Информ технологии в СМС (скинул Павликов)

. QAM #' &. 2 '( #) # * '

'( $( # * ' * * ',

. * «!» $ #.

13.2. FDM-

! * ' %3 % FDM-

$ # QPSK-#', . #' &

& * * ' ( ! ):

−00 –1–1j;

−01 –1+1j;

−10 +1–1j;

−11 +1+1j.

# ( . # * ': a = [11 01] ( . . 13.2)

- . 13.2. & % * '

* ' ! 2 '' '( . ( #'

2):

−11 +1+1j.

−01 –1+1j;

161

' '( %3 * ! !. #' *

! * ! 0# (:

:

&

1

N −1

j2πkn

Cn

=

∑x(k ) exp

−

N

N k =0

!:

N −1

j2πkn

&

x(k ) = ∑Cn

exp −

n=0

N

' . $'

−

&

= +1

+ 1 j ,

C0

−

&

= −1

+ 1 j

C1

) !' ! * ! 0# (:

N −1

&

j2πkn

&

j2π 0 0

&

j2π 0 1

x(0)

= ∑Cn

exp −

N

= C0

exp −

2

+ C1 exp −

2

=

n=0

&

&

= +1 + 1 j

− 1 + 1 j = 0 + 2 j

= C0

+ C1

N −1

&

j2πkn

&

j2π 1 0

&

j2π 1 1

x(1) = ∑Cn

exp −

= C0

exp −

2

+ C1 exp −

2

=

n=0

N

&

&

= +1 + 1 j

− (− 1 + 1 j ) = 2 + 0 j

= C0

− C1

0 # : (x(0) x(1)) = (0 + 2 j

2 + 0 j ),

−Re(x(0) x(1)) = (0 2) # 4

*$% # & % sin(2πft ) ( . . 13.3 );

−Im(x(0) x(1)) = (2 0) # 4

*$% # & % cos(2πft ) ( . . 13.3 !).

162

!

- . 13.3. * ' ' 0 4:

(.#) – Re (x(0) x(1)), (#) – Im (x(0) x(1)), ! (.#) – f4[Re (x(0) x(1))]· sin(2πft ) , ! (#) – f4 [Im (x(0) x(1))]· cos(2πft )

# % * ' ' ! % ' ! % OFDM-* ',

% # # '#$ ( .

. 22). !$

fRe(t)= f4[Re (x(0) x(1))]· sin(2πft ) , fIm(t)= f4[Im (x(0) x(1))]· cos(2πft ).

+ * OFDM-* ': fOFDM(t) = fRe(t) + fIm(t).

- . 13.3. OFDM-* ' *

163

%	OFDM-* ' # '' '(	!'
' %	*$ # & sin(2πft ) ,	cos(2πft )

( . . 13.4), ' $* # ) !' 0, * ) '(

*, ' . % $% * ' ( . . 13.5).

!

- . 13.4. * ' . . ' %:

fOFDM (t )sin(2πft ) ( ), fOFDM (t )cos(2πft )(!)

- . 13.5. * ' ' 0

164

- % &, . / #

# & ) sin(2πft ) $% $ :

T		T
∫ f OFDM (t )sin(2πft )dt =∫( f Re (t )+ f Im (t ))sin(2πft )dt =
0		0
= T∫{f (t )[Re(x(0)		x(1))]sin(2πft )+ f (t )[Im(x(0) x(1))]cos(2πft )}× sin(2πft )dt =
0
T
= ∫ f (t )[Re(x(0)		x(1))]sin(2πft )sin(2πft )dt +
0	(t )[Im(x(0)	x(1))]cos(2πft )sin(2πft )dt = f (t )[Re(x(0) x(1))]
+ ∫ f
T

0	2
* T – ' OFDM-* '. 2 $ # '
& ' $' $ f.
	4 ' *$ , * OFDM-* '

cos(2πft ).

( #', OFDM-* ' '

. $ 0 # (3, 6 #

( & ), ' # # * ' 3 ) . '#$ * ', # ) 4 ( . . 13.6), #

' '(:

- . 13.6. 0 . ' '( % (' 4)

165

. *, * '

#) * ' $ :

Re(x(0) x(1)) = (0 2)

Im(x(0) x(1)) = (2 0)

:

x(0) = Re(x(0))+ j Im(x(0)) = 0 + 2 j

x(1) = Re(x(1))+ j Im(x(1)) = 2 + 0 j

. ! 0# (:

&

1

N −1

j2πkn

Cn

=

∑x(k ) exp

−

N

N k =0

&

1

j2π 0 0

C

0

=

x(0) exp −

+ x(1) exp −

2

2

=

0 + 2 j + 2 + 0 j

= 1 + 1 j

2

&

1

j2π 1 0

C

=

x(0) exp −

+ x(1) exp −

1

2

2

=

0 + 2 j − 2 − 0 j

= −1 + 1 j

2

&

= 1 + 1 j

C0

&

= −1 + 1 j

C1

j2π 0 1		x(0)+ x(1)
	=			=
2		2

j2π 1 1	x(0)− x(1)
=			=
	2
2

' '( ( C0	= 1 + 1 j # * '# [11]
&
' '( ( C1	= −1 + 1 j # * '# [01]
&

+ !, ' !" '#$ : [11 01], %

* ' ( . . 13.7)

166

- . 13.7. % * ' (.#), % * ' ( &),

( # * ' (#)

13

1.+ . ' * OFDM ' ! % ! % #' &,

% '( # * '( . #/..

2.* '( ( #/ . * $ '(

! * ! 0# (.

3.#/ '( ! '(3 % !" .,

# ( #/ . # $'( %

!" &.

4.' '( ( ' #/ % $'( ! '(3, $

& . ., $ ' # 3 ! (

'( % & % (,).

5.' ! (! , ' '( '( # . % ' – # # OFDM-'.

6.OFDM- $ '( #) . ' * . ADSL, DVB-T, WiMAX, LTE.

167

7.' ( .$% ' & OFDM '$

! % 0# (, 6 # ! ' '#$

'( * ! 0# (.

- 13

1.( !! # OFDM?

2.3 & '( * * ' OFDM.

3.' $* !. . % '?

4.2 . . ' * . $ '( # OFDM?

5.9 $ $* $ '( OFDM ! ' # %$

'( % &?

6.' * $# # ( * ' * '(

#/?

8

1.! * ' FDM- $ # QPSK-#'. QPSK-#' & & * * ' (

! ):

−00 → –1–1j;

−01 → –1+1j;

−10 → +1–1j;

−11 → +1+1j.

. % * ': a = [01 01].

2.! * ' FDM- $ # QPSK-#'. QPSK-#' & & * * ' (

! ):

−00 → –1–1j;

−01 → –1+1j;

−10 → +1–1j;

−11 → +1+1j.

. % * ': a = [11 00].

168

% 14. Wi-Fi

& ' &: Wi-Fi, .

Wi-Fi, 6' & # & . ' * % $ OFDM

$* , ' * % ! . %. '( ' &: #$( & ! Wi-Fi *# & ) ! . %.

14.1. ' Wi-Fi

2 1990 *. IEEE 802 (Institute of Electrical and Electronic Engineers) ' !$#) * # # ' ! . ' '( . % 802.11. 7 * # ' ( ! %

!/ * ' ! # %, ! )/ . $

2.4 11& 1 2 ,!/ .

2 / 3 '( # #/

* # IEEE 802.11 ( . !'. 14.1).

+ !'. 14.1. . * # IEEE 802.11

	802.11g	802.11a	802.11n
%	2,4-2,483	5,15-5,25	2,4 ' 5,0
, 11&
, $	DSSS,OFDM	DSSS,OFDM	MIMO
(, ,!/	1-54	6-54	6-300
(	802.11 b/n	802.11 n	802.11 a/b/g
, #' &	BPSK, QPSK,	BPSK, QPSK,	BPSK, 64-QAM
	OFDM	OFDM
'( (	20-50	10-20	50-100
/,
'( (	250	150	500
/,

14.2. " IEEE 802.11g

IEEE 802.11g, % 2003 * #, ' ' *$

802.11b ' * $# .
$ , ! ' .
, '( ( $ .	802.11g
' 54 ,!/ .

169

C 802.11g 3: $

! . ) . ' * OFDM CCK, & '(

# '( . ' * PBCC.

$* (Packet Binary Convolutional Coding, PBCC) ')$ ' #)/. 2. / ' '( (

& . ! ! # $ !, $! # . # ! # ' ! ' * . *. +

( $% ! ' ' #) !$#) & )

. % ' '(. ', #, # . # ! #

#) . ., * $

() % 1/2. ' # . ! #)

. ., ( $* !# ' ( #

2/3.

1' $. '

. # %$( # % ' '(. ' , $

!$ '#$ 3 !

. ' '( ( ! ! ( ! 3 !$ '. ' ' . % ' '( !

2 !.

' 22 ,!/ ) # %

. % PBCC $ . !. *,

8-& #' & (8-PSK), ( * '

( ( '$. $%, $ '

' ( # !. *, . #, ')$

$* , ! ' # # % (Puncture). ' *

3 '( : !$( $* , 2 (

% . % ! . . .), $

' . # ' . . % ! ' ' 3 %, 6 #

# (3 ( !$(, $!, #, # . ! ' ... ' 6 * , $ ,

! ( #)/ % $% , '#$3 ! ( . #

& '( % # # % , % !# #$ ( ' 3 !. #, # # % # ' ! . $.

. . !. + * $ . / ! !# # (

. /.. ( * ' 4/3. ' %

170