Page 213 - Radar Technology Encyclopedia

203 frequency stability FUNCTION, random

ern radars using the master oscillator power amplifier between transmitted power P and receiver power P in a one-
r
t
(MOPA) technique, the master oscillator is the source of RF way, free-space radio link:
signals for both the transmitter and receiver. Short-term fre- 2
P G G l
t
t
r
quency stability (i.e., from pulse-to-pulse for a pulse radar, or P = ------------------------
r 2 2
within the signal integration time for a continuous wave ( 4p ) R
(CW) radar), is a principal issue in modern radar design. In where G and G are the transmitting and receiving antenna
t
r
CW, MTI, and pulsed doppler radar, short-term frequency gains, l is the wavelength, and R is the distance between
variations generate spurious modulation sidebands on main- antennas. This formula serves as a basis for deriving the radar
beam clutter, causing serious degradation of radar perfor- range equation. SAL
mance against targets in clutter. Long-term instability, or fre- Ref.: Johnson (1984), p. 1.12.
quency drift, can affect the accuracy of target parameter
“FRUIT” is the type of interference caused by beacon replies
measurements, and, under some conditions, create spurious
to interrogation asynchronous with the observer’s interroga-
targets from PRF harmonics, but long-term frequency drift
tor. The acronym stands for false replies unsynchronized with
specifications that prevent these problems are easily met for
interrogator transmission. SAL
monostatic radars.
Frequency stability requirements for coherent radar are Ref.: Johnston (1979), p. 60; Stevens (1988), p. 288.
largely driven by the magnitude of the received clutter- FUNCTION, random. A function f q is random when x
()
power-to-noise spectral density ratio (C/N ) in which the exhibits a random dependence on its arguments, q . The vec-
0
radar is expected to operate. For a properly designed coherent tor q can represent a set of parameters (e.g., coordinates of
radar, the clutter level at the output of the doppler filters cov- the target, x, y, z) or a single parameters (e.g., time t). In the
ering the frequency band of expected targets would be below latter case, when q = t the random function is called a ran-
thermal noise, if all of the radar frequency sources were ideal. dom process. It is a set of random variables with time t run-
Any actual source, such as a master oscillator, will experience ning through all real numbers, and in this case the random
short-term frequency fluctuations that give rise to AM and function x t ()
is represented by the set of sample functions
FM noise spectra which are impressed on the received clutter x(t) with associated probabilities.
signal. Some components of the resultant clutter-reflected The complete probabilistic description of an arbitrary
noise spectrum spread into the radar’s target doppler filters, random function requires knowledge of the nth-order proba-
reducing the signal-to-interference (S/I) ratio and, under some bility distribution function, which, for a random process, is
circumstances, presenting false targets. defined as the probability that at times t , t , ... , t the func-
n
2
1
For components such as master oscillators, which supply tion x t ()
will be less than the corresponding levels defined by
signals to both transmitter and receiver, a mixing process per- a sample function, x(t):
mits cancellation of a large part of the undesired short-term
,
=
£
=
£
P x t () xt () x ¼x t () xt () x }
,
{
frequency fluctuation effects, especially at short ranges where 1 , , 1 , 1 , n n n
1
n
n 1
the clutter return is strongest. This “common mode” cancella- = F x ¼ x t ¼ t , n
tion is not available to several other radar components such as If the probability distribution function has a derivative
the transmitter power amplifier, waveform generator, or any n
¶
other oscillators in the system not associated with the master ( x ¼ x t ¼ t , n ) = n ( 1 , , n 1 , n ) ,
,
, f x ¼ x t ¼ t ,
,
,
1
1
n
¶ ( x ¼¶x , )
,
oscillator. All such sources must be included in an overall 1 n
noise error budget for the system. Noise specifications for fre- this derivative is called the probability density function (pdf).
quency sources and other noise sources within the radar are In practical cases it is difficult to obtain the nth-order sta-
generally given in terms of allowable AM and FM noise tistics of a random function, and its consideration is limited to
power density per Hertz relative to carrier power (dBc), as a first- and second-order statistics, the mean value or mathe-
function of frequency offset from the carrier. PCH matical expectation:
Ref.: Skolnik (1970), pp. 19.18–19.22; N. Slawsby, “Frequency Control ¥
Requirements of Radar,” Proc. of the 1994 IEEE International Fre-
=
m t () á xt ()ñ = ò xf xt ,( ) x d
quency Control Symposium, 1–3 June 1994. x 1
– ¥
Video frequency is a term understood to mean the frequen-
the variance:
cies of the components of the video (envelope-detected or
¥
baseband) signal spectrum. The video signal (video pulse) in 2 2 2
s t () á [ xt () m t ()]ñ = ò [ xt () m t ()] f xt ,( ) x d
–
–
=
a radar is shaped at receiver detector output and occupies a x x x 1
band from tenths to several megahertz. AIL – ¥
and the correlation function:
FRESNEL-FRAUNHOFER TRANSITION POINT (see ¥ ¥
FIELD, antenna).
K t t ,( ) á xt ()xt ()× ñ = ò ò x x f x x t t ,( , , ) x d d x
=
x 1 2 1 2 1 2 2 1 2 1 2 1 2
FRIIS TRANSMISSION FORMULA. This formula, origi- – ¥ – ¥
nally published by Friis in 1946, gives the relationship Here, <y> denotes statistical averaging of y.