Прикладные математические методы в статистической радиотехнике. Федосов В.П. - 42 стр.

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ɷɮɮɟɤɬɚ ɜ ɨɞɧɨɦ ɢɡ ɞɜɭɯ ɤɚɧɚɥɨɜ, ɨɧ ɨɛɹɡɚɬɟɥɶɧɨ ɫɨɡɞɚɫɬ ɟɝɨ ɜɨ ɜɬɨɪɨɦ ɤɚɧɚɥɟ.
ɋɥɟɞɨɜɚɬɟɥɶɧɨ, ɬɚɤɢɦ ɨɛɪɚɡɨɦ ɫɧɢɠɚɸɬɫɹ ɩɨɬɟɪɢ ɜ ɨɛɧɚɪɭɠɟɧɢɢ, ɨɛɭɫɥɨɜɥɟɧ-
ɧɵɟ ɧɟɢɡɜɟɫɬɧɨɣ ɧɚɱɚɥɶɧɨɣ ɮɚɡɨɣ. Ɏɭɧɤɰɢɹ ɜɵɛɨɪɨɱɧɵɯ ɞɚɧɧɵɯ
Z ɧɟ ɡɚɜɢɫɢɬ ɨɬ
ɫɥɭɱɚɣɧɨɝɨ ɩɚɪɚɦɟɬɪɚ - ɮɚɡɵ
M ɢ ɹɜɥɹɟɬɫɹ ɢɧɜɚɪɢɚɧɬɨɦ ɨɬɧɨɫɢɬɟɥɶɧɨ ɷɬɨɝɨ ɩɚ-
ɪɚɦɟɬɪɚ (ɞɥɢɧɚ ɜɟɤɬɨɪɚ).
ɇɚɣɞɟɦ ɜɵɪɚɠɟɧɢɹ ɞɥɹ ɜɟɪɨɹɬɧɨɫɬɟɣ ɥɨɠɧɨɣ ɬɪɟɜɨɝɢ ɢ ɩɪɚɜɢɥɶɧɨɝɨ ɨɛɧɚ-
ɪɭɠɟɧɢɹ. Ⱦɥɹ ɷɬɨɝɨ ɨɩɪɟɞɟɥɢɦ ɩɥɨɬɧɨɫɬɶ ɜɟɪɨɹɬɧɨɫɬɢ ɜɟɥɢɱɢɧɵ
Z:
f(Z) =
³
S
2
0
f(M)f(Z/M)dM = [1/(2S)]
³
S
2
0
f(Z/M)dM. ɉɪɢ ɧɚɥɢɱɢɢ ɫɢɝɧɚɥɚ:
f(Z/s
1
)= Z/E exp[-E/S
0
(1+Z
2
/Q
2
)]I
0
(Z),
ɩɪɢ ɨɬɫɭɬɫɬɜɢɢ ɫɢɝɧɚɥɚ
f(Z/s
0
)=Z/E exp(-Z
2
/Q
2
).
ɋɪɚɜɧɢɬɟɥɶɧɵɣ ɚɧɚɥɢɡ ɩɨɥɭɱɟɧɧɵɯ ɜɵɪɚɠɟɧɢɣ ɩɨɤɚɡɵɜɚɟɬ, ɱɬɨ ɪɚɫɩɪɟɞɟ-
ɥɟɧɢɟ ɦɨɞɭɥɹ ɤɨɪɪɟɥɹɰɢɨɧɧɨɝɨ ɢɧɬɟɝɪɚɥɚ ɩɪɢ ɧɚɥɢɱɢɢ ɫɢɝɧɚɥɚ ɨɬɥɢɱɚɟɬɫɹ ɨɬ
ɬɚɤɨɝɨ ɠɟ ɪɚɫɩɪɟɞɟɥɟɧɢɹ (ɧɨ ɩɪɢ ɨɬɫɭɬɫɬɜɢɢ ɫɢɝɧɚɥɚ) ɫɦɟɳɟɧɢɟɦ ɜɩɪɚɜɨ. ɗɬɨ
ɫɦɟɳɟɧɢɟ ɡɚɜɢɫɢɬ ɨɬ
Q. ɂ ɱɟɦ ɛɨɥɶɲɟ Q, ɬɟɦ ɛɨɥɶɲɟ ɫɦɟɳɟɧɢɟ. Ɍɟɦ ɫɚɦɵɦ ɭɜɟ-
ɥɢɱɢɜɚɟɬɫɹ ɜɟɪɨɹɬɧɨɫɬɶ ɩɪɚɜɢɥɶɧɨɝɨ ɨɛɧɚɪɭɠɟɧɢɹ ɩɪɢ ɮɢɤɫɢɪɨɜɚɧɧɨɦ ɩɨɪɨɝɨ-
ɜɨɦ ɭɪɨɜɧɟ (ɮɢɤɫɢɪɨɜɚɧɧɨɣ ɜɟɪɨɹɬɧɨɫɬɢ ɥɨɠɧɨɣ ɬɪɟɜɨɝɢ).
8.6.Ɉɬɧɨɲɟɧɢɟ ɩɪɚɜɞɨɩɨɞɨɛɢɹ ɢ ɯɚɪɚɤɬɟɪɢɫɬɢɤɢ ɨɛɧɚɪɭɠɟɧɢɹ
ɞɥɹ ɫɢɝɧɚɥɚ ɫɨ ɫɥɭɱɚɣɧɵɦɢ ɧɚɱɚɥɶɧɨɣ ɮɚɡɨɣ ɢ ɚɦɩɥɢɬɭɞɨɣ
ɋɢɝɧɚɥ ɜ ɷɬɨɦ ɫɥɭɱɚɟ ɦɨɠɟɬ ɛɵɬɶ ɡɚɩɢɫɚɧ ɜ ɬɚɤɨɦ ɜɢɞɟ:
s(t,A,M) =As(t)cos[Z
0
t+I
s
(t)+M], ɝɞɟ M - ɫɥɭɱɚɣɧɚɹ ɧɚɱɚɥɶɧɚɹ ɮɚɡɚ, ɪɚɫɩɪɟɞɟɥɟɧɧɚɹ ɩɨ ɪɚɜɧɨɦɟɪɧɨɦɭ
ɡɚɤɨɧɭ ɜ ɩɪɟɞɟɥɚɯ ɨɬ 0 ɞɨ 2
S; Ⱥ - ɫɥɭɱɚɣɧɚɹ ɚɦɩɥɢɬɭɞɚ, ɪɚɫɩɪɟɞɟɥɟɧɧɚɹ ɩɨ ɪɟɥɟ-
ɟɜɫɤɨɦɭ ɡɚɤɨɧɭ
f(A)=AV
-2
exp(-A
2
/(2V
2
)), At0. ɋɥɭɱɚɣɧɵɟ ɜɟɥɢɱɢɧɵ M ɢ Ⱥ ɧɟɡɚɜɢɫɢɦɵ ɢ ɢɯ ɫɨ-
ɜɦɟɫɬɧɨɟ ɪɚɫɩɪɟɞɟɥɟɧɢɟ
f(M,Ⱥ) ɪɚɜɧɨ ɩɪɨɢɡɜɟɞɟɧɢɸ ɨɞɧɨɦɟɪɧɵɯ ɡɚɤɨɧɨɜ ɪɚɫ-
ɩɪɟɞɟɥɟɧɢɹ. ɉɪɢ ɬɚɤɢɯ ɢɫɯɨɞɧɵɯ ɞɚɧɧɵɯ ɭɫɥɨɜɧɨɟ ɨɬɧɨɲɟɧɢɟ ɩɪɚɜɞɨɩɨɞɨɛɢɹ
ɢɦɟɟɬ ɜɢɞ
l(X/M,A) =AZcos(M - ]). ɗɧɟɪɝɢɹ ɫɢɝɧɚɥɚ ɡɚɜɢɫɢɬ ɨɬ ɫɥɭɱɚɣɧɵɯ ɩɚɪɚ-
ɦɟɬɪɨɜ
Ⱥ ɢ M ɢ ɞɨɥɠɧɚ ɛɵɬɶ ɭɫɪɟɞɧɟɧɚ ɩɨ ɜɫɟɦ ɷɬɢɦ ɩɚɪɚɦɟɬɪɚɦ. Ⱦɥɹ Ⱥ/V ɷɬɚ
ɫɪɟɞɧɹɹ ɷɧɟɪɝɢɹ ɪɚɜɧɚ
ȿ (ɩɪɢɛɥɢɠɟɧɧɨ ɩɪɢ ɬɟɯ ɠɟ ɫɨɨɬɧɨɲɟɧɢɹɯ, ɱɬɨ ɢ ɞɥɹ ɫɥɭ-
ɱɚɣɧɨɣ ɧɚɱɚɥɶɧɨɣ ɮɚɡɵ). ɂɫɩɨɥɶɡɭɹ ɮɨɪɦɭɥɵ ɩɪɟɞɵɞɭɳɟɝɨ ɩɨɞɪɚɡɞɟɥɚ, ɨɩɪɟɞɟ-
ɥɢɦ ɨɬɧɨɲɟɧɢɟ ɩɪɚɜɞɨɩɨɞɨɛɢɹ, ɭɫɪɟɞɧɢɜ ɟɝɨ ɩɨ
Ⱥ ɢ M: l
AM
(X)=
=
S
0
/(E+S
0
)exp[Z
2
S
0
/(4(E+S
0
))]. Ɍɚɤɢɦ ɨɛɪɚɡɨɦ, ɫɬɪɭɤɬɭɪɭ ɨɛɧɚɪɭɠɢɬɟɥɹ ɦɨɠɧɨ
ɩɨɥɭɱɢɬɶ, ɩɪɨɥɨɝɚɪɢɮɦɢɪɨɜɚɜ ɨɬɧɨɲɟɧɢɟ ɩɪɚɜɞɨɩɨɞɨɛɢɹ. Ɉɛɧɚɪɭɠɢɬɟɥɶ ɞɥɹ
ɫɥɭɱɚɣɧɵɯ ɚɦɩɥɢɬɭɞɵ ɢ ɧɚɱɚɥɶɧɨɣ ɮɚɡɵ ɧɟ ɨɬɥɢɱɚɟɬɫɹ ɩɨ ɫɬɪɭɤɬɭɪɟ ɨɬ ɨɛɧɚɪɭ-
ɠɢɬɟɥɹ ɞɥɹ ɫɥɭɱɚɣɧɨɣ ɮɚɡɵ. Ɉɬɥɢɱɢɟ ɜɵɪɚɠɚɟɬɫɹ ɬɨɥɶɤɨ ɜ ɩɨɪɨɝɨɜɨɦ ɭɪɨɜɧɟ, ɫ
ɤɨɬɨɪɵɦ ɫɪɚɜɧɢɜɚɟɬɫɹ ɤɜɚɞɪɚɬ ɦɨɞɭɥɹ ɤɨɪɪɟɥɹɰɢɨɧɧɨɝɨ ɢɧɬɟɝɪɚɥɚ. Ɋɚɫɩɪɟɞɟɥɟ-
ɧɢɟ
Z ɜ ɨɛɥɚɫɬɢ ɝɢɩɨɬɟɡɵ (G
0
) ɢ ɚɥɶɬɟɪɧɚɬɢɜɵ (G
1
) ɨɬɥɢɱɚɟɬɫɹ ɬɨɥɶɤɨ ɜɟɥɢɱɢɧɨɣ
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