The phenomenon of incoherent signal interference

Transcription

1 The phenomenon of incoheent signal intefeence.. Goshenkov #, Y.N. Klikushin #, K.T. Koshekov *3 # Depatment "Technology of electonics", Omsk tate Technical Univesity, OmGTU, Omsk, Russia goshenkov@omgtu.u iit@omgtu.u * Depatment of "Enegetics and instumentation", Noth-Kazakhstan tate Univesity, NKU, Petopavlovsk, Kazakhstan 3 kkoshekov@mail.u bstact in this wok the methodology, tools and esults of modeling the evolution of a binay mixtue of signals ae descibed, and theefoe the phenomenon of incoheent signals intefeence was found. This phenomenon is appeaed in the fact that the linea summation of the components of a binay mixtue of signals and the signal wavefom of the mixtue changes, depending on the elation of the amplitudes of summable components. Keywods identification teste, measuing of signal fom, intefeence, coheency, andom signals summation I. INTRODUCTION The concept of intefeence in physics has two levels of intepetation. To wide extent, the intefeence oscillations is consideed as a change in the natue of sound, heat, light and electical phenomena, explained by the vibational motion []. In adio engineeing, this coesponds to the definition of intefeence, as anything that changes o damages the infomation tansfeed by a signal fom the tansmitte though a communication channel to the eceive (e.g. sola intefeence in satellite communication). In the naow sense, intefeence is a supeposition of waves, with which they ae mutually einfocing in some points of space and weakening - in othes. Heewith the esult of intefeence depends on the phase diffeence of supeimposed waves. The theoy of such intefeence (i.e. intefeence in the naow sense) is based on the vecto summation of two oscillations []. In paticula, the two simultaneously popagating sinusoidal spheical waves and, geneated by point souces B and B, will cause the vibation in the point M, which, accoding to the pinciple of supeposition, is descibed by fomula +. ccoding to the fomula of a spheical wave: sin( ω t k sin( ω t k + α ), + α ), whee: Φ and Φ the phases of popagating waves; k and k the wave numbes; ω and ω cyclical fequency of each wave; α and α the initial phases; and the distances fom the point M to point souces B and B. In the esultant wave: + sin the amplitude and the phase ae detemined by fomulas: Φ actg + + cos( Φ +. cos Φ + cos Φ Φ Φ The theoy states that only coheent waves may intefee. In the theoy of signals [3] the concept of coheence has seveal definitions. Fistly, coheence is consideed as an ageed behavio of seveal vibational o wave pocesses in the time. econdly, the vibations ae called coheent, if the diffeence of thei phases emain constant o changing egulaly. Thidly, the coheent signals ae consideed with the same fequency (ω ω ), and fluctuations which occu along the same diection. This esult of the intefeence will be detemined by the phase diffeence: Φ Φ Φ α α + k ( Fouthly, the coheence is intepeted as a measue of the spectal width of the signal. In this case, the smalle the spectal width of the signal is, the degee of coheence is highe. The esults of intefeence, called the intefeence figue, depending on the wavelength and the distance between the point souces ae shown in fig. [4]. ). ),

2 Fig.. The esults of intefeence, depending on the wavelength and the distance between the point souces Fo a fully coheent souces, the intefeence figue is an endless altenation of light and dak aeas (bands), which coespond to the sum and diffeence of the amplitudes of the inteacting oscillations. n example of nealy coheent light souces ae lases with vey naow spectal line of adiation. With egad to the adio-technical souces, absolutely coheent can be only those that geneate a stictly peiodic sinusoidal signals. uch signals have minimal spectal width, because the spectum consists of a single hamonic. To patially coheent efe geneatos of non-sinusoidal peiodic signals, fo example, of tiangula shape. The spectum of this signal contains seveal hamonics, distibuted in a cetain way. Patially coheent signals ae also such signals, which coespond to the mixtue of peiodic sinusoidal component and andom noise, whose intensity is much smalle than the intensity of useful component. The geneatos of andom signals, having a continuous spectum in a cetain ange of fequencies ae consideed to be absolutely incoheent. Thus the spectal powe density of a andom signal may have a diffeent fom of distibution. In paticula, the andom signal which has a unifom spectal density, is called "white noise". Random signal which has an abitay, iegula spectal density, is called "coloed noise". ccepting the tems of coheence it tuns out that the phenomenon of intefeence (like a pictue of altenation light and dak bands) of incoheent souces must be absent. But thee is an exception. If two signals ae foming fom the same incoheent souce and thee is a phase shift between the signals, the intefeence can still be obseved. In paticula, the sun emits incoheent light waves, that is equivalent to the andom noise with nealy unifom density. Howeve, we can see the intefeence colo pictues on the suface of thin films on the wate fom sunlight. The theoy of signal links the concept of intefeence with the concept of coelation, consideing any laws of vaiation of the components fo the amplitude of the esulting signal which is popotional to the poduct of the amplitudes of the souces and the cosine of the phase shift in equation (). Fo two independent andom signals, the coelation coefficient is 0, which coesponds to the othogonality popeties (cos Φ cos π / 0) and, thus, the squae of the amplitude of the esulting signal is equal to the sum of the squaes of the amplitudes of the components. Fo coheent souces the amplitude of the esulting wave is equal to the sum of the amplitudes of the components (amplification effect) in cases whee the phase shift is 0 degees. When the phase shift is 80 degees, the amplitude of the esulting wave is equal to the diffeence between the amplitudes of the components (the effect of attenuation). This conclusion is fully coesponds to the established undestanding in physics of the phenomenon of intefeence. The analytical desciption () of the intefeence phenomenon is supposed that the shape of the esulting fluctuations + does not change at any atio of amplitudes and phases of tems. Howeve, the authos caied out special studies which showed that the intefeence is moe complex, that appeas in changes of shape of the esulting signal depending on the atio of the amplitudes of the inteacting oscillations [5,6]. Howeve, this phenomenon is absent in coheent souces, but occus fo incoheent souces. In this wok the methodology, tools and esults of modeling the evolution of a binay mixtue of signals ae descibed, and theefoe the phenomenon of incoheent signals intefeence was found. II. METHOD ND TOOL OF REERCHE Methods of eseach is explained by the stuctual scheme (Fig. ), containing the geneatos of and signals, combine, powe metes, signal geneatos output, indexing divide, calculating the powe atio of signals and identification scale which is used to measue the distibution fom of the mixtue signal at the combine output. Fig.. Block diagam of the method fo conducting expeiments The essence of eseach is to study the evolution of binay additive mixtues of signals U (t) Ua (t) + Ug (t). The evolution in this case, is [7] a mixtue of tansition

3 fom one bounday state to anothe with the change of components amplitudes atio ( / ) fom 0 to indefinitely lage value (ideally to ). In paticula, if the atio ( / ) 0, then the output signal of the combine U (t) Ua (t) is the same as the fom of the output signal of the -th geneato. If the atio ( / ), then the output signal of the combine U (t) Ug (t) coincides in fom with the output signal of the -nd geneato. In this egad, the question aises: how will the shape of the signal U (t) be changed within the ange 0 <( / ) <? To answe this question, an expeiment should be made as to adjust the amplitude of the signal geneato, measue the atio ( / ), fo example, in the fom of powe signal s elation (PR), and also to measue the wavefom of the mixtue. The tool, called NF-teste fo the identification of the type [8] was used to measue the wavefom of the mixtue. The stuctue code (pogam LabVIEW-7.) of the NF-teste is shown in Fig. 3. IdPNF, N- mount of signal Mean (NF), N0000, L00 Eo (р0,95),% nalogues among peiodic signals TBLE. NF-TETER IDENTIFICTION CLE mod Kind of distibution of a andom signal sin Even 3 imp 4 Gaus 5 Lapl 6 Kosh ,003,5,7 3, qu in Ti, aw This table is called the identification scale (I) [8], because the linguistic stuctues appeas to be odeed in it, in the fom of names of distibutions (mod two-modal, asin - acsine, even - even, simp - tiangula, gaus - nomal, lapl - Bilateal exponential, kosh - Koshy) of andom signals. The objects of the eseach wee andom signals with the distibutions pointed above, and also peiodic signals of ectangula (squ), sine (sin), tiangula (ti) and sawtooth (saw) foms. If the components Ua ( t), Ug ( t) of the mixtue have the same name, then a mixtue U ( t) is called auto-sum, in othe cases - coss-sum. In paticula, the examples of auto-and coss-sum can be the mixtues that wee obtained by summation of andom signals and shown in Fig Fig. 3. tuctue code of the NF-teste Mathematical model of the teste is based on computation of the signal amplitude atio to its standad deviation (D): max{ x } min{ x } NF i i K N, f N ( x X ) N i i and intepets the teatment values (X) of the signal as the tansfomation the amount of infomation of size N at the input of the ecognition system to the amount of infomation of size NF at the output. Identifying paamete NF, called a vitual volume, displays the fom of distibutions of andom signals numeically, as it s shown in Table.. Fig. 4. The example of the mixtue wavefom depending on the atio of powes of andom components to auto-sum () and coss-sum (B,C) s it s seen fom the gaphs, the dependence NF (PR) have a clealy defined extemum (in this example, maximum), that is equal to the sum of the identification numbes of inteacting components, and it indicates the change in the wavefom of the mixtue. Exactly this effect the authos

4 popose to call «the phenomenon of incoheent intefeence». The position of the maximum fo the auto-sum coincides with the condition of equality of components powe (fig. ). Fo the coss-sum the position of maximum is shifted fom the condition PR in the lage (Gaph B) o less (Gaph C) side, depending on which of the components is subjected to egulation. In othe wods, in this type of summation of components of the mixtue the commutative law is not obseved. It indicates the nonlinea natue of thei inteaction. III. THE REULT OF REERCH The esults of evolution eseach of the auto-sums of andom signals, which distibution names ae given in Table., ae shown in Fig. 5. unlimited distibutions. In the biggest degee, the effect of the inteaction of components of the mixtue fo these goups of signals, occus when thei capacities ae equal. Thid goup of signals ae the signals with so called stable [9] distibutions (5-gaus, 7-kosh), whose EIC does not depend on the powe tems atio. Theefoe, these chaacteistics have the fom of staight lines, paallel to abscissa axis. It should be noted anothe peculiaity, which appeas in egula, deteministic natue of the EIC family. Consequently, these chaacteistics, fist, can be modeled by the geneatos of peiodic signals and, second, it s possible to ceate the analytical desciptions that will theoetically allow to estimate the effects of the inteaction of andom signals, fo example, to pedict. To test these assumptions, the authos poposed and studied the deteministic model of the phenomenon of incoheent intefeence, which is built on geneatos of peiodic signals. The stuctue of the pogammed code of the model is shown in Fig. 6. Fig. 5. Evolutionay identification chaacteistics of auto-sums of andom signals (-mod, -asin, 3-even, 4-simp, 5-gaus, 6-lapl, 7-kosh) The educing of andom fluctuations in the gaphs is achieved by aveaging of a lage numbe (L 00) of the individual implementations of dependencies such as Fig. 4,. The volume of andom ealizations was N 000. The numbes (fom to 7) of dependencies coespond to seial numbes of the names of allocation fom the table.. Fo example, the numbe 5 efes to the dependence which was obtained by summation of two andom signals with a nomal (gaus) distibution. The values of powe atio (Powe ignal s Relation) of summable components ae situated on abscissa axis, and the value of identification numbe (NF) is on the odinate axis. The fom of evolutionay identification chaacteistics (EIC) allows to make an objective classification of andom signals into thee goups as follows. The fist goup is fomed fom the signals, whose autosum has a maximum. These signals (-mod, -asin, 3-even, 4-simp) belong to the class of signals with limited distibutions. The second goup is fomed fom the signals (6-lapl), whose EIC has a minimum. These signals have Fig. 6. The deteministic model of obtaining EIC of andom signals mixtue The stuctue contains two functional geneato of type FGen_3.vi, combine, NF-teste, the visualization block of EIC, the elements of shaping, amplitude and fequency signal geneatos. The cycle of type Fo-Next is intended fo automatically building EIC, and as the diving paamete is the amplitude of the signal geneato located inside the loop. The amplitude of the second signal geneato vaies fom 0,0 to 00, simulating, thus, the changing of intensity atio of summable components, because the amplitude of the fist signal geneato is fixed at a constant level, fo example, which is equal to. NF-teste measues the shape of the output signal of the combine, as a function of the atio of intensities. In ode to get a paticula dependency (Fig. 7) with the help of this model, it is necessay to tune the fequencies of the fist F and F of the second geneatos accoding to the data fom table.. The settings of geneatos fo auto-sums of andom signals ae pesented in the diagonal elements of the table. These configuation options allow to geneate EIC mixtues fo auto-sum with an eo of no moe than %. In

5 the emaining cells the paametes of settings of geneatos fo coss-sums ae specified. Fig. 7. The gaphs EIC of mixtues of peiodic signals fo the model in Fig. 6 TBLE THE FORM OF PERIODIC IGNL OF TNDRD GCCF ND THEIR IDENTIFICTION NUMBER Geneic paametes F;F; Delta,%; hift The fom of peiodic signals of standad GCCF and thei identification numbes (NF-teste) quae ine Tiangle awtooth Cos quae ,08 0,3 0,55,7 0,3 ine 0 5 9,5 7,8 0,05 0,4,87 0,64 0,5 0,5 0,5 Tiangle ,5 8 0,05 0,86 0,66,4,8 awtooth 4,5 3,5 9,9 0, 0,4,66 0,6, Cos ,05 0,6,4 0,5 0,5 0,5 0,5 In paticula, the data fom table show that in the case of addition of -sinusoidal signals, the phenomenon of incoheent intefeence down to the limit is appeaed at the diffeence of geneatos fequency between each othe 5 times (the intesection of the column and the ow with the name of INE). t the same time, thee is no intefeence, if the oscillato fequencies ae equal, that, in fact, the esults of expeiments pesented in Fig. 7 confimed. The figues 7 and 7, B, espectively, illustate the esults of the intefeence of two sinusoidal signals when the fequency of the geneatos diffe 5 times (non-coheent signals), and when the fequency of the geneatos ae equal (coheent signals). In the figues 7 C and 7 D ae shown the esults of incoheent intefeence (the fequency geneatos diffe 9 times) of sinusoidal and tiangula signals while changing the ode of summation. If we compae these esults with those that elate to the summation of andom signals (Fig. 4 and 5), then the high degee of confomity can be noted. IV. CONCLUION The expeiments, fist, confim the existence of the phenomenon of incoheent intefeence with the addition of two signals. It is clea that the phenomenon is indiffeent to the natue (peiodic, andom) of summable components. Thee ae the optimal conditions of setting the fequency fo the peiodic geneatos at which the effect is to maximize. The conditions of setting depend on the shape of summable signals. The law of the mixtue wavefom changing is sensitive to which of the two components is subjected to the egulation. The egula natue of the phenomenon of incoheent intefeence allows to descibe it in an analytical fom. Howeve, the latte cicumstance equies a sepaate eseach. REFERENCE [] aveliev I.V. The couse of geneal physics. In 4 vols. - Moscow: " Publishing KnoRus", [] aveliev I.V. The couse of physics. In 3 vols. Volume. Electicity. Oscillations and waves. Wave optics. Ed. 3d, a steeotype. - Moskau: "Publishing Lan", [3] Collegiate Dictionay. Electonic vesion. [4] Univesal Encyclopedia. Intenet esouce. [5] Klikushin Y.N., Koshekov K.T. tudy of the evolution of binay mixtues of signals // Bulletin of KazNU. - lmaty: " Publishing KazNU", (44), 005, [6] Klikushin Y.N., Koshekov K.T. Models of the evolution of the additive mixtue of signal-noise atio. / / Bulletin of KazNU. - lmaty: " Publishing KazNU", (44), 005, [7] Klikushin Y.N. Technology identification of scales in the poblem of ecognition of signals: Monogaph. - Omsk: " Publishing OTU", [8] Klikushin Y.N. Classification scheme fo pobability distibutions. Intenet aticle // Russian Jounal of Radio Electonics, Publishing IRE R, (Novembe), 000: [9] Zolotaev V.M. One-dimensional stable distibutions. - Moskau: "Nauka", 983, 365.