JPRS ID: 8341 TRANSLATIONS ON USSR SCIENCES AND TECHNOLOGY PHYSICAL SCIENCES AND TECHNOLOGY

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16 !.lARCN 1979
m m
(FOUO i6179)
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JPRS L/a341
16 March 1979
TRANSLATIONS ON USSR SCIENCE AND TECHNOLOGY
PNYSICAL SCIENCES AND TECHNOLOGY
(FOUO 16/19)
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JPRS L/8341
16 March 1979
TRANSLATIONS ON USSR SCIENCE AND TECHNOLOGY
PNYSICAL SCIENCES AND.TECHNOLOGY
(FOUO 16/79)
* . .
I,ONTENTS PhGE ,
ELECTRONIC9 AND I;LECTRICAL ENGINE'ERLNG -
Spatial-Time Procesaing of Radio Signals in Radio Measurement
3ystems in the General Case (Review)
(I. Ya. Kremer; C. S. Nakhmans on; IW'L RADTOII,EICPRONZKA,
, Nov 78) 1
The Synchronous Excltation of the Primary Harmonic of a
Field With a PL-riodic Structure by an Incident
Nonrelativistic Flaw
(G. A. Alekseyev, et al.; IVUZ RADIOIIIIfiPRONIKA,
Nov 78) 18
Postdetector Storage in Signal Detection Channels .
(Yu. L. Mazor; IVUZ RA.DIOELEKTRONIKA, Nov 78) 24
Processing a Signal With a Ra.ndom Delay Using a Digital
, Matched Filter
- (I. P. Knyshev; IVUZ RADIOELEUROIVIKA, Nov 78) 31
The Noise Immunity of the Optimum Detection of Fluctuating
Signals in Noise of a.n Unknawn Level
. (K. K. Vasillyev; IVUZ RADIOEI,FKTRONIKA, 'Nov 78) 34 - The Reflection of a Quasicontinuous Signal From the Surf,ace
- of the Earth at Small Grazing Anglea
(L. F. Vasilevich, N. A. Vinogradov; IVUZ RADIpLEKTRONII{A,
Nov 78) 39
Modeling the Processes in a SelP-Cscillating System Which Is
Acted Upon by a Reflected Delaying Signal
� (V. G. Lysenko, A. R. Niileslavskix; IW'L RA.UIpEI,EIMpNIKA.,
-
Nov 78 44
- a- (aii - UssR - 23 s& T FoUoI
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CONTENTS (Continued) Page
- GEOPSY8IC8O ABTRONOMY AND BPACE
~
Corpu.scular Model of Gravitation end Inertia
(IC. Ye. Veselov; PR710GAUNAYA aEOFIZ]:KAp No 87) 1977) 49
Methods of Eatimsting the Accuracy, Network Density and
Isoanoma].y Gross Section of a Gravimetric Survey
(s. P. 3urovtsm; PR.IiQADNAYA QPOP'IZIKA, N0 87, 1977)� 66 _
PUBLIGATION3
List of Soviet Articles Dealing With Compoai.te Mater3als
(GpgUDARgTVM1Nyy gQNLLTEi' SOVETA MINISTROV SSSR PO
~ NAUKE I TEKHNM. AKADIIMYA NAUK SSER. SIGNAL' NAYA
INFaMSIYA. KQMPOZl'PSIONNYYE MATEEtTALY., No 24,
1978) 78
a
- b -
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ELECTRONZCS ANU ELECTRICAL ENGZNEEkTNG
UDC 621.391.161
SPATIAL-TIME PROCESSING OF RADIO SIGNALS IN RADIO MEASURIIMENT SYSTEMS IN
THE GENERAL CASE (REVIEW)
Kiev IVUZ RADIOELEKTRONIKA in Russian Val 21 No 11, Nov 78 pp 3-15
[Article by I.Ya. Kremer and G.S. Nakhmanson, manuscript received following
revision 10 May, 1978] .
[Text] Optimal apatial-time processing of signals is
considered in the general case, including t1ie location
of the objecta and external interference sources being
observed in both Che far field of the receiving antenna
systems as well as in the Fresnel zone. Also analyzed
are the possibilities of utilyzing information on the
curvature of the wave frnnt of eignals and interfer-
ence to increase the precision in the determination of -
the location of the observed objects, increase the re-
solving power of the system and discriminates signals
from interference generated by external sources.
Introduction
- The baeic principles of the theory of optimal spatial-time processing of
signals ir; determining the position of observed objects and the parameters
- of their motion have been rather thoroughly worked out in the literature
[11- 31, etc. However, specific results in this field have been primarily _
obtained as applied to the apecial case where the wave fronts of the signals
in the external interference can be considered planar, i.e., the observed
obJects and interference sourcea are located in the far field of the receiv-
in$ antenna systems, something which is justified only when the following
- condition is met:
R.c R,,.== 2L cosep (1)
where R is the distance of the radiation source from the center of the
antenna; RA3 is the radius of the far field; L is the overall dimension
of'the receiving antenna system; 0 is the angle between the normal to the
plane of the antenna and direction to the source; a is the wavelength.
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The eEfort Co increase the resolving power o� radio measuremenC systems _
and, relatad to this, the trend towards the uae of large aneenna syatems
- auci t:he mastery of increasingly ahorter wavelengths, as well as the use of -
_ diversiCy receiving systems [4, 51 is leading Co the fact in a number oE
cases, condieion (1) is not met and it is impossible to consider the wave
' fronta of the signals heing processed to be planar ones. T us, the basic
relAtionships derived for the case of plane electromagnetic waves are not -
applicable to the analysis and synthesis of optimal spaCial-time signal
procesaing algorfthma in a number of radio measurement systems and the
theory of several auch systems (mulCiposition radar systems [5], hyperboli.c
radio navigation systema [6]; etc.) are at times developed independenrly
of the general theory of spatial-time processing signals. This makes the
analysis nf such signals diff icult based on uniform methodological principles
of optimal recepCion theory, as well as the estimation of the closeness of
their chAracteristics to the potential achievable ones and the determinaCion
_ of ways of optimizing them. What has been said above can also apply to
sonar systems. For this reason, an urgenC problem is the generalization of
theory of optimal spatial-time processing for the case of the recepti.on of
aignals with both planar and epherical fronts, i.e., for the general case -
of the location of the obaerved objects and external interference sources _
in Uoth the far field and the Fresnel zone of the receiving antennasl.
In this treatment, the electromagnetic field of the signal has an addiCional
parameter (as compared Co the case of a plane wave), the curvature of the
wave front, which can be employed as a source of information. For small
sized ("point") signal sources, the curvature of the wave front is uniquely
related to the range to the source. With suitable processing of the signal,
this allows for the realization of the followirig additional capabilities,
which are m3nifest more strongly, the greater the ratio of the dimensions
of the antenna system to the range to the signal and interference sources,
- and the amaller the wavelength:
--The spatial resolution of the objects with respect to range, by virtue of =
the difference in the curvature of the wave fronts of the signals generated
by them [2, 7, 81;
--Tlie discrimination of the useful signals:from interference generated by
external sources, by means of selection based on the curvature of the wave
Cronts [9];
--7'lie determination of the range of "point" signal sources based on the
curvature of the wave fronts;
1 I7or multipoaition measurement sysrems, the antenna is understood to be
the set of antennae of all the receiving statians.
2
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In l�}inse active radar sysrema, where the ran$e is measured based on the
gignal delay time, the uae of a supplemental independent information source
wi11 permit increasing rhe precision oF Che range determination [10, 11,
12, 13, 14]2.
This paper is a survey of the basic principles And specific features of the
optimum spnCial-t�Lme proc:essing of signals in the general case, including
the proceasing of both plane and spherical waves, and a brief analysis is
given of the poCential characteristics of such processing (resolving power,
= noise tmmunity, and precision in the derermination of the location of nbjects). _
This ttnalyais is based on both published and new resulta. To aimplify the
mathematical derivations, the treatment uses the example of n plane problem, '
where the antenna system is oriented along one of the cooroinate axes, while
the objects and interference sourcea being observed are located in the same
plane. The basic: governing laws ascertained using the plane problem example -
are alsn jueCified when the objects and interFerrnce sources being obaerved
are posiCioned in three-dimensional space, as well as for antennas of any
size (linear, planar, three-dimensional).
_ The Ambiguity Function of a Space-Time Signal and the Spatixl ResoluCion
Posibilitiea
A deecription of antenna systems and signaZs, geometric re7ationships. An
antenna system with an overall dimension L and a center at the origin of
the coordinates is oriented along the Ox axis (Figure 1). The geometry of
the antenna system and the gain distribution in it are defined by the aper-
ture function i(x) (3]. Basically, two forms of the functions i(x) will be -
considered: a function corresponding to a continuous linear aperture wi.th
uniform gain (I(x)12 = I when Jxl j L/2; II(x)12 = 0 when Ixi > L/2 and the
n
- discrete function l1(x)1zaEb(x-xr), , where xi are the coordinates of the
receiving elements. A continuous aperture for the case of reception in the
Fresnel zone is samewhat of an idealization, however, such a representation
of t(x) permits the derivation of the basic relationships in compact form,
while the numerical results, as calculations show, practically coincide with
thie results obtained for an antenna array consisCing of a large number of
isbtropic elements with spacings between adjacent elements less than A. The
diiscrete function II(x)J2 ia a sufficiently good descripCion of an antenna
arxay of isotrapic (nondirectionxl) elements with an arbitrary number of
2
Data on an active radar system are given in [15j, in which the range
meaeurement is based on the curvature of the wave front and the informa-
tion on the time delay is not used.
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Pt
44
z0 80 dp~
PNC. 2. 0
Figure 1. Figure 't.
_ e.lemenCS and arbitrary spacings between them, as well as�of the anCenna systems
of mulCiposition radio measurement system3 under the same,conditions and with
relatively smAll anrenna dimensions at the individual receiving stationa.
Let the observed object take the form o� a smaXl (point) isotropic radiation ~
source, located at the point Mp with coordinates of R and 0. The �orm of
the signal radiated by the object (for the case of passive radar) or the
sounding s ignal (in the case of active radar) is def ined by the eapression:
so(~a Re{so(t)} - Re {l!(~ ll�g}, (2)
where U(t) is the complex envelope of the signal. If the sounding signal is
radinted from point 0, then when there are no distortions in it in the pro- '
pagation process and the corresponding normalizing of the amplitude so(t),
the spaCial-time signal being processed has the form:
_ s(t,X)=aol(x)r~ ) sort- R ~~~X~ll~a'', (3) ~
where �p is the random initial phase which is uniformly distributed over the
range [0, 2w); r(x) is the range from the object to point x of the receiving
antenna, equal to
r(x) = r(x, R, A) = jl R= x1- 2Rx si n 6, -
(4)
~
ap is the amplitude of the received singal at the point x= 0. Under the
~
same conditions, in the case of passive radar, if the time is read out with
respect ta the aignal arriving at point 0, the signal being processed has the farm:
s(t,x)-QoI(X)rR) sort_. r(X)^ R 1lpm.:
1 1 (5)
r(x) at values of the range R which considerably exceed the overall dimen-
sions of the antenna system L, can be approximately represented by three
terms of series (the Fresnel approximation):
4
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_ r(x)_R_xsine+ X, cos=e
2R_ (6)
The near boundary of the field in wtiich the k'res-al approximatien can be uaed
is determined from the condiCion where a/16 does not exceed the value of the
fourth term of series (6), and when 0= 0, the fifCh term of the series.
R1 a R~,, ~ RA, r. S2 e, R3 > R~ns = Rn, L2 " 5 sin3 A
16 (7)
The region of the locatien of the objecta being observed, Rdn LRnearl
a
R= RA3 [Rfar fieldl, Where it is necessary tn Cake into nccount Che
sphericity of the wave fronta and the Fresnel approximation cnn be used, we
- shall ca11 the Freanel region.
_ The ambiguity funetion of a space-time signaZ. Let two observed objecta
(signal sources) be posikioned at pointa having coordinates of (R1, 01) and
(R2, 02). Taking formulas (2), .(3) and (5) into account, and neglecCing the
lack of equality of the amplitudes of the signal at the di�ferenC points in
, the antenna system, something which is permissible when RL Z> L[16], the
range and direction ambigvity functions for the case of Active and paesive
radars wi11 have the foZl.,owing forms reapectively [6]:
/ri -I- R, - a --12a 2n
. J I 1(X) 12 P~ I c r) exP I~(r, -f- R, - rs - R2) dx
~
p (Ri, e,, R,, e,
00 ,
f I t (x) Is dx (a )
.
j(1 wll~ r r,- Rf- rz -I- Rz 1 eX 2n r-
~ ` ~ ~ P i j~ R, - r= RJdx
P (R,, e,, R2, a,) _
, (9)
. f I 1(X) pdx
where pT(T) is the normalized complex autocorrelation funct3on of signal (2);
rl and r2 are the distances from the signal sourres to the point x of the
antenna system.
In (9), the argument pT is the difference in the time shifts of the signals
received by the antetina system at the points x and 0. For the case of noC
very large antenna system dimensions (or a rather narrow epectrgl bandwidth
Afc), the following conditions are observed
ra - RZ ri - R,
� ~ '
c - c ~fo ~ Ps (lo)
and the ambiguity function (9) does not depend on the wave form of the signal
s0(t). We shall introduce the following symbols: AR = R~_ R2 is the differ-
- ence in the ranges of the objects being resolved; Rp = R 1R2 is the mean
seometric value of the ranges. Then, in case direcCional resolution is im-
posaible (01 = OZ = 0), taking approx imation (6) into account, the expressions
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- for the range ambiguity functiona for acrive (8) and passive (9) radar can
be repreaented in the form
P(oR,R,.e)=
(1l)
( ii>
N (2 ~R + xa AR cosa e eXP/ 2 eR xzAR 1 dx I
f(x) la*
� 2cRo ) ~ 2n( c 2cRo cos A1
, f (1(x) J1 dx 
. '
. � a(eR,Ro.e)= (12)
(12)
1(x) I~ Ps ( x~eR cosz9 ex 2n( x'~R 1 ~ _
\ 2~?0~ ) P 1~, 2Ro cos 8~dx f i f(x) I dx.
_
-
' As follows from (11), in the case of active radar, the resolving power with
respect to range is due to two �actors;
--The resolution with respect to the delay time (time re3olution), determined
by the 26R/c term in the pT argument (when (10) is met, the values of the func-
tion pT are determined by this term alone);
--The resolution due to the difference in the curvature of the wave fronts of
the signals (spatial resolution).
In the case of passive radar, the range resolving power is due only to the
spatial resolution. Formula (12) shows that the range resolving power due
_ to the curvature of the wave front of the signals increases with an increase
_ in the square of the ratio of the overall dimension of the antenna system L
to the distance to the objects being resolved Ro, with a widening of the signal
snectrum and a decrease in the wavelength. For a linear antenna of length L
with uniform gain, if condition (10) is met, (12) yields the following [2]:
at. (oR.Ro, e)=c(Ya )/Ya (13)
.
~
where C(x) = c:os n 2 dt is a Fresnel cosine integral, a==eRL2cos~/(2a~Ro).
The grapli of the function pL(AR, Rp, 0), determined by (13), is shown in
Figure 2. The width of this function at the 0.5 level is determined by the
expression
s
- dRo, a- LZ ~2 e k - 16 Ro/Ra,.
(14)
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Formulu (14) ehowa thaC in syatems with narrow band signals, reaolurion with
respect Co the curvAture of the wave front can be effective only at ranges
aign3ficantly less than the far field radius of the receiv~.ng anCenna system.
_ Tlte 1aCrer condition is usually met for mulCipoF;itior: radio systems. In such
radio syaCema, the values of the range Ro Are of the same order of magnitude
as the overall dimens:Lons of the antenna system L[5]. In thia case, the
- range resolution inCerval runs Co units or tens of wavelengths, i.e., an
exCremely high spatial resolukion can be achieved. 'Phe failure to meeC con-
= di,tjoil (10) leads to an additional improvement in the reaolution wiCh respect
- to the curvature of the front.
Optimal Spatial-Time Processing and the Discrimination of 5ignals from
_ Interference
We shall cQnsider signal processing for the case of activA radar wiCh a small
- :IsotrupIca1.l.y reradiating Carget, l.ocated at A point with coordinatea of (R, 0)
(Figure 1). The following resulta, as applied Cc the spatial processing of
- the signals, are also ~ustified for the case of passive radar for ama11 radia-
tion sourcea. The signal (3) is received by the antenna against a background
of internal antenna sysCem noise with a spectral density of N0, which is un-
correlated at different points in the anterina system, as well as against a
background oE noise generated by an internal, small isotropic source of
gaussian white noise, located at point Mn having coordinates of Rn and On.
The correlation functions of the inCernal and external interference at the
antenna inputi have the form: .
; Bu (fi, tz, xs, xa) = 2-� 8(xi - xa) b(t, -tZ); B., (ri, ta+ Xi;z,) -
, . . - N, ~ S rts ~ _ r"! r"=1 � . . . � (15)
~nftnZ ~ r; ~ \ c .
EBBH � Binternall Where N1 is the spectral noise power density of the external
source in the antenna aperture; rnl and rn2 are the distances from the noise
source to the poi.nts xl and x2 of the antenna system, determined from (4).
, Signaz processing atgorithms. Jhen receiving spatial-time signals with a
random initial phase against a background of gaussian noise, the absolute
- talue of the correlatiion integral of [1] is taken as the outpit of the optimal
_ (in the aense of a criterion of the probability ratio) sigral processing system:
Z= 21S u(t, x) v(t, x) dtdx I.
cr~ c  `
(16)
- where u(t, x) is an additive mixture of the signal and interference; v(t, x)
- is the reference signal which determines the signal processi.ng algorithm;
(T) and (L) are the time and space intervals, in which the signal processing
is accomplished. The reference signal is defined by the relation:
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aCi~x,~~~ tt. x, xi)s(rit x') ~lditi, (17
~ )
where s(t, x) ia the uae�ul signa1, while 0(e, e1, x, xi) is the inverae
correlation Punetiidn of the ineer*erence, defined from the integral equgtion:
~ tf$ xis xj)B(lo tt# xo xI)dtidxi we 8(1 (x _xt~ (ig)
' f 1f
where B(t, t1, x, xl)  B$H(t, el, x, xi) + Hn(t) el, X, xi) ip, the Cdl'r@I.A-
_ tion function of the interference at the gntenna input. For a 12negr untenna
with uniform ggin, the reference gignal which natifies equgtl.on (17) aesumeg
the form: Q~t~x~~ 2 R~(t.R--i x Nt !
~ { r x) c ) + i rjl (x) re (xj dx X
s
~w
- x l ~z~ R. ~ `t _ R `f' r(xi) - Q (xi)~- rn (z) ~i, (19) (19
)
and fnr the i-th receiving element of a diacretE antenna gysCem (antenna array)s
~ R$Ct-R ~~R;~ t-R`f' r" crn-f'Ln) (20)
where
1V, ~~~r ~N~ ~1- No) ~ j ~ �
.
The firet terms on the right side of expreasion (20) and (19) describe pro-
cessing matched to the received uaeful signal (3). In the folloaing, we shall
call spatial-time proceising using such a reference signal matched processing.
This proceeaing ie optimal only in the absence of noise generated by an external
source. With matched proceaeing, the antenna ayatem ie "focused" with reapect
to range and direction. The aecond terms in (19) and (20), eubtracted from the
tirst, provide for optimal compensation of ex:irnal inte*ference. The essence
of optimal apatial-.*.ime proceseing in the preaence of internal and external
noise is more clearly aeen in the case ahere expansion (6) can be uaed, and
the signal is a narrow band one in the spatial-timeaise aense (the correlation
time of the signal 1/Afc is many times greater than the maximum value of the
time ahift between the aignal values at the extreme points of the antenna
system). For the case of range valuea which exceed the overall dimensions of
the nntenna syatem, one can neglect the inequality of the amplitudes of the
signals at different poinCs in the anCenna. Then formula (19) assumea the
fnrm: /
l - ~imp zsin9 z~ooss9
No ~ . ~C- -~11 -
/J
- PL (RQ. 9n. R. e x sin 6� x+ooss ~
1 ~ (21,
~ ~ uP [J% --~~'~J
w'Ca~
~
8
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e
ahere � t
P` (Rio ~tso 8i, O,~ ~ exp f x (ytn 0, stn Oj

r~R lll (22)
t ~ : If (
The expregsi,on which defineg the fdrm of the reference signa1 fnr the anCenna
array is deCetmined on analogy aith (21), gubgtituting xi Pnr x. Ie ia ndt
diffiCUlt to see from (21) that with gpaciai-narrow band signals, time and
spatial prdcessing are separatedt the fgctor in front di the curly braces
determineg the optimum timewise pxoceseing nf a signa1, and the expressinn
in the curly bracee dptermines itg spatial procesaing, whieh rpduces to the
matched epatial proCeasing of the ugeful end interference signblg, end the
eubtraction from the reeulte of the firet operation of the xpeult of the second.
The subtraction ie cnrried ouC with the areighCing Pactor 1316L(ittt, Ott, R, 0)/
/(Na + N1), defined by the mutual pogieidning of the earget and the noiae
source, ao weil ae the relationehip af the external and internal noise inCen-
sity. Where eeverel pxternal noige gnurces gre prespnt, matched epatial pro-
ceesing should be cgrried dut for each source, jtgt ae in (19), vith weight-
ing Cneffi4iente Which depend on the relationship of che intena'iCiee of the
noige sourCea and their mutual arrangement (9). Uaually, the coordinates and
intensities of the noiae eourcn_s are unknown beforehand, and for thie reagon,
they should be determined by the proceseing system in the process of generating
the reference eignal. The design af guch processing eysteme ig possible by
meana of ueing the principlpe analyzed in (Z, 17j.
The suppreaeion of noipe generat8d by e.xtgrnaZ aourcee. The effectiveneas
of the suppresaion of naise generated by external eourcea can be evalugCed
in terms of the eigngl to noiae ratio at the outpuk of the procegeing system.
The poWer sigttal to noise ratio for the case of apatial-time signal process-
ing is equal to [1]:
x) o(t. x) dldzl.
(23)
To eatimate the level o� external noise suppression, we ahall introduce the
following coefficiente:
k � 9'/90; ! ~ 9'/9'0,,�
- (24)
ahere q2 is the output signal to noise ratio for the case of optimum procesa-
fng of a signal with aspherical front againat a background of internal and
external noise; qA, ie the same for the optimal pruceasing of a signal with
a plnne wave front under the same conditions; qg applies in the abaence of
external noiae. The coefficient k indicates the degradatiun of the output
aignal to noise ratio by virtue of the presence of external noise; the coef-
ficient Z is the level of suppresaion of external noiae through the use of
information on the curvature of the wave Pronts.
9
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In the dptimal proceseing of ngrrow band signalg in a linear nnCenna of lengeh _
L, formulg (23), taking (21) into aCCOUnt, yieldg the gollowing [9]:
~
k':' 1.._ N . N ~ AL (Iln~ en ~ E2~ 1m r 1.}. .k 1 k.
\ / (2 5)
The valuee of the noefficients k and I a,�e ehown in Figurea 3a gnd 3b (ehe
pI9 , where RA~ ig the far field
snlid 11nes) ge a functinn of Y~. 17-Rn R'" R
rndiug of (1), for the cgee where the angular coordinates of the noiee source
and thu target coincide (On - 0), and geting of thp external noise is pogsible
only through the diffQrence in the curvature of their aavefronts. As followg
from Figure 3, w3.th a eignificant difference in range betveen the eignal and
noise eourcea (Y � 1) ka 1, i.e., Che external naiae can be suppreseed almoet
completely. in this case, the adventage gained in the gignal to noise rgtio
ae Compered Ca the cgee of processing a plgne wave Z ie approximgtely equal
to the rgtio of the speCtral densitiea of the external and internal noise at
the antenna aperture. The gain falls off in etep with a decrease in the curva-
ture of the wave fronti.
It Was nnted above that the realizatior of optimal spaCigl-time processing
of eignals Where exCernal noise aources are present ig rather complicated.
Por thig regeon, it ie of interest to aesese Che pogeibilities of euppressing
external noiae for the case of eimpler (fram a design viesapoint) matched
proceseing. In this case, the coefficiente k and Z are defined ns:
k� N~ 1� (1-- J-1 k. (26)
Ni~-N,IP~(Re. B.. R, e)P ~ ` N0
l
7'he values of k and Z With matched processing for the case of Aff � 0 are
shown in Figuree 3a and 3b by the dashed line. A comparision of theae curves
With the curvea for the caee of optimal processing ahowa that aC extremelq
emnll (Y = 0) and extremely large (Y > 20) curvatures of the wave front,
matched processing provides for iipproximately the same degree of external
noise suppreasion as eptimal proceeeing, while in intermediate cases (1 < Y<
< 20), optimal processing is more effective.
Figure 4 illuetrates the suppresaion df external noise for the cgse of optimal
apatial-time processing fn multipoeition radio syatems, where the aumber of
receiving pointe is small, while the spacings between them are � A. The cutwes
are plotted for the case where there ie no gaCing With respect to direction
(0ff = 8), While the noise source is located in the far field (Y U Rgg/R).
The dashed linee apply to a three-position system (xl --0.45 L, x2 = 0,
x3 - 0.55 L), and the solid lines apply to a five-position system (xl ! .
~-0.45 L. x2 - -0.2 L, x3 - 0, x4 - 0.25 L, xs - 0.55 L). The curvea in
Figure 4 atteet to the fact that in multiposition systems, the input signal/ -
noise retio expressed as a lunction of Ya Rgf/R is of an oscillating nature.
An increase in the number of receiving positions leads to a emoothing of the
oecillatione.
10
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Fur ehe cusp of acCive radar: ~
: c.' 4 (r16 ' [1+ Ls Ccoss 9 `
~q r , ~ sin! Al
090 ~ ~ II~ +11 o u
16
~

cos' 9(7 - 31 s ins 6) L-'-~ L' cos' 9 . (28)
In Cormulgs (27) and (28), L2 and L4 are the normalixed gecottd gnd foureh
moments nf the square nf the aperture functionslI(x)12 (1, 31, determine2
~ by the geometry of the gntenne eyatem gnd the gain dieCribution in it; q8
is the signal/floi8e rerfo; c is the gpeed of 1ight; n2 ie the gquare of the equivalenC width of the etgnal epecerum, defined as the second central
moment of the epectrum. The formulag gre de.rived ueing the approximate ex-,
pansion (6). . 1
~
~
l4'
ro,
~
h'igure 5.
For the caee of range meagurement based only on the
curvature of the wave front, the meaeurement error
as fo11oas from (27), is prnportional to the wavelength
a and the squarp of the ratio of the range R to the
overall eize of the antenna L, and the error depends
slightly on the epectral width of the signal. Shown
in Figure 5 is the nottinalized dispprsion of the range
measurement ag a function of the ratio L/2R for a
linear antenna of length L. aith a uniform gain dis-
tribution, and for an equally apaced antenna grray of
the eame length consisting of three elements where
(tta/Wo)Z � 1.
Zn act:ve radar, for the case of optirial spatial-time
processing of the signals, the range is determined by
meang of the joint utilization of the information on the delay time and the
curv;iture of the Wave front of the signals. To eatimate the influence of
wave front curvature information on-the precision of range measurement, shown
in Figures 6a and 6b are the rgtio of the dispersiona of the range eatimate
for the case of optimal apatial-time procesaing of the signals (vj) and for
the cnge of ineasurement based on the delay time (oRO) for a linear antenna of
lenRtli l. (Figure 6a) and for an -iqually spaced antenna arrey of the same
lengtli (Figure 6b). As can be seen from Figures 6a and 6b, the use of wave
front curvature informntion permisg a substantial increase in the range measure-
ment precision when L/R > L/Rbound a 2 n �
h'or ex,imple, ai[h n relntive spectral width of R3/wp = 10-6, the influence of
the InEormation on ttie curvature of the Wave front begins to have a substantial
rf[cct at ranges of R2 I 103L. M analysis of Figur.es 4, 5 and 6a ahoWa that
tor [clentical vttlues of the output signal/noise ratio and identical overall
JimenHionH of the antenna, the range measurement precesion when using "dis-
persed" antennu arrnya ie higher than ahen using antennas vith a continuous
12
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I
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4
~
l
/
i
~
/
/
6
6
4
2
0 ~ t 5 /025rorr o
c
(al.
N

'
i
/
/

l1? ~10?5/0`r
(b)
K m VA i a ir5 ~ r3 I
Q~
I ~ps 1 ~ ~
42
J
0 12 510 2 5 /0 Y
Figure 3. Figure 4.
; [fnsed on the values of the signgl/noise ratio at the output of the proceseing
gyetem cdmputed from formulas (19)--(23), the probabiliey of detecting bn
nbject by meung o� the wsll-known detection curvps cnn be determined. In Chig
cnHe, iC is necessnry to consider Che fact ChgC xt gmall valuee of R/L, an
increaqc: in thc range resolving power by virtue of resolution of the curvature
of the wave front leads to an incregse in the number of resolution elements
in ehe scanning field, and conaequently, to an increase in the false alarm
probability.
lletermining the Positiun of Objecte and Their Peremeters of Motion
q!
qc
Q~
Q~
The posgibility of determining range based or, r'ie curvature of a wave froni
arises wiCh spati.al-time processing of signals wteh spherical wave fronts.
In passive radar sysCeme, this is the sole primary source of information con-
cerning ttle range; in active radar :,stems, the information on the Wave front
curvnture cmn be emplayed in con,junction with the information on the delay
time of the signals to increase the precision in detennining the location of
objects, and in aome cases, it cen be used independentl.y [15]. For the case
of interference in the form of gaussian white noise, which is not correlated
nt Chn different pointa in the receiving antenna system, as well as for large
siKnnl/noise ratiog, the precision in the estiTaaCion of the range R using
tlic maximum probability method is characterized by the following expression:
For the case of pasaive radar
Q'�1'o ~T 1((00)I
+ 11 L' - Ll)-t ;
(27)
11
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- nperture, und bcaomey higher the Hma11er Chci number of elementa nC the nrray.
Hnwever, Enr lnrge vnlues nf L/J, a reduction in rhe number of 'e1emenCs af
the array cnn 1ead to ambiguiry in tiic measuremenes which can ba eliminhted
by menns df axpnnding the epectrum o� the signal being processed. The re-
~ quiremente placed dn Che signgl snectrum eo eleiminate measurement nmbiguity
in tihe angular coordinaCes when ueing "disperged" arrAys in the general cage
ax the positioning of the objecta being observed do noe differ dubsr.antinlly
- i;xom the requiremenes which nre see when the objeCts are ldcated in the fnr
field of the anCenna array. mhe ambiguiry phenomenon uf range measurcmenCs
nrises in the spaCial-time processing of signals wieh a spherical fronC. Tt
can Ue shown ehat ambiguity in the range measurement can ariae when receiving
signnls with a lineur, equally spaced antenna nrray containing n elements,
where n 4 ~ R ~og e) .
(29)
;0
0,/64"M1
1,4 opt
6A,
0,!
QI
~?R
~k `0 _ Q? Q< l/IR
(a) � � (b)
Figure 6. Figure 7.
In paper [11], the potential p?-ecisian in the estimate of coordinates is
analyzed for the case of an antenna of any size. A comparison of the results
obtained in Chis paper for a circular antenna, with those results given above
for n linera antennn ahows thut for the case of equal overall aize, the ad-
v;uitahe gnined in precision by virtue of using information on the Wave.front
curvuture ie approximaCely the same for both antennas.
An anzilysis ot the precision in eatimating the angular coordinate of an object
!n the genernl case shows that when receiving signals with spherical wave
CrcintH, the potential precision of the determination of directions is practical-
ly tite same As when recei.ving signels with plane wave fronts.
Ignoring the wave front curvature in spatial-time processing of signals can
le;id tn n substnntial degredation of the signallnoise ratio and the range
me;tsurement precision. Thus, When R= 0.02 Rgf, the signal/noise ratio falls
uEf by trns of timcs [11j. The range measurement precislon, ds a result of
fniling to tnke into account the information coneained in the curvature of the -
wave front, tor R s 25L and L/J = 100, decreases by ten times ahen 1i3/w0 '
= 10-3 and by 100 timea s.�hen ii3/wp - 10-6 (181.
13
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_ The poCenCial possibilieies for increasing the accuracy of multipogiCinn
radio sysCeme nperating in the F'resnel zong can be illuetrated by meane of
compnring the precigion of range measurement in a range difference (hyper-
bnlic) radio naviagaeinn systiem [6] and in a system with the same arrange-
mene o� the receiving etatione, which carriea out the opCimal gpatiial-Cime
proGessing oE the aignal. Shown in Figure 7is the ratio of the dispereiona
nP the range esCimate oh itt a Cwo-base hyperbolic system with receiving sta-
ttons at the pointa xl A L/2, x2 - 0, x3 - -L/2, gnd in a syatem which realizeg
the opCimal processing of the gignals received at the same statione: 0o t
_ (dg was determined on the basis of the relationahipa given 3n [6], and the
vnlues uf oo t were determined from formula (29) twice. It can be seen from
rigure 7 Chat the preciaion which can be attained in hyperbolic radio naviga-
Cion systems ia extremely fo.r from the potenCial accuracy obtainable with
optimnl coherenC processing of the aigngl.
Ttte rclutionghipsggiven above were derived with the assumption that the signal/
noisc rntio is rather high, and the range eatimate ia reliable, i.e., the pro-
bability of anomolous errors is neglectibly small.' With amall values of the
piirameter R/L, the reaolving power with respect to range increases sharply by
virtue of the resorution based on the curvature of the wave front, gnd cdn-
sequently, the probability of anomolous errors also increases. In this case,
higher values of the aignal to noise raCio can be necessgry to assure relia-
bility of the eatimate than is true of the case of range measurement based
only on the signal delay time. An analysie of this phenomenon ie given in
the literaCure [19], the reaulte of which show that for signal to noise ratioa
of q0 1 20, the increase in anomolous errors muat be taken into account at
rcletively small values of ChL range (as compared to the dimensions of the
antenna system) and at a relatively small signal spectral width (for tt3/wo _
m 10-3--10-4 when R 500.
Thus, na a result of the anelyaig made here, precise and approximate formu-
lns were derived w}iich are needed to egtimate the noise immunity of optimal
detectidn of packeta of fluctuating sigaals in noise with an unknown disper-
gion. -
BIBLIOGRAPHY
1. Levin B.K., "Teoreticheskiye osnovy statisticheskoy radiotekhniki"
("The Theoreticel principles of Statisrical Radio Engineering"], Moscow,
Sovetskoye Rndio Publishers, 1976, Book 3.
'l. 1'rokoE'yev V.N., "Obnaruzheniyc pachki signalov s neizvesCnymi parametrami
- v shumnkh neizvestnogo urovnya" ["The Detection of a Signal Packet wt,th
Unknown Purameters in Noise of an Unknown Level"], IZV. Vi1zOV -
tAl)IUELEKTRONIKA (PROCEEDINGS OF THE HIGHER EbUCATIONAL INSTITUTES,
W1DI0 FLECTRONICSJ, 1972, 15, No 10, p 1,234.
3. 1'rokof'yev V.N., "K zadache obnaurzheniya signalov v shumakh neizvestnogo
urovnya" ["On the problem of Signal Detection in Noise of an Unknown Level"]
� itADIOTEK}{NIKA I ELEKTRONIKA, 1969, 14, No 10, p 1,895.
3?
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G. Krnmer C., "Mneemnticheakiye metody atatiseiki" ["Mathemntical Meehode of
SCaCietiCs"] , Moecow, Mir Publiehers, 1975.
5. Grxdehteyn, I.S., Ryzhik I.M., "Tabl3Cgy integrglov, eumm, ryadov, i
prnixvedeniy" ["Tablee of Integrale, Sums, 3eriee and Producte"), Moscow,
Nauka Publ3sheYS, 1971.
GOPYRIGHT: "Ixvestiya vuzov SSS1t - Rgdioelektronikg," 1978
8225
CS0:1870
38
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- =CTRONIC3 AND LLECTRICAI, Mt}INEEiING
UDC 621.396.96
'CIIL 1tLF'!,L'CTInN Or AQUASICdN'1'INUUUS 5iGNAL FRdM 'CNE SUEtFACE 0F THC EAtt'I'H
A'C SMALI. G1tAZING ANGLLS
Kiev IVUZ ttADIdELl:KTItONIKA in Rusgian Vol 21 Na 11, Nnv 78 pp 133-135
(Article by L.F. Vuailevinh and N.A. Vinngrndov, menuecript received 14
Derembcr, 1977J
[kext] in gtudyinK qrnundrpCurng, g gtatigeically r4ugh surfaGe ie usunlly
emp.toyed itg the mndel of the reflecting nrea 11j. In thie paQer$ Chig surface
lt+ treated na a�ilter wieh randomly changing characteristiCS.. SuCh an
apprunc:h pcrmits the use of the well develnped toolg of parametric gyetemg
Chcory.
We shall write thc tieFlected signal in the form of the sum of the returne
from the elemcntal areag: ,v
r(9-~ 2~~'~ Q(9,)x(I-r,)&; d-~,
r.~
where K(t, ti) is the reflection factor of the i-th reflecting area; AD is
thesize of an elemental area, aithin the bounds of which one can coneider
the reflection characteristic to be constant; c is the propagation velocity
of the radio waves; Q(#i) is the shading futtctfon of (i): Q(#i) MQ(arc04n 2A�
Qi ig the grazing angle; hg is the height of Che antenna. d
lt is usually asgumed thnt the signal reflected from an elemental reflector
clneK not inf.luence other signals. It Was noted in [2) that the setting of
cuncllcicros ahich define the mutual influences of the elemental reElectors
JneK nut produce uny marked change in the resulta.
Taking this tnLo account, one cxn go to the limit Where At 0 and N
s~
V(nw f Q(i)~U.s)x(t-t)ds,
~
attere Tmin end Tmax are the delay limts of the reflected aignels; k(t, T) �
a~ l K ie the pulse characteriatic of the reflection of the aurface
_ gegment.
39
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IE n pulned Hignnl with an amplieude A nnd g period Tn [Tp] in uged gg
the naunding gignnl, M
x (J) �'I A(t - mTe) aP ("1W tI
a.1
ehen the reflecred s3gna1 geswneg the furmt
Ma M
Y(0 f~' Q(t) R(f mTn, t) A(! - mT,, - t) uD Ir-'j'lfti (I - e7'n r' t)Mt.
sfm� 0-1
Let dndther get of elemental reflectore be loegeed at a cereain distance
n2. The signgl refiected from it wi11 bes
stnra
Yt~) ~ j QIti1R (I -o, t)x(f-n-S) di,
where ~
20
Whcn computfng the correlation funetion (Itlt) of the refleeted ai$na1, it ig
ne~~ssary to congider the statiseical chnracterisrics of the roughness oP
the reEleCting surface. Taking this into account, we t+rite the correlation
f.uiiCCinn in the farm:
I? p. c1 - J J y U, hJ Y(I - a M) Os Ut. MJ dhldhs
Where N2(hl, h2) is the tWO-dimensional law for the distribution of the
heightg.
The assumption thut the diatribution of the heights of the pointe of the
reElecting surface is close to a normal distribution is substantiated in -
11, 3, 4j. Considering W2(h1, h2) to be normal, following aeveral cwnbersome
trangfo mations, the correlation function can be reduced to the form:
N
rr
kt J J y( 3). Then the certainty of detecting the effective anomaly is practically
equal to unity (4~(3) = 99.7 percent). Undoubtedly, detection of the eYfec:t
- o� a mildly sloping structure with this certainty practically excludes the
poasibility of missing it. But in the case of low strength of the effect
this imposes quite strict requirements on the accuracy of the survey. In
particular, the employment of seandard gravimeters ensuring a measurement
error of 0.05 to 0.06 mgal can become simply impossible. And this, in turn,
can restrain the introduction of gravitational prospecting in the practice
oE prospecting work. In addition, the instructions do not give an answer
to the question of the required observation network density and of the possi-
bility of varying it in relation to the accuracy of the survey. Of course,
in practice an attempt is always made to make more than three observations
per profile within the limita of an anoznaly. But in each specific instance
this number ia determined arbitrarily,
In V.V. Kotlyarevskiy's method og x'elative e;-rors, eVidently for the first
Cime in domestic practice precise relati.onships were establi,shed between
the certainty of detecting anomalies and the accuracy and observation network
density requixed for this. Typically, the relative error itself, Em = o/gm ,
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ie a value xepreaenttng the inverae og the eggective^eigna7,-to-noise ratio
intxoduced by the tnetxuctf,ona (s m I/E Furthezmoxe, unltke the Instruc-
tions, here thie value I8 not afixsd oie. xC can vAZy, being bound only
ae the lower limtt (s t- 2). The asaigniqant oR 9 auCOmatically determines
the required accuracy and obeervation network deneity. Furthermore, the
cereainey og datecting the anomaxyr is dexined ae 0 w0(1/E Tn addition,
this method 8saumea ehat it Ia pose3,ble to varyr the parameters of accuracy
and obaervation network density while nutintaining the required certainCy of
detection. On the whole thia method broadens the capabilitiea of gravitational
proapecting in formulating d3fferent problems.
0f all the methods enumerated above, the moet effective, evidently, is A.A.
Nikitin's method. x'his is explained by the fo11ow3ng reasona. First, here
_ ia moaC aimply expreased the relat3onship between aurvey parametere and the
certainty of eignal deeection. Unlike other methods, it can be used for
detecting anomalies whose intensity is equal to the atrength of the noise and
is slighter. Thia method ie the only one in which estimal::es are made with
reference to area and in which the case of correlated noir,�e ia considered.
Survey parameters are determined here on the baeis of an apriori asaigned
cerCainty of detecting the aubject of the search or of prospecting. With
assigned certainty, it is posaible to vary both the network denaity and the
observation accuracy. A11 this makes it posaible Co recommend this method
as the basic one 3n estimating aurvey parametera, in particular, in prospecting
mildly sloping structures.
Let us now discuas the certainty of signal separation againat a background
of random non-correlated no3se. Generally, this certainty is determined
by the accuracy and network denaity of the survey, the ratio of the useful
signal and noise strength, and the law for variation of the strength of the
useful aignal, and, as a consequence of all this, by the isoanomaly cross
section and the survey acale. Formally, both in "Technical Instructior,a for
Gravitational Prospecting Operatione" and in B.V. Kotlyarevskiy's method,
the certainty is assigned by selecting the isoanomaly crass section. In the
instructions this problem is solved on the basis of the principle that the
cross section must equal triple the measurement error.
Furthermore, a necessary condition for nutlining an anomaly is the presence
within its limits of not less than thrr�e points obtained on independent trips.
As far as the scale of the survey is concerned, it is determined on the basis
oE its formal relationahip to the isoanomaly cross section chosen. The con-
dition imposed on selection of the cross section assumes a degree of certainty
_ in outlining anomalies with lsolines which is practically equal to unity
(00) - 99,7 percent). But this concerns only anomaliea which are two times
~ greater in strength than the measuretoent errors. 0f couxae, this method cannot
be employed fox the purpose of outlining anoma].i.es equal to and slighter than
the noise. Tn othex worda, these anomali,es will be omitted, since they will
not be ourllned.
The employment of B.V. Kotlyarevskiy's method makes it possible in selecting
the cxoss section to operate with the set of parameters of the anomaly to be
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lqntared. Tha ee],oeklnct og the cgaee ReGCi.on iCae]�t here dependm nn the
apriori aesigned cextainCy wixh whi,ch wa Wish tp tao1ate the artomaly in
quest4on, 0 m O(7./D And ehie coxtAinty, in turn, depando nn the eelected
neCwork dansiCy, Che qccuxitcy of the aurvey and the elgnal-Co-noieg raCio
(the ],aw o,t varl~tton of the strength nf Ctie uselux aigna]. Ie nesigned
apriori, in th3s maChod). This has A d3tcect xe1nCionehip ro the problem of
ieolaring low-etrengkh anomaliee. Actually, Chi,s ntethod eeCAbllehee the
required quantitarive r.elntionshi,pg between the certainty of ieolating the
effective anomely, survey parameters and the isoanonAly crosa section (survey
ecale), for the case when the intensity of the effective anomaly ia commenau-
rate witli the obeervation errnr, 0(],/DM ) d0(l) .
The comparaCive analyeis of ineehods made fiere can be conducive to imprnving
the geologica1 and economic ePfeceivenega of graviCat3anal prospQCting.
zn conclusion, 1eC ue 311uatrate the cnpabil:leieg of these methods witli g
epecifi.c example. We a8sume that the subject for proapecting is a mildly
sloping sCrucrure with the following parametera:
= Number of gravitationally active bnundaries 1
Excesa denaity wiehin 11miCe of graviCationally acttve boundary,
Ap , in g/cm3 0.2
Mean bed depth of gravitationully active boundary, tl , in km Z
- Axisymmetric aurocorrelation radiua of boundary, R, in km 2
Mean atatistical amplitude of structure, Z, in kmZ 0.1
Linear dimeneiona of anomaly of atructure, 2t 4
Mean statietical inteneity of effective anomaly, g, mgal 0.2
Maximum intensity, g, mgal 0.3
Ratio of autocorrela?ion radiua of noise to interval between
neighboring eurvey pointa 1.5
1~
. .
R
3)pa3
4)
~
5)
o
`
~
6)
np,~HerP
~
~ a$
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e a
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ci� x~ g
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oaroe~HnwlT ~r.~ n~p:~~~
=O
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ocs R p
to
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B
~ ry 3
p K,e
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npneMa A, A. }IttttgTtl80

p
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(If0 tt110t1(N,~tl)
S
C
ba
axx ce
7) lforpamaocn xnie-
0,07
0,05 0,10
0,05
0,05
0,10
0,15
peaux, uran
8) !'ycTor.i ceTtr, iac
1,5
1,5 2,2
-
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94 x

-
q) 1(acmreG chewmi,
I: 25 000
1: 25 CUO l: 100vU
-
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[IGey on following page]
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Key:
J.. Paxameter
2. MeChode
3, Oiyen in Cechnical In-
etructione, (by prQgtle)
4. B.V. KoelyAxevak3.yr'e
meChod of re1,ative
exrotca (by profile)
S. K.V. alAdic3,yls method of
QquaCing erroxe v and s
(by pro�i.le)
6. Baeed on A.A. Nikttints
theory of optimum recepe3.on
(by area)
7. MsaauxeMsnt Gxxox, MSaI
8. Netwoxk denatcY', km
9, Suxvey ece;Ie 0 tngal
10. Cxoes eection, p
11. Certainty of IsolaCing ef4ecti.ve
anom1y
xn ehe rable are given the resulte of eetimatee by each method, wi.th an indica-
Cion of the certainty of detecting, y1 , and ieolating, -Y2 , t1ae effecCive
anomaly.
Bibliography
1. Gladkiy, K.V. "Gravirazvedka i magnitorazvedka" [Gravitational and Magnetic
Prospecting], Moecow, Nedra, 1967, 318 pagea with illuetrationa.
2. "Inatruktaiya po provedeniyu gravimetricheskikh rabot" [Inatructions on
Carrying Out Gravimetric Work], Moecow, Nedra, 197` 46 pagea with illus.
3. Kotlyarevakiy, B.V. "Eatimating the Accuracy of a Gravimetric Survey and
Selection of an Intelligent Obaervation Network and Gravity Isuanomaly
Croas Section," PRIKLADNAYA GEOFI7.IKA, No 20, Moscow, Nedra, 1958, pp 34-
62 with illus.
4. Nemteov, L.D. "Vysokotochnaya gravirazvedka" [High-Current Gravitational
ProapectingJ, Moscow, Nedra, 1967, 230 pagea with illus.
5. Nikitin, A.A. "Statistical DeCection of Slight Geophyeical Anomalies
Against a Background of Random Noise" in "Avtoreferat diss. na soisk.
uch, step. kand. tekh. nauk" [Author'e Abatract of Dissertation for the
Academic Degree of Candidate in Technical Sciencea), Moscow, MGRI, 1967,
115 pages with illus.
6. Savinskiy, I.D. "Tabli.tsy vexoyatnostey podaecheniya elli.pti,cheskikh
ob"yektov PrYamougol'noy set'yu nablyudeniy" [Tables of Probability of a
Sub-Croas-Section Rox Elliptical Objects with an Oxthogonal Obaervation
Network], Moecow, Nedxa, 1964, 36 pages with 3lJ.us.
7. Serkerov, S.A. "Tnvestigation of Optimal Transformations of Gravitational
and Magnetic Anomalies" in "Avtorefcrat di.ss. na soisk. uch. step. kand.
tekh. nauk," Moacow, MINKhiGP, 1965, 136 pages with illus.
76
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FoR orFrcinL crsE ornY
. ,
6. SuroytaeY, B.P. "High-Cuxxent Gxavltattona7. Pxoapect~z~g In Scanning
and Pxoapsctin$ Mildly S1,oping Srructux~a In Che Centxal Rag~ons of the
Ruasian Plzltfom," Pki1KGAANAYA. GFOF1ZxKA� NQ 65, MQSCOv, Nedxa, 1972,
PP 151-163 wi.th illud. -
COPYRIGIIT; lxtla,tel'srva Nedxa, 1978
8831
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