JPRS ID: 8338 TRANSLATIONS ON USSR SCIENCES AND TECHNOLOGY PHYSICAL SCIENCES AND TECHNOLOGY

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- PNYSICAL SCIENCES AND TECHNOLOGY
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JPRS L/8338
].5 March 19 79
TRANSLATIONS ON USSR SCIENCE AND T~CHNOLOGY -
PNYS,ICAL SCIENCES AND. TECHNOLOGY
cFOUO i5/~9~ ~
CONTENTS PAGE
ELECTRONICS AND ELECTRICAL ENGINEERING ~
Matched Surface.Acoustic Wave Filter for Low Transmiasion Rates
(A. Ye. Znamenskiy, Ye. S. Murat~r; ELEKTROSVYAZ',
No 11, 1978) 1
Noncoherent ltadar Systems ~
(V.~V. Karavayev, V.V. Sazonov; RADIOTEKHNIKA 2
ELEKTRONIKA, rlov 78) 8
Range and Bearing Accuracy Uaing Antenna Arrays
(I. Ya. ~Cremer, G.S. Nakhmanson; RADIOTEKHNIKA I
ELEKTRONIKA, Nov 78) 17
ElectromagneCic Interactions in Transmission Lines
(D.V. Sokolov, et. al.; RADIOTEKHNIKA I ELEKTRONIKA,
Nov 78) 27
Signal Uetection on CRT Againat Noise Background: Nonparametric
Model
(V.N. Budko, et. al.; RADIOTEIQiNIKA I ELEKTRONIKA,
� Nov 78) 38
Side-Lobe Filters for Phase-Manipulated Signals
~V.P. Ipatov; RADIOTEKHNIKA I ELEKTRONIKA, Nov 78)..... 43
Amplification of Wide-Band Signals in Type 0 Traveling-
Wave Tubes
' (B. Ye. Zhelezovskiy, et. al.; RADIOTEICFINIKA I
ELEKTRONIKA, Nov 78) 48
CEOPHYSICS, ASTRONOMY AND SPACE
A Specialized Computer for Marine DiQital Gravimeters -
(A.V. Staklo; PRIKLADNAYA GEOFIZIKA, No 88, 1977)...... 53
-a- (III -USSR-23S &T FOUOJ
FOR OFFICIAL US~ 0'~LY _
� s.
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CONTENT5 (Continued)~ ~ ~ Page
rirsC Re~sulCe oC SCientific Experimente on 'Venera-11' and
'Venera-12' ~ -
(PIS'MA V ASTRONOMICHESKIY ZHURNAL, Vol 5, No 1,
~1979) 64
PHYSIC5
Invesrigating the Noise Characteristics of an Optical
AmpliFier in a XE-HE MixCUre = 3.51 microns)
- (V.P. Logvinov, et. al.; RADiOTEKHNbKA I ELEKTRONIKA,
No 1, 1979) 70 -
Inveatigating the Noise of a DC Discharge Plasma in an
Optical Amplifier Operating in a Mixture of HE and XE
(V.I. Logvinov, et.�al..; RADIOTEKHNIX~ I ELEKTRONIKA,
No 1, 1979) 76
~ Controlling 'he Parameterrs of Microsecond Einisaion Pulses .
_ .(V.V. ~rsen'yev, et. a1.; RADtOTEKHNIKA I ELEKTRONIKA,
No 1, 1919) 85
A Method of Restoring Laser Beam Energy Distribution From
Data Obtained From a Bolometric Sensor Array
, (V.V. Yefremenko; RADIOTEKHNIKA I ELEKTRONIKA,
N~ 1, 1979) 92
PUBLICATIONS -
New Publication Reviews Lateat Geophysical Instruments,
Applications . -
(GEOFIZICHESKAYA APPARATURA, Issue 64, 1978)........... 99
. _b_
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~L~CTRONICS AND ~LCCTRICAL ENGINEERING
MATCHCD SURFACE ACOUSTIC WAVE FILTER FOR LOW TRANSMISSION RATES
Moscow EL~KTROSVYAZ' in Russian No 11, 1978 pp 58-61 -
[Article by A. Ye. Znamenskiy and Ye. S. Murator]
- (Textj An optimal receiver for relative phase transmissions contains a
filter matched to baseband or radio-frequency pulses.
_ Filters matched to baseband pulses for low transmission rates R= 5ti25 kbaud
are made using active RC networks (hybrid construction) while those corres-
pondinq to high ratea R> 1Mbaud are made using miniature lumped parameter
multitapped delay lines.
In many cases equipment size is smaller and receiver circuitry is simpler,
while its specifications are better when rf pulse-matched filters are useci
instead of baseband matched filters.
Surface acoustic wave (SAW) device technology ts widely used in constructian
of rf pul~e matched filters [1, 2, 3]. The advantages of SAW technology is -
fully evident at information transmission rates exceeding R=20 N30 kbaud.
The lower limit for these rates is defined by two factors: 1) permissible
temperature deviation of the center frequency of the most stable (with re-
- spect to temperaCure) piezo-electric element (ST-cut of quartz at -50 ~ t
~+SO�C), and ~lso 2) the actual dimensions of the working matched filter
as will be shown.
_ SAW devices are highly stable ir, a wide temperature range, a fact which iR
very important at low information transmission rates, their manufacturing
technology is higlily developed, they are very reliable and small in size as
compared wttl~ the dimensions of series 153, 155, and 157 mi~rocircuits.
The SAW Cilter structure is shown in Fig 1 where 1) is an acoustic guide;
2) is ,7n interdigltnl transducer (IDT); 3) is a wideband IDT; 4) is an
:il�nrbtnb layer. As we know the filter's amplitude-frequency charactertistic
tl(w) r~nd Its pulse response ii(t) are related by an inverse Fourier transform:
1
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P
~
h(t)' ~ ~ H(w)e~ti d a. (1)
� os =
Moreover, there exists a aingular relationship between the pulse response h(C)
and the Ahape of the envelope of the ID electrodes. Electrodea are position-
ed ~t T= 1/2fo intervals along the acoustic guide, and the el~ctrode length
15 Proportional to h(t) at the corresponding reference pointT� (see Fig 1). .
In general, during calculations involving h(t) it is also necessary to in-
- clude the amplitude-frequency characteri~tic of a aecord IDT
~~N)�Hl~~)H2~w)� ~2)
As ~ rule, in practice the second IDT has a much wider bandwidth so thaC
the resul[ant amplltude-frequency characteristic is mainly defined by a -
s ing l e nr~ rrow-band trnnsducer, i. e. H(w) Hl (w) .
13n~ic requiremenCs Eor matched filter parameters:
CentPr frequency of the passband, Hz f, ~ 0.03R `
Form af ampl3tude-frequency characteristic Sin x/x x=(f-fo)/fo
Frequency band between the zeros of the main lobe
of Sin x/x, Hz 2(R !'O.a3R)
Deviation of phase-frequency characteristic
from liner response, degrees + 5 '
- Insertion loss, db < 30
Relative level of crosstalk components, db -20
4 � 2 1 3 y
� ^
i
~c I
b'
tn
c
F~g 1
2 '
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From tl~is as~umpt~.oti it fo].lowa that Che deaired pulse response h(t) is fully
drfined by the s}~r~pe nf Che envelope of Che diaCributed transducer electrodea.
The great~st d~lfficulties are encnuntered during manufacturc of SAW filCers
at the lower end of~realizable transmission rates (R a 20 h�34 kbaud). 1'he
_ amplitude-frequency response of a filter matched to a rectangular pulse is
� H(w) = Sin x/x where the pulse width is defined as: ~
'~=1/R. (3) -
Since n reduction of R leads to an ir~crease in the transducer lengCh 1; -
1= r v whe:e v i$ th~ velocity of propagation of the aurface wave in the
acoustic guide. Thus, for R~ 25 kbaud where v= 3,158 mm/,~Sec in an ST-cut _
quartz 1~126 mm. If we consider that the acoustic guide must be even
longer by about 20 ~.30 mm, then it is evident that s~ch a filter is not an
- optimum one.
A seco?~d deficiency of the filter shown in Fig 1 is the difficulty of tuning ~
_ ~ center frequency witl~ high accuracy. It is a,hown that the velocity devia- .
- tion in quartz ~coustic guides is on the order of 10-4. From the above it
is cteur that even if deviations involved during filter manufacture are ex- -
cluded, it ia very difficult to obtain the required accuracy for fa at low -
trunsmission rates. Although methods used for tuning are known [4J these
were carried out on small-size acoustic guides (i.e. for those used in high -
transmission rates). The method of applying a unifoXm-thickness metalized
layer over the entire acoustic structure and the aging of this layer remains
~
questionable. r_
~ A method is described beloW for making matched filters for low transmission
rates which permits a reduction in the length uf the acoustic guide by a
- factor o�,2 and which allows for tuning the filter's center frequency while
using relEtively simple manufacturing methods.
The complex transfer fvnction c,f IDT using equidistant electrode spacing and
a constant aperture may be expressed as [5]
H(w)~H, si~ ~ 1 wt+ `2'
e � (4)
wt
2
_ where Ho t:: a constant multiplier; t is the time; and w= 2'n'(f - f o) . _
_ ~
3
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Urop~~ing the e!~'C multiplier, which corresponds t~ a linear phase chnractnr- ~
isCic, for Che sake of eimplicity, expression (4) may be presented as:
J _
~ wC ieJC iat �
H~N~~Ho sin 4 4 2
e 'l+e .
. wt -
~4 -
~
The Eirsr term corresponds to a transfer function of a maCched filter for a
transmi9sion rate equaY to R= 2/t; whi]~ the second term may be consf.dered
n tr~nafer function of a transducer ~onsisting ot 2 IDTs shifted with re-
specC to one unother by ~/2. The general. form of theae IDTs is simi~~r to -
the ch~racteristic of comb f ilters. ~ -
E'igure 2 shows the structure of a matched filter for R- 1/~ rate, synChe-
sized by cascading a matched filte: (in the uppe. part of the Fig) for, R=
, 2/~- rate and a comb filter (in the lower part of the Fig) where 1) is the
~ic~usttc ~uide; 2) ia the shaping IDP of the matc.hed filter for rate 2R; 3)
i~ u wideband IDT; 4) is an abaorbing layer; 5) is a shapin.g IDT of a comb
fL~Lter; 6) is a mettalic layer. .
~ 2 ~ d Z =d~'�V -
� 3
IIIIIIIIIIIIilllll(fl~ll~ ~L , ~
- ~T ~ -
4 i = (~~1). y
6 5
Fig 2
y I~ath circuit sections are laid out on a single aCOUStic guide and are
~ cc~nnec[ed electricnlly. M a~sorbing layer is deposited between circuits
tc> eliminate a~oustlc cross-talk between channels.
r l 2 3 ' _
/
? ~ ~ S, 6 ~ ~
I'
~ _j I j ? I g6 ~ 1 ~
i 1 I I j I ~0,4 1 ~ -
I i
' ' ~ 1 1 ~ ~ ~Ij 1 ~ 1 1 ~ .
- - . _
~ ~ 0~ ~ ~ 1
~ 3
/p-,~ f0-,~, /0 f0 f~+~ fp{'~
Fig 3 ~
4 .
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tn compnrison with a single sectio!~ maCched�~fil-ter~with�transducer length ~ ~
equiil to~ ra 1/R, a two-section conatruction permits a reduction in length
by u ftictor of almoet 2(the higher R, the closer Co 2).
In the above-descz~ibed method of synthesis of a marched filCer for low trans- ~
~ mission raCes permits, to a certain extent, varying the filter's center
- frequency. This is accomplished by ch~nging the distance ~/2 between trans-
_ ducer sections in the comb portion of the filter at the expense of increaaing
or decrer~sing the pxopagation velocity of the SAW in this reg:ton. It is
known that the presence of a metalized layer in the propagation path of a
SAW chnnges its velociCy (6]. Thus, if a section of a continuuusiy metal-
ized lAyer 'between transducer secti4ns is removed or deposited (see Fig 2)
iC is possible to vary the center frequency of Che main amplitude-frequency
- ,reaponse peak of the comb filter inside the wider amplitude-frequency respohse
- of the mntched filter with R= 2/~ . Correaponding amplitude-frequency
cliaracteristics are shown in Fig 3 where 1) is the amplitude-frequency
characteristic of the matched filCer Lor rate equal to 2R; 2) is the ampli- -
tude-frequency characteristic of the comb filter before returning; 3) is the _
ampl~tude-Erequency ~haracteristic of the comb filter after retuning.
In fact, at the center frequency f, phasing condition 2 71'(-2 ~ f a) = 2 n ~
~ is ac h ieve d (n is a w ho le number). Thus, fo = 2 n~ . At the same time Z'/2 =
' L/V where L is the distance between centers of the comb fil.ter sections; V is
' the propagation velocity of the SAW. -
Deposition (removal) of the layer causes a corresponding reduction (increase)
�of ti~e velocity in the region between sections V Then
equiv' _
f �(v f e v.Ka)
o� ~
- Th,is method of frequency tuning is not optimal because of a certain assymetry ~
- of side lobes. But, since the principal portion of th~ signal energy is con-
- centrated in the center lobe it is more important to tune to the center fre-
quency even at the expense of a certain deviation in the level of sidelobes _
from the degign values in the range of + 3db, a fact which was confirmed ex-
perimentally..
It is noted that the formulas used for synthesis of matched filters cited
' liere d~ not include the finite length of small electrodes, i.e. wideband
transducers in the two-section structure. This is deemed permissible where
the relationship 4'C (~1~/2 holds.
Second-order effects (spreading and scattering losses, losses due to disper-
sion of the acoustic wave by the IDT grating in lieu of electrical and
mecirintcal surface loading), the influence of matching networks on the input
:ind ~utput [7j cause distortions in the amplitude-frequency characteristic
S
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' responbe ttnd nn increase in crosswalk levels. These effects increase with ~
decreasing R. In nrder to reduce Cheae effecCs it is necessary to introduce
c~r.rectlona in the trnnqducer nperture r~nd to uCilize n construction wiCh
~ s~illt elecCrodey, ~nd nlan to consider the nmplitude-frequency characteris-
Clcs of the electrical circuita on the filter's input and output.
Experimental results.
'The construated matched filtc:r was designed for two information transmission
raCes R1 ~ 256 kb~ud; R2= 64 kbaud and fo = 12 MHz. Calculations have in-
dicated that the dimensions of Che filter are optimal if one of its parCs
is made using a two-section structure (for R2= 64 kbaud rate) and the
second - using a single section (for R1 = 256 kbaud rate) with subsequent
positioning of both parts on a single acoustic guide (Fig 4).
The filter was constructed using a thermally stable SR-cut quartz plate _
measuring 45X20X2.5 mm. The IDT structure was formed using metal photo-
etching techniques on chemically deposited silver O.l.t~thick. Aperture of
Fill IDTs was 0.3 mm. The number of electrodes making up the R1 IDT section
~ was 47, which agrees with the given information transmission rate, and in
= the case of R2 - 94, which corresponds to the doubling of tlie transmission _
rate.
~~p , Output 1
_ ~ Baix.1 ' ~
~ R=64rr6aa k Band ~
I . -~1-~1-1 ~ i L~ RM~
T~T ~i 1 I I! I
~~x . ~ - . -
ax. Lz RNp Output 2
Input . Be~x.2
R=7S6x6oa k Band
The absorbing layer was deposited at the ends of the acoustic guide at inter-
channel spacing using the FL - 03 coating in order to reduce crosstalk.
[n order to reduce the insertion losses of the filter, its static transducer -
ca~p.7r.tty w:is compensated by inductances. The input resistance of emitter _
F~~ll~wers were used as high~impedance loads. The losses in the band of in- �
tr~rest were 18 + 2db. Deviation of side-lobe levels of the function Sin x/x
from tlie theoretical values in the + 3R range of tuning did not exceed ldb.
_ Other p,lrnmeters emt the'given requirements.
'Plie two-section matched filter was designed for R= 25.6 kbaud f, = 12MHz. -
An SR-cut quartz plate measuring 80X20X5 mm was used for the acoustic guide.
I':tlter structure was two-sectional. The above-described construction tech-
_ . 6 -
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~ n(que ~wn:t utilized. 'i'tie aperCure for all IUTe was 4 mm. There were 2:15
� electrode pairs in the shaping IDT which corresponds to a doubling of infor-
matlon Cransmission rate. Fi1Cer coupling into the R~~ strip and the sCatic
Cransducer capaciCance compensation method did not differ from those in Fig 4
- for R= 64 kbaud. Losses at Che center frequency of the passband of interest
were 14 + ldb. Deviation of side lobes of the function Sin x/x in the + 3R
range of tuning did not exceed 2 db. Other parameters met the given require- .
ments. '
Thus, experimental charncteristics of small-size �ilters with simple center -
_ frequency tuning agree fairly well with results of calculations according to
given formulas. _
- ,The authors consider i~ their pleasant duty to express appreciation to A. F. -
Beletski for his careful review of the manuscript and his observations which
hnve helped improve the quality of the article.
$IBLTOGRAPHY
~ 1. 'l,n~~menskii A. E., "Fil'try poverkhnostnykh akusticheskikh volt~" ["Sur-
- Eace ur.oustic wave filters"] ELEKTOSVYAZ', 1977, No 12.
2. Hays R., Hartmann C. "Surface acoustic wave devices for communications" -
Proceeding of the IE~E, 1976, Vol 64, No 5., -
3. Dodonov A. B. et al. "Kompleksnaya mikrominiaCurizatsiya priyemousilitel'-
_ nykh rraktov na osnove integral'nykh aredstv chastotnoy selektsii "["Com- _
- plex microminiaturization of receiver sections using frequency selective _
integrated devices"] ELEKTRONNAYA TEKHNIKA Series 11, 1976, 3rd edir.ion -
_ (7). ~
_ 4. Hayde W., "Precision narrowband surface wave bandpass filters" 1974
� Ultrasc~nics Symposium, Proceedings of the IEEE, Boston. _
5. A. De Vries et al. "Characteristics of surface wave integratable filters"
- II:I:C Transactions, 1971 Vol BTR-17, No 1. _
_ 6. Karinskty S. S. "Ustroystvo obrabotki signalov na ul'trazvukovykh _
_ poverkhnos[nykh volnakh" ["Signal processing devices using ultrasonic
surface waves"] M., SOV. RADIO 1975.
7. 13ondarenko, V. S, et al "Osobennosti raboty uzkopolosnogo fil'tra
~~overklmost}iykh akysticheskikh voln v razlichnykh rezhimakh nagruzki" _
["Pc~rCormcm ce peculiarities of narrowband surface acoustic wave f ilter
_ rit dLfferent loads"] VOPROSY RADIOELEKTRONIKI: SER OBSHCHETEKHNICHESKAYA,
]976, Cd 7. '
- Suhmitted Oct 6, 1977
COPYRIGHT: Izdatel'stvo "Svyaz'," "Elektrosvyaz'," 1978
6981
CSO: 1870 ~
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.
' ~LEC`i'ltONiC5 ANn CLECTl21CAL ~NG1N~~~2WG
NONCOh1ERENT RADAI2 5YST~MS
~ Mosrow R~1DiOTEtGHNIKA i EL~KTRONIK.A in Russian No 11, Nov 78 pp 2306-
2313
(i~rticlr by V. V. Kar~vayev and V. V. 5azonov: "On the Theory of Non-Cohere~~~
Det~r. t ion"]
[Text] The use of phased transmitting antenna arrays has several shortcomings =
in sc~r~~~inK space. Some af these stiortcomings are as follows: energy dissipation
in sl~aping a coherent prbbe signal in each element of the ~ctive array, and _
r.onr.e~itration n[ the beam to ic~tensify emissivity due to increased antenna
~ dim~r1510hS. in order to surmount these shortcomings, in [1l it was proposed to
drop thr phasing of individu~l elements of the transmitting array, avoid emitting
si~n:~ls with diff~rent (prrhaps, random) modulation relationships; but coherent
processin~; of the received signal was do be done with the aid of a set of
- rr.ferrncr si~;nals gener~ted for each angular bearing by a spec~al device based on
kn~wn or measured time relationships of amplitudes and phases of excitation of
rach emitter. Modulation probe signals is needed to suppress gaps in
transrnitter direction~lity in non-cophase power conditions. A deficiency in this
arrangement is the complex nature of producing a set of ad justabte matching
filters. Consequently, it is worth considering the characteristics of a system
which does not employ time-matched filtration of an incoming noise signal
(replacing it with band filtration). We shall demonstrate that with an optimum
selection of system parameters, power losses due to noncoherent processing are
not grcat.
If the transmittinp antenna array is not phas~ scintillation of the target can ~ae
s~ippressed by separation o[ the transmitters. Tw~: versions of a transmitting
system df:si~;n will bc examined below, differing in the manner of separation of _
tt~c probr sibnal. In thc first version, several spatially-sepat ated transmitters are '
~mployccl wfiich simultaneausly irradiate the target at different angles. In the
~cc�ond vcrsion~ the transmitters are superposed~ but a multiple frequency probe
si~nal is ~~tilized. C'ormulation of this problem here differs from that usually
fnund in the literature (cf., for example, [2)) in' that the incoming signal here has
double modulation with different inherent times, occurring as a result of the ~
r::ndom fietd of the transmitter and coefficient of reflection of the target.
, ~
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~
~ l. 't'HEtC~-nIMCN510NALLY 5EpAEtATED 5Y5T~M
- LCt us c~nslder that th~ prncessing channel Cont~ins a fllter whos~ bandwldth
matches the sNectrum of tN~ emltt~d sign~l; connected to its output are a square-
law deteetor and a signal�length memory. The output ~ffect of this prdcessing ,
is
r
(1) a- f Is(!)-t�~(~)I'dt,
_ .
_ wl~ere s(t) and (t) are independent signal and noise components of the filtered out
input process and T is processing time. in conformity with the above, the signal
component may be represented in the form
.
(2) a(t)d~ yaie"'8,~~~~
,
wlicrr. s~(t) is ~ r~ndom signal emitted by the j-th transmitte~; n is their number;
- 6~ is the e[ier.tive cross section of the target towards the receiver when it ~s
irrudiated by the j-th transmititer; and e~ is the phase shift nccurring vrith
rc~tlcction from the t~~rget.
With fixed coefficients A~ = yo,~'�~ in (2) and large n,~ignal s(t) may be
r.onsidered gaussian. In this case the d3stributive function of the quantity z is
well described by the principle ~(,Z:
' ~31 Z~''e'~~:e~
P~:!{A,))ma:~lm~~~m~ ~
whcrc 2m is the number of degrees of freedacn and Q2 is dispersion p~r degree
- of freedom. These parameters are expresscd thraugh the effective band of the
signal ~f and signal dispersion Us2 and noise Q'.~ 2 in the folio�~ving manner: m=
I~.fT,Q2 = 0's2 +a'~2 = (I~'I~~ I~I~')~"-�~f.
It is usually c�onsidered that the coefficients of reflection of target A~ are n~r-
mal. f~or the s~me rc~son, if ali A~ arc independent and have identical dis-
p~~rsions, thrn the rand~m quantity ~52 is distributed according to the principleX2
witfi N- 2n degrccs of frcedom and dispersion P2 per degree.
Tl~r c�I~arac�teristic function z is obtained by averaging the arbitrary charatteristic
tur~ction r.(u/Gm2) -(i - iu2(6'S2 + 6,~ 2)-m in terms of the distribution
652. Let us find
~ c._.~uis ~
r ~s -t- 4p'u / X .
~
i
x~X~~~.�;+ ~ ~ w + i
~n: ~{~~:u ~~-*-~ri:,~*-Min Clp= 4p'u ~ !
. (4D c~u)~=
(-E4p'u)'^ '
9
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~dit c1~~tCfAL USL ONLY
whcrc~ Wi,k~x) is thc Whittakrr funetion. To derfve the distributive taw it is
nrcrsti:?ry tn trantifnrm (4) ar.cording tn ~ourier. In the gen~ral c~se this ~an not
bc donr. t3~t in the detection problem the c~se wh~rp the signa~l signific~ntly
rxreeds nois~ is most substantial; herp n~ise ~ffe~ts ~ly the chaic~ di thre~hdld.
- And in ~xamtning th~ st~tlstics of the signal, nolse may be [gnored, Then
~ -
~S~ ~11�tm1N~f1~~ \ ~r~ ~
n-n?
P ) ~
, ~~~n~I~~~n~2n+m-Ipn}n~ ~
where K.~ (x) is a Macdonald funCtion.
In thr absence af a signal, z is distributed according to the Z 2 p~inciple.
TfirrrCorr, prob~bility of a false alarm is equal to
�
y~n-~e_~~~un~ " y~-~e_:i~
1~
6 d: ~
~ ~ 'r'�1'(m)a l,~l'(m) dx~
i h ~
whrrr c�* = c/6r~ 2, c is detection thresholii. Probability of detection is ea!~al ~
to _
~ xn~*n-1
U f . K~-m(z)ds
- ~'~m,i�C~~2nfm-i ~
wf~~rr c* = 1'~'~,'/~~2. This integ~al, for integral and haif-integral values of m
is reduced to tabular definitions. For integral m
m}n-1 m-1 ~
' UQ c. 2K~_M~~~1(~�)
~~~~,~~~.~-n c.'C(m-1) ~ _
r...
whilc tar h;rlf-intcgral m
(2rn-2)1 !
- ~y~ ~ 1�~ni~l�~n~2,~*~_: X
:~c,-, 1
~ x ~ C 1~~..- ~ ��A-M*~+~~C�/ '
L ~.'cz?,~--zcc+>� u
~
7t:n. n/: ~ � ~n~~ �
1.1 I C , (l--l~�-~~~~~�)L*-,~~c.)-
2
~ ~'`w-';r~C~~Kw-7~~C�/~
1~
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Hrrr L.~ (x) is t~ Struvr funr.tion.
- The relat~onship P(c*) = 1- D(c*) as a function ~f c* Is glven in Figures 1~nd
_ 2 for n= 3and S~nd m= l, x, 3, 5, 10.
h is worth comparing the dcrfved deteCtlon characterlsti~s wlth thos~ of the
system in which ~mission and receptfon of the signal oc~urs ~oherently ~nd
where, as in the system in question, separation of slgr~al through Independ~nt -
channels is utilized. In this fnstance, with quadrgtic composition, the
- distrtbution of the output effect Is described by'~2 with 2n d~grees of fre~dom,
. whilc th~ det~~tion Chara~teristics are given by the formul~s in C2~
" x�-~~-=is
, ~
(10) ~ r~ ~
" x*-~Q-~n
D " f dr~
~�re~~t~+r) 2~I~~n~
wl~ere � is the sum si~n~i-to-noise ratio, defined as nN~; ~t~ is the avcrage
signal-to-noitie ratio in the j-th channel.
- A comparison of the detection char~cteristics of noncoherent and coherent
systcros shall be done for iden~ical energies of the signai arriving at the input.
in this case. the ordinates of the curves in Figurps 1 and 2 ar~ defined at
pointse.~y?mn~�'(n)/~~,and c~(n) is derived according to ~ormula (10) for given
F and n. Examples of the relationship nf the threshold signal-to-noise ratio
versus m are cited in Figures 3 and 4 for n= 3 and n= S, respectively. It
- can be seen that for each value ~f n there exists an e~timum m at which -
thc threshold level of the signal is minimal. Here, in the form of horizon-
- tal lines, are also depicted the threshold characteristics of a coherent system.
Minimal losses are defined by the distance from these lines to the extreme
puints of the corresponding curves. This losses are obviously not great. For
Q= 0. S th~y are ~-0.6 to + 0.6 dB) and for D= 0.99 they rise to 2.4 to 2.6
d H.
- 11
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~'l'c~)
P(c,l ' ~ '
n�~ n"S -
_ Q f � 4~ .
~ :
' O,UI , F : h ; U0i � ~ ~ ~ ~ o =
C ~ ' E " ~
, F ~ E ~ ~ ,
QDDI.. 1 , 4~1 ~ ~
�JO' -:0 -f0 U W lulgc, �?0 ~10 0 lo ?Otgc~
~igure ~ 1 Eigure z
do ~tt,d6
i0
n �J n-S ~
JO - JO
~p�poyu
' ~,1 ^ U,99 ~D -0.999
20 pQ D-Q99
;~D �0,9
'D=~9
- D-QS D-O,S
_ ~0 10 ~
1 i J~r 56 8 10 m?.^ 1 1 J Z 56~8 f0 m10
Figure 3 Figure 4
12
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2. SY5TEM WIThi ~R~t~U~NCY SEPARATION
� 1'o suppress fluctuat[ons of ~ Raylelgh targ~t, this system utilizes frequency
retuning of the signal from impulse to impulse. Processing conslsts af band
filtration of earh frequency chann~l, square-law memory nf signnl dur~tion and
_ m~mory of frequency ch~nnels.
Consequently, the output effect of this system appears as
* * r
z~~g~~ ~ f I~~s~~~~~~l~t~~s(;t~
J+1 0
whrrr s~(t) and 1~~(t) are independent signal and nofse cornponents in the band of
oF tt~e j-th frequency channel and A~ is the randc~m coefflcient of reflection of
tl~r. t~rget ~t the j-th frequency. We shall assume that freq~ency separation is
r.I105Ch so A~ ~r~ independent.
At fixed vatues of A~ the quantities zJ~, as before, may be considered as
distributed ~ccording to x 2 with 2m = 2efT degrees of freedom. Consequently,
thr arbitrary (for given A~) characteristic function of quantity z~ is given by the
expression
(l2) (u/{:l~})'�I4-2lu(~~1~~=Q~'~1-o.')I-M
,
whcre ~j2 and 6p2 are dlspersions per degree of freedom of signal sl�(t) and noise
+~�~t), respectively. The absdlute characteristic function is obtained by averaging
~12) in terms of the distribution of the random quantity (A~I2 (scattering cross -
section) v~hich we, as before, consider to be exponential with average unit
powcr. Employing [3], we find
(l3) �
( er'dU
J ~ i-'ltu (o,'~-ho.') 0
~�~~..,-II/21re~~l'rf-,n 21uo,'-1
\ ~ 2fu0~s /
-
(-2?ua,~~"'
wherr r(-~, x) is an incomplete gamma function.
13
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~
H'Ult UI~I~ [GIAL IISL ~1NLY
N ~ tl M
(~4) U~' f p(c)clz~1...._.~ f f~,(il)~~~4~dudzm+
~ 2n o
~iuoo'~ i !uc
~ 1 W 1. nxp ~ n ztuo,' u 2~
~n f X
(r2tuo,')"'^
2tuoo'--i ain 2 .
X I'" (1~m' ?tuo,' ~ u du'
2
whcrc r. is the threshold defined by the required valu~ of false alarm. This
intcgr~l r.an bC r.nmputed nnly for n ~ 1. Thus we Calculated the characteristlcs
c~f deter_tinn by constructing an integral law of dlstribution of th~ quantity z
usin~; thr rnethod of mathematical simulation. Heing concerned with a region of
rathcr higli probability of detection and small false alarms at that, we will, as
rarlirr, consider noise only in calculating threshold. Notably, the integral law of
distribution was calculate~ of the quantity _
h ~
t15) ~~vla~~=~Ib~RI',
�
wherr a� and b~k are independents for different j and k and on~ from another
are ranc~om quantities with unit dispersions of the quadrature terms.
lntcgral laws P( y) for various m and n= 3 and n= 5 are shown in Figures 5
and 6 as a function of lOlog Using these graphs it is easy to construct
characteristics of detection for any probability of false alarm which, as before,
is given by the integral law x2 (6), but now with 2mn degrees of freedom:
~16~ � ~~~_~~-~i:a~ds
Y
11 ~1 ~ ~.r. ~ d
` ~'"~I�~mn)o~'"~
pr ~MII_,e_,~i ~
~ J Lm~r~mn~ dS, C' = Q~, .
~
E~rob~bility of detection is then derived according to
(c'2mn1
tl7) D~i-P~ \ 1
�
whc~e 'J~. , as before, is the sum signal-to-noise ratio.
Wl~rn tlie latter formula ~nd Figures S and 6 are utilized, relationships of
threshold signal-to-noise ratio for va~ious probabilities of detection are obtained
as ~ funrtion o[ the number m of time cells in each fcequency channel. They
:?re shown in t'igures 7 and 8 for n=3 and n= 5 with a probability of false alarm
1' - 10-6. Characteristics ot detection of a coherent system (horiaontal lines)
witti thc appropriate number of independent separation channels n are given here
f~r comparison.
14
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~
r'Uk Oi~ 1~' CC CAL US1: ONLY
P(C)
P(G) ~
1
~ ~
n-s
n-3 Qt
R1
F p a QD/ ~ ~"a ~
O,Of F ~ E ~ ~ ~ ~
,
Qooi 4�~
-m o ~o totgc o ro ~r~g
Figure 5 Figure 6
~r, ~6
- ~.~6
JO
n�5
D �0.999
D~0,99 D-Q999
~O ~ ~ 499
%D-R9 D�Q9
jp..Qs D-QS
l~ - i0
_ 1 i J~ 3 67d t~m 1 t J 1 S 67d tOm
Figure 7 Figuce 8
1S
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Th~ figur~s pr~sented shdw that just ~s in the casp of three-dfinenslonal
' sCp~r~tion, with lnr.raase m(for given n) losses in ~.t for D> 0.5 ~t first
dr.r.rr~se c~nd thcn gruw. But this ~ff~ct is m~nifested more sherply. . It is
assoclated with the fact that the quantity vf noncoherently stored discrete units -
with frequency s~paratfnn is equal to mn, whereas in three-dimenslon~l
separation It is equ~l tr~ m. Consequently, in the first case, due td noncoherent
_ storage, losses being to show at much lower values of m. Accordtngty, uptimum
- vnlues of m lie betw~en one to two (versus 5 to 10 f~r three-dimen~ional
s~p~r~tion), and losses are siightly higher (by 0.5 t~ 1 d~). -
- CdNCLU51dN
Th~ char~cteristiCS of detection of a Rayleigh target by radar ldcatinn are
ex~min~d: there is no ph~sing of components of the tr~nsmitting system. For the
~as~ of great three-dirnensional separation of tr~nsmitters, an~lytical ex-
pressi~ns are nbtained which des~ribe the char~cteristi~s of dete~tion. ~'or the -
case of frequency separ~tion the appropriate formulas are derived in quad- -
ratures, and calculation of chara~teristics of detc~ction was done by the rriethod
of m~thematical simulation.
it was found that with optimum selection of the band of a random probe signal
~nd numbrr oi branches of separation, ~bandonment of the use nf phasing does
not lead to substantiai losses in the signal-to-noise ratio. According to the
probability of detection, they range from 0.5 to 3 dB. A system with three-
dimrnsion~l s~paration has minimal losses.
1'he authnrs express th~ir gratitude to I. G. Korobkova, who performed the _
ralculations on computer.
RCFERENCES
l. H. N. Woerrlein, Pat. USA No. 3, 680.100, 25 Jul 72. ~
2. f~. A. gakut, I. A. Bol'shakov, B. M. Gerasimov et al. Problems of
statistic~l th~ory of r~diolocation [Voprosy statisticheskoy teorii ra-
diolok~tsii], 1, izd. 5ove:skoye radio, 1963. _
3. 1. 5. Cradshteyn, i. M. Ryzhik, Tables of integrals, sums, series and
derivations [Tablitsy integralnv, summ, ryadov i proizvedeniye], 4th
ed., GIFML, 1962.
COPYRiCIi'P: Izdatel'stvo "Nauka". "Radio[ekhnika i elektronika", 1978
8617
cso: i $~o
t~
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_ EI.~CTRdN1t:S AN1~ E1,~C1'12[CAL ENGIN~El21NC
. RANC~ AND BEARING ACCURA~Y USiNG AN1'ENNA ARRAYS
Moscow RADIOTEKHNIKA i ELEKTRONIlCA fn Russian No 1l, Nov 78 pp 2314-
2320 ~
C/lrtir.le by I. Y~. Kremer and G. S. Nakhmanson: "C~~ the Potential Ac~uracy of
Estim~ting Itange ~nd Angular Coordinate of a Target wlth Signai Reception by
~n /lntenn~ Array In the General Case"~ -
[1'ext I INTEtODUCTION
1'he prirnary current assumptions ~f the theory of time-space processing of
signais C4, 2] are valid gor arbitrary time-space signals. But specific results in
' thc literature havr mainly been nbtained as they apply to the special case where
the wave frnnts of signais ran be considered flat, i.e., the signal sources are in -
thr remnte znne of the receiving antenna. If the signal source is situated in the
Fresnel zone of the receiving antenna, an estimate of the parameters o~ time-
spac:e signals has substantia! peculiarities associated with the curvature of the
signal wav~ front. These distinctive aspeCts have been investigated in studies
[1, 2, 6] as they apply t~ antennas with continuous linear apertures.
In this article the potential accuracy of estimates of range and angular position -
ot a t~rget are considered for reception of signals by an aiitenna array in the
Kcnrral case, which includrs positioning of the target both in a remote zone and
in a rresi~el zone. The rise in potential accuracy of range analysis owing to
cnnsideration of signal wav~ front curvature is analyzed as a function of the
nwnbcr df arr~y elements. The ambiguity of range measurement is considered
for rer_eption in "widely spaced" arrays and conditions to eliminate this problem ~
~re discussed.
y
M
Ra
B ~o
Z �
m- ~ ~---e--�r
~ Figure 1
17
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1. POTENTIAL ACCURACY O~ ANALYSIS OF TARGET COORDINATES
W1TH SPACE dc TIME PROCESSING OF SIGNALS IN AN ANTENNA _
_ ARRAY
.
~ Let us consider an equidistant linear array whose length is L and whose distance
between elements is d having N= 2m + 1 elements (F~gure 1). -
� Let us first conslder the case of active location. A sounding signal is emitted
from point 0
` (1) s(t)~U(t) cns f~ot-1~~(~)l� -
A srnall target is situated at point M with coordinates (R0, A~). The vector the
arriving signal may then be represented as
(2) Ilx~(~) Ilr~lls~(t, no, eo~ v~~) II-~-IIn~(~) il,
where i=-m, 0, m is the number of the receiving array element.
in forrnula (2) Ilni(t)II is a vector of gaussian interference with zero average
values and correlation matrix IIBI~(tl,t2) = II