of the ranges R ₁ , R ₂ and the parameters T and Δf _D are set by the forecast of the flight of the detected COs, therefore, the maximum attainable value of SS _{OUT is} uniquely determined by the formula for the probability of error (BO) of the detection of COs from the input noise power level P _Ш measured in the experiment ^VX taking into account the method of modulation (coding) of the received signal, in this case, Doppler linear-frequency modulation of the luminal signal:

VO = Ф (СШ _ОТ ), where Ф is the normalized error probability integral.

Thus, the parameters of the synthesized optimal filter uniquely determine the possibility of detecting various QoS of different area of the shadow contour with a given probability of detection error.

The block diagram of the algorithm of the implemented complex optimal filter is shown in FIG. four.

          As a coherent storage device, the matched filter described above was used with compensation of the ionosphere distortion of the Doppler frequency of KOs by introducing an a t² to the model chirp signal f_D =  k · t / 2 (see Fig. 4), and the synchronous quadrature detector of the complex output signal of the coherent (matched) filter was used as a multiplicative incoherent drive. Moreover, in the computer algorithm of the detector, the current output signal U was supplied to the first signal input of the detector_out coherent storage (filter correlation response) with nonlinear weighting in the form of a tenth root of U_out ^0.1 using a weighing filter (see Fig. 4). All previous multiplicatively accumulated output complex signals of this incoherent storage ring were supplied to the second reference input of the detector in all previous shifts of the input window of the matched filter (coherent storage) with a convolution time of T = 6 sec, which was equal to the CO flight time over the radar detection area. Voltage U_out ^SD at the output of an incoherent multiplicative storage device (synchronous detector) at the N-step of accumulation is equal to the iterative product (in the feedback circuit)

(U _output ^LED ) _N = (U _output ^0.1 ) _N · [(U _output ^0.1 ) _N-1 · (U _output ^LED ) _N-1 ] · cos (Δφ _{N, N-1} ),

where the phase difference Δφ_{N, N-1}≈0 and cos (Δφ_{N, N-1}) ≈1 for two  sequential complex correlation responses (U_out ^0.1)_N  and (U_out ^0.1)_N-1, since the phases of the complex correlation functions of the matched filter do not change according to the fundamental property of these filters, and the initial value of the product [(U_out ^0.1)₀(U_out ^SD)_about] = 1 by the definition of multiplicative accumulation. It is important to note that the functional form of the nonlinear weighting filter is not fundamental, if only it would be a function with a signal limitation, for example arctg (U) or another similar, not even an analytic function.

           The resulting signal-to-noise ratio of the detector increased by more than 20 dB. A program for processing recorded information by the method of a complex optimal filter is given in APPENDIX A and is implemented in the MATLAB language by the WinradHD_ARIANE_sinhronDETEC.m file.

Proof of the feasibility of the method of complex optimal filtering.

         In order to prove the feasibility of the principle of operation of a space radar, a bistatic radar complex was created with antennas, transmitters, receivers and digital signal processing, the parameters of which are described above. The operation of the information processing system has proved the feasibility of the method proposed in the application for a complex optimal filtering of the luminal signal of KO flying through the bistatic detection area.

Numerous experiments were carried out to configure various optimal filters and study their functioning to detect the lumen signal. A series of final control experiments were conducted with typical QoSs with a large shadow contour area of about 20 m ² , with an average shadow contour area of about 6 m ² and CO with a small area shadow contour no more than 3 m ³ . These space objects are listed in table 1.

              In this section, in order to reduce the number of demonstration materials for comparison, typical examples of CRs with the largest shadow area of the ARIANE-5 upper stage and CRs with the smallest shadow area such as the NOAA-3 geophysical satellite are presented, which convincingly prove the feasibility of the method.

Experimental conditions : radiation pattern of the receiving antenna - tracking a narrow beam with a width of about 0.3 ⁰ , recorder - measuring radio receiver from the analog-to-digital complex with ADC at an intermediate frequency of 249 MHz based on the monitoring digital radio receiver Rs-Rus.

The order of the experiment : first, the tracking mode of the ground antenna is selected according to the forecast of the CO, then, with the monitoring radio receiver turned off from the antenna LNA, the noise level of this radio receiver is measured from its output by the spectrogram and by the "waterfall conversion" on the computer screen using the Winrad program. Then, the signal from the LNA output is fed to the input of the measuring radio receiver and the total noise of the LNA and the Rs-Rus receiver is recorded, and then the diffraction signal from the QoS span is recorded.

The results of measurements of the noise floor of the Rs-Rus receiver are shown in FIG. 5.

In FIG. Figure 5 shows that the noise floor of the Rs-Rus receiver is -140 dBW in the 40 kHz band, taking into account its noise factor of 6 dB. The gain of this measuring radio was set to 1. After connecting this radio to the LNA output, the total direct and translucent signal was measured by UDN, when it should appear in accordance with the forecast.

Signal recording from the overclocking block ARIANE-5.

           At the moment of passage of the CO and the axis of the ground antenna of the ground antenna accompanying it through the maximum of the antenna bottom of the KA transmitter antenna (axis KP-KA antenna), the maximum response is observed in the “waterfall diagram” in FIG. 6 and the spectrogram in FIG. 7.

In FIG. 6 and 7, a direct signal is detected (the transmission signal is not visible in the noise) near the carrier frequency f = 249011 kHz of the spacecraft transmitter with a slowly varying satellite Doppler addition of about 2 Hz / s. It is noteworthy that at the moment of passage of the axis “antenna KP-KA antenna”, a maximum of a direct signal is observed at a level of -50 dBW at a frequency of 249011 kHz and interference radiation at side frequencies of 249011 ± 2.3 kHz with a local maximum of power at a level of -91 dBW That is, the excess of the direct signal over the interference is not more than 41 dB. It should be noted an important fact that the band of the Doppler signal is predicted to be Δf _D = 2880 Hz (the deviation of this frequency f _D = ± 1440 Hz), therefore, the interfering signal does not interfere with the detection of QoS in the indicated frequency band smaller than the frequency band of the interference, in addition , in the process of optimal processing, the spectrum of the interfering signal will be additionally subtracted programmatically from the total signal (interference + translucent signal).

         A periodic change in the signal amplitude by 2–3 dB with a period of 10–12 sec is observed, apparently due to the known extremely low-frequency (ELF) and ultra-low-frequency (ULF) oscillations of the ionosphere permeability, such oscillations are traced on all recorded files.

            In accordance with the forecast, the time of flight of the CO detection barrier is 5 seconds. The height of the spacecraft is 768 km and is almost equal to the inclined range of the spacecraft, since the height of the spacecraft is almost 84 degrees.

Remarks: The transmission signal for the shadow contour area of about 24 m ² theoretically has a power level on the ground antenna of -185 dBW, and a direct signal is -108 dBW. Therefore, the theoretical direct signal / lumen signal ratio is 77 dB. After amplification by 70 dB, the experimentally observed direct signal is -50 dBW (-38 dBW-12 dBW), taking into account the total noise factor of 12 dB (LNA, PCB, Rs-Rus receiver), the transparency signal is at the level of -120 dBW. Since the experimentally observed noise level is -110 dBW, the translucent signal is theoretically lower than the noise level by 10 dB.

             Analysis of the results for this QoS and all subsequent QoS was carried out after the optimal processing of the recorded signal. The algorithm for processing and selecting filter parameters is the same for all QoS.

Analysis of the signal parameters of an unstabilized KO type acceleration block ARIANE-5

     After optimal processing in an optimal filter with a quadratic additive coefficient a = 30, a correlation response function was obtained when flying KO near the axis “KP antenna-KA antenna” with the maximum amplitude shown in FIG. 8. Processing was carried out in the frequency domain using the FFT at Nz = 32768 points in the window of time T = 6 sec (according to the forecast, the time of flight of the main lobe of the luminous signal is 5 sec), the window was shifted through Nz / 16 = 2048 points or time T / 16 = 0.375 seconds to search for the maximum signal. The entire recording file for 4 min with a volume of 20 MV was preliminarily scanned visually to search in time for the section with the maximum direct signal at the position of the QO near the axis “antenna KP-antenna of the SC” in the region of 28 seconds with a deviation of ± 14 seconds relative to the maximum signal. Then the file was divided into 10 files of 2 MB each and a file was selected containing the found area with the maximum direct signal in time. This time coincided with an accuracy of ± 1 s with the predicted time spent by the QoS in the detection barrier. Then this file was subjected to optimal processing.

                 In FIG. Figure 8 shows the graphs of the signals at the position of the KO before approaching the axis "antenna KP-KA antenna".

In the lower graph of FIG. Figure 8 shows the maximum amplitude of the response of the translucent signal 14 ÷ 15 dB above the noise in the form of a correlation function at a time mark of 0.6 seconds from the end of the span of the spacecraft for 6 seconds. The fine structure of the luminal signal is visible during diffraction by a QoS. The middle figure shows the spectrogram of the filter output signal, and its frequency response is shown in FIG. 11, which does not match the standard frequency response of the Doppler LFM filter. In the upper FIG. Figure 8 shows a graph of the line of a noisy translucent signal at the output of the Rs-Rus receiver visually filled with solid red in the 40 kHz frequency band. The blue line shows the nonlinear frequency modulated model signal, and its frequency response is shown in FIG. 11. In FIG. Figure 9 shows the same lines as in Figure 2.36, but for the case where the center of the window, and, therefore, the QoS, is located on the axis "KP-SC antenna".

It can be seen from this figure that when the QoS position is on this axis, the Doppler frequency shift of the QoS relative to the Doppler frequencies of the SC is equal to the predicted zero and there is no correlation response.

In FIG. 10 the same graphs are shown, but after the passage of the KO axis of the KP-KA antenna, the shape of the correlation function does not coincide with its shape before approaching this axis (see Fig. 8), which indicates the asymmetry of the shadow contour of the spacecraft. The maximum response is 14 dB above the noise.

               In FIG. 11 it can be seen that the frequency response of the filter is fundamentally different from the frequency response of the optimal filter with a model LFM signal. It is this frequency response that is involved in the formation of a convolution with a noisy luminal signal when using FFT.

              To investigate the possibility of earlier detection of CO

outside the region of T = 6 sec (according to the forecast of T = 5 sec), that is, outside the main lobe of the transillumination signal, a convolution was performed from a time of -14 s until the position of the QO on the axis "KP-KA antenna". The result of the convolution is shown in FIG. 12. On the upper part of this figure, the entire received signal for 28 seconds is shown in red, the same as in FIG. 6 - 8. However, according to the program, the model signal (black graph) is shifted along the received signal graph in steps of Nz / 16, so the response of the optimal filter (the correlation function is the blue graph) is shifted synchronously along this received signal. In the lower part of FIG. 12 shows on an enlarged scale a graph of the response of the filter, where it can be seen that the response exceeds the average noise level by 5 dB. The maximum response value of 14 dB is achieved near the axis "antenna KP-KA antenna", as shown in FIG. 13. When the processing window (and QoS) is positioned on the axis “antenna KP-KA antenna”, there is no response, as can be seen in FIG. 14 similarly to FIG. 9. With the location of the QoS at the end of the interval of 28 sec (with a deviation of +14 sec relative to the axis “antenna KP-KA antenna”), a response graph is obtained in FIG. 15, where it can be seen that it is 5 dB above the noise level. Thus, the reception of the translucent signal is possible on asymmetric side lobes with a signal excess of 5 dB with an error probability of no more than 10 ^-2 . It should be recalled that the graph amplitudes are normalized to a level of 20 dB relative to 0 dB - the average noise level, although the direct signal power level (red line) is 80 dB higher than the transparency signal power (blue line). And the luminal signal itself is below the noise level with a mark of "0 dB" by 20 dB.

         It is important to note that in all FIGS. 8–15, the ELF and ULF oscillations in the amplitude of the received signal with a period of 10–12 sec are noticeable, apparently due to a change in the permeability of the ionosphere. These oscillations do not correlate with a change in the luminal signal in the frequency band up to 3000 Hz. In addition, these oscillations are suppressed by the zero-Doppler frequency rejection filter before the optimal filter; therefore, these oscillations do not affect the final filtering result.

          In the main lobe of the transmissive signal, in the time interval of 6 sec (± 3 sec), the response is constant and equal to 14 dB above the noise level, with the exception of the region near the axis “antenna KP-KA antenna” with a beam width of a ground antenna with a width of 0.3 degrees and a duration of the order of 0 , 3 sec. The nature of the change in response maximum over a period of 28 seconds is shown in the upper part of FIG. 15 dotted black line. This type of curve corresponds to the angular movement of the beam of the ground antenna precisely along the asymmetric multi-leaf beam of the translucent beam. The fine structure of the response graph is determined by the shadow profile of the QoS and can serve as an identifier of the type of QoS.

          The maximum response of the optimal filter is calculated using the formula for the signal-to-noise ratio of the undistorted Doppler chirp signal:

signal / noise _output = signal / noise input _* Δf _D * T.

In relation to the overclocking block ARIANE-5 input

signal / noise ratio _in = -10 dB (see. Note)

Δf_D = 2880 Hz (the predicted value coincided with the selected value in the filter program),

T = 5 s (predicted value),

Δf _D * T = 2880 · 5 = 42 dB compression ratio or base of undistorted Doppler chirp signal.

Theoretically, the limit value of the output signal-to-noise ratio for this signal is

signal to noise_out ^theor = -10 dB + 42 dB = 32 dB.

In a computer experiment, a displacement coefficient along the frequency axis b = ω _max = 2π · f _D , a quadratic additive coefficient a = 30 for a nonlinear frequency modulated signal was selected. The maximum value of the response above the noise is taken from the graph in FIG. 8 or FIG. 10 and the response value matches the signal / noise ratio _O ^ex = 14 dB, which is 18 dB less than the theoretically attainable values for the undistorted chirp signal. This indicates a lesser degree of compression of the response of the correlation function of the nonlinear frequency modulated signal than the chirp signal. That is, after passing through the ionosphere, the transparency LFM signal is distorted towards a decrease in its compression, it is highly dispersively diffused for 1 s to a value of T = 6 s, which is a programmatically selected duration of the model FM signal instead of T = 5 s according to the forecast. The fact of dispersion spreading of the LFM signal is confirmed theoretically and experimentally when monitoring the ionosphere by probing the transmitter of the geostationary satellite with its LFM signal.

               Using a more sophisticated optimal filter with coherent and incoherent signal accumulation, a theoretical limit response of 33dB was achieved (with an allowable error of ± 1 dB of the model). The matched filter described above was used as a coherent drive, and the synchronous quadrature detector of the complex output signal of a coherent (matched) filter was used as a multiplicative incoherent drive.

         The resulting detector output modulo increased by more than 10 dB, as shown in FIG.

            It is noteworthy that the graph of the correlation function of the response of the described complex optimal filter more clearly and with high resolution displayed the structure of the shadow profile of the QoS, which is important for the accurate identification of the QoS.

CONCLUSIONS on the analysis of the recording results for the ARIANE-5 block.

1) It was established that the luminal LFM-signal is distorted, dispersively spreading for 1 s in duration with respect to the predicted value of 5 s equal to the duration of the LFM signal corresponding to the predicted time of flight of the QO over the detection zone.

2) It was found that using a complex optimal filter, a correlation response was obtained for a transmissive distorted FM signal above the noise by 32 dB, which corresponds to a theoretically achievable value.

3) It was established by selection in the program (upon reaching the maximum response of the correlation function) that the frequency band is 2880 Hz and deviation

frequency ± 1440 Hz of the FM signal corresponds to the predicted value.

4) It was established by selecting in the program (upon reaching the maximum response of the correlation function) that the coefficient of the quadratic additive a = 30.

5) It was found that a change in the given parameters by only 10% in either direction results in the disappearance of the response in noise, which indicates an undesirable high parametric sensitivity of the synthesized complex optimal filter.

6) It was established that the side lobes of the transmissive signal are observed, exceeding the noise by 5 dB before the approach to the detection zone 14 seconds before the maximum response near the axis "antenna KP-satellite antenna" and after the passage of this zone after 14 seconds. In this case, the shape of the side lobes corresponds to the movement and position of the TO body relative to the axis of the lumen beam, which is important for determining possible TO maneuvers.

7) A fine structure of the luminal signal corresponding to the profile of the shadow contour of the QoS has been established, which is important for identifying the QoS.

8) The absence of false targets (LC) in the observation band over the entire observation interval of 28 seconds, taking into account the side lobes and in the main lobe of the luminous ray during the flight time of 6 seconds, was established. Such an appearance of LCs is impossible precisely in gates in time, in space (in angle), according to the parameters of a model FM signal (Doppler frequency, rate of change of this frequency, coefficient of quadratic additive, signal amplitude) selected with an accuracy of 10%, and for all of the listed QoS recorded at different times for different points in space with their own selected parameters of the model FM signal.

To prove the feasibility of the method of complex composite filtering of very weak signals near the level of -200 dBW, an experiment was conducted with the detection of a satellite of the smallest area of the shadow contour, that is, an extremely small translucent signal. The results of signal recording and analysis are given below.

Signal recording from a stabilized satellite of a very small area of the shadow contour NOAA-3.

            In FIG. 17 for the NOAA-3 satellite, the record of the “waterfall transformation” signal is shown at the top, and the spectrogram of this signal at the bottom. It can be seen from the spectrogram that the average level of total noise is -110 dBW in the 40 kHz band.

At the moment of passage of the CO and the axis axis of the ground antenna accompanying it through the maximum of the antenna of the spacecraft transmitter antenna (axis antenna of the KP-antenna of the spacecraft), the maximum direct signal response is observed in the "waterfall diagram" in FIG. 17 at the level of -70 dBW, this signal is very time-spread for 30 seconds due to its strong dispersion in the ionosphere. No interference at lateral frequencies is observed, as the signal is deeply drowned in noise. According to the forecast, the Doppler signal band is Δf _D = 2170 Hz (deviation of this frequency f _D = 1085 ÷ -1085 Hz), the time of flight of the CO detection barrier is 8.1 seconds. Altitude (slant range) KO equal to 1524 km.

Remarks: The light signal for the area of the shadow contour of the order of 1 m ² theoretically has a level of -198 dBW, and the direct signal is -108 dBW. The difference between the direct and transparent signal is 90 dB. After amplification in the LNA by 70 dB, the experimentally observed direct signal is -70 dBW, then the transmission signal is at the level of -160 dBW. Since the experimentally observed noise level is -110 dBW, the translucent signal is theoretically lower than the noise level by 50 dB.

Signal analysis of a stabilized QoS type satellite signal of a very small area of the shadow contour NOAA-3

                     After optimal processing in a simple optimal filter, the function of the correlation response was calculated during the passage of the QoS near the axis “antenna KP-antenna of the SC” in the region of the second side lobe of the transillumination signal 15 seconds before approaching this axis, this correlation signal is shown in the middle graph of FIG. 18, but the maximum response is unobservable in noise. Moreover, in this average graph of FIG. 18 shows the result of processing only with the help of a simple optimal filter, but with the selected parameters of the distorted translucent FM signal.

The predicted value of the flight time T = 8.1 sec is equal to the time of flight of the main lobe of the lumen of the translucent beam,

Doppler frequency deviation f _D = ± 1085 Hz,

frequency band Δf _D = 2170 Hz,

compression ratio or base of a linearly frequency modulated signal

Δf _D * T = 2786 * 8 = 42 dB.

The selected displacement coefficient along the frequency axis b = ω _max = 2π · f _D. The selected coefficient of the time quadratic in time addition to the model Doppler LFM frequency is equal to a = 10.

In the middle graph of FIG. 18 shows that at each moment of counting and calculating the correlation response of this response in noise is not visible. The bottom graph shows the result of processing using a complex optimal filter with a synchronous detector. The output values of the matched filter were supplied to the first input of the synthesized synchronous detector with a nonlinear weight in the form of a fractional degree of the output signal U of the matched filter U ^0.1 . From the bottom graph of FIG. Figure 18 shows that the correlation response accumulated over 186 responses increases to 20 dB above noise. In the graph of FIG. 19 shows the result of the accumulation of 371 responses, where the response increases to 40 dB above the noise. In FIG. 20 shows the result of the accumulation of 724 responses, where the response of a complex optimal filter increases to 70 dB above noise. In all these cases, the observation window is ~ 30 sec, but the shift step of the convolution window lasts 8 sec, the number of points for the FFT is Nz = 32,768. The shift steps are chosen to be equal to Nz / 8, Nz / 16, Nz / 32. It is important to note that in the observation window ~ 30 sec the signal is measured from many side lobes of the lumen of the translucent beam (at least 4 side lobes in an angle of no more than 20 degrees).

Since the transmission signal is theoretically lower than the noise level by 50 dB (see Note ), the theoretical limit value of the output signal-to-noise ratio for an undistorted LFM signal is

signal to noise_out ^theor = -50 dB + 42 dB = -8 dB.

This suggests that, theoretically, we do not observe a response with a classical optimal filter, which was observed in the experiment, only the use of a complex composite optimal filter made it possible to detect a weak transparency signal in the form of a large multiplicatively accumulated response.

CONCLUSIONS on the analysis of the results of recording the signals of a stabilized satellite of a very small area of 1.3 m ² shadow circuit type NOAA-3.

It is reliably impossible to detect a satellite with such a small area of the shadow contour using a simple optimal filter, however, using a complex optical filter, the QoS transparency signal is detected with a signal-to-noise ratio of more than 20 dB and an error probability of 10 ^-10 . This experiment convincingly proves the possibility of observing KO sizes and the feasibility of the method of complex composite optimal filtering of weak signals.

CONCLUSION

       The above experimental studies convincingly showed the principal feasibility of the method of complex composite optimal filtering of weak signals claimed in the invention. This method can be used in terrestrial and space complexes of radio communications, broadcasting, radar, radio navigation, radio direction finding, radio astronomy, as well as for remote monitoring of the ocean, atmosphere, ionosphere and subsurface layer of the Earth.

LIST OF DRAWINGS

FIG. 1 - Qualitative frequency arrangement.

FIG. 2 - Organization chart of a bistatic radio link.

FIG. 3 - Scheme of the general method of optimal filtration, which shows a compression coefficient equal to T · Δf _D = 50 dB.

FIG. 4 - Block diagram of the algorithm of complex optimal filtering with coherent and incoherent signal accumulation.

FIG. 5 - Result of recording own noise of the monitoring radio receiver Rs-Rus.

FIG. 6 - “Waterfall diagram” for recording the total and transparent signal of the ARIANE-5 satellite.

FIG. 7 - Spectrogram for recording the total and transparent signal of the ARIANE-5 satellite.

FIG. 8 - Graphs of signals before the approach of the spacecraft to the axis "antenna KP-KA antenna".

Figure 9 - Graphs of signals in the case of the location of the TO on the axis of the "antenna KP-antenna KA", at the time of zero clearance signal.

FIG. 10 - Signal graphs in the case of the location of the KO after the passage of the axis "antenna KP-KA antenna".

FIG. 11 is a graph of the frequency response of the optimal filter with a quadratic time addition to the frequency of the model LFM filter signal.

FIG. 12 - Signal graphs with the position of the QO at the beginning of the observation window lasting 28 seconds.

FIG. 13 - Graphs of signals when the QO is located at the maximum of the lumen signal near the axis "antenna KP-KA antenna".

FIG. 14 - Graphs of signals when the QoS is located on the axis "antenna KP-KA antenna" at the zero of the translucent signal.

FIG. 15 - Signal plots at the position of the QoS at the end of the observation window lasting 28 seconds.

FIG. 16 - Graphs of the result of a complex optimal filter.

FIG. 17 - Recording graphs of the total direct and transparent signal during the passage of a stabilized satellite NOAA-3.

FIG. 18 - The result of the accumulation of 186 responses matched filter in an incoherent multiplicative drive.

FIG. 19 - The result of the accumulation of 371 matched filter responses in an incoherent multiplicative accumulator.

FIG. 20 - The result of the accumulation of 724 responses matched filter in an incoherent multiplicative drive.

Table 1

Title
KO Type of
KO Shadow
area
KO Height
KO CO flight time Doppler frequency deviation ARIANE-5 overclocking.
block 24 m ²     767 km 5 sec 1440 ÷ -1440 Hz SL-14 (1) overclocking.
block 5.72 m ² 1419 km 7 sec 1436 ÷ -460 Hz IRS-1 satellite 6 m ² 916 km 7 sec 1434 ÷ -1434 Hz Cosmos
2451 satellite 2 m ² 1522 km 5 sec   656 ÷ -646 Hz Cosmos-198 satellite 3 m ² 947 km 6.8 sec 1393 ÷ -1393 Hz NOAA-3 satellite 1.3 m ² 1524 km 8.1 sec 1085 ÷ -1085 Hz      SL-14 (2) overclocking.
block 5.72 m ² 1570 km 12 sec 1440 ÷ -1440 Hz H-2a overclocking.
block 24 m ² 606 km 3 sec 1100 ÷ -1100 Hz      ERS-1 satellite 12 m ² 807 km 5.5 sec 1400 ÷ -1400 Hz Cosmos-2297 satellite 3 m ² 872 km 6.3 sec 1430 ÷ -1430 Hz

Correction of the list of sources used.

1. Reference radar. Editor M. Skolnik. M .: "Soviet Radio". T.3. 1976. P.339

2. P.A. Bakulev, V.M. Stepin. Methods and devices for moving targets selection. M .: Radio and communication. 1986. P.117

3. Proceedings of the Institute of Applied Geophysics named after Academician E.K. Fedorova, issue 87 Radiosounding of the ionosphere by satellite ground-based radio probes. M .: IPG them. Academician E.K. Fedorov. 2008.P.14.

4. I. B. Vlasov. Global navigation satellite systems. M .: "Rudomino". 2010. S. 93-100.

5. P. B. Petrenko, A. M. Bonch-Bruevich. Modeling and estimation of ionospheric broadband radio signals in location and communication // Issues of information protection. 2007, No.3, S.24-29

6. I.S. Gonorovsky. Radio circuits and signals. M .: "Soviet Radio". 1972. S. 344-346.

7. A.A. Kharkevich. Fighting interference. M .: "Science". 1965. S. 61, S. 78.

Claims (2)

1. The method of complex optimal filtering of a weak signal of a space radio link, consisting in the fact that the reference signal used for the convolution process in the optimal filter contains an additive that compensates for the Doppler distortion of the frequency of the space radio line, characterized in that the compensation additive is a predetermined nonlinear time the change in the frequency of the model (reference) signal f _d , almost repeating the form of distortion of the Doppler signal of a space target in the form:
f _d = k · t / 2 + a · t ² ,
where k is the rate of linear change of the Doppler chirp signal (selected for each space object in the programming process until the maximum response of the convolution-type correlation function is obtained),
a is the coefficient of the quadratic additive in time due to nonlinear distortion of the Doppler signal in the ionosphere (it was selected during programming to obtain the maximum response of a convolution-type correlation function),
t is the current time. 2. The method of complex optimal filtering of a weak signal, which consists in the fact that the input signal is filtered with noise in a matched filter with coherent signal accumulation, followed by conversion in a detector with incoherent additive accumulation of correlation responses, characterized in that in the process of matched filtering with coherent signal accumulation a frequency addition is introduced to compensate for the frequency distortion of the space radio line, which is a predetermined non-linear in time measurement nenie frequency model (reference) signal f _d, almost repeating the shape distortion of the Doppler signal in a target space:
f _d = k · t / 2 + a · t ² ,
where k is the rate of linear change of the Doppler chirp signal (selected for each space object in the programming process until the maximum response of the convolution-type correlation function is obtained),
a is the coefficient of the quadratic additive in time due to nonlinear distortion of the Doppler signal in the ionosphere (it was selected during programming to obtain the maximum response of a convolution-type correlation function),
t is the current time,
then, the output correlation response of the matched filter is subjected to nonlinear transformation of the type of nonlinear weighting with restriction, after which the signal is converted by the method of synchronous detection with multiplicative accumulation of correlation responses.

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