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5 Performance Characteristics of Radar Location …
Random process constantly presented in a radar is internal electrical noises of a
receiver. Energy or spectral density of internal noise in linear (up to detector) part of
a receiver is expressed as follows:
E n = K n kT 0 ,
(5.8)
where K n —noise coefficient of radar receiver, estimating a degradation of signalto-noise ratio (in power or energy) in comparison to receiver input; T 0 —absolute
temperature, at which a noise coefficient is measured. Usually, a noise coefficient of
receiver is measured at T 0 = 290 K, and sometimes, a corresponding recalculation of
a noise coefficient is required at high deviation of input temperature of radar from a
standard one. In most cases, the deviation of real temperature from a standard one is
neglected. Boltzmann constant k = 1.38 × 10
−23 in this case gives an increment value
of spectral noise density at temperature increase in one degree. Spectral noise density
in the mentioned above conditions with an idealized receiver will comprise a value
kT 0 = 4 × 10
−21 J or W/Hz. A transition to a real receiver requires a multiplication
of this spectral density into a noise coefficient. Formula (5.8) expresses that physical
fact that a reason, inducing electrical noises, preventing a detection process is a
heat motion of charged particles in stages of a receiver. As long as amplification
coefficient is not included in formula but coefficient K n exists considering noises
of the whole receiver, so a value E n represents noises of a receiver recalculated by
its input. Herewith, it is more convenient to compare them with a desired (useful)
signal, usually measured at the output. Finally, a relation of energy (power) of noise
gives a real signal-to-noise ratio at output of receiver linear part (e.g., at output of
intermediate-frequency amplifier). By using an expression (5.8), let us refer all noises
of receiver to some fictive active impedance (resistance) standing at receiver output
and heated up to K n T 0 temperature; herewith, a receiver itself can be assumed as
noiseless. It will be recalled that a noise power of active impedance does not depend
on resistance value. Since a spectral noise density E n is a noise power coming on a
frequency band of 1 Hz, a total power of receiver noise, correlated to input (arriving)
signal, will have a value:
P n = E n f = K n kT 0 f.
(5.9)
where f —pass band of receiver linear part.
Now then, (5.8) and (5.9) formulas give a possibility to consider one fluctuation process, limiting a detection possibility, internal noises of receiver. To consider
another fluctuation processes, external noises, target RCS fluctuations and to consider
an effectiveness of a certain method of signal processing at the background of all
fluctuations processes, a recognition (discrimination) coefficient is introduced:
K r =
E rcv min
E n
=
P rcv min
P n
.
(5.10)
5 Performance Characteristics of Radar Location …
Random process constantly presented in a radar is internal electrical noises of a
receiver. Energy or spectral density of internal noise in linear (up to detector) part of
a receiver is expressed as follows:
E n = K n kT 0 ,
(5.8)
where K n —noise coefficient of radar receiver, estimating a degradation of signalto-noise ratio (in power or energy) in comparison to receiver input; T 0 —absolute
temperature, at which a noise coefficient is measured. Usually, a noise coefficient of
receiver is measured at T 0 = 290 K, and sometimes, a corresponding recalculation of
a noise coefficient is required at high deviation of input temperature of radar from a
standard one. In most cases, the deviation of real temperature from a standard one is
neglected. Boltzmann constant k = 1.38 × 10
−23 in this case gives an increment value
of spectral noise density at temperature increase in one degree. Spectral noise density
in the mentioned above conditions with an idealized receiver will comprise a value
kT 0 = 4 × 10
−21 J or W/Hz. A transition to a real receiver requires a multiplication
of this spectral density into a noise coefficient. Formula (5.8) expresses that physical
fact that a reason, inducing electrical noises, preventing a detection process is a
heat motion of charged particles in stages of a receiver. As long as amplification
coefficient is not included in formula but coefficient K n exists considering noises
of the whole receiver, so a value E n represents noises of a receiver recalculated by
its input. Herewith, it is more convenient to compare them with a desired (useful)
signal, usually measured at the output. Finally, a relation of energy (power) of noise
gives a real signal-to-noise ratio at output of receiver linear part (e.g., at output of
intermediate-frequency amplifier). By using an expression (5.8), let us refer all noises
of receiver to some fictive active impedance (resistance) standing at receiver output
and heated up to K n T 0 temperature; herewith, a receiver itself can be assumed as
noiseless. It will be recalled that a noise power of active impedance does not depend
on resistance value. Since a spectral noise density E n is a noise power coming on a
frequency band of 1 Hz, a total power of receiver noise, correlated to input (arriving)
signal, will have a value:
P n = E n f = K n kT 0 f.
(5.9)
where f —pass band of receiver linear part.
Now then, (5.8) and (5.9) formulas give a possibility to consider one fluctuation process, limiting a detection possibility, internal noises of receiver. To consider
another fluctuation processes, external noises, target RCS fluctuations and to consider
an effectiveness of a certain method of signal processing at the background of all
fluctuations processes, a recognition (discrimination) coefficient is introduced:
K r =
E rcv min
E n
=
P rcv min
P n
.
(5.10)