ISSN 0010-9525, Cosmic Research, 2018, Vol. 56, No. 3, pp. 190–198. © Pleiades Publishing, Ltd., 2018. Original Russian Text © V.D. Zakharchenko, I.G. Kovalenko, O.V. Pak, V.Yu. Ryzhkov, 2018, published in Kosmicheskie Issledovaniya, 2018, Vol. 56, No. 3, pp. 209–217.

Fundamental Constraints on the Coherence of Probing Signals in the Problem of Maximizing the Resolution and Range in the Stroboscopic Range of Asteroids V. D. Zakharchenkoa, *, I. G. Kovalenkoa, O. V. Pakb, and V. Yu. Ryzhkova a

Volgograd State University, Volgograd, 400062 Russia b LLC First Service, Volgograd, Russia *e-mail: [email protected] Received July 19, 2016

Abstract—The problem of coherence violation in stroboscopic ranging with a high resolution in the range due to mutual phase instability of probing and reference radio signals has been considered. It has been shown that the violation of coherence in stroboscopic ranging systems is equivalent to the action of modulating interface and leads to a decrease in the system sensitivity. Requirements have been formulated for the coherence of reference generators in the stroboscopic processing system. The results of statistical modeling have been presented. It was shown that, in the current state of technology with stability of the frequencies of the reference generators, the achieved coherence is sufficient to probe asteroids with superresolving signals in the range of up to 70 million kilometers. In this case, the dispersion of the signal in cosmic plasma limits the value of the linear resolution of the asteroid details at this range by the value of ~2.7 m. Comparison with the current radar resolution of asteroids has been considered, which, at the end of 2015, were ~7.5 m in the range of ~7 million kilometers. DOI: 10.1134/S0010952518030085

INTRODUCTION Radar astronomy has a number of specific features, which makes its application in the problems of studying small bodies of the solar system (asteroids, comet nuclei, and in the distant future of dwarf planets closest to the Earth), which are often preferable compared with the use of traditional astronomy (we will conditionally call it astronomy using passive methods of measurement). The disadvantage of passive ways of determining the linear dimensions of celestial bodies and their surface details is that the measurement error increases proportionally to the range to the measured object. The matter is that passive measuring systems created based on telescopes are goniometric such that the error in determining the angle leads to error in estimating the transverse linear dimensions proportionally to the range to the object under study. Moreover, passive methods for the ground-based optical telescopes are subject to dependence on the state of optical transparency and turbulence in the atmosphere. These deficiencies are deprived of active measurement methods, including the methods of the radar sounding of space, the resolution of which along the line of sight is determined by the properties of the used signals and does not depend on the range to the object.

In addition, the use of radar methods when studying celestial bodies by probing them with broadband signals in the super-resolution mode allows one to obtain additional information on the reflecting properties of objects in the third dimension (along the line of sight in depth) in the form of a radar portrait, while traditional astronomy allows one to construct only two-dimensional portraits of bodies in the picture plane. Increasing the spatial resolution of three-dimensional images of remote space objects during radar sounding from Earth is an important problem of astronomy. At present (late 2015–early 2016), the record values of the radar resolution of asteroids were ~7.5 m in the range of ~7 million kilometers [1, 5]. The factors that prevent the achievement of maximum resolution are the fundamental constraints dictated by both the physics of the processes of radiation and propagation of radio signals and by the current level of technology development, including (1) the limitations on the power of the radio signal, (2) the loss of signal coherence due to the nonideality of the equipment (instability of reference frequency generators), and (3) the dephasing of the signal, as it propagates in cosmic plasma due to dispersion. In this paper, we confine ourselves to the discussion of the second and third items, the question on the requirements for the power of

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191

R ΔR

x(t)

t

2ΔR/c Fig. 1. Formation of a radar portrait of a space object.

radio signals is important and worthy of detailed consideration in a separate publication. It should be noted that the interpretation of the concept of fundamental constraints, which we use, is determined simultaneously by physical laws and current engineering and technical capabilities; this is typical for applied science in general. For example, the diffraction limit is a fundamental physical constraint and is established by the laws of the wave nature of light; however, the specific maximum achievable angular resolution due to the diffraction limit is determined by the aperture, the choice of which reflects the currently available technological capabilities of humanity. The development of methods to increase the accuracy of determining the dimensions of asteroids is important for a correct estimate of the degree of damage that asteroids can inflict on the planet. It is known that space bodies with dimensions of less than 10 m usually do not reach the Earth’s surface, as they burn up in the atmosphere, and there are no dangers to the planet or population [3]. Bodies with dimensions of several dozen meters when burning are capable of exploding and creating serious destruction, and objects with dimensions of hundreds of meters or more lead to regional or global catastrophes. In this case, namely, bodies with dimensions of several dozen meters are the greatest danger for humanity at the characteristic time of its existence, since the probability that they will collide with Earth is higher than that of larger bodies and their average destructive action is maximized [2, 4]. Thus, the questions of estimating the dimensions of cosmic bodies crossing the Earth’s orbit are already pressing, and interest in them as technology advances and a clearer understanding of the degree of threats will only increase. For example, in [20], it has been suggested that the lower limit of the dimensions COSMIC RESEARCH

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of potentially dangerous asteroids be lowered from 140 to 50 m. At the same time, these developments can be of interest to specialists studying small bodies of the solar system from the point of view of determining their shape and the details of the relief. Radar systems that use traditional narrowband signals of long duration (0.5–1 μs or more) do not allow one to estimate the linear dimensions of space objects with the required accuracy due to insufficient resolution. This problem can be solved by using signals with high resolution in the range δr ~ c Δf ! L , where c is the speed of light, Δf is the frequency band of the signal, and L is the characteristic dimensions of the object reflecting the signal [16]. These signals make it possible to obtain a radar portrait of the object and the reflected signal x(t), provided that the resolution element in the range is significantly smaller than the linear dimensions of the target L. The corresponding dimensions of the asteroid can be determined by the duration of the radar portrait [13], which is determined by the radial dimension ΔR of the illuminated part of the object (Fig. 1). The resolution of individual elements of the asteroid surface makes it possible to study the fine structure of the surfaces of small celestial bodies, as well as to construct three-dimensional models of the studied objects. The resolution in the range required to obtain radar portraits is determined by the density of the range of the local reflection parts (brilliant points) on the object surface. Since the real space objects have a complex (fractal) surface structure, the problem of increasing the resolution is important and actual. For example, for the radial asteroid dimension of ~10–50 m, it is necessary to provide the resolution in the range δr ~ 0.5 m, which corresponds to the duration of the probing radar pulse of ~3.5 ns.

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The recording and processing of these signals presents considerable difficulties due to the wide band of occupied frequencies. However, the periodic nature of the sounding signal makes it possible to use the stroboscopic effect in radio engineering, which occurs when gating investigated signals with a sequence of window functions that have a close repetition frequency. This procedure for VHF signals can be implemented in a balanced mixer when the heterodyne pulse signal repeating the sounding signal is fed into the reference channel. STROBOSCOPIC TRANSFORMATION OF REFLECTED SIGNALS: RADIO-PULSE GATING SCHEME Stroboscopic methods of time scale conversion widely used in measuring technology allow one to record broadband signals using low-frequency equipment [17, 18]. The stroboscopic converter model consisting of a mixer that multiplies the investigated x(t) and gating a(t) signals and low-pass filter (LPF) is shown in Fig. 2a. Figure 2b illustrates the principle of stroboscopic transformation, where N

x(t ) =

∑ x (t − kT ); 0

k =0

N

a(t ) =

∑ a (t − kT ) 0

1

(1)

k =0

are the input and gating signals with the repetition period T and T1 of single signals x0(t) and a0(t), respectively; τk = k ΔT is the shift in the gating pulse a0(t) relative to x0(t) in the kth period of the input signal. In this case, the value of the coefficient of spectral transformation (signal stretching) is determined by the ratio N = T ΔT , where ΔT = T1 − T is the so-called reading step; in this case, ΔT ! T ,T1. The latter circumstance determines the high coefficient of spectral transformation N, which is usually 10 4–106. For a fairly short gating pulse a0(t), the output signal of the stroboscopic converter with an accuracy of the constant factor α and possible delay in the filter τ repeats the input signal x0(t) stretched in time by N times: y(t ) = αx0 t − τ . N Potential possibilities of stroboscopic transformation are most fully implemented in the oscillographic technique. Figure 3 shows the parameters of analog and stroboscopic oscilloscopes of some domestic and foreign companies (Tektronix, Hewlett-Packard, Iwatsu) [14]. The axes are Δf (MHz), the band, and S (mm/V), sensitivity over the screen. As seen from the figure, the corresponding product SΔf for stroboscopic instruments is higher than that of analog ones by a factor of 102–10 4. A stroboscopic transformation of the time scale of the envelope of periodic signals obtained by modulation of high-frequency oscillations of the VHF generator is performed in the so-called radio pulse gating

(

)

x(t)

~ y(t)

y(t)

(a)

F a(t) NT

(b)

T

x(t) ΔT a(t) kΔT y(t) T1 ~ y(t) t Fig. 2. Stroboscopic transformation of nanosecond pulses: (a) mathematical model of a stroboscopic converter and (b) principle of stroboscopic processing.

S, mm/V 104

C1-68

HP-140 (United States)

C1-19 C7-24

103

C8-13 C7-13

C1-159 C1-49

T-568 (United States)

C1-67

86100C DCA-J (United States)

C1-126

102

C1-31 C1-11

SAS-509B (Japan)

ACK-8064 (United States, Japan) T-7104 (United States)

10

1.0

C7-10A

1.0

10

102

103

104 105 ΔF, MHz

Fig. 3. Sensitivity and band of operating frequencies of some oscillographic devices. Circles and hollow squares show characteristics of analog and stroboscopic instruments, respectively.

scheme, where the gating signal represents the same sequence of short radio pulses with similar repetition frequencies and carriers (Fig. 4). This scheme makes it possible to increase the sensitivity of the system by carCOSMIC RESEARCH

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193

T

x(t)

(k – 2)T

t

kT

(k – 1)T kΔT

a(t) t T1 Fig. 4. Input x(t) and gating a(t) signals in the radio pulse gating scheme.

Ω

. |Sy(ω)|

Ω

–2π/T1

–Ω

0

Ω

Ω

Ω

2π/T1

Ω

Ω

4π/T1

ω

Fig. 5. Spectrum of the signal y(t) at the output of the stroboscopic mixer for Ω < π T . Filtered spectral components are marked by shading.

rying out the coherent accumulation in the narrowband filter. The VHF mixer is used when radar sounding the object as a multiplier, and the input signals are represented by the complex models N

x(t ) =

∑ A (t − kT )e

a(t ) =

∑

0

k =0 N

j ω0t

; (2)

jω t A1(t − kT1)e 1 ,

k =0

where A0(t), A1(t) are complex envelopes of the input and gating radio signal; ω0, ω1 are carrier frequencies, respectively; T and T1 are the repetition periods of radio pulses as in Eq. (1). The form of the signal spectrum at the output of the stroboscopic mixer is shown in Fig. 5. The output signal is filtered in the radio pulse gating scheme by a narrowband filter tuned to the difference frequency of the carriers Ω = ω0 − ω1, where Ω ! ω0, ω1 [6]. For a fairly short envelope of the gating radio pulse a(t ) = A1(t ) cos(ω1t ), the output signal of the radio pulse gating scheme is adequate for the input signal x(t ) = A0(t ) cos[ω0t + ϕ(t )] with a time-stretched COSMIC RESEARCH

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envelope by N times at a difference frequency of the carriers Ω as follows [8, 12]:

y(t ) ~ A0(t N ) cos [Ωt + ϕ(t N )] .

(3)

The scheme combines the principle of the operation of superheterodyne receiver (transformation to the difference frequency of carriers) and stroboscopic converter; in this case, only the envelope of nanosecond radio pulses is transformed in the time scale. Thus, provided the resolution of individual brilliant points on the asteroid surface, the envelope of the output signal of the radio pulse gating scheme will describe the radar portrait of the object on the transformed time scale. VIOLATION OF COHERENCE IN STROBOSCOPIC PROCESSING When analyzing the transformation of the time scale of broadband radio signals [8, 13], it is assumed that the carrier frequencies of the investigated and reference oscillations are completely coherent. This representation corresponds to the absence of phase instabilities in the processing system. In real devices, this condition can be violated due to the departure of frequency and

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phase of the reference generator, instability of delays in the signal propagation path and other factors. These factors limit the possibilities of coherent processing methods and lead to deterioration in the signal-to-noise ratio at the output of the stroboscopic system. Since the resulting interference is of a multiplicative nature, their level varies with the signal level and does not depend on its power. In this regard, it should be noted that increasing the power of sounding signals (including the use of complex signals) will not increase the signal-to-noise ratio, and, thus, the range of the radar system operation will be limited by the instability of the reference frequencies, regardless of its energy potential. In this regard, the estimate of the stability requirements of the reference generators of coherent stroboscopic processing systems is very important. Let us consider the influence of mutual phase instability of the carrier frequencies of the investigated and reference signals on the statistical characteristics of the transformed signal when stroboscopic processing. We will characterize the violation of coherence by the random process θ(t ), the fluctuation component of the phase difference of the received and gating radio signals, the statistical characteristics of which are assumed to be known. During analysis, we will assume that the spectral transformation coefficient N is large enough to use asymptotic estimates. In the stroboscopic processing model (Fig. 2a), when using sounding radio signals, the low-frequency filter must be replaced by tracking bandpass filter adaptively tuned to the difference frequency of carriers taking into account the Doppler shift. To accurately determine the difference frequency Ω , the radial velocity of the asteroid Vr must be measured independently by narrowband methods at the center of gravity Ω0 of the spectrum of the Doppler signal. An effective method is the method of estimating the radial velocity in real time1 using fractional differentiation of the Doppler signal [7].

Taking into account the phase instability θ(t ), complex models of the received x(t ) and reference a(t ) signals (2) will take the form N

x (t ) =

12

of half-integer order Dt

from the signal by the formula

2

2 Ω0 = Dt y(t ) y(t ) . Fractional derivative Dtα of an arbitrary order α of function y(t ) can be represented as linear inte∞ gral operator Dtα y(t ) = ∫ y(t')hα (t − t')dt'. The difference kernel −∞ of operator hα (t ) in the case of an integer order α is representable as a superposition of infinitely close delta functions. This means that integrating the signal with this impulse response equivalent to computing an integer derivative is a local procedure. In the case of fractional order α, the difference kernel of the operator is nonlocal, since it includes power functions that are different from zero on the positive semiaxis. The difference kernel of operator hα (t ) makes it possible to implement the procedure for 12

12

calculating Ω0 in the form of the filter that calculates Dt y(t ) without spectral processing as the signal reflected by the target arrives [7], which significantly reduces the processing time of y(t ) after the arrival of the signal without losing accuracy.

j[ω0t +θ(t )]

k =0 N

a(t ) =

∑ A (t − kT )e 1

; (4)

j ω1t

1

.

k =0

The value of stroboscopic sampling of the signal in the kth sounding period can be represented in the form

yk = 1 2T

(k +1)T

∫

j [Ωt +θ(t )] A (t − kT )A1*(t − kT1)e dt.

kT

We will consider θ(t ) to be a stationary random process with zero mean and correlation interval τθ that exceeds the duration of the gating signals. Let us also assume that the slow phase shifts are tracked by the stabilization system so that the correlation of neighboring reading samples {θk } can be neglected and assume that θi θk = σ2θδik , where σ2θ is the dispersion of phase fluctuations. This allows us to represent the readings yk in the form

yk ≈ e

j [ΩkT1 +θk ] T

2T

∫ A(t')A*(t' − k ΔT )dt = y

k 0e

1

j θk

,

(5)

0

where θk = θ(kT1) is a sample of the random process θ(t ), and yk 0 is the value of the stroboscopic sample (5) in the absence of phase instability in the processing system. To provide the super-resolution mode of radar portraits of asteroids [13], it is necessary to use the nanosecond signals with pulse ratio of about 103–106; therefore, the obtained approximations are completely permissible. The average value (mathematical expectation) of readings (5) of the signal obtained by averaging over the phase θk can be represented in the form Myk = yk = β yk 0,

1 The

position of the center of gravity of the signal spectrum can be expressed in terms of the Riemann–Liouville derivative [19]

∑ A(t − kT )e

where β = exp[ j θk ] = χθ(1); χθ(ν) is a characteristic function of the law of the distribution of phase fluctuations W (θk ). For a normal process with zero mean W (θk ) = N (0, σ2θ ), this value is β = exp[−0.5σ2θ ] < 1. The dispersion of readings yk under the consid2 ered assumptions will be Dyk = yk − Myk =

yk 0 (1 − β2 ) . The ratio of the dispersion to the square of the modulus of the mean value of readings 2

Dyk 1 − β2 (6) = . 2 2 β Myk has the meaning of a relative level (in terms of power) of the output interface due to phase fluctuations. This η=

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1

m=5 2

3

σθ, rad 4

5

10

0

1

195

σθ, rad m = 25 2 3 4

5 σE , dB E y0

10

15

15

20

20

25

25

σE , dB E y0

Fig. 6. Results of statistical simulation of the output signal of the stroboscopic processing system in the case of the coherence violation: σθ is rms phase noise; E y is the average value of the signal energy at the output of the stroboscopic system filter; σE is rms value of the signal energy spread at the filter output; E y0 is the value of signal energy at full coherence (σθ = 0 ); m is the number of reading steps ΔT that fit into the duration of the signal τ.

ratio can be significantly reduced by increasing the coefficient of spectral transformation N = T ΔT by reducing the reading step ΔT and using the accumulation in the digital filter system. In this case, the value of dispersion Dyk will be reduced by m times, where m is the accumulation coefficient [12]. The value m at adaptive matching of the filter with the band of the signal compressed over the spectrum asymptotically corresponds to the number of reading steps ΔT that fit into the duration of the probing signal τ x : m ~ τ x ΔT . RESULTS OF SIMULATION AND QUANTITATIVE ESTIMATES In this paper, we have performed a numerical simulation of the processing in the radio-impulse gating scheme of signal of the form A(t ) cos[(ω0 + Ω)t + θ(t )] reflected by a single brilliant point of the surface of a moving asteroid. The envelopes of the probing and gating signals A(t ) cos(ω0t ) were selected by Gaussian signals A(t ) = A0 exp[−π (t τ)2 ] with an effective duration τ determined from the condition ∞

τ = 1 A(t )dt. A0 −∞

∫

(7)

Random process θ(t ) was specified by a sequence of uncorrelated readings θk = θ(kT ) with the normal distribution W (θk ) = N (0, σ2θ ). The frequency response of COSMIC RESEARCH

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the filter was consistent with the amplitude spectrum of the stroboscopically converted signal. Since the energy of the received signal is important for problems of optimal receiving under conditions of additive interference [17], the effect of phase instability was estimated by reducing the average energy of signal 2 E y = y(t ) at the filter output of the processing system with respect to energy E y0 at full coherence (σθ = 0 ). Figure 6 shows the statistical characteristics of the output signal of the stroboscopic processing system for the accumulation coefficients m = 5 and m = 25 obtained by statistical modeling. The model parameters are as follows: Ω = 2πF ; F = 512; τ = 0.015; the number of signal readings N = 2048. On the ordinate, the value E y E y0 is plotted, which corresponds to a decrease in the energy of the output signal of the bandpass filter of the stroboscopic system when phase instability appears. The figure also shows the relative error σE E y0 due to phase instability. The results of statistical modeling presented in Fig. 6 were obtained by averaging over 100 values. It was previously noted [8] that, for a space object with a dimension of ~50 m, the resolution in range δr ~ 0.5 m can be provided by coherent stroboscopic processing of signals with the duration of ~3 ns in the X-ray band ( f0 ~ 10 GHz) with a band of Δf ~ 300 MHz. As can be seen from Fig. 6, for phase instability σθ ~ 1 rad, a decrease in the average power of the

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received signal by 4 dB is observed. In this case, the relative level of interference at the output of the stroboscopic system does not exceed the value of –12 dB with an accumulation coefficient m > 25. To ensure this accumulation mode for the object velocity of ~20 km/s, the repetition rate of the stroboscopic radar should be ~1 MHz. The value of the phase advance θ due to the shortterm instability of the frequency Δω and the finite propagation time of the signal t0 = 2 R c t + t0

θ(t ) ≤

∫ Δω(ξ)d ξ

(8)

t

is the Wiener process [15] with normal distribution and dispersion t0 t0

Dθ(t0 ) = σθ2 =

∫∫K

Δω(ξ

− μ)d ξd μ ≈ σ2Δωt0τω,

(9)

0 0

where K Δω(τ) is the correlation function of frequency drift Δω(t ); τω is correlation interval; σ2Δω is the dispersion of fluctuations of the cyclic frequency. For the operation of the stroboscopic radar in range R with allowable phase instability σθ < 1 rad, it is necessary to ensure that

σΔω < σθ

c . 2R τω

(10)

At the current level of technology development, the stability of the frequency of reference generators with a relative error not worse than δ ~ 10−12 is implemented [9], which in the X-ray band is the value of dispersion for frequency fluctuations σΔf ~ 0.01 Hz (σΔω = 2πσΔf ). Assuming that the frequency stabilization system has time constant of τω ~ 0.5 s, the estimate of the maximum range of the system operation at the considered assumptions is ~70 million kilometers. VIOLATION OF SIGNAL COHERENCE DUE TO DISPERSION IN COSMIC PLASMA Another important factor that contributes to a reduction in the signal coherence is the dispersion of electromagnetic waves in interplanetary plasma. For plasma with electron concentration ne the refractive

index

is

n(ω) = 1 − ω2pe ω2,

where

ω pe = 4πne e me is the electron plasma frequency, e and me are charge and mass of the electron, respectively. For typical values of the electron concentration in the solar wind in the Earth’s orbit ne ≈ 8 cm–3 [10], the 2

12

5 electron plasma frequency is ω2pe ≈ 1.6 × 10 s–1, which is much less than the carrier frequency of the probing signal in the X-ray band ω0 ≈ 6.3 × 1010 s–1. Because of the dispersion, the spectral components of the pulse acquire different individual phase shifts and, if the medium is inhomogeneous, i.e., ne = ne (z ), where z is the coordinate along the radar–asteroid route, then also different amplitude variations. All of this combined leads to a distortion of the pulse when it is propagated.

The phase delay Δϕ for a harmonic with the frequency ω in the detected reflected signal is given by relation R

∫(

)

−1 Δϕ(ω) = 2ω n (ω; z ) − 1 dz c 0 R

2 ω pe ≈ 2ω dz = 4πe DM , 2 c 0 2ω mecω

∫

where DM =

∫

R

0

2

(11)

ne (z )dz is the measure of dispersion.

The difference in phase delays (dephasing of the signal) for harmonics with boundary frequencies of the spectrum ω and ω + δω, where δω is the width of the spectrum, is δϕ = Δϕ(ω + δω) − Δϕ(ω) . Since for the radar signals, as a rule, the condition δω ! ω0 is satisfied, the value of the dephasing of the signal in view of Eq. (11) can be estimated as 2 δϕ ≈ 4πe DM2 δω . mecω

(12)

We will assume that the effect of loss of coherence becomes significant when the dephasing exceeds the angle 30°. Thus, the condition for preserving coherence is the fulfillment of inequality

δϕ ≤ π . 6

(13)

Substituting (12) into inequality (13), replacing approximately the electron density ne (z) with its average value ne , and taking into account the fact that the width of the spectrum δω is related to the linear resolution δr of the asteroid surface element by the relation δr ≈ (2δf )−1c = πc δω , we find the relationship between the allowable range and resolution 2 R ≤ 1 ω2 δr. 6 ω pe

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For the above characteristic values of the plasma frequency and the frequency of the sounding signal, we find

R ≤ 25.8 ( δr 1 m ) million kilometers. 

(15)

Thus, for the above estimate of the maximum range of the radar system operation of ~70 million kilometers, the dispersion in cosmic plasma limits the linear resolution of the asteroid details to the value of ~2.7 m. These values exceed the achieved values of the radar resolution of asteroids, which are ~7.5 m for the range of ~ 7 million kilometers [1, 5]. The resolution can be increased if the sounding is performed in the antisolar direction. According to [10], the electron concentration decreases upon moving away from the Sun, as ne (r ) = ne (1 AU r )2, respectively, at a range of 70 million kilometers, the concentration becomes smaller of the value ne by a factor of ~2.1, the dispersion measure decreases by a factor of ~1.5, and the resolution δr increases to ~1.8 m. When calculating the influence of dispersion, we did not take into account the contribution of the ionosphere, which is significant. The possibilities of increasing the information capacity of astronomical radar systems evaluated in this paper by significantly (by an order of magnitude compared with the currently available) increasing the maximum range of their operation obviously dictate the high requirements to the power of the sounding radio signal. These capacities can be implemented when using spacebased radar stations far beyond the ionosphere, for example, in the geostationary orbit using phased antenna arrays. The above estimates allow us to hope that the current potential of radar technology is not yet fully exhausted in radar astronomy. CONCLUSIONS In addition to limiting the range of operation of radar systems with the power of radiation, the use of coherent methods for receiving broadband radio signals encounters fundamental constraints on the phase stability of the used signals when maximum resolution and range are reached. The violation of coherence in stroboscopic ranging systems caused by phase instabilities of reference oscillation sources leads to a decrease in the sensitivity of the system and is equivalent to the effect of modulating interference. Noise reduction at the output of the stroboscopic converter due to the violation of coherence can be achieved by reducing the reading step ΔT = T N with a corresponding increase in the time of analysis. COSMIC RESEARCH

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ACKNOWLEDGMENTS We are grateful to Prof. Yu. N. Parshin (Ryazan State Radio Engineering University) for their attention to work and for a number of useful advices. This work was supported by Russian Foundation for Basic Research, project no. 15-47-02438-r-povolzhie_a. REFERENCES 1. Marshall, S.E., Howell, E.S., Brozovich, M., et al., Potentially hazardous asteroid (85989) 1999 JD6: Radar, infrared, and lightcurve observations and a preliminary shape model, Am. Astron. Soc., DPS Meeting no. 47, 2015, id 204.09. 2. Morrison, D., Defending the earth against asteroids: The case for a global response, Sci. Global Secur., 2005, vol. 13, pp. 87–103. 3. Morrison, D., Chapman, C.R., Steel, D., and Binzel, R.P., Impacts and the public: Communicating the nature of the impact hazard, in Mitigation of Hazardous Comets and Asteroids, Belton, M.J.S., Morgan, T.H., Samarasinha N.H., and Yeomans, D.K., Eds., Cambridge: Cambridge Univ. Press, 2011, pp. 353–390. 4. Study to Determine the Feasibility of Extending the Search for Near-Earth Objects to Smaller Limiting Diameters, Stokes, G., Ed., Report of the NEO SDT, NASA, 2003. http://neo.jpl.nasa.gov/neo/neore port030825.pdf. 5. Taylor, P.A., Richardson, J.E., Rivera-Valentín, E.G., et al., Radar observations of near-earth asteroids from Arecibo and Goldstone, 47th Lunar and Planetary Science Conference: The Woodlands, Texas, 2016, LPI Contribution no. 1903, pp. 2772–2772. 6. Zakharchenko, V.D., Stroboscopic selection of broadband RF signals with coherent probing, in 21st International Crimean Conference: Microwave and Telecommunication Technology (CriMiCo-2011), id 6068856, pp. 1124–1125. 7. Zakharchenko, V.D. and Kovalenko, I.G., On protecting the planet against cosmic attack: Ultrafast real-time estimate of the asteroid’s radial velocity, Acta Astronaut., 2014, vol. 98, pp. 158–162. 8. Zakharchenko, V.D., Kovalenko, I.G., and Pak, O.V., Estimate of sizes of small asteroids (cosmic bodies) by the method of stroboscopic radiolocation, Acta Astronaut., 2015, vol. 108, pp. 57–61. 9. Belov, L., Reference generators, Elektron.: Nauka, Tekhnol., Biznes, 2004, no. 6, pp. 38–44. 10. Veter solnechnyi. Sostav, kontsentratsiya chastits i skorost’. GOST 25645.136-86 (Solar Wind: The Composition, Particle Concentrations and Velocity. GOST 25645.136-86), Moscow: Izd. standartov, 1986. 11. Gonorovskii, I.S., Radiotekhnicheskie tsepi i signaly (Radio Engineering Circuits and Signals), Moscow: Drofa, 2006. 12. Zakharchenko, V.D., Self-gating of fast-moving targets in early warning radio engineering systems, Fiz. Vol-

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Translated by N. Topchiev

COSMIC RESEARCH

Vol. 56

No. 3

2018