Прикладные математические методы в статистической радиотехнике. Федосов В.П. - 43 стр.

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f(Z/s
0
) =Z/Eexp(-Z
2
/Q
2
);
f(Z/s
1
)=ZS
0
/[E(E+S
0
)]exp[-Z
2
S
0
2
/(4E(E+S
0
)).
Ɍɨɝɞɚ ɜɟɪɨɹɬɧɨɫɬɢ ɥɨɠɧɨɣ ɬɪɟɜɨɝɢ
p
F
ɢ ɩɪɚɜɢɥɶɧɨɝɨ ɨɛɧɚɪɭɠɟɧɢɹ p
D
ɨɩɪɟ-
ɞɟɥɹɸɬɫɹ ɩɨ ɫɥɟɞɭɸɳɢɦ ɮɨɪɦɭɥɚɦ:
p
F
=
³
f
0
z
f(Z/s
0
)dZ=exp(-S
0
2
/(2Q
2
)); p
D
=(p
F
)(1-Q
2
/2)
-1
.
Ƚɪɚɮɢɤɢ ɤɪɢɜɵɯ ɨɛɧɚɪɭɠɟɧɢɹ ɞɥɹ ɬɪɟɯ ɬɢɩɨɜ ɫɢɝɧɚɥɨɜ ɩɨɤɚɡɚɧɵ ɜ [6,
ɪɢɫ.8.2], ɝɞɟ ɜɢɞɧɨ, ɱɬɨ ɱɟɦ ɛɨɥɶɲɟ ɚɩɪɢɨɪɧɨɟ ɧɟɡɧɚɧɢɟ ɨɬɧɨɫɢɬɟɥɶɧɨ ɩɚɪɚɦɟɬ-
ɪɨɜ ɫɢɝɧɚɥɨɜ, ɬɟɦ ɛɨɥɶɲɟ ɬɪɟɛɭɟɬɫɹ ɨɬɧɨɲɟɧɢɟ ɫɢɝɧɚɥ/ɲɭɦ ɞɥɹ ɞɨɫɬɢɠɟɧɢɹ
ɪɚɜɧɨɣ ɜɟɪɨɹɬɧɨɫɬɢ ɩɪɚɜɢɥɶɧɨɝɨ ɨɛɧɚɪɭɠɟɧɢɹ ɩɪɢ ɮɢɤɫɢɪɨɜɚɧɧɨɣ ɜɟɪɨɹɬɧɨɫɬɢ
ɥɨɠɧɨɣ ɬɪɟɜɨɝɢ. Ɉɞɧɚɤɨ ɩɪɢ ɦɚɥɵɯ ɨɬɧɨɲɟɧɢɹɯ ɫɢɝɧɚɥ/ɲɭɦ ɷɬɚ ɬɟɧɞɟɧɰɢɹ ɧɚ-
ɪɭɲɚɟɬɫɹ: ɫɢɝɧɚɥ ɫ ɮɥɸɤɬɭɢɪɭɸɳɟɣ ɚɦɩɥɢɬɭɞɨɣ ɢ ɧɟɢɡɜɟɫɬɧɨɣ ɧɚɱɚɥɶɧɨɣ ɮɚɡɨɣ
ɨɛɧɚɪɭɠɢɜɚɟɬɫɹ ɥɭɱɲɟ, ɱɟɦ ɫɢɝɧɚɥ ɫ ɧɟɢɡɜɟɫɬɧɨɣ ɧɚɱɚɥɶɧɨɣ ɮɚɡɨɣ. ɗɬɨ ɦɨɠɧɨ
ɨɛɴɹɫɧɢɬɶ ɭɜɟɥɢɱɟɧɢɟɦ ɞɢɫɩɟɪɫɢɢ ɨɬɧɨɲɟɧɢɹ ɩɪɚɜɞɨɩɨɞɨɛɢɹ ɡɚ ɫɱɟɬ ɮɥɸɤɬɭɢ-
ɪɭɸɳɟɣ ɚɦɩɥɢɬɭɞɵ, ɱɬɨ ɩɪɢɜɨɞɢɬ ɤ ɭɜɟɥɢɱɟɧɢɸ ɜɟɪɨɹɬɧɨɫɬɢ ɩɪɟɜɵɲɟɧɢɹ ɩɨɪɨ-
ɝɨɜɨɝɨ ɭɪɨɜɧɹ
z
0
.
8.7. Ɉɛɧɚɪɭɠɟɧɢɟ ɩɚɱɤɢ ɪɚɞɢɨɢɦɩɭɥɶɫɨɜ ɧɚ ɮɨɧɟ ɛɟɥɨɝɨ ɲɭɦɚ
ɋɢɝɧɚɥ ɩɪɟɞɫɬɚɜɥɹɟɬ ɫɨɛɨɣ ɩɚɱɤɭ (ɩɚɤɟɬ) ɪɚɞɢɨɢɦɩɭɥɶɫɨɜ ɫɨ ɫɥɭɱɚɣɧɵɦɢ
ɧɟɡɚɜɢɫɢɦɵɦɢ ɧɚɱɚɥɶɧɵɦɢ ɮɚɡɚɦɢ ɨɬɞɟɥɶɧɵɯ ɪɚɞɢɨɢɦɩɭɥɶɫɨɜ
s(t,M
1
,...,M
m
) =
¦
m
i 1
s
i
(t)cos[Z
0
t+I
i
(t)+M
i
] ɢ ɫ ɩɥɨɬɧɨɫɬɶɸ ɜɟɪɨɹɬɧɨɫɬɢ ɧɚɱɚɥɶɧɵɯ
ɮɚɡ, ɪɚɜɧɨɣ ɩɪɨɢɡɜɟɞɟɧɢɸ ɨɞɧɨɦɟɪɧɵɯ ɩɥɨɬɧɨɫɬɟɣ ɜɟɪɨɹɬɧɨɫɬɟɣ ɤɚɠɞɨɣ ɢɡ ɧɚ-
ɱɚɥɶɧɵɯ ɮɚɡ ɪɚɞɢɨɢɦɩɭɥɶɫɨɜ, ɪɚɫɩɪɟɞɟɥɟɧɧɵɯ ɪɚɜɧɨɦɟɪɧɨ ɨɬ 0 ɞɨ 2
S.
ɉɨɫɤɨɥɶɤɭ ɨɛɧɚɪɭɠɟɧɢɟ ɩɪɨɢɡɜɨɞɢɬɫɹ ɧɚ ɮɨɧɟ ɧɨɪɦɚɥɶɧɨɝɨ ɲɭɦɚ, ɬɨ
ɫɬɪɭɤɬɭɪɚ ɨɛɧɚɪɭɠɢɬɟɥɹ ɞɨɥɠɧɚ ɛɵɬɶ ɨɫɧɨɜɚɧɚ ɧɚ ɤɨɪɪɟɥɹɰɢɨɧɧɨɦ ɢɧɬɟɝɪɚɥɟ,
ɡɚɩɢɫɚɧɧɨɦ ɩɪɢ ɩɪɨɢɡɜɨɥɶɧɨɣ ɧɚɱɚɥɶɧɨɣ ɮɚɡɟ
i-ɝɨ ɢɦɩɭɥɶɫɚ:
z [x(t)/M
1
,...,M
m
]=
¦
m
i 1
Z
i
cos(M
i
-]
i
),
ɝɞɟ
Z
i
=(z
ci
2
+z
si
2
)
1/2
, ]=arctg[x(t)/M
1
,...,M
m
]. ȿɫɥɢ ɜ ɩɪɟɞɟɥɚɯ ɞɥɢɬɟɥɶɧɨɫɬɢ ɤɚɠɞɨɝɨ
ɪɚɞɢɨɢɦɩɭɥɶɫɚ ɭɤɥɚɞɵɜɚɟɬɫɹ ɦɧɨɝɨ (ɛɨɥɶɲɟ 100) ɩɟɪɢɨɞɨɜ ɡɚɩɨɥɧɟɧɢɹ, ɬɨ ɷɧɟɪ-
ɝɢɹ ɩɚɱɤɢ ɢɦɩɭɥɶɫɨɜ ɧɟ ɡɚɜɢɫɢɬ ɨɬ ɫɥɭɱɚɣɧɵɯ ɧɚɱɚɥɶɧɵɯ ɮɚɡ ɢ ɪɚɜɧɚ ɫɭɦɦɟ
ɷɧɟɪɝɢɣ ɤɚɠɞɨɝɨ ɢɡ ɪɚɞɢɨɢɦɩɭɥɶɫɨɜ.
Ȼɟɡɭɫɥɨɜɧɨɟ ɨɬɧɨɲɟɧɢɟ ɩɪɚɜɞɨɩɨɞɨɛɢɹ ɩɨɥɭɱɚɟɬɫɹ ɩɨɫɥɟ ɭɫɪɟɞɧɟɧɢɹ ɭɫ-
ɥɨɜɧɨɝɨ ɨɬɧɨɲɟɧɢɹ ɩɪɚɜɞɨɩɨɞɨɛɢɹ ɩɨ ɜɫɟɦ ɧɚɱɚɥɶɧɵɦ ɮɚɡɚɦ
l(X)=
m
i 1
exp(-
E
i
/S
0
)I
0
(Z
i
), ɤɨɬɨɪɨɟ ɩɨɫɥɟ ɥɨɝɚɪɢɮɦɢɪɨɜɚɧɢɹ ɩɪɢɧɢɦɚɟɬ ɜɢɞ lnl(X) =

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