Технические науки / 6. Электротехника и радиоэлектроника

Doctor of Sciences Artyushenko V.M.¹, candidate of Sciences Volovach V.I.²

¹Technological University, Korolev, Russia

²Volga Region State University of Service, Togliatti, Russia

Research and analysis of statistical characteristics of useful signal reflected from an object with spatially-distributed reflective elements

Lead. The article shows that in the analysis and implementation of radio-technical devices operating at close ranges, one should be aware of the extensive nature of the detected object, multipath nature of the reflection of signals from the object, etc.

In the article we examine the results of experimental studies of the statistical characteristics and of the parameters of the Doppler signal spectrum for different models of extended objects. Analysis and generalization of the obtained results was carried out based on a big selection of fragments of the Doppler signal spectrum that allows us to consider these results as statistically reliable. It is shown that acceleration motion of the extended object has the greatest influence on the width of the spectrum of the Doppler signal and, consequently, on the accuracy of the measurement of its speed of movement.

Key words. The short-range radar systems (SRRS), the extended object, the vehicle, the spectrum of the Doppler signal, the effective width of the spectrum, scattering cross-section, the speed of the motion, the acceleration of the motion.

Introduction. Short-range radar systems (SRRS) are widely applied in various systems of measurement of movement parameters, protection systems of various objects, classification identification systems use the principle of short-range radar-location. [1,2]. Consequently, they should also use other characteristics than those applied in the theory of long range radio systems.

Doing the theoretical justification and practical implementation of any devices belonging to the class of SRRS, for example, measuring device of motion parameters of various objects, you should consider a number of specific features for short range, such as the extended nature of the detected object, the comparability of geometric dimensions of the object with the distance to it, multipath nature of the reflection of signals from such objects, etc.

As a result, it is necessary to analyze the characteristics of reflection of the sounding signal, to define the width of the Doppler spectrum of the signal, to select the method of definition and experimental determination of the scattering cross-section, and also to create on their basis mathematical models corresponding the real physical phenomena in SRRS taking into account the extended nature of the detected objects, constantly changing range, various laws of instantaneous detection probability, a priori uncertainty about the position of the object and its motion parameters [1,2].

Body. A priori knowledge of the statistical characteristics of signals and disturbing influences allows us to formulate more accurate mathematical models of the reflected signal as well as interferences influencing this signal and reasonable approach to the development of devices of SRRS. Previously the authors [3] have selected and justified models of disturbing influences on electronic detection devices (EDD) of high frequency type, which is a special case of SRRS taking into account multipath nature of the signals reflected from extended objects. It was noted that the probability density of the envelope of such a signal is well approximated by the PDF of Nakagami, and the PDF of the instantaneous values at specific values of the distribution parameters is clearly bimodal.

One of the objects of detection, changing motion parameters, ensuring traffic safety in the group, etc. SRRS are various vehicles of railway transport and road transport, which by their structure can be attributed to the extended objects of complex shape. Particularly interesting is the study of the above mentioned vehicles in connection with the special character of the reflections of the sounding signal coming from them. It is known [4,5] that a vehicle as an object of detection is a complex spatially distributed radar target. Characteristics of the signal reflected from such a target, not only affect the range of SRRS, but also largely determine the number of other important indicators for such systems as: the accuracy of measurement of speed, resolution and other.

As is known, when we measure the motion parameters of any extended object with radio methods, the speed of its movement is determined by the Doppler frequency offset of the signal:

, (1)

where V_R – is the radial velocity of movement of the detected extended object; λ_о – is the wavelength of the probing signal; j – is the angle between the direction of the axis of the main lobe of the antenna directional diagram and the direction of movement of the extended object.

One of the most important statistical characteristics of the signal reflected from the extended object, affecting the accuracy of measurement of speed of its movement, is the spectrum of the Doppler signal (SDS). The main parameters of the SDS are the average frequency of spectrum F_D.A, the shape of the envelope, the effective width DF and power Р_D.

The effective width of the SDS is determined by the resulting pattern of the directivity of the antenna in the plane of the angle j. As noted by the authors previously [4] the effective width DF, is also affected by the correlation interval. The interval characterizes the rate of change of a random process in time:

, (2)

It is also shown that at a certain mutual arrangement of radio-technical sensor (RS), measuring the speed of the object and the vehicle, when the vehicle moves in the direction RS, the width of the Doppler spectrum of the received signal can be estimated by the formula

, (3)

where 2Da – is the angular size of the vehicle (in horizontal plane).

Determination of the parameters of the reflected signals, including the spectral parameters can be used in various applications [6-10].

Next, let us proceed to study results of SDS parameters.

It should be noted that the methodology we use now was proposed by the authors before [1,2,10]. Also earlier on the basis of the proposed method the authors experimentally determined the average values of scattering cross section (SCS) s_V, the width of the SDS is DF_V and root-mean-square deviation of the SCS on the example of different types of vehicles. To summarize the obtained results it was interesting to carry out the research of more extended objects such as vehicles of railway transport, as well as the study of the influence of acceleration of these objects on the parameters of the SDS.

An experimental study of the parameters of the SDS reflected from extended objects (train rolling-stock, single cars, in some cases for a shunting locomotive), was performed using microwave oscillations of serial rate meter RIV-V2 with wavelength l = 8 mm. Analysis and generalization of the study results of the parameters of the spectrum produced from the numerous fragments of the Doppler signal reflected from the vehicle of the same model. The number of the considered fragments from the vehicles of each type was 380...400.

All of the spectra of the reflected signals can be divided into three groups. The first group will include the SDS under irradiation of the vehicle (train rolling-stock) at an angle close to zero when the vehicle is at a relatively large distance of about 50...60 m. For this case is characteristic the spectrum of the reflected signal, potentially providing a good accuracy of measurement of speed and, consequently, acceleration and high resolution. The spectral width at the level of 0,707 is ΔF = 8…10 Hz.

The second group of spectra corresponds to positive angles of irradiation of the vehicle α₀ ≥ 17^о. In this case, the width of SDS increases significantly and is ΔF = 20...25 Hz, which corresponds to the location the vehicle at relatively small distances of about 10...20 m from the RIV velocity meter. The angular dimensions of the vehicle often exceed the beam width of the antenna. Moving vehicle rapidly changes its angle, which is accompanied by rapid fluctuations of reflecting centers, which leads to the expansion of the SDS, the deterioration of the accuracy potential of the velocity meter and frequency resolution. In addition, this case is characterized by a sharp decrease in the scattering cross-section (SDS) for some types of cars caused by the oblique fall of the ray on a smooth surface of the vehicle (mirror reflection), as well as some decrease of scatter of the values of SCS for different types of cars, due to the fact that the narrow beam of antenna irradiates only a part of the surface (projector mode).

The third group of spectra corresponds to the deceleration mode of the vehicle from the trigger point to the moment of release the car retarders. In this case the body of a railroad car as well as the velocity meter is exposed to strong vibration. In this case the spectrum of the reflected signal is expanded so that its width reaches ΔF = 30…40 Hz. Under these conditions the accuracy of the velocity measurement is the worst.

A significant expansion of the range is observed in Doppler signals reflected from shunting locomotives, because their body continuously vibrates from the running engine. Moreover, SDS does not only expand, but also has a "parasitic" harmonics, the amplitude of which is comparable with the spectrum of the main signal, which significantly affects the measurement accuracy, and can lead to errors in the velocity measurements.

The results of processing of the experimental data show that when rotating wheels of the vehicle or its oscillating parts (for example, the rear and side doors, hatches, covers and accessories for fastening cargo) are irradiated, in the spectrum of the reflected signals appear additional components. Moreover, the frequencies of these components can be both above and below the frequency of the main signal, and their level is 10...40 dB below the main signal. It should be noted that the results obtained in this part of the study are absolutely identical to the earlier obtained results of study of similar parameters of SDS for road transport [5]. At low speeds of rolling of the vehicle the spectrum of the reflected signal is exposed to stronger "parasitic" effects than the spectrum of the signal reflected from the vehicle at a higher speed. This is because at low speeds of rolling of the vehicle the spectrum of the reflected signal falls within the frequency domain of additive noise, whose spectrum and the SDS "overlap". As a result of this not only the expansion of ΔF can occur, but its "splitting" as well, which greatly reduces possibility of accurate measurement of the Doppler frequency signal.

As a result of experimental studies it has been shown that the vehicle movement acceleration has the greatest influence on the width of the SDS and, consequently, on the accuracy of speed measurement of the extended object movement (railway cars, vehicles in general). Moreover, the bigger is its absolute value, the wider is the energy spectrum of the reflected signal, which is fully consistent with the theoretical analysis.

Conclusions. Considering a good compliance between theoretical and experimental results we can draw the following conclusions. The average value of the acceleration of railway cars rolling into brake position is within (+0,45)…(+0,55) м/с². At the time of braking, the acceleration is in the range of (–1,9)…(–2,1) м/с²; respectively, in the output of the moderator it is (–0,05)…(+0,05) м/с². It should be noted that while technically implementing the tracking velocity meter for increasing accuracy of measurement of the average frequency of spectrum of the reflected signal, the time constant of the measurement must be chosen from the condition of minimum width of the Doppler reflected signal at the maximum possible acceleration value of the vehicle, taking into account the required processing speed of the meter in receiving and issuing information about velocity of the vehicle movement. As can be seen from the presented results, the time constant of the measurement must be within 80...120 ms.

References:

1. V. M. Artyushenko, Research and development of the radar measuring instrument of parameters of movement of extended objects (monograf), Moscow, NOU VPO FTA, 2013. – p. 214.

2. V. I. Volovach, Methods and analysis algorithms of short-range radio engineering devices, (monograf), Moscow, Radio and communication, 2013. – p. 228.

3. Artyushenko V. M., Volovach V. I. Statistical Characteristics of Envelope Outliers Duration of non-Gaussian Information Processes. In the Proceedings of IEEE East-West Design & Test Symposium (EWDTS’2013), pp: 137-140.

4. V. M. Artyushenko, V. I. Volovach, “The analysis of parameters of a range of the signal reflected from extended object”, News of higher education institutions. Instrument making. – 2012. – 9 (57). – , pp. 62–67.

5. Lu N. H., Bruce A. Eisenstein. Detection of Weak Signals in Non-Gaussian Noise // IEEE Trans. – 1981. – Vol. IT-27, 6. – Р. 755-771.

6. Prokopenko N. N., Serebryakov A. I., Budyakov P. S. Perspective high-frequency correction in differential and broadband amplifiers. In the Proceedings of Papers – 5th European Conference on Circuits and Systems for Communications, ECCSC'10, art. no. 5733875, pp: 135-139.

7. Budilov V. N., Volovach V. I., Shakurskiy M. V., Eliseeva S. V. Automated Measurement of Digital Video Cameras Exposure Time. In the Proceedings of IEEE East-West Design & Test Symposium (EWDTS’2013), pp: 344-347.

8. Shakurskiy M. V., Shakurskiy V.K., Ivanov V. V. Digital converter of frequency deviation based on three frequency generator. In the Proceedings of IEEE East-West Design & Test Symposium (EWDTS’2013), pp: 316-319.

9. Anfalov K.V., Volovach V. I. Comparative Analysis of Coding Effectiveness in Telecommunication Systems with ARQ. In the Proceedings of IEEE East-West Design & Test Symposium (EWDTS’2013), pp: 320-324.

10. Volovach V. I. Accumulating probability of detecting the objects in the control zone of radio security devices // Electrical engineering and information systems. – 2011. – 1, v. 7. – pp. 17-20.