Graphics Programs Reference
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noise power. and are, respectively, the output signal and noise power.
Substituting Eq. (1.50) into Eq. (1.51) and rearranging terms yields
S
o
N
o
S
i
=
kT
e
BF SNR
(
)
o
(1.52)
Thus, the minimum detectable signal power can be written as
S
min
=
kT
e
BF SNR
(
)
o
min
(1.53)
The radar detection threshold is set equal to the minimum output SNR,
. Substituting Eq. (1.53) in Eq. (1.48) gives
(
SNR
)
o
min
14
⁄
P
t
G
2
λ
2
σ
4(
3
kT
e
BF SNR
-------------------------------------------------------
R
max
=
(1.54)
(
)
o
min
or equivalently,
P
t
G
2
λ
2
σ
4(
3
kT
e
BFR
max
(
SNR
)
o
min
=
-------------------------------------------
(1.55)
4
In general, radar losses denoted as
reduce the overall SNR, and hence
L
P
t
G
2
λ
2
σ
4(
3
kT
e
BFLR
4
(
SNR
)
o
=
-----------------------------------------
(1.56)
Although it may take on many different forms, Eq. (1.56) is what is widely
known as the Radar Equation. It is a common practice to perform calculations
associated with the radar equation using decibel (dB) arithmetic. A review is
presented in Appendix A.
MATLAB Function Ðradar_eq.mÑ
The function
Ðradar_eq.mÑ
implements Eq. (1.56); it is given in Listing 1.1
in Section 1.10. The syntax is as follows:
[snr] = radar_eq (pt, freq, g, sigma, te, b, nf, loss, range)
where
Symbol
Description
Units
Status
pt
peak power
Wa t t s
input
freq
radar center frequency
Hz
input
g
antenna gain
dB
input
sigma
target cross section
input
m
2
te
effective noise temperature
Kelvin
input
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