Wave Propagation 2010 Part 19 ppt

So, the instantaneous distribution of scattered field power in the space as the function of the positional angle θ is formed by the union of elementary scatterer radar cross section (4 items) plus 6 cosine oscillations. It is not difficult to see that every cosine functions are caused by the interference effect between the fields scattered by a pair of elementary scatterers forming the RCRO. The number of this pairs can be found with the use binomial coefficient ( ) !/ ! ! N M CMNMN = ⎡−⎤ ⎣ ⎦ , where M is a number of values, N is a number elements in the combination. In the case when 4 M = , 2N = , we have 2 4 6C = . So, the angular response function of the complex radar object considered will include 6 space harmonic functions as the interference result summarize how it follows from the expression (48) where the values 12 1 2 ;dXX=− 13 1 3 14 1 4 23 2 3 24 2 4 34 3 4 ;;;;dXXdXXdXXdXXdXX=− =− =− =− =− are the space diversity of scattered elements for every interference pair. The space harmonic function ( ) cos 2 ik ik kd σ σθ corresponds to the definition that was done in (Kobak, 1975), (Tatarinov et al, 2007) . In accordance with this definition, the harmonic oscillation in the space having the type () cos 2kd θ is defined by the full phase ( ) ( ) 22/2kd d ψ θθπλθ == , the derivative from which is the space frequency 2/ SP fd λ = having the dimension 1 Rad − . The period 1/ /2 SP SP Tf d λ == has the dimension Rad , which corresponds to this frequency. So, a full power distribution of the field, scattered by complex radar object, is an union of the interference pictures, which are formed by a collection of elementary two-points interferometers. Thus, we can write a scattered power random angular representation, depending on the positional angle, in the form () () 2 11 2cos2 MC mikik m Pkd θ σσσ θ = =+ ∑∑ , where 2 M CC= is combinations number, M is a full number of RCRO elementary scatterers. It was demonstrated above that the electromagnetic field Stokes parameter 03 , SS angular distribution at the scattering by two-point distributed object has the form () ()() () 00000 33300 2cos0,5; 2cos0,5, ab ab ab ab ab ab SSSSSN SSSSSD θ ξϕ θ ξϕ =++ + =++ − where 2 kl ξ θ = . It follows from this expression that the space harmonics functions ( ) cos 2kl θ η ± are having amplitudes 00 ab ab SSN or 00 ab ab SSD. Here the values , ab ab ND are a proximity (distance) of distributed object elementary scatterers polarization states respectively. Taking into account above mentioned, we can write the Stokes parameters angular distribution for the field, scattered by random complex radar object as an union of the generalized interference pictures, which are formed by a collection of elementary two-points interferometers (see Fig.13): () () 0000 11 2cos MC m i k ik ik ik m SSSSN θ ξη = =+ + ∑∑ , () () 3300 11 2cos MC m i k ik ik ik m SSSSD θ ξη = =+ + ∑∑ , where 2 M CC= is combinations number. An amplitude of every space harmonics and initial space phases of these harmonics will be stochastic values and the further analysis must be statistical. First of all we will find a theoretical form of scattered field Stokes parameter S 3 angular distribution autocorrelation function. As far as we would like to find the autocorrelation function (not covariance function!), we must eliminate a random constant item 3 1 M m m S = ∑ from the stochastic function ( ) 3 S θ for the guarantee of zero mean value. Taking into account that the value 3 1 M m m S = ∑ can be as no stationary stochastic function, the average must be made using a sliding window. After a mean value elimination and normalization we can write stochastic stationary function S 3 (θ) in the form () () 3 1 cos 2 C ik ik ik SDkd θ θη =+ ∑ Its autocorrelation function can be found as () () [][ ] ()() 2 2 1 cos2 cos2 ( ) , C SNNN N B D kd kd W D d D d θ θη θ θ η η η ∞∞ = −∞ −∞ Δ= + +Δ+ ∑ ∫∫ . (49) Here amplitudes D and space initial phase η of space harmonics are random values, which can be characterized by two-dimensional probability distribution density ( ) 2 ,WD η , and 12 θ θθ Δ= − . We will suppose that random amplitudes and phases are independent variables. For this case two-dimensional probability distribution can be presented as two one-dimensional distributions densities product ( ) ( ) () 211 , WD WDW η η = . Let’s suppose also that random phase has the uniform probability distribution density on the interval ( ) , π π − i.e. ( ) 1/2W η π = . A probability distribution density for the random amplitude D can be preassigned, however for all cases it will be one-sided. After the integration we obtain the value of double integral in the form () () ()() () 2 1 0 0,5 cos 2 0,5 cos 2 2 NN NN I D kd W D d D d D kd π π θ ηθ π ∞ − =Δ=<>Δ ∫∫ , (50) where N D<> is the polarization distance mean value, which was found by the average along the statistical ensemble of random values N D for all space harmonics having the space frequency 2 / N SP N fd λ = . Thus, we can write the theoretical form of scattered field Stokes parameter angular distribution autocorrelation function in the form () () 1 0,5 cos 2 C SNN N BDkd θ θ = Δ =<> Δ ∑ . (51) Taking into account that the every item of the union (51) is the autocorrelation function for an isolated space harmonic oscillation ( ) ( ) cos 2 NNNN SDkd θ θη =+ having random amplitude N D and random initial space phase N η , i.e. ( ) ( ) 0,5 cos 2 SN N N BDkd θ θ Δ =<> Δ (52) it is not difficult to see that the autocorrelation function of the Stokes parameter stochastic realization is the union of individual autocorrelation functions of all space harmonics: () () 1 C SSN N BB θ θ = Δ =Δ ∑ . (53) Let’s now to find a complex radar object averaged space spectra using the expressions (8) for polarization-angular response autocorrelation function. The power spectra for the case of isolated space harmonic can be found as the Fourier transformation above the autocorrelation function (52): () () () () ()() exp 0.5 [ ] NN SP SN SP N SP SP SP SP PB jd D θθθ δ δ ∞ −∞ Ω = Δ −ΩΔ Δ= < > Ω−Ω + Ω+Ω ∫ , (54) where ( ) 222/ SP SP fd π πλ Ω= = is a space frequency. The spectra lines are placed on the distances N SP ±Ω from the co-ordinates system origin and their positions are defined by the space frequency 2 / N SP N fd λ = of two-point radar object. This space frequency is corresponding to space diversity of two reflectors distributed in the space. The intensity of power spectra lines is determined by polarization distance between polarization states of two scatterers forming the radar object. The full space spectra of stochastic polarization-angular response, i.e. Fourier transformation of the autocorrelation function (53) is: () ()() 1 0,5 [ ] C NN SP N SP SP N PD δδ = Ω= < >−Ω++Ω ∑ . (55) It is necessary to indicate here that a connection between scattered (diffracted) field polarization parameters and polarization parameters distribution along a scattering (diffracting) object in the form of Fourier transformation pair is established in the first time. However, this connection is correct for fourth statistical moments: scattered field intensity correlations (include mutual intensity) and polarization proximity (distance) distribution along a scattering (diffracting) object. In the conclusion we consider some results of scattered field polarization parameters investigation at the scattering by random distributed object having a lot of scattering centers – “bright” points. It follows also both from theoretical and experimental investigations results that polarization-angular response function of a RCRO in the form of the 3-rd Stokes parameter angular dependence corresponds to a narrow-band random process. The experimental realization of this parameter has shown on the fig.7. The angular interval for this dependence is 0 20± . The rotated caterpillar vehicle (the sizes 5,5x2,5x1,5 m) placed on the distance 2 km was used as complex radar object. The autocorrelation functions (ACF) of this object response ( ) 3 S θ Δ are shown on the fig.14. The ACF on the angular interval 0 20± concerning the direction to the object board is designated by dotted line and the ACF into the same interval in direction to the stern of the object is continue line. The measurements in these directions allow us to take into account the difference in the radar object space spectra band at its observation in areas of perpendiculars to the board and to the stern of the object. On the fig. 15 RDRO mean power spectra are shown. Dotted line is corresponding to direction to the object board and continue line corresponds to object stern. -1 0 1 -0,5 0 0,5 1 Fig. 14. Autocorrelation functions of RDRO Fig.15. Mean power space spectra of RDRO stochastic polarization-angular response 6. Conclusion In the conclusion we can to indicate that in the Chapter proposed a new statistical theory of distributed object polarization speckles (coherent images) has been developed. The use of fourth statistical moments and emergence principle allow us to find the answers for a series of problems which are having the place at the electromagnetic waves coherent scattering by distributed (complex) radar objects. 7. References Proceedings of the IEEE. (1965). Special issue. Vol. 53., No.8, (August 1965) Ufimtsev, P. (1963). A Method of Edge Waves in Physical Diffraction Theory, Soviet Radio Pub. House, Moscow, Russia Proceedings of the IEEE. (1989). Special issue. Vol. 77., No.5, (May 1965) IEEE Transaction on Antennas and Propagation . (1989). Special issue. No.5, (May 1965) Ostrovitjanov, R. & Basalov F. (1982). A Statistical Theory of Distributed Objects Radar, Radio and Communication Pub. House, Moscow, Russia Shtager, E. (1986). Waves Scattering by Complicated Radar Objects, Radio and Communication Pub. House, Moscow, Russia Kell, R. (1965). On the derivation of bistatic RCS from monostatic measurements. Proceedings of the IEEE, Vol. 53, No. 5, (May 1965), pp 983-988 Stratton, J. & Chu, L. (1939). Diffraction theory of electromagnetic waves. Phys. Rev., Vol. 56, pp 308-316 Tatarinov, V. ; Tatarinov S. & Ligthart L. (2006). An Introduction to Radar Signals Polarization Modern Theory (Vol. 1 : Plane Electromagnetic Waves Polarization and its Transformations), Tomsk State University Publ. House, ISBN 5-7511-1995-5, Tomsk, Russia Shtager, E. (1994). Radar objects characteristics calculation at random earth and sea surface. Foreign Radioelectronics, No. 4-5, (May 1994), pp 22-40, Russia Steinberg, B. (1989). Experimental localized radar cross section of aircraft. Proceedings of the IEEE, Vol. 77, No. 5, (May 1989), pp 663-669 Kobak, V. (1975). Radar Reflectors, Soviet Radio Pub. House, Moscow, Russia Kanareikin, D.; Pavlov, N. & Potekchin V. (1966). Radar Signals Polarization, Soviet Radio Pub. House, Moscow, Russia Pozdniak, S. & Melititsky V. (1974). An Introduction to Radio Waves Polarization Statistical Theory, Soviet Radio Pub. House, Moscow, Russia Franson, M. (1980). Optic of Speckles. Nauka Pub. House, Moscow, Russia Peregudov, F. & Tarasenko, F. (2001). The Principles of Systems Analysis, Tomsk State University Publ. House, Tomsk, Russia Azzam, R. & Bashara, N. (1977). The Ellipsometry and Polarized Light, North Holland Pub. House, New York-Toronto-London Tatarinov, V. ; Tatarinov, S. & van Genderen P. (2004). A Generalized Theory on Radar Signals Polarization in Space, Frequency and Time Domains for Scattering by Random Complex Objects. Report of IRCTR-S-004-04, Delft Technology University, the Netherlands Born, M. & Wolf, E. (1959). Principles of Optics. Pergamon Press, New-York-Toronto-London Potekchin, V. & Tatarinov, V. (1978). The Coherence Theory of Electromagnetic Fielg, Svjaz Pub. House, Moskow, Russia Tatarinov, V. ; Tatarinov S. & Kozlov, A. (2007). An Introduction to Radar Signals Polarization Modern Theory (Vol. 2: A Statistical Theory of Electromagnetic Field ), Tomsk State University Publ. House, ISBN 978-5-86889-476-3, Tomsk, Russia 1. Introduction In the solar system, debris whose mass ranges from a few micrograms to kilograms are called meteoroids. By penetrating into the atmosphere, a meteoroid gives rise to a meteor, which vaporizes by sputtering, causing a bright and ionized trail that is able to scatter forward Very High Frequency (VHF) electromagnetic waves. This fact inspired the Radio Meteor Scatter (RMS) technique (McKinley, 1961). This technique has many advantages over other meteor detection methods (see Section 2.1): it works also during the day, regardless of weather conditions, covers large areas at low cost, is able to detect small meteors (starting from micrograms) and can acquire data continuously. Not only meteors trails, but also many other atmospheric phenomena can scatter VHF waves and may be detected, such as lightning and e-clouds. The principle of RMS detection consists in using analog TV stations, which are constantly switched on and broadcasting VHF radio waves, as transmitters of opportunity in order to build a passive bistatic radar system (Willis, 2008). The receiver station is positioned far away from the transmitter, sufficiently to be bellow the horizon line, so that signal cannot be directly detected as the ionosphere does not usually reflect electromagnetic waves in VHF range (30 - 300 MHz)(Damazio & Takai, 2004). The penetration of a meteor on Earth’s atmosphere creates this ionized trail, which is able to produce the forward scattering of the radio waves and the scattered signals eventually reach the receiver station. Due to continuous acquisition, a great amount of data is generated (about 7.5 GB, each day). In order to reduce the storage requirement, algorithms for online filtering are proposed in both time and frequency domains. In time-domain the matched filter is applied, which is optimal in the sense of the signal-to-noise ratio when the additive noise that corrupts the received signal is white. In frequency-domain, an analysis of the power spectrum is applied. The chapter is organized as it follows. The next section presents the meteor characteristics, and briefly introduces the several detection techniques. Section 3 describes the meteor radar detection and the experimental setup. Section 4 shows the online triggering algorithm performance for real data. Finally, conclusions and perspectives are addressed in Section 5. Eric V. C. Leite 1 , Gustavo de O. e Alves 1 , Jos ´ e M. de Seixas 1 , Fernando Marroquim 2 , Cristina S. Vianna 2 and Helio Takai 3 1 Federal University of Rio de Janeiro/Signal Processing Laboratory/COPPE-Poli 2 Federal University of Rio de Janeiro/Physics Institute 3 Brookhaven National Labaratory 1,2 Brazil 3 USA Radar Meteor Detection: Concept, Data Acquisition and Online Triggering 25 2 Electromagnetic Waves 2. Meteors Meteoroids are mostly debris in the Solar System. The visible path of a meteoroid that enters Earth’s (or another body’s) atmosphere is called a meteor (see Fig. ??). If a meteor reaches the ground and survives impact, then it is called a meteorite. Many meteors appearing seconds or minutes apart are called a meteor shower. The root word meteor comes from the Greek μτωρoν, meaning ”high in the air”. Very small meteoroids are known as micrometeoroids, 1g or less. Many of meteoroid characteristics can be determined as they pass through Earth’s atmosphere from their trajectories, position, mass loss, deceleration, the light spectra, etc of the resulting meteor. Their effects on radio signals also give information, especially useful for daytime meteor, cloudy days and full moon nights, which are otherwise very difficult to observe. From these trajectory measurements, meteoroids have been found to have many different orbits, some clustering in streams often associated with a parent comet, others apparently sporadic. Debris from meteoroid streams may eventually be scattered into other orbits. The light spectra, combined with trajectory and light curve measurements, have yielded various meteoroid compositions and densities. Some meteoroids are fragments from extraterrestrial bodies. These meteoroids are produced when these are hit by meteoroids and there is material ejected from these bodies. Most meteoroids are bound to the Sun in a variety of orbits and at various velocities. The fastest ones move at about 42 km/s with respect to the Sun since this is the escape velocity for the solar system. The Earth travels at about 30 km/s with respect to the Sun. Thus, when meteoroids meet the Earth’s atmosphere head-on, the combined speed may reach about 72 km/s. A meteor is the visible streak of light that occurs when a meteoroid enters the Earth’s atmosphere. Meteors typically occur in the mesosphere, and most range in altitude from 75 to Fig. 1. Debris left by a comet may enter on Earth’s atmosphere and give rise to a meteor. 538 Wave Propagation Radar Meteor Detection: Concept, Data Acquisition and Online Triggering 3 100 km. Millions of meteors occur in the Earth’s atmosphere every day. Most meteoroids that cause meteors are about the size of a pebble. They become visible in a range about 65 and 120 km above the Earth. They disintegrate at altitudes of 50 to 95 km. Most meteors are, however, observed at night as low light conditions allow fainter meteors to be observed. During the entry of a meteoroid or asteroid into the upper atmosphere, an ionization trail is created, where the molecules in the upper atmosphere are ionized by the passage of the meteor (Int. Meteor Org., 2010). Such ionization trails can last up to 45 minutes at a time. Small, sand-grain sized meteoroids are entering the atmosphere constantly, essentially every few seconds in any given region of the atmosphere, and thus ionization trails can be found in the upper atmosphere more or less continuously. Radio waves are bounced off these trails. Meteor radars can measure also atmospheric density, ozone density and winds at very high altitudes by measuring the decay rate and Doppler shift of a meteor trail. The great advantage of the meteor radar is that it takes data continuously, day and night, without weather restrictions. The visible light produced by a meteor may take on various hues, depending on the chemical composition of the meteoroid, and its speed through the atmosphere. This is possible to determine all important meteor parameters such as time, position, brightness, light spectra and velocity. Furthermore it is possible also to obtain light curves, meteor spectra and other special features.The radiant and velocity of a meteoroid yield its heliocentric orbit. This allows to associate meteoroid streams with parent comets. The deceleration gives information regarding the composition of the meteoroids. From statistical samples of meteor heights several distinct groups with different genetic origins have been deduced. 2.1 Meteor observation methods There are many ways to observe meteors: – Visual Meteor Observation - Monitoring meteor activity by the naked eye. Least accurate method but easy to carry out in special by amateur astronomers. Large numbers of observations allow statistically significant results. Visual observations are used to monitor major meteor showers, sporadic activity and minor showers down to a zenithal hourly rate (ZHR) of 2. The observer can count and estimate the meteor magnitude using a tape recorder for later to plot a frequency histogram. The visual method is very limited since the observer cannot work during the day or cloudy nights. Such an observation can be quite unreliable when the total meteor activity is high e.g. more than 50 meteors per hour. The naked eye is able to detect meteors down to approximately +7mag under excellent circumstances in the vicinity of the center of the field of view (absolute magnitude - mag - is the stellar magnitude any meteor would have if placed in the observer’s zenith at a height of 100 km. A 5th magnitude meteor is on the limit of naked eye visibility. The higher the positive magnitude, the fainter the meteor, and the lower the positive or negative number, the brighter the meteor). – Photographic Observations - The meteors are captured on a photographic film or plate (Hirose & Tomita, 1950). The accuracy of the derived meteor coordinates is very high. Normal-lens photography is restricted to meteors brighter than about +1mag. Multiple-station photography allows the determination of precise meteoroid orbits. Photographic methods can hardly compete with video advanced techniques. The effort to be spent for the observation equipment is much lower than for video systems. For this reason photographic observations is widely used by amateur astronomers. On the other hand, the photograph methods allow to obtain very important meteor parameters: accurate 539 Radar Meteor Detection: Concept, Data Acquisition and Online Triggering 4 Electromagnetic Waves position, height, velocity, etc. The sensitivity of the films must be considered. There is now very sensitive digital cameras with high resolution for affordable prices, which produce a great impact to this technique. This method is restricted also to clear nights. – Video Observations - This technique uses a video camera coupled with an image intensifier to record meteors (Guang-jie & Zhou-sheng, 2004). The positional accuracy is almost as high as that of photographic observations and the faintest meteor magnitudes are comparable to visual or telescopic observations depending on the used lens. Meteor shower activity as well as radiant positions can be determined. Multiple-station video observations allow the determination of meteoroid orbits. Advanced video techniques permit detection of meteors up to +8mag. Video observation is the youngest and one of the most advanced observing techniques for meteor detection. Professional astronomers started to use video equipment at the beginning of the seventies of the last century. Currently the major disadvantage is the considerable price of a video system. – Telescopic Observations - This comprises monitoring meteor activity by a telescope, preferably binoculars. This technique is used to determine radiant positions of major and minor showers, to study meteors much fainter than those seen in visual observations ones, which may reach +11mag. Although the narrower field, the measurements are more precise. – Radio Observations - Two main methods are used, forward scatter observations and radar observations. The first method is easy to carry out, but delivers only data on the general meteor activity. The last is carried out by professional astronomers. Meteor radiants and meteoroid orbits can be determined. Radar meteors as well as telescopic ones may be as faint as +11mag. Radio meteor scatter is an ideal technique for observing meteors continuously, day and night and even in cloudy days. Meteor trails can reflect radio waves from distant transmitters back to Earth, so that when a meteor appears one can sometimes receive small portions of broadcasts from radio stations up to 2,000 km away from the observing site. The technique is strongly growing in popularity amongst meteor amateur astronomers. In the recent years, some groups started automating the radio observations by monitoring the signal from the radio receiver with a computer and even in cloudy days (see Fig. 2). Even for such high performance, the interpretation of the observations is difficult. A good understanding of the phenomenon is mandatory. 3. Meteor radio detection Measurements performed by Lovell in 1947 using radar technology of the time showed that some returned signals were from meteor trails. This was the start of a technique known today as RMS, which was intensely developed in the 50’s and 60’s. Both experimental and theoretical work have been developed. Today, radio meteor scatter can be easily implemented having in hands an antenna, a good radio receiver and a personal computer. There are two basic radar arrangements: backscattering and forward scattering. Back scattering is the traditional radar, where the transmitting station is near the receiving antenna. Forward scattering is used when the transmitter is located far from the receiver. Both arrangements are used in the detection of meteors. Back scatter radar tends to be pulsed and forward scatter continuous wave (CW). Forward scatter radar shows an increase in sensitivity 540 Wave Propagation [...]... electromagnetic waves propagating in the vicinity of a building that is exceedingly great in comparison with the wavelength is 556 Wave Propagation measured or in case in-room propagation on a spot where a base station is located in the building is measure, it is easy to comprehend what shape of structure of the wall in the inside or outside of the building will exercise influence on the electromagnetic waves... waves are reached, two methods, i.e the one to measure the waves and the other one in accordance with simulation are available Despite the above, it might be next to impossible to recognize the field strength of the electromagnetic waves in the whole area where wireless communication is utilized Therefore proposals for a simulation method that can adjust the settling position of the base 554 Wave Propagation. .. to estimate attenuation loss of the electromagnetic on a propagation route utilizing the building height in the communication area obtained by residence maps and its distribution (Kita et al., 2007; Kitao & Ichitsubo, 2008; Xia, 199 7) together with the state of the roads (Ikegami et al., 198 4; Walfisch & Bertoni, 198 8) or the one to estimate the propagation route in accordance with the Ray Tracing method... as to allow the electromagnetic waves to reach the place where no Electromagnetic Waves Propagating Around Buildings 555 electromagnetic waves generated in the vicinity of a specific building are reached Nothing has been obtained with the result explaining that it is possible to shut the electromagnetic waves intruding from the outside or to allow the electromagnetic waves propagating through the room... transform (STFT) was applied (Oppenheim, 198 9) Then, the PSD 14 550 Electromagnetic Waves Wave Propagation Amplitude (V) is estimated via periodogram Considering the sampling frequency of 22,050 Hz, windows of 256 samples correspond to a time length of approximately 11 ms, which provides a good resolution for the detection and allows wide-sense stationarity (Papoulis, 196 5) The 30 s of acquired data were... Type-II: Accept H0 when H1 is true (which means to miss a target signal) 8 544 Electromagnetic Waves Wave Propagation The probability to commit a type-I error is called false alarm probability, denoted as PF , and the probability of type-II error is called probability of a miss (PM ) (Shamugan & Breipohl, 199 8) In addition, we can define PD = 1 − PM , which is called the detection probability The decision... 27, 861-874, 2006 16 552 Electromagnetic Waves Wave Propagation Guang-jie, W., Zhou-sheng, Z.Video observation of meteors at Yunnan Observatory Chinese Astronomy and Astrophysics, Volume 28, Issue 4, October-December 2004, Pages 422-431 Hayes, M.H Statistical Digital Signal Processing and Modeling, ISBN: 0-471-59431-8, John Wiley and Sons Inc., New York, 199 6 Hirose H., Tomita, K., Photographic Observation... model is a model building taken up based on the idea that the size of the building is made smaller by shortening the wavelength of the wave source used for the measurement, keeping constant the ratio of the size of the real building complying with the wavelength of the electromagnetic waves used for general mobile wireless devices such as mobile telephones, in-room wireless LAN, RFID, etc Incidentally... noise 10 546 Electromagnetic Waves Wave Propagation process The whitening transformation applied to the development set (see next section) results on a perfect diagonal matrix and the results are well generalized for the testing set (see Fig 5) 4.2.2 Stochastic process detection In this case, matched filter design may be generalized for stochastic process detection (Trees - Part III, 2001) For this more... Estimation, and Modulation Theory, Part III, ISBN: 0-471-10793-X, John Wiley & Sons, New York, 2001 Whalen A D Detection of Signals in Noise Second Edition ISBN: 978-0127448527, Academic Press, 199 5 Willis, N.C., ’Bistatic Radar’, chapter 23 in Radar Handbook, third edition, (M.I Skolnik ed.), ISBN 978-0-07-148547-0, McGraw-Hill, New York, 2008 Wislez, J M Forward scattering of radio waves of meteor trails, Proceedings . electromagnetic waves coherent scattering by distributed (complex) radar objects. 7. References Proceedings of the IEEE. (196 5). Special issue. Vol. 53., No.8, (August 196 5) Ufimtsev, P. (196 3). . Edge Waves in Physical Diffraction Theory, Soviet Radio Pub. House, Moscow, Russia Proceedings of the IEEE. (198 9). Special issue. Vol. 77., No.5, (May 196 5) IEEE Transaction on Antennas and Propagation. (May 199 4), pp 22-40, Russia Steinberg, B. (198 9). Experimental localized radar cross section of aircraft. Proceedings of the IEEE, Vol. 77, No. 5, (May 198 9), pp 663-669 Kobak, V. (197 5).