1. (SS) さ (11/13)

Ⅴ さ PSD SS

2. PSD ┞ (11/20)

PSD PSD ┞

--------- モ -------------------- 3. リ GPS

リ SS Ⅴ GPS SS Ⅴ

(SS: SS: Spread Spectrum) さ リ Ⅴ

┈

々 ㊪ () (fading) さ

10 100 ㊪

㍇

!

x( t) = m( t)c( t) 2 cos(2"f ct +# )

!

y(t) = x(t)

!

z( t) = m( t)c2( t)2cos2(2"f ct +# )

= m( t){1+cos(4"f ct + 2# )}

!

w( t) = m( t)

BPSK

!

2 cos(2"fct +# )

PN

PN

Low-pass Filter

!

0

Tb

"

!

2 cos(2"fct +# )

!

t = Tb

!

x(t)

!

y(t)

!

z( t)

!

w( t)

!

m( t)

!

c(t)

!

c(t)

PSD(Power Spectral Density)

!

fc

!

fc

!

fc

!

fc

m(t)

m(t)c(t)

c(t)

!

Tb

!

Tc

!

m(t) 2 cos(2"fct +# )

!

x( t)

!

y(t)

!

z( t)

!

fc

!

w( t)

!

2 f c

!

PSD

!

PSD

!

PSD

!

PSD

!

PSD

!

m( t)

!

PSD

PN ㊪ m 2m-1

1/Tc = Rc

!

N =R

c

Rb

=T

b

Tc

m(t) SS

┞

!

"c

!

" <|Tc

|

!

" >|Tc

| ┞ ┞

!

"c1c2

SS

ck ぜ k

!

xk(t) = 2m

k( t"#

k)c

k( t"#

k)cos[$

c(t"#

k)]

= 2mk( t"#

k)c

k( t"#

k)cos($

ct +%

k)

k

!

zk(t) = 2m

k(t "#

k)c

k(t "#

k)c1( t)cos($

ct +%

k)cos($

ct)

Low-pass Filter

!

wk(t) = m

k(t "#

k)c

k(t "#

k)c1( t)cos($

k)

!

0

!

Tb

!

0

!

Tb

!

"k

!

b1

!

b2

!

m1( t)

!

mk(t"#

k)

!

t

!

t

1 0 1 0 1 0 101010

110101

0

1

011010 0

001101 1 63

!

Ik

= cos("k) m

k( t#$

k)c

k( t#$

k)c1(t)

0

Tb% dt

0

!

"k

!

"k

Tb (-1 or 1) b1 b2

!

Ik = cos("k ) b1 ck (t # $ k )c1(t)dt0

$ k% + b2 ck (t # $ k )c1(t)dt$ k

Tb%& ' (

) * +

┞ ┞

!

"c1ck

= c1( t)ck( t#$ )dt

0

Tb% PN

!

c1(t)

!

ck (t)

っ CDMA(Code Division Multiple Access)

㍇

2. PSD(Power Spectral Density) ┞

PSD g(t) -T/2 T/2 gT

!

gT (t) =g( t) | t |"T / 2

0 | t |>T / 2

# $ %

gT

!

EgT = gT

2( t)dt = | GT ( f ) |2 df

"#

#

$"#

#

$

g(t)

!

Pg = limT"#

EgT

T= lim

T"#

1

T| GT ( f ) |2 df

$#

#

%& ' ( ) * +

= limT"#

|GT ( f ) |2

Tdf

$#

#

%

!

Sg ( f ) = limT"#

|GT ( f ) |2

T(PSD)

PSD ┞

!

"g(# )

g(t) ┞

!

" g (# ) = g(t)g(t +# )dt$%

%

&

x = t+

!

" g (# ) = g( x)g( x$# )dx$%

%

&

x t

!

" g (# ) = g(t)g(t $# )dt$%

%

&

!

"g(# ) ="

g($# )

g(t)

!

"T = g( t)g( t#$ )dt#T / 2

T / 2

%

!

F["T (# )] = e$ j 2%f# g( t)g( t$# )dt$T / 2

T / 2

&' ( ) * + , d#

$-

-

&

= g(t) g(t$# )e$ j 2%f#

$-

-

& d#' ( )

* + , dt

$T / 2

T / 2

&

= G($ f ) g( t)e$ j 2%ft dt$T / 2

T / 2

&= G($ f )G( f ) =|G( f ) |2 (when T .-)

!

Rg (" ) = limT#$

1

Tg(t)g(t +" )dt

%T / 2

T / 2

&

!

F Rg (" ){ }= limT#$

F[%T (" )]

T= lim

T#$

|G( f ) |2

T= Sg ( f )

!

Rg (" ) = limT#$

1

Tg(t)g(t %" )dt

%T / 2

T / 2

&

!

Rg (" ) = limN #$

1

NTb

g(t)g(t %" )dt%NTb / 2

NTb / 2

&

!

" <Tb

/ 2

!

N (Tb

/ 2"# )

!

Rg (" ) = limN #$

1

NTb

NTb

2%"

&

' (

)

* +

,

- .

/

0 1

=1

21%

2"

Tb

&

' (

)

* + (" <Tb / 2)

!

Rg (" )

!

Rg (" ) =1

21#

2"

Tb

$

%

& &

'

(

) ) ( " <Tb / 2)

!

Tb

!

Tb

/ 2

!

"

!

g(t)

!

g( t"# )

!

0.5

!

Rg (" )

!

"T

b

2

!

Tb

2

!

0

!

"

!

" >Tb

/ 2

!

Rg (" ) = 0

!

Sg ( f ) =Tb

4sinc2 Tb f

2

"

# $

%

& '

!

Q"(x)# sinc2( f )

3. リ GPS

リ SS Ⅴ

リ リ

リ (MTSO) リ

リ MTSO さ

リ リ リ ┞ リ

┞ リ

MTSOリ Ⅴ

!

1

!

"(x)

!

"1

!

1

!

0

!

x!

1

!

sinc2( f )

!

"1

!

1

!

0

!

f

!

2

!

"2

!

Sg ( f )

!

0

!

f

!

4

Tb

!

"4

Tb

!

"2

Tb

!

2

Tb

!

Tb

4

!

"

!

MTSO(mobile telephone switching office)

!

Telephone central office

!

base station

1. 2. ぜ 3. 4. 5. CDMA

Global Positioning System(GPS) SS Ⅴ GPS 々

GPS 24 424 22,000km 6 12

┐っ

ゝ PNPN GPS

PN PNゝ

┘ ゝ

GPS Ⅴ 1. ㌱ ┘ GPS 2. 100Hz

3. PN ┞ ┞ 0 ├ ス

PN

PN