Efecto No Lineal de OFDM en La Transmisión de RoF
3
Nonlinear Effect o f OFDMn Radio-over-Fiber transmission Zhang B o, Lu Yinghua, Zhang Jinling, Yang Biao Beijing University of Posts a n d Telecommunications P O Bo x 214, X i T u Cheng Road 1 0 , BeiJing, CHINA, 100876 Tel: 86-10-62283303, E-mail: zhbomailWgmail.com Abstract - This paper i s concerned with t he analysis o f t h e nonlinear distortion o f Orthogonal Frequency-Division Multiplex OFDM) signals caused b y semiconductor laser i n a Radio-over- Fiber link. A third order polynomial without memory i s used t o present th e nonlinearity of semiconductor laser. T h e expression of in-band noise d u e t o nonlinear distortion i s then derived. Moreover, t h e relation of carrier-to-noise ratio with optical modulation index i s analyzed. T h e analytical method i s applicable f o r nonlinearity analysis a n d useful t o select th e optical modulation index o f OFDM- R O F system. Index Terms- radio over fiber; nonlinearity; OFDM;. I . INTRODUCTION I n t h e case o f further wireless communication system significant effort i s done t o reduce t h e multipath fading a n d t o have low-cost a n d small base station matched t o demands made b y t h e bigger number o f mobile cells a n d high frequency applications. T o meet these requirements o n e o f best solution i s t h e combination o f Orthogonal Frequency Division Multiplexing OFDM) modulation a n d radio over fiber (ROF) technology. OFDM i s seen as t h e modulation technique f o r future broadband wireless communications because i t provides increased robustness against frequency selective fading a n d narrowband interference, a n d i s efficient i n dealing with multi- path delay spread [l] I t present a suitable solution f o r indoor wireless access, wireless LAN a n d LMDS. However, this modulation scheme i s sensitive t o t he nonlinear effects i n t h e in[2]. in k T h e u s e radio over fiber t o provide radio h a s a number o f advantages including th e ability t o deploy small, low- cost remote antenna units a n d ease o f upgrade. Actually, some kinds o f R O F link h a s been developed t o support further wireless system, such as WLAN, I T S a n d next generation cellular system[3]. Transmitting analog R F signal through R O F link, a common problem i s semiconductor laser nonlinearity[45]. There have been a number o f publications on t h e laser nonlinearity analysis when u s e standard modulation scheme including multilevel QAM, CDMA , etc[6,7]. T h e nonlinearity knowledge o f OFDM i s useful f o r system design a n d performance analysis. Some works have done t o study OFDM transmission performance through the nonlinearity o f fiber-radio link, however these researches mainly focus on discussing t he nonlinearity o f external modulator such as Mach-Zehnder modulator89]. With semiconductor laser nonlinearity i t i s necessary t o select an optimal modulation index that provides a maximum carrier-to-noise ratio (C/N).A third order polynomial without memory i s used t o present laser nonlinearity[10] a n d nonlinearity on CDMA i s analyzed i n [ 7 , 1 1 ] using this method. I n this paper, we deal with R O F link applying direct intensity modulation a n d direct detection (IM-DD). A n analytical method i s proposed t o evaluate the effects of semiconductor laser nonlinearity on OFDM signal. A nd t h e relation o f C / N ratio a n d optical modulation m s also studied. RE in RE o u t R F out RE in Fig. 1. t h e layout o f a RO F optical link using direct modulation laser diodes. I I . RADIO OVER FIBER LINK IM-DD links are used i n cellular applications f o r reasons o f simplicity a n d cost. Fig.1 shows the layout o f a simple bidirectional directly modulated radio over fiber link. I n each direction t h e imput R F signal is applied t o a laser diode where i t modulates t he intensity of t h e output light. I n most cases this light was semiconductor laser which i s operated a t 1300nm or 1550 nm f o r l o w transmission loss i n silica fiber. Th e optical receiver usually consists o f a p-i-n photodiode, which provides an R F powe r output proportional t o t he square o f t he input optical power. - aserdiode Photodiode fiber -Photodiode Laserdiode <
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Transcript of Efecto No Lineal de OFDM en La Transmisión de RoF
Nonlinear E f f e c t ofOFDMn Radio-over-Fiber
t r a n s m i s s i o n
Z h a n g
Bo, Lu Y i n g h u a ,
Z h a n g J i n l i n g ,
Yang B i a o
B e i j i n g U n i v e r s i t y o f
P o s t s a n d T e l e c o m m u n i c a t i o n s
PO Box 2 1 4 , X i Tu C h e n g R o a d 1 0 , B e i J i n g , CHINA, 1 0 0 8 7 6
T e l :
8 6 - 1 0 - 6 2 2 8 3 3 0 3 , E - m a i l : z h b o m a i l W g m a i l . c o m
A b s t r a c t
-
paper
i s c o n c e r n e d w i t h t he a na ly si s o f t h e
n o n l i n e a r d i s t o r t i o n o f O r t h o g o n a l F r e q u e n c y - D i v i s i o n
M u l t i p l e x
OFDM) s i g n a l s c a u s e d
b y s e m i c o n d u c t o r l a s e r i n a R a d i o - o v e r -
F i b e r l i n k .
A
t h i r d o r d e r p o l y n o m i a l w i t h o u t memory i s u s e d t o
p r e s e n t t h e n o nl i n e ar i t y o f s e m i c o n d u c t o r l a s e r . T h e e x p r es s i o n o f
i n - b a n d n o i s e d u e t o n o n l i n e a r d i s t o r t i o n
i s t h e n d e r i v e d . M o r e o v e r ,
t h e r e l a t i o n o f c a r r i e r - t o - n o i s e r a t i o w i t h o p t i c a l
m o d u l a t i o n i n d e x
i s a n a l y z e d . T h e a n a l y t i c a l m e t h o d i s a p p l i c a b l e f o r n o n l i n e a r i t y
a n a l y s i s
a n d
u s e f u l
t o s e l e c t t h e o p t i c a l
m o d u l a t i o n
i n d e x
o f OFDM-
s y s t e m .
I n d e x T e r m s - r a d i o over f i b e r ; n o n l i n e a r i t y ; OFDM;.
I . I N T R O D U C T I O N
I n t h e
case
o f f u r t h e r w i r e l e s s c o m m u n i c a t i o n
s y s t e m
s i g n i f i c a n t
e f f o r t i s
d o n e t o r e d u c e t h e
m u l t i p a t h f a d i n g
a n d t o
h a v e l o w - c o s t a n d s m a l l b a s e s t a t i o n m a t c h e d t o d e m a n d s m a d e
b y
b i g g e r
n u m b e r o f m o b i l e c e l l s a n d
h i g h
f r e q u e n c y
a p p l i c a t i o n s .
To meet t h e s e
r e q u i r e m e n t s
one o f b e s t s o l u t i o n i s
t h e
c o m b i n a t i o n o f
O r t h o g o n a l
F r e q u e n c y
D i v i s i o n
M u l t i p l e x i n g
OFDM)
m o d u l a t i o n a n d r a d i o over f i b e r
( R O F )
t e c h n o l o g y .
OFDM i s seen as t h e m o d u l a t i o n
t e c h n i q u e
f o r
f u t u r e b r o a d b a n d w i r e l e s s c o m m u n i c a t i o n s b e c a u s e
i t
i n c r e a s e d
r o b u s t n e s s
a g a i n s t f r e q u e n c y
s e l e c t i v e f a d i n g
a n d
n a r r o w b a n d i n t e r f e r e n c e , a n d i s e f f i c i e n t
i n
w i t h m u l t i -
p a t h d e l a y s p r e a d [ l ] I t
p r e s e n t
a s u i t a b l e s o l u t i o n f o r i n d o o r
w i r e l e s s
access,
w i r e l e s s LAN a n d LMDS.
H o w e v e r ,
t h i s
m o d u l a t i o n s c h e m e i s s e n s i t i v e t o t h e
n o n l i n e a r e f f e c t s
i n
r a d i o over
f i b e r
t o
r a d i o h a s a
n u m b e r o f
a d v a n t a g e s i n c l u d i n g t h e a b i l i t y
t o
d e p l o y s m a l l , l o w -
c o s t
r e m o t e a n t e n n a u n i t s a n d
ease o f
u p g r a d e . A c t u a l l y ,
some
o f
h a s b e e n
d e v e l o p e d
t o
w i r e l e s s
s y s t e m ,
s u c h
I T S a n d n e x t
g e n e r a t i o n
c e l l u l a r
s y s t e m [ 3 ] .
T r a n s m i t t i n g
a n a l o g
RF
s i g n a l t h r o u g h
ROF
p r o b l e m
i s s e m i c o n d u c t o r l a s e r n o n l i n e a r i t y [ 4 5 ] .
T h e r e h a v e
b e e n
a n u m b e r o f
p u b l i c a t i o n s
on t h e l a s e r
n o n l i n e a r i t y
a n a l y s i s when use s t a n d a r d m o d u l a t i o n
s c h e m e
i n c l u d i n g
m u l t i l e v e l
QAM,
CDMA
e t c [ 6 , 7 ] . T h e
n o n l i n e a r i t y
k n o w l e d g e
o f OFDM
i s u s e f u l f o r s y s t e m d e s i g n
a n d
p e r f o r m a n c e a n a l y s i s .
Some w o r k s h a v e d o n e t o
s t u d y
OFDM
t r a n s m i s s i o n p e r f o r m a n c e t h r o u g h
t h e
n o n l i n e a r i t y
o f f i b e r - r a d i o
l i n k , h o w e v e r t h e s e r e s e a r c h e s m a i n l y f o c u s on d i s c u s s i n g t h e
n o n l i n e a r i t y o f e x t e r n a l m o d u l a t o r
s u c h as M a c h - Z e h n d e r
m o d u l a t o r 8 9 ] . W i t h s e m i c o n d u c t o r l a s e r n o n l i n e a r i t y i t i s
necessary t o
s e l e c t an o p t i m a l m o d u l a t i o n i n d e x t h a t p r o v i d e s a
maximum c a r r i e r - t o - n o i s e r a t i o ( C / N ) . A t h i r d o r d e r p o l y n o m i a l
w i t h o u t memory
i s u s e d t o p r e s e n t l a s e r n o n l i n e a r i t y [ 1 0 ] a n d
n o n l i n e a r i t y
on
CDMA i s a n a l y z e d
i n
[ 7 , 1 1 ] u s i n g t h i s
m e t h o d .
I n t h i s paper, we d e a l w i t h ROF l i n k a p p l y i n g d i r e c t i n t e n s i t y
m o d u l a t i o n a n d d i r e c t d e t e c t i o n ( I M - D D ) .
A n
a n a l y t i c a l m e t h o d
i s p r o p o s e d t o e v a l u a t e t h e e f f e c t s o f
s e m i c o n d u c t o r
l a s e r
n o n l i n e a r i t y on OFDM s i g n a l .
And
t h e r e l a t i o n o f C / N r a t i o a n d
o p t i c a l m o d u l a t i o n
m
s t u d i e d .
RE
in
RE in
l a y o u t
o f a RO F o p t i c a l
l i n k
using d i r e c t m o d u l a t i o n l a s e r d i o d e s .
I I . RADIO OVER
IM-DD l i n k s
are u s e d i n c e l l u l a r a p p l i c a t i o n s f o r reasons o f
s i m p l i c i t y
a n d c o s t .
F i g . 1
l a y o u t
o f a
s i m p l e
b i d i r e c t i o n a l
d i r e c t l y
m o d u l a t e d r a d i o over f i b e r
l i n k . I n
e a c h
d i r e c t i o n t h e
i m p u t
RF
i s
a p p l i e d
t o a l a s e r d i o d e
w h e r e
i t
m o d u l a t e s t h e i n t e n s i t y o f t h e
o u t p u t l i g h t .
I n
most cases t h i s
l i g h t was
s e m i c o n d u c t o r l a s e r w h i c h i s o p e r a t e d a t 1300nm
or
1 5 5 0 nm
f o r l o w t r a n s m i s s i o n l o s s i n
s i l i c a f i b e r . T h e
o p t i c a l
r e c e i v e r
u s u a l l y
c o n s i s t s o f a p - i - n p h o t o d i o d e ,
w h i c h
p r o v i d e s
an
RF
power
o u t p u t p r o p o r t i o n a l
t o
o p t i c a l
power.
P h o t o d i o d e
f i b e r
<
I I I . R E P R E S E N T A T I O N OF IN-BAND D I S T O R T I O N N O I S E
T h e OFDM s i g n a l c a n
b e m o d e l e d
( f o r a h i g h n u m b e r o f
i n d e p e n d e n t l y m o d u l a t e d c a r r i e r s ) l i k e a c o m p l e x G a u s s i a n
p r o c e s s w i t h R a y l e i g h e n v e lo p e d i s t r i b u t i o n [ 2 ] .
T h i s
t h e
a n a l y t i c a l t r e a t m e n t
o f
n o n l i n e a r OFDM s y s t e m s
m a k i n g
u s e o f
t h e m o r e g e n e r a l r e s u l t s f o r n o n l i n e a r d i s t o r t i o n s
o f
G a u s s i a n
s i g n a l s . T h e r e f o r e ,
R i c e s t r a n s f o r m
m e t h o d 1 2 ]
w a s a p p l i e d t o
d e r i v e t h e p o w e r s p e c t r a o f t h e o u t p u t
a n d t h e i n d u c e d d i s t o r t i o n
n o i s e
f a l l i n g i n t o t h e s i g n a l b n d S p e c i f i c a l l y , t h e
o u t p u t
a u t o c o r r e l a t i o n
f u n c t i o n c a n b e e x p r e s s e d a s
FR
r1
R X ( I )
i s t h e
a u t o c o r r e l a t i o n
f u n c t i o n o f t h e i n p u t OFDM
s i g n a l , a n d t h e
c o e f f i c i e n t s
* k
2 g ( x ) e x d x d u ( 2 )
2 / 7 Z ( X
T h e
f i r s t t e r m i n ( 1 )
i s t h e
DC t e r m , t h e n = 1 t e r m i s t h e s i g n a l
t e r m , a n d
n > 1 t e r m s r e p r e s e n t t h e i n d u c e d
d i s t o r t i o n n o i s e .
T h e s e e x p r e s s i o n s a r e i n a g r e e m e n t
w i t h [ 1 2 ] . T h e n t h e
t o t a l
d i s t o r t i o n n o i s e s p e c t r a l d e n s i t y i s g i v e n b y
m o d u l a t i o n b a n d w i d t h , a n o n l i n e a r s e m i c o n d u c t o r
l a s e r
w i t h o u t
memory c a n b e p r e s e n t e d b y a t h i r d o r d e r p o l y n o m i a l a s [ 7
1 0 ]
+ a 3 x ( 6 )
w h e r e y i s h e o p t i c a l p o w e r
o u t p u t
m o d u l a t e d b y c u r r e n t s i g n a l
x
a n d a 1 , a 2 , a 3
a r e c o n s t a n t s d e t e r m i n e d b y t h e s e m i c o n d u c t o r
l a s e r u s e d . F o r i d e a l
l i n e a r l a s e r , a 2 = a 3 = 0 , t h e o p t i c a l
p o w e r
o u t p u t i s p r o p o r t i o n a l t o t h e m o d u l a t i n g s i g n a l s . F o r
p r a c t i c a l
s e m i c o n d u c t o r l a s e r , a 2 a n d
a 3 a r e
u n e q u a l t o z e r o
w h i c h p r o d u c e
t h e n o i s e . I n - b a n d n o i s e i s
p r o d u c e d b y
x 3 t e r m ,
s o we
s u b s t i t u t e
a 3 x 3
i n
( 2 ) t o g e t h k . I t i s
n o t d i f f i c u l t
t o i n t e g r a t e , a n d o n l y
h 3
t e r m e x i s t s
i n
t h e r e s u l t . I t
c a n b e e x p r e s s e d
h 3
2
= R
( O ) .
A s
a c o n s e q u e n c e , t h e i n - b a n d n o i s e e x p r e s s i o n o f OFDM c a n
b e d e r i v e d
b y
( 5 ) .
I V . C A R R I E R - T O - N o I S E A N A L Y S I S OF OFDM-ROF
SYSTEM
B e s i d e t h e n o n l i n e a r
e f f e c t ,
s e m i c o n d u c t o r l a s e r r e l a t i v e
i n t e n s i t y
n o i s e ,
s h o t n o i s e a n d t h e r m a l c i r c u i t n o i s e a r e h e
f a c t o r s t h a t
r e d u c e t h e s y s t e m p e rf o rm a n c e. A t t h e t r a n s m i t t e r ,
t h e s e m i c o n d u c t o r l a s e r h a s
i n t e n s i t y
f l u c t u a t i o n
t h a t
i s
p r e s e n t e d b y
[ 7 ]
K
3 )
t i m e s
c o n v o l u t i o n o f
S f f ) ,
w h i c h i s t h e F o u r i e r
t r a n s f o r m o f
R X ( l ) .
T h e s p e c t r a l d e n s i t y
S , f )
i s o f r e c t a n g u l a r s h a p e , t h a t i s
S f)
I n t e g r a l
range i s f o r m
f o - B / 2
f o + B / 2
b e c a u s e we o n l y c o n s i d e r
i n - b a n d n o i s e . And
i n - b a n d
n o i s e
can b e e x p r e s s e d a s [ 1 2 ]
h 2
2 h 3
l i n k
b e t w e e n BS a n d C S ,
OFDM s i g n a l i s u s e d t o
m o d u l a t e t h e
o p t i c a l i n t e n s i t y
o f s e m i c o n d u c t o r l a s e r . T h e
n o n l i n e a r c h a r a c t e r i s t i c s o f s e m i c o n d u c t o r l a s e r i n f l u e n c e t h e
s y s t e m p e r f o r m a n c e .
B e c a u s e
t he s i g n a l
b a n d w i d t h
i s s m a l l
c o m p a r e d
w i t h t h e b a n d w i d t h o f s e m i c o n d u c t o r l a s e r
w h e r e RI N i s r e l a t i v e
i n t e n s i t y n o i s e ( R I N ) d e n s i t y f o r t h e
s e m i c o n d u c t o r
l a s e r o u t p u t .
A l s o ,
a t t h e r e c e i v e r ,
t h e r e a r e s h o t
n o i s e a n d t h e r m a l c i r c u i t n o i s e b e i n g p r e s e n t e d , r e s p e c t i v e l y ,
a s
R L
w h e r e i s t h e B o l t z m a n n
c o n s t a n t ,
T
i s t h e a b s o l u t e
t e m p e r a t u r e ,
F
i s t h e n o i s e
f a c t o r , R L
i s l o a d
i m p e d a n c e ,
q
c h a r g e ,
r
i s t h e
s e n s i t i v i t y
o f P I N ,
P ,
i s t h e a v e r a g e
t r a n s m i t t i n g o p t i c a l
p o w e r .
n t )
FDM
s o u r c e d o d e
d e c t e c t o r
F i g . 2 .
a n a l y t i c a l
m o d e l o f
f i b e r - o p t i c
l i n k
T h e C / N
a n a l y t i c a l m o d e l o f f i b e r - o p t i c l i n k i s s h o w n i n F i g . 2 .
T h e r e f o r e , c o n s i d e r i n g
t h e a b o v e n o i s e f o r a g i v e n
b a n d
t h e C / N
f o r t h i s l i n k
B 7 7
P r ) 2
+ P i b a n d
I t i s o b s e r v a b l e
t h a t , i n ( 8 ) ,
C / N i s t h e f u n c t i o n o f o p t i c a l
m o d u l a t i o n i n d e x .
T h e
o p t i c a l m o d u l a t i o n i n d e x must b e
s e l e c t e d t o a v o i d
o v e r m o d u l a t i o n .
I n
F i g . 3 , C / N as a f u n c t i o n o f
o p t i c a l m o d u l a t i o n i n d e x i s s h o w n .
O p t i c a l
d e v i c e p a r a m e t e r s i s
same as
As
s h o w n i n F i g . 3 , a t l o w m o d u l a t i o n i n d e x ,
o p t i c a l d e v i c e n o i s e i s d o m i n a n t
a n d t h e
C / N
i n c r e a s e s w i t h
m o d u l a t i o n i n d e x up t o 0 . 3 . A t h i gh m o d u l a t i o n i n d e x , t h e
n o n l i n e a r e f f e c t b e c o m e s l a r g e r
a n d
C / N i n c r e a s e s s l o w l y w i t h
m o d u l a t i o n i n d e x . W i t h i n t h e
range
0 . 0 1 t o 0 . 3 , t h e
m a x i m a l C / N
i s 3 6 d B
when m = 0 . 3 .
0 1 2 5
O p t i c a l
m o d u l a t i o n i n d e x
F i g . 3 . C/ N versus o p t i c a l
m o d u l a t i o n i n d e x m
( 1 . 3 pm
D F B - L a s e r : R I N = -
- l 5 d B / H z ;
P , = 2 m W .
p - i - n P h o t o d i o d e : i = 0 . 8 . )
V. CONCLUSION
T h e b e h a v i o r o f an OFDM s i g n a l
i n IM-DD r a d i o - o v e r - f i b e r
l i n k
i s
i n v e s t i g a t e d . By u s i n g
t h e t h i r d - o r d e r
w i t h o u t
memory p r e s e n t i n g
s e m i c o n d u c t o r
n o n l i n e a r i t y ,
t h e i n - b a n d
n o i s e o f OFDM d u e t o
n o n l i n e a r i t y
o f s e m i c o n d u c t o r l a s e r i s
a n a l y z e d .
And
f i b e r - o p t i c
l i n k i s
i n v e s t i g a t e d .
W i t h
t h e
n o n l i n e a r i t y
o f
s e m i c o n d u c t o r l a s e r
i t
i s
an
m o d u l a t i o n
i n d e x t o
p r o v i d e
a m a x i m a l
C / N .
T h e
t h e o r e t i c a l
a n a l y t i c a l
m e t h o d
i s
a p p l i c a b l e
t o
On t he o t h er
h a n d ,
p r o d u c e d b y
a m p l i f i e r
a n d
I F i n t h e c i r c u i t w a s n o t c o n s i d e r e d i n t h i s p a p e r , a n d t h e s e
f a c t o r s w i l l
b e t h e s u b j e c t o f f u t u r e w o r k .
ACKNOWLEDGMENT
T h e p r o j e c t w a s
s u p p o r t e d
b y O p e n F u n d o f Key L a b o r a t o r y
o f O p t i c a l C o m m u n i c a t i o n a n d L i g h t w a v e T e c h n o l o g i e s
( B e i j i n g U n i v e r s i t y
o f P o s t s a n d
T e l e c o m m u n i c a t i o n s ,
M i n i s t r y
o f
E d u c a t i o n P . R . C h i n a ) . T h e r e s e a r c h w a s a l s o s u p p o r t e d
b y
N at i on a l S ci e nc e F o u n d a t i o n
( N o . 6 0 6 7 1 0 5 5 ,
w h i c h
i s
f r o m
C o m m i t t e e o f C h i n a .
REFERENCES
[ 1 ] R a s h i d F a r r u k h , M a n i k a s A t h a n a s s i o s . T r a n s m i t d i v e r s i t y f o r m u l t i b a n d
OFDM UWB
I E E
P r o c e e d i n g s
o n
C o m m u n i c a t i o n s , V o l
1 5 3 ,
I s s u e 4 , A u g u s t 2 0 0 6
P a g e ( s ) : 5 7 3
-
5 7 9 .
[ 2 ] P a o l o B a n e l l i , S a v e r i o C a c o p a r d i . T h e o r e t i c a l A n a l y s i s a n d P e r f o rm a n c e
o f OFDM S i g n a l s
i n
N o n l i n e a r AWGN C h a n n e l s .
IEEE
T r a n s a c t i o n s o n
C o m m u n i c a t i o n s ,
V o l u m e
4 8 ,
3 ,
P a g e ( s ) : 4 3 0
-
C .
J - P . V i l c o t .
P o t e n t i a l s o f R a d i o o v e r M u l t i m o d e
F i b e r S y s t e m s f o r t h e I n - B u i l d i n g s C o v e r a g e o f M o b i l e a n d W i r e l e s s L A N
A p p l i c a t i o n s .
IEEE
P h o t o n i c s T e c h n o l o g y L e t t e r s , V o l u m e 1 7 , I s s u e 1 2 ,
-
[ 4 ]
M a r o z s a k T . , K o v a c s A . , U d v a r y E . . D i r e c t m o d u l a t e d l a s e r s
i n r a d i o o v e r
f i b e r
a p p l i c a t i o n s .
I n t e r n a t i o n a l
T o p i c a l M e e t i n g
o n
M i c r o w a v e P h o t o n i c s ,
N o v . 2 0 0 2
P a g e ( s ) : 1 2 9
- 1 3 2 .
Lu
Y i n g h u a , Z h a n g J i n l i n g . E f f e c t s o f
a M i c r o c a v i t y o n
H a r m o n i c a nd I n t e r m o d u l a t i o n D i s t o r t i o n s o f a V e r t i c a l C a v i t y S u r f a c e
E m i t t i n g
L a s e r . C h i n e s e
J o u r n a l
o f S e m i c o n d u c t o r s , 2 0 0 6 , 2 7 ( 9 ) : 1 6 2 5 -
1 6 2 9 .
P e d r o
M i g u e l L a v r a d o r ,
Nuno
B o r g e s
d e C a r v a l h o , J o s e C a r l o s
P e d r o .
E v a l u a t i o n o f
S i g n a l - t o - N o i s e
a n d D i s t o r t i o n R a t i o
D e g r a d a t i o n
i n
S y s t e m s .
IEEE
T r a n s a c t i o n s o n M i c r o m a v e
T h e o r y
a n d
T e c h n i q u e s , V o l u m e 5 2 , I s s u e
3 ,
P a g e ( s ) : 8 1 3
-
W . ,
a n d
N a k a g a w a M . N o n l i n e a r e f f e c t o f d i r e c t
s e q u e n c e
CDMA
i n
o p t i c a l t r a n s m i s s i o n . I E I C E T r a n s a c t i o n s C o m m u n i c a t i o n , V o l
E 7 8 - B ( 5 ) ,
1 9 9 5
7 0 2 .
M .
B .
K l e i n ,
e t a l . N o n l i n e a r e f f e c t s i n
o p t i c a l -
w i r e l e s s OFDM
s i g n a l
t r a n s m i s s i o n .
I n t e r n a t i o n a l
T o p i c a l M e e t i n g
o n
N o v . 2 0 0 2
P a g e ( s ) : 2 2 5
-
H o r v a t h ,
I s t v a n F r i g y e s .
E f f e c t s o f t h e
N o n l i n e a r i t y
o f a M a c h -
Z e h n d e r
M o d u l a t o r o n OFDM R a d i o - o v e r - F i b e r T r a n s m i s s i o n .
IEEE
C o m m u n i c a t i o n s L e t t e r s . V o l u m e
9 ,
1 0 ,
P a g e ( s ) : 9 2 1
-
F i b e r
o p t i c
i n t e r m o d u l a t i o n d i s t o r t i o n .
IEEE
T r a n s a c t i o n s o n
C o m m u n i c a t i o n s . V o l u m e
3 0 ,
8 , A u g
1 9 8 2
1 9 5 4
J o h n K o s h y ,
P . M . S h a n k a r .
S p r ea d - Sp e c t ru m T e c hn i q u es
f o r F i b e r - F e d
M i c r o c e l l u l a r N e t w o r k s . IEEE T r a n s a c t i o n s o n V e h i c u l a r
T e c h n o l o g y ,
V o l u m e
4 8 ,
3 , May
-
Qu n S h i . OFDM i n
B a n d p a s s N o n l i n e a r i t y .
IEEE
T r a n s a c t i o n s o n
C o n s u m e r
E l e c t r o n i c s ,
V o l u m e
4 2 ,
3 , A u g .
1 9 9 6
-
t r a n s m i s s i o n
Z h a n g
Bo, Lu Y i n g h u a ,
Z h a n g J i n l i n g ,
Yang B i a o
B e i j i n g U n i v e r s i t y o f
P o s t s a n d T e l e c o m m u n i c a t i o n s
PO Box 2 1 4 , X i Tu C h e n g R o a d 1 0 , B e i J i n g , CHINA, 1 0 0 8 7 6
T e l :
8 6 - 1 0 - 6 2 2 8 3 3 0 3 , E - m a i l : z h b o m a i l W g m a i l . c o m
A b s t r a c t
-
paper
i s c o n c e r n e d w i t h t he a na ly si s o f t h e
n o n l i n e a r d i s t o r t i o n o f O r t h o g o n a l F r e q u e n c y - D i v i s i o n
M u l t i p l e x
OFDM) s i g n a l s c a u s e d
b y s e m i c o n d u c t o r l a s e r i n a R a d i o - o v e r -
F i b e r l i n k .
A
t h i r d o r d e r p o l y n o m i a l w i t h o u t memory i s u s e d t o
p r e s e n t t h e n o nl i n e ar i t y o f s e m i c o n d u c t o r l a s e r . T h e e x p r es s i o n o f
i n - b a n d n o i s e d u e t o n o n l i n e a r d i s t o r t i o n
i s t h e n d e r i v e d . M o r e o v e r ,
t h e r e l a t i o n o f c a r r i e r - t o - n o i s e r a t i o w i t h o p t i c a l
m o d u l a t i o n i n d e x
i s a n a l y z e d . T h e a n a l y t i c a l m e t h o d i s a p p l i c a b l e f o r n o n l i n e a r i t y
a n a l y s i s
a n d
u s e f u l
t o s e l e c t t h e o p t i c a l
m o d u l a t i o n
i n d e x
o f OFDM-
s y s t e m .
I n d e x T e r m s - r a d i o over f i b e r ; n o n l i n e a r i t y ; OFDM;.
I . I N T R O D U C T I O N
I n t h e
case
o f f u r t h e r w i r e l e s s c o m m u n i c a t i o n
s y s t e m
s i g n i f i c a n t
e f f o r t i s
d o n e t o r e d u c e t h e
m u l t i p a t h f a d i n g
a n d t o
h a v e l o w - c o s t a n d s m a l l b a s e s t a t i o n m a t c h e d t o d e m a n d s m a d e
b y
b i g g e r
n u m b e r o f m o b i l e c e l l s a n d
h i g h
f r e q u e n c y
a p p l i c a t i o n s .
To meet t h e s e
r e q u i r e m e n t s
one o f b e s t s o l u t i o n i s
t h e
c o m b i n a t i o n o f
O r t h o g o n a l
F r e q u e n c y
D i v i s i o n
M u l t i p l e x i n g
OFDM)
m o d u l a t i o n a n d r a d i o over f i b e r
( R O F )
t e c h n o l o g y .
OFDM i s seen as t h e m o d u l a t i o n
t e c h n i q u e
f o r
f u t u r e b r o a d b a n d w i r e l e s s c o m m u n i c a t i o n s b e c a u s e
i t
i n c r e a s e d
r o b u s t n e s s
a g a i n s t f r e q u e n c y
s e l e c t i v e f a d i n g
a n d
n a r r o w b a n d i n t e r f e r e n c e , a n d i s e f f i c i e n t
i n
w i t h m u l t i -
p a t h d e l a y s p r e a d [ l ] I t
p r e s e n t
a s u i t a b l e s o l u t i o n f o r i n d o o r
w i r e l e s s
access,
w i r e l e s s LAN a n d LMDS.
H o w e v e r ,
t h i s
m o d u l a t i o n s c h e m e i s s e n s i t i v e t o t h e
n o n l i n e a r e f f e c t s
i n
r a d i o over
f i b e r
t o
r a d i o h a s a
n u m b e r o f
a d v a n t a g e s i n c l u d i n g t h e a b i l i t y
t o
d e p l o y s m a l l , l o w -
c o s t
r e m o t e a n t e n n a u n i t s a n d
ease o f
u p g r a d e . A c t u a l l y ,
some
o f
h a s b e e n
d e v e l o p e d
t o
w i r e l e s s
s y s t e m ,
s u c h
I T S a n d n e x t
g e n e r a t i o n
c e l l u l a r
s y s t e m [ 3 ] .
T r a n s m i t t i n g
a n a l o g
RF
s i g n a l t h r o u g h
ROF
p r o b l e m
i s s e m i c o n d u c t o r l a s e r n o n l i n e a r i t y [ 4 5 ] .
T h e r e h a v e
b e e n
a n u m b e r o f
p u b l i c a t i o n s
on t h e l a s e r
n o n l i n e a r i t y
a n a l y s i s when use s t a n d a r d m o d u l a t i o n
s c h e m e
i n c l u d i n g
m u l t i l e v e l
QAM,
CDMA
e t c [ 6 , 7 ] . T h e
n o n l i n e a r i t y
k n o w l e d g e
o f OFDM
i s u s e f u l f o r s y s t e m d e s i g n
a n d
p e r f o r m a n c e a n a l y s i s .
Some w o r k s h a v e d o n e t o
s t u d y
OFDM
t r a n s m i s s i o n p e r f o r m a n c e t h r o u g h
t h e
n o n l i n e a r i t y
o f f i b e r - r a d i o
l i n k , h o w e v e r t h e s e r e s e a r c h e s m a i n l y f o c u s on d i s c u s s i n g t h e
n o n l i n e a r i t y o f e x t e r n a l m o d u l a t o r
s u c h as M a c h - Z e h n d e r
m o d u l a t o r 8 9 ] . W i t h s e m i c o n d u c t o r l a s e r n o n l i n e a r i t y i t i s
necessary t o
s e l e c t an o p t i m a l m o d u l a t i o n i n d e x t h a t p r o v i d e s a
maximum c a r r i e r - t o - n o i s e r a t i o ( C / N ) . A t h i r d o r d e r p o l y n o m i a l
w i t h o u t memory
i s u s e d t o p r e s e n t l a s e r n o n l i n e a r i t y [ 1 0 ] a n d
n o n l i n e a r i t y
on
CDMA i s a n a l y z e d
i n
[ 7 , 1 1 ] u s i n g t h i s
m e t h o d .
I n t h i s paper, we d e a l w i t h ROF l i n k a p p l y i n g d i r e c t i n t e n s i t y
m o d u l a t i o n a n d d i r e c t d e t e c t i o n ( I M - D D ) .
A n
a n a l y t i c a l m e t h o d
i s p r o p o s e d t o e v a l u a t e t h e e f f e c t s o f
s e m i c o n d u c t o r
l a s e r
n o n l i n e a r i t y on OFDM s i g n a l .
And
t h e r e l a t i o n o f C / N r a t i o a n d
o p t i c a l m o d u l a t i o n
m
s t u d i e d .
RE
in
RE in
l a y o u t
o f a RO F o p t i c a l
l i n k
using d i r e c t m o d u l a t i o n l a s e r d i o d e s .
I I . RADIO OVER
IM-DD l i n k s
are u s e d i n c e l l u l a r a p p l i c a t i o n s f o r reasons o f
s i m p l i c i t y
a n d c o s t .
F i g . 1
l a y o u t
o f a
s i m p l e
b i d i r e c t i o n a l
d i r e c t l y
m o d u l a t e d r a d i o over f i b e r
l i n k . I n
e a c h
d i r e c t i o n t h e
i m p u t
RF
i s
a p p l i e d
t o a l a s e r d i o d e
w h e r e
i t
m o d u l a t e s t h e i n t e n s i t y o f t h e
o u t p u t l i g h t .
I n
most cases t h i s
l i g h t was
s e m i c o n d u c t o r l a s e r w h i c h i s o p e r a t e d a t 1300nm
or
1 5 5 0 nm
f o r l o w t r a n s m i s s i o n l o s s i n
s i l i c a f i b e r . T h e
o p t i c a l
r e c e i v e r
u s u a l l y
c o n s i s t s o f a p - i - n p h o t o d i o d e ,
w h i c h
p r o v i d e s
an
RF
power
o u t p u t p r o p o r t i o n a l
t o
o p t i c a l
power.
P h o t o d i o d e
f i b e r
<
I I I . R E P R E S E N T A T I O N OF IN-BAND D I S T O R T I O N N O I S E
T h e OFDM s i g n a l c a n
b e m o d e l e d
( f o r a h i g h n u m b e r o f
i n d e p e n d e n t l y m o d u l a t e d c a r r i e r s ) l i k e a c o m p l e x G a u s s i a n
p r o c e s s w i t h R a y l e i g h e n v e lo p e d i s t r i b u t i o n [ 2 ] .
T h i s
t h e
a n a l y t i c a l t r e a t m e n t
o f
n o n l i n e a r OFDM s y s t e m s
m a k i n g
u s e o f
t h e m o r e g e n e r a l r e s u l t s f o r n o n l i n e a r d i s t o r t i o n s
o f
G a u s s i a n
s i g n a l s . T h e r e f o r e ,
R i c e s t r a n s f o r m
m e t h o d 1 2 ]
w a s a p p l i e d t o
d e r i v e t h e p o w e r s p e c t r a o f t h e o u t p u t
a n d t h e i n d u c e d d i s t o r t i o n
n o i s e
f a l l i n g i n t o t h e s i g n a l b n d S p e c i f i c a l l y , t h e
o u t p u t
a u t o c o r r e l a t i o n
f u n c t i o n c a n b e e x p r e s s e d a s
FR
r1
R X ( I )
i s t h e
a u t o c o r r e l a t i o n
f u n c t i o n o f t h e i n p u t OFDM
s i g n a l , a n d t h e
c o e f f i c i e n t s
* k
2 g ( x ) e x d x d u ( 2 )
2 / 7 Z ( X
T h e
f i r s t t e r m i n ( 1 )
i s t h e
DC t e r m , t h e n = 1 t e r m i s t h e s i g n a l
t e r m , a n d
n > 1 t e r m s r e p r e s e n t t h e i n d u c e d
d i s t o r t i o n n o i s e .
T h e s e e x p r e s s i o n s a r e i n a g r e e m e n t
w i t h [ 1 2 ] . T h e n t h e
t o t a l
d i s t o r t i o n n o i s e s p e c t r a l d e n s i t y i s g i v e n b y
m o d u l a t i o n b a n d w i d t h , a n o n l i n e a r s e m i c o n d u c t o r
l a s e r
w i t h o u t
memory c a n b e p r e s e n t e d b y a t h i r d o r d e r p o l y n o m i a l a s [ 7
1 0 ]
+ a 3 x ( 6 )
w h e r e y i s h e o p t i c a l p o w e r
o u t p u t
m o d u l a t e d b y c u r r e n t s i g n a l
x
a n d a 1 , a 2 , a 3
a r e c o n s t a n t s d e t e r m i n e d b y t h e s e m i c o n d u c t o r
l a s e r u s e d . F o r i d e a l
l i n e a r l a s e r , a 2 = a 3 = 0 , t h e o p t i c a l
p o w e r
o u t p u t i s p r o p o r t i o n a l t o t h e m o d u l a t i n g s i g n a l s . F o r
p r a c t i c a l
s e m i c o n d u c t o r l a s e r , a 2 a n d
a 3 a r e
u n e q u a l t o z e r o
w h i c h p r o d u c e
t h e n o i s e . I n - b a n d n o i s e i s
p r o d u c e d b y
x 3 t e r m ,
s o we
s u b s t i t u t e
a 3 x 3
i n
( 2 ) t o g e t h k . I t i s
n o t d i f f i c u l t
t o i n t e g r a t e , a n d o n l y
h 3
t e r m e x i s t s
i n
t h e r e s u l t . I t
c a n b e e x p r e s s e d
h 3
2
= R
( O ) .
A s
a c o n s e q u e n c e , t h e i n - b a n d n o i s e e x p r e s s i o n o f OFDM c a n
b e d e r i v e d
b y
( 5 ) .
I V . C A R R I E R - T O - N o I S E A N A L Y S I S OF OFDM-ROF
SYSTEM
B e s i d e t h e n o n l i n e a r
e f f e c t ,
s e m i c o n d u c t o r l a s e r r e l a t i v e
i n t e n s i t y
n o i s e ,
s h o t n o i s e a n d t h e r m a l c i r c u i t n o i s e a r e h e
f a c t o r s t h a t
r e d u c e t h e s y s t e m p e rf o rm a n c e. A t t h e t r a n s m i t t e r ,
t h e s e m i c o n d u c t o r l a s e r h a s
i n t e n s i t y
f l u c t u a t i o n
t h a t
i s
p r e s e n t e d b y
[ 7 ]
K
3 )
t i m e s
c o n v o l u t i o n o f
S f f ) ,
w h i c h i s t h e F o u r i e r
t r a n s f o r m o f
R X ( l ) .
T h e s p e c t r a l d e n s i t y
S , f )
i s o f r e c t a n g u l a r s h a p e , t h a t i s
S f)
I n t e g r a l
range i s f o r m
f o - B / 2
f o + B / 2
b e c a u s e we o n l y c o n s i d e r
i n - b a n d n o i s e . And
i n - b a n d
n o i s e
can b e e x p r e s s e d a s [ 1 2 ]
h 2
2 h 3
l i n k
b e t w e e n BS a n d C S ,
OFDM s i g n a l i s u s e d t o
m o d u l a t e t h e
o p t i c a l i n t e n s i t y
o f s e m i c o n d u c t o r l a s e r . T h e
n o n l i n e a r c h a r a c t e r i s t i c s o f s e m i c o n d u c t o r l a s e r i n f l u e n c e t h e
s y s t e m p e r f o r m a n c e .
B e c a u s e
t he s i g n a l
b a n d w i d t h
i s s m a l l
c o m p a r e d
w i t h t h e b a n d w i d t h o f s e m i c o n d u c t o r l a s e r
w h e r e RI N i s r e l a t i v e
i n t e n s i t y n o i s e ( R I N ) d e n s i t y f o r t h e
s e m i c o n d u c t o r
l a s e r o u t p u t .
A l s o ,
a t t h e r e c e i v e r ,
t h e r e a r e s h o t
n o i s e a n d t h e r m a l c i r c u i t n o i s e b e i n g p r e s e n t e d , r e s p e c t i v e l y ,
a s
R L
w h e r e i s t h e B o l t z m a n n
c o n s t a n t ,
T
i s t h e a b s o l u t e
t e m p e r a t u r e ,
F
i s t h e n o i s e
f a c t o r , R L
i s l o a d
i m p e d a n c e ,
q
c h a r g e ,
r
i s t h e
s e n s i t i v i t y
o f P I N ,
P ,
i s t h e a v e r a g e
t r a n s m i t t i n g o p t i c a l
p o w e r .
n t )
FDM
s o u r c e d o d e
d e c t e c t o r
F i g . 2 .
a n a l y t i c a l
m o d e l o f
f i b e r - o p t i c
l i n k
T h e C / N
a n a l y t i c a l m o d e l o f f i b e r - o p t i c l i n k i s s h o w n i n F i g . 2 .
T h e r e f o r e , c o n s i d e r i n g
t h e a b o v e n o i s e f o r a g i v e n
b a n d
t h e C / N
f o r t h i s l i n k
B 7 7
P r ) 2
+ P i b a n d
I t i s o b s e r v a b l e
t h a t , i n ( 8 ) ,
C / N i s t h e f u n c t i o n o f o p t i c a l
m o d u l a t i o n i n d e x .
T h e
o p t i c a l m o d u l a t i o n i n d e x must b e
s e l e c t e d t o a v o i d
o v e r m o d u l a t i o n .
I n
F i g . 3 , C / N as a f u n c t i o n o f
o p t i c a l m o d u l a t i o n i n d e x i s s h o w n .
O p t i c a l
d e v i c e p a r a m e t e r s i s
same as
As
s h o w n i n F i g . 3 , a t l o w m o d u l a t i o n i n d e x ,
o p t i c a l d e v i c e n o i s e i s d o m i n a n t
a n d t h e
C / N
i n c r e a s e s w i t h
m o d u l a t i o n i n d e x up t o 0 . 3 . A t h i gh m o d u l a t i o n i n d e x , t h e
n o n l i n e a r e f f e c t b e c o m e s l a r g e r
a n d
C / N i n c r e a s e s s l o w l y w i t h
m o d u l a t i o n i n d e x . W i t h i n t h e
range
0 . 0 1 t o 0 . 3 , t h e
m a x i m a l C / N
i s 3 6 d B
when m = 0 . 3 .
0 1 2 5
O p t i c a l
m o d u l a t i o n i n d e x
F i g . 3 . C/ N versus o p t i c a l
m o d u l a t i o n i n d e x m
( 1 . 3 pm
D F B - L a s e r : R I N = -
- l 5 d B / H z ;
P , = 2 m W .
p - i - n P h o t o d i o d e : i = 0 . 8 . )
V. CONCLUSION
T h e b e h a v i o r o f an OFDM s i g n a l
i n IM-DD r a d i o - o v e r - f i b e r
l i n k
i s
i n v e s t i g a t e d . By u s i n g
t h e t h i r d - o r d e r
w i t h o u t
memory p r e s e n t i n g
s e m i c o n d u c t o r
n o n l i n e a r i t y ,
t h e i n - b a n d
n o i s e o f OFDM d u e t o
n o n l i n e a r i t y
o f s e m i c o n d u c t o r l a s e r i s
a n a l y z e d .
And
f i b e r - o p t i c
l i n k i s
i n v e s t i g a t e d .
W i t h
t h e
n o n l i n e a r i t y
o f
s e m i c o n d u c t o r l a s e r
i t
i s
an
m o d u l a t i o n
i n d e x t o
p r o v i d e
a m a x i m a l
C / N .
T h e
t h e o r e t i c a l
a n a l y t i c a l
m e t h o d
i s
a p p l i c a b l e
t o
On t he o t h er
h a n d ,
p r o d u c e d b y
a m p l i f i e r
a n d
I F i n t h e c i r c u i t w a s n o t c o n s i d e r e d i n t h i s p a p e r , a n d t h e s e
f a c t o r s w i l l
b e t h e s u b j e c t o f f u t u r e w o r k .
ACKNOWLEDGMENT
T h e p r o j e c t w a s
s u p p o r t e d
b y O p e n F u n d o f Key L a b o r a t o r y
o f O p t i c a l C o m m u n i c a t i o n a n d L i g h t w a v e T e c h n o l o g i e s
( B e i j i n g U n i v e r s i t y
o f P o s t s a n d
T e l e c o m m u n i c a t i o n s ,
M i n i s t r y
o f
E d u c a t i o n P . R . C h i n a ) . T h e r e s e a r c h w a s a l s o s u p p o r t e d
b y
N at i on a l S ci e nc e F o u n d a t i o n
( N o . 6 0 6 7 1 0 5 5 ,
w h i c h
i s
f r o m
C o m m i t t e e o f C h i n a .
REFERENCES
[ 1 ] R a s h i d F a r r u k h , M a n i k a s A t h a n a s s i o s . T r a n s m i t d i v e r s i t y f o r m u l t i b a n d
OFDM UWB
I E E
P r o c e e d i n g s
o n
C o m m u n i c a t i o n s , V o l
1 5 3 ,
I s s u e 4 , A u g u s t 2 0 0 6
P a g e ( s ) : 5 7 3
-
5 7 9 .
[ 2 ] P a o l o B a n e l l i , S a v e r i o C a c o p a r d i . T h e o r e t i c a l A n a l y s i s a n d P e r f o rm a n c e
o f OFDM S i g n a l s
i n
N o n l i n e a r AWGN C h a n n e l s .
IEEE
T r a n s a c t i o n s o n
C o m m u n i c a t i o n s ,
V o l u m e
4 8 ,
3 ,
P a g e ( s ) : 4 3 0
-
C .
J - P . V i l c o t .
P o t e n t i a l s o f R a d i o o v e r M u l t i m o d e
F i b e r S y s t e m s f o r t h e I n - B u i l d i n g s C o v e r a g e o f M o b i l e a n d W i r e l e s s L A N
A p p l i c a t i o n s .
IEEE
P h o t o n i c s T e c h n o l o g y L e t t e r s , V o l u m e 1 7 , I s s u e 1 2 ,
-
[ 4 ]
M a r o z s a k T . , K o v a c s A . , U d v a r y E . . D i r e c t m o d u l a t e d l a s e r s
i n r a d i o o v e r
f i b e r
a p p l i c a t i o n s .
I n t e r n a t i o n a l
T o p i c a l M e e t i n g
o n
M i c r o w a v e P h o t o n i c s ,
N o v . 2 0 0 2
P a g e ( s ) : 1 2 9
- 1 3 2 .
Lu
Y i n g h u a , Z h a n g J i n l i n g . E f f e c t s o f
a M i c r o c a v i t y o n
H a r m o n i c a nd I n t e r m o d u l a t i o n D i s t o r t i o n s o f a V e r t i c a l C a v i t y S u r f a c e
E m i t t i n g
L a s e r . C h i n e s e
J o u r n a l
o f S e m i c o n d u c t o r s , 2 0 0 6 , 2 7 ( 9 ) : 1 6 2 5 -
1 6 2 9 .
P e d r o
M i g u e l L a v r a d o r ,
Nuno
B o r g e s
d e C a r v a l h o , J o s e C a r l o s
P e d r o .
E v a l u a t i o n o f
S i g n a l - t o - N o i s e
a n d D i s t o r t i o n R a t i o
D e g r a d a t i o n
i n
S y s t e m s .
IEEE
T r a n s a c t i o n s o n M i c r o m a v e
T h e o r y
a n d
T e c h n i q u e s , V o l u m e 5 2 , I s s u e
3 ,
P a g e ( s ) : 8 1 3
-
W . ,
a n d
N a k a g a w a M . N o n l i n e a r e f f e c t o f d i r e c t
s e q u e n c e
CDMA
i n
o p t i c a l t r a n s m i s s i o n . I E I C E T r a n s a c t i o n s C o m m u n i c a t i o n , V o l
E 7 8 - B ( 5 ) ,
1 9 9 5
7 0 2 .
M .
B .
K l e i n ,
e t a l . N o n l i n e a r e f f e c t s i n
o p t i c a l -
w i r e l e s s OFDM
s i g n a l
t r a n s m i s s i o n .
I n t e r n a t i o n a l
T o p i c a l M e e t i n g
o n
N o v . 2 0 0 2
P a g e ( s ) : 2 2 5
-
H o r v a t h ,
I s t v a n F r i g y e s .
E f f e c t s o f t h e
N o n l i n e a r i t y
o f a M a c h -
Z e h n d e r
M o d u l a t o r o n OFDM R a d i o - o v e r - F i b e r T r a n s m i s s i o n .
IEEE
C o m m u n i c a t i o n s L e t t e r s . V o l u m e
9 ,
1 0 ,
P a g e ( s ) : 9 2 1
-
F i b e r
o p t i c
i n t e r m o d u l a t i o n d i s t o r t i o n .
IEEE
T r a n s a c t i o n s o n
C o m m u n i c a t i o n s . V o l u m e
3 0 ,
8 , A u g
1 9 8 2
1 9 5 4
J o h n K o s h y ,
P . M . S h a n k a r .
S p r ea d - Sp e c t ru m T e c hn i q u es
f o r F i b e r - F e d
M i c r o c e l l u l a r N e t w o r k s . IEEE T r a n s a c t i o n s o n V e h i c u l a r
T e c h n o l o g y ,
V o l u m e
4 8 ,
3 , May
-
Qu n S h i . OFDM i n
B a n d p a s s N o n l i n e a r i t y .
IEEE
T r a n s a c t i o n s o n
C o n s u m e r
E l e c t r o n i c s ,
V o l u m e
4 2 ,
3 , A u g .
1 9 9 6
-
