Optics and Photonics Journal, 2011, 1, 179-188
doi:10.4236/opj.2011.14029 Published Online December 2011 (http://www.SciRP.org/journal/opj)
Analysis of the Impact of P-Ratio on BER, Q-Factor and
OSNR of Radio over Fiber (RoF) System
Vishal Sharma1, Amarpal Singh2, Ajay K. Sharma3
1Shaheed Bhagat Singh College of Engineering and Technology, Ferozepur, India
2Beant College of Engineering and Technology, Gurdaspur, India
3Dr. B.R. Ambedkar NIT, Jalandhar, India
Received September 15, 2011; revised October 15, 2011; accepted November 6, 2011
Abstract
The impact of p-ratio i.e. ratio of carrier power to total received RF power at control office (CO) on Bit error
rate (BER), Q- performance parameter and Optical signal noise ratio (OSNR) of RoF communication system
is theoretically analyzed using angular full-linewidth at half maximum (FWHM) of Lorentzian shape for the
RF oscillator in this paper. As reduction in Laser linewidth improves the performance of RoF system, the RF
oscillator linewidth at FWHM also plays an important role in improving the performance of RoF system.
Keywords: RoF System, OSNR Parameter, BER, Q-Parameter, Fiber Dispersion, Matlab 7.0
1. Introduction
For realization of future high performance integrated
networks, broadband distribution & access networks and
to meet the increasing demand of multimedia services
with a guaranteed quality of service, RoF technology
comes out as the most promising technology. RoF tech-
nology combines the capacity of optical networks with
the flexibility and mobility of wireless networks. Reduc-
tion in complexity at the antenna site, reduction in in-
stallation cost of access networks, possibility of dy-
namically allocation of radio carriers to different an-
tenna sites, transparency and scalability are the few ad-
vantages of RoF technology. These systems have several
advantages including lower attenuation compared to the
coaxial cable, higher bandwidth, immunity to the RF
interference and durability [1-4]. Modulation technique
is one of the most significant processes in RoF system
where the RF electrical signal is applied to modulate the
optical carrier. RoF modulation methods can be catego-
rized into two main groups: direct modulation and exter-
nal modulation. Direct modulation, a simple technique,
directly modulates the amplitude of the laser beam but
suffers from a laser-frequency chirp effect that degrades
severely the performance of the system. However, this
can be eliminated by using the external-modulation
scheme [5] used to modulate the phase of the optical
carrier. Furthermore, the conventional optical double
sideband (ODSB) external modulation scheme degrades
the received RF signal power due to fiber chromatic dis-
persion drastically. For frequency range beyond 5 GHz
external modulation is needed for higher speeds. No
doubt such systems are capable of meeting the future
requirements of High speed high data transfer services
but some degradations effects the performance of such
systems such as fiber dispersion and modulator’s non-
nearity. For overcoming this power degradation, an opti-
cal single sideband (OSSB) external modulation scheme
is employed [5]. The effect of phase noises from a laser
and an oscillator on OSSB-RoF system is analyzed and
discussed [6]. Barry and Lee [7] and Salz [8] also ana-
lyzed the performance of coherent optical systems with
laser phase noise by utilizing a wiener process as coher-
ent detection provides better sensitivity than that of di-
rect detection. A number of techniques have been in-
vented to analyze and improve the performance of RoF
system by mitigating these problems. Minimization of
fiber dispersion using OSSB technique, reduction of
laser linewidth [9] and using external modulators are
the few important techniques. In this paper, we have
analyzed theoretically the impact of p-ratio over per-
formance parameters of RoF communication system us-
ing angular full-linewidth at half maximum (FWHM) of
Lorentzian shape of the RF oscillator at different optical

V. SHARMA ET AL.
180
span and responsivity. In section II we present the theo-
retical analysis of OSNR for a radio over fiber (RoF)
communication system. Section III presents results and
discussion for system. Finally, section IV concludes the
paper findings.
2. Theoretical Analysis of OSNR in Rof
System
In a simple and compact architecture of RoF system as
shown in Figure 1, the data is up-converted by a RF os-
cillator and optically modulated by a laser diode (LD) by
means of a Mach Zehnder (MZM) external modulator in
a control office (CO). The output signal of the MZM is
transmitted via a standard single-mode fiber (SSMF) and
detected by a PD to generate the photocurrent at a base
station (BS). This photocurrent goes through a band-pass
filter (BPF) and an amplifier to be launched into a wire-
less channel in the BS. The wireless channel makes sig-
nals vulnerable to amplitude and phase distortion. A user
terminal (UT) amplifies and filters the received signal to
detect the transmitted RF signal. Finally, the data are
extracted through RF demodulation.
In this paper, an optical single sideband (OSSB) signal
is generated by using a DEMZM external modulator to-
gether with a phase shifter to overcome the power deg
radation due to fiber dispersion. This RF signal is opti-
cally modulated by the LD with a Dual electrode MZM
external modulator. The optically modulated signal is
transmitted to the PD and the photocurrent corresponding
Figure1. Overall downlink architecture [6] of a RoF system.
to the transmitted RF signal is extracted by the BPF. First,
the optical signals from the laser and the RF oscillator
are modeled as follows:


() .exp()
() .cos()
LDLD LD
RFRFRF RF
x
tA jt
x
tVj tt




(1)
where A and VRF define amplitudes from the LD and the
RF oscillator, ωLD and ωRF define angular frequencies
of the signals from the LD and the RF oscillator, and
φLD(t) and φRF(t) are phase-noise processes. φLD(t) is
characterized by a Wiener process [7].
0
()'( )dLD LD
t
t

  (2)
The time derivative φ’
LD(t) is not flat at low frequen-
cies due to 1/f noise. The white phase noise, however, is
the principal cause for line broadening and is associated
with quantum fluctuations [8]. Thus, φ'
LD(t) can be mod-
eled as a zero-mean white Gaussian process with a power
spectral density (PSD) function as
'() 2π
L
DS  LDv

 (3)
where, ΔvLD defines a laser line-width. Unlike the
phase-noise process from the laser, the phase-noise
process φRF(t) from the RF oscillator is difficult since
the spectrum consists of various noises like flicker
frequency, a white frequency noise, and a white phase
noise. After optically modulating xRF(t) by xLD(t) with a
DE-MZM, the output signal of the DE-MZM is repre-
sented [6] as (see Equation (4))
where ()
RF
x
t
 denotes the phase-shift version of()
RF
x
t,
πdc
VV


and π 2
RF
V  Vdefine a normalized dc
and ac value, V

is the switching voltage of the
DEMZM, LMZM is the insertion loss of the DEMZM, and
θ is the phase shift by the phase shifter. Note that the
input RF signals into the DEMZM are () 2
RF
xt and
()2
RF
xt
 rather than ()
RF
x
t and ()
RF
x
t
because the
RF signal is 3dB attenuated by utilizing the power split ter.
By controlling the phase shifter, the output signal can be the
OSSB or the optical dual sideband (ODSB) signal. Among
the two signals, only the OSSB signal will be dealt with in
this paper since the ODSB signal suffers from fiber chro-
matic dispersion severely and requires double bandwidth




.
ππ
()() () ππ
(0,)expπ.exp.
22
.exp π() πcos( )
2
exp( )πcos( )
LD
MZMRF RF
MZM
LDLDRF RF
LD LDRFRF
Lxtxt xt
Et jj
VV
AL jttt t
jt tt t

 
 


2

 



 

 



 



(4)

181 V. SHARMA ET AL.
than that of the OSSB signals. For generating the OSSB
signal, θ and γ are set to π/2 and 1/2, respectively. By
using Equation (4) and the mentioned conditions, the
OSSB signal at the DE MZM can be modeled as follows:


 
π
(0,)exp( )exp(πcos( ))
2
2
π
exp( )exp(πcos( ))
2
(0,)exp( )cosπcos( )sinπcos (
2
2
MZM
LD LDRF RF
LD LDRFRF
MZM
LDLDRF RFRF RF
AL
Etj ttjtt
jt tjt t
AL
Etj ttttjtt
 
 

 







 








 

)
ππ
exp( )cosπcos( )sinπcos( )
22
LD LDRFRFRFRF
jt tt tjtt   








 

 


 



(5)
  





 
02
1
21
0
02
1
2
cos πcos( )(π)2(π)cos2( )
sin πcos(( )2(1)(π)cos(21)[( )]
cos πsin( )(π)2 (π)cos2( )
sin πsin( )2
RF RFnRF RF
n
n
RF RFnRF RF
n
RF RFnRF RF
n
RF RFn
ttJJ ntt
ttJn tt
ttJJ ntt
tt J
 
 
 









 

 




1
0
(π)cos(21)[( )]
RF RF
n
ntt 




Now by using the Jacobi’s expansion for cos- and sin-terms and after simplification, Equation (5) can be written as

01
π
(0, )..(π).exp( )2(π) exp()()
4
SMZMLD LDLDRFLDRF
EtALJjt tJjtt tt 
 


 


 

(6)
By neglecting the high-order components of the Bessel
function since the value of π

in the Bessel function is
very small due to the fact that π
R
F in general. The
output signal at the DEMZM is transmitted via the SSMF
experiencing different group delays, due to the fiber
chromatic dispersion, at a different wavelength. After the
transmission of
VV
F
iber
L km, the signal at the end of the
SSMF becomes

.
20
0
1
01 2
0
(,)10 (π)
2(π) π
exp()exp()()
4(π)
fiber Fiber
L
SMZM add
LD LDLDRFLDRF
ELt ALLJ
J
jt tjtt tt
J



   



 
 
  
 
 


 
 
(7)
where Ladd denotes an additional loss in the optical link,
f
iber

is the SSMF loss,
F
iber
L is the transmission dis-
tance of the SSMF, 0

and


define group delays for a
center angular frequency of
L
D

and an upper sideband
frequency of
L
DRF

 , 1

and 2

are phase-shift
parameters for specific frequencies due to the fiber
chromatic dispersion. For performance evaluation of RoF
system, we determine and analyze OSNR performance
parameter by employing the ratio between the signal
power and the noise power by using an autocorrelation
and a PSD- function. By using a square-law model, the
photocurrent i (t) can be obtained from (7) as follows:
 
22
110 2
()(,)2cos(()()())
SRFLDLDRF
itE LtABttt1










  (8)
where
.
1
20
101
0
2
1
2(π)
10( π), ,
(π)
1
Fiber Fiber
L
MZM add
J
AAL LJJ
B

 


 

where,

defines the responsivity of the PD and 2 .is
the square-law detection. From Equation (8), the auto-
correlation function ()
I
R

is obtained as
() ().()
I
Ritit

 
(9)

V. SHARMA ET AL.
182
1
2 2
1
2
24 22
2
11
1
2cos( ),
()
2cos( ),
e
LD RF
RF
I
RF
e
RB
Ae

 


1








 


(10)
where,
L
D
v and
R
F
v are the laser- and RF oscilla-
tor- line-width respectively and 2(2π)
L
D
vLD

 and
2(2π)
R
F
vRF

 define the angular full line-width at
half maximum (FWHM) of the Lorentzian shape for the
laser and the RF oscillator, respectively. The2t

, termed
as total line-width, is not given as 2π2π
L
DR
vv
as 2ππ
L
D
vv
RF

 . The term 1

is the differential delay
due to the fiber chromatic dispersion and is dependent on
the optical wavelength

, carrier frequency
R
F
f
, fiber
dispersion parameter, D and optical length,
F
ibe
Lr and
mathematically, given [10] as
2
1
R
F
Fiber
f
DL c    (11)
where, c is the light velocity. The PSD function of the
photocurrent is given by the Fourier transform of (8).
The PSD function SI (f) can be written as
F
but

 


11
1
24
1
2 22
2
11 21
22
22
2
12
2
()
() ()
2cos2π() 4
()
2π() (2)2π()
4π.()( )
cos2π() sin2π(
2π()
et
t
I
II
RF RF
RF RFtRF
LD LDRFRF
tt RF
RF RF
Sf
Sf FRA
effe
Bf
ff ff
ff
eff ff
ff
 


 


 



 
 
 

 


1
)()
R
FR
Gf f 
 
 
 
 
 F
(12)
The first term of Equation (12) represents a dc compo-
nent, the second and third is the broadening effects due
to the fiber chromatic dispersion and the line-widths of
the laser and the RF oscillator. By using Equation (12),
the received RF carrier power
I
P is approximately rep-
resented as follows [6]
 
1 1
1
2
2
2 2 2 2
22 2
24 2111
122
22
22 2
2
2()d
2..cos(2π() 4.
2()d d
2π() (2)2π()
.c
RF
RF
RF
RF
RF RFRF
RF RFRF
t t
RF RFRF
RF RFRF
t
B
f
II
B
f
BB B
ff f
RF RF
I
BB B
RF RFtRF
ff f
tt
PSff
effe
PABff f
ff ff
e
 






 
 
 



 
 








11
1 1
2
2
242
22 11 11
1
4π.()( )
os 2π() sin2π()
2π()
4π.π.
(1)tantan
2
forπ1,
tt
LD LDRFRF
RF RF
RF RF
RF RF
tRF
RF
ff
ff ff
ff
ABB
ee
B
 






 

 
 

 

 
 

  
 
  





1
1
242
21
11
21
4tan
π
t
ttRF
RF
RF
and
AB
e










(13)
In Equation (13), the last condition, 1 2
t1

  and
tRF

, is reasonable because the laser line- width is
much greater than the RF-oscillator line- width and the
fiber length is usually less than a few tens of kilometers
in RoF systems. Note that the coefficient 2 of Equation
(13) is due to the real and imaginary spectrum. The cos
and sin terms in Equation (12) are approximately equal
to 1 and 0 in the integrand when 1RF πB1

 is satis-
fied.The received RF signal power is a function of dif-
ferential delay1

, laser- and RF oscillatorline-width and
bandwidth of electrical filter
R
F
For evaluating the total RF power excluding dc
power, we utilize Equation (10) as follows:
B.
24224
1
(0) 2
tI
PRABA2
11

 (14)
By using (14), we define the ratio p between the total
carrier power and the required power as follows [6]:
1
1
1
242
21
11
242
1
21
1
4π.
tan
π
2
π. 2tan
π
for 21
t
t
I
t
RF
RF
RF
RF
ttRF
P
pP
AB
e
A
B
e
and






 













(15)

183 V. SHARMA ET AL.
From (14), the required bandwidth for the p- ratio is ob-
tained as
1
2
π
tan( )
π2
t
RF
RF
B


 ep
1
(16)
The required bandwidth increases as we need more
received signal power. Note that the required band-
width for a specific received carrier power is domi-
nantly dependent on the phase noise from the RF os-
cillator rather than that from the laser for 1 2
t

 
and tRF

 . By using Equations (14) and (16),
OSNR is calculated as
1
242
1
0
4
.
2
20
2
2
0
OSNR
Signal 2
Noise Noise2.
2
(π)
1.10
2()
π.
20 tan()
2
fiberFiber
t
power t
powerpower RF
L
rf
MZM add
PAB
N
B
VAL L
V
pe
N







 









(17)
The value of Bit error rate (BER) by using the direct
relation among BER, Q-parameter and OSNR [10] can
be predicted as
2
2
2
2
BERError probability of Q
11
d1
2
π2
1
.
2π
x
Q
Q
Q
ex erf
e
Q






 




(18)
where,
22OSNR
Q114OSNR


3. Results and Discussion
The impact of p ratio using angular full-linewidth at half
maximum (FWHM) of Lorentzian shape for the RF os-
cillator can be easily observed graphically of the RoF
system at different optical span by varying responsivity
of photo detector. The OSNR decreases as we increases
the optical span but reduces as we decreases the p ratio
from p = 0.6 to p = 0.5 as shown in Figures 2-3. Also it
is observed that OSNR increases with increasing the re-
sponsivity (R-parameter) of the photodetector along with
by using the angular full-linewidth at half maximum
(FWHM) of Lorentzian shape the RF oscillator. The
OSNR increases about 3dBm by using the RF oscillator
linewidth at FWHM as shown in Figures 2(a) and 3(a).
The performance parameter Q also increases by de-
creasing the p-ratio of the RoF system and by increasing
the R- parameter. The Q-parameter is also improving by
using the RF oscillator linewidth at FWHM as shown in
Figures 4-5. The BER of RoF system is also improving
in the same manner depending upon the parameter such
as R-parameter, p-ratio and gamma RF as shown in Fig-
ures 6-9. The results obtained and shown graphically if
Figures 2-9 reveals that the performance of the RoF
system improves if the RF oscillator is defined at angular
full-linewidth at half maximum (FWHM) with increasing
the R-parameter.
(a) (b)

V. SHARMA ET AL.
184
(c) (d)
Figure 2. OSNR vs optical length for (a,b) R = 1 and (c,d) R = 0.5 with . π
RF
 
(a) (b)
(c) (d)
Figure 3. OSNR vs optical length for (a,b) R = 1 and (c,d) R = 0.5 with π2
RF
 .

185 V. SHARMA ET AL.
(a) (b)
(c) (d)
Figure 4. Q-parameter vs optical length for (a,b) R = 1 and (c,d) R = 0.5 with . π
RF
 
(a) (b)

V. SHARMA ET AL.
186
(c) (d)
Figure 5. Q-parameter vs optical length for (a,b) R = 1 and (c,d) R = 0.5 with π2
RF
 .
(a) (b)
(c) (d)
Figure 6. BER vs optical length for (a,b) R = 1 and (c,d) R = 0.5 with . π
RF
 

187 V. SHARMA ET AL.
(a) (b)
(c) (d)
Figure 7. BER vs optical length for (a,b) R = 1 and (c,d) R = 0.5 with π2
RF
 .
(a) (b)
Figure 8. BER vs OSNR for (a) R = 1 and (b) R = 0.5 withπ
RF


.

V. SHARMA ET AL.
188
(a) (b)
Figure 9. BER vs OSNR for (a) R = 1 and (b) R = 0.5 with π2
RF
 .
4. Conclusions [4] J. Hecht, “Understanding Fiber Optics,” 4th Edition, Pren-
tice Hall, Upper Saddle River, 2002.
In this paper, we have analyzed the impact of p-ratio on
OSNR, Q-parameter and BER of RoF communication
system at FWHM of RF oscillator linewidth in conjunc-
tion with variable value of fiber length (LFiber) up to 100
Km. An improvement of 3 dBm in OSNR have been
observed for p-ratio = 0.5 and π2
RF

along with
R-parameter of 1. A considerable improvement in Q-
parameter and BER has also been observed for lesser
value of p-ratio.
[5] G. H. Smith and D. Novak, “Overcoming Chromatic-
Dispersion Effects in Fiber-Wireless Systems Incorpo-
rating External Modulators,” IEEE Transactions on Mi-
crowave Theory Technology, Vol. 45, No. 8, 1997, pp.
1410-1415. doi:10.1109/22.618444
[6] T.-S. Cho, C. Yu and K. Kim, “Analysis of CNR Penalty
of Radio over Fiber Systems Including the Effects of
Phase Noise from Laser and RF Oscillator,” Journal of
Lightwave Technology, Vol. 23, No. 12, 2005, pp. 4093-
4100.
[7] J. R. Barry and E. A. Lee, “Performance of Coherent
Optical Receivers,” Proceeding of Institute of Electrical
Engineering, Vol. 78, No. 8, 1990, pp. 1369-1394.
5. References
[1] N. Uesugi, T. Horiguchi, M. Nakazawa and Y. Murakami,
“Optical Fiber Cable Measurements in the Field,” IEEE
Journal on Selected Areas in Communications, Vol. 4,
No. 5, 1986, pp.732-736.
doi:10.1109/JSAC.1986.1146373
[8] J. Salz, “Modulation and Detection for Coherent Light-
wave Communications,” IEEE Communication Magaga-
zine, Vol. 24, No. 6, 1986, pp. 38-49.
doi:10.1109/MCOM.1986.1093099
[9] V. Sharma, A. Singh and A. K. Sharma, “Analysis the
Impact of Laser- and RF Oscillator-Line width over Car-
rier-to- Noise Ratio in Optical Single Sideband (OSSB)
RoF Transmission Systems”, Optics and Lasers in Engi-
neering, Vol. 47, No. 11, 2009, pp. 1145-1149.
doi:10.1016/j.optlaseng.2009.06.012
[2] M. Sauer, A. Kobyakov, J. E. Hurley and J. George, “Ex-
perimental Study of Radio Frequency Transmission over
Standard and High-Bandwidth Multimode Optical Fi-
bers,” International Topical Meeting on Microwave Pho-
tonics, Seoul, 12-14 October 2005, pp. 99-102.
doi:10.1109/MWP.2005.203549 [10] U. Gliese, S. Nørskov and T. N. Nielsen, “Chromatic Dis-
persion in Fiber-Optic Microwave and Millimeter-Wave
Links,” IEEE Transaction of Microwave Theory Tech-
nology, Vol. 44, No. 10, 1996, pp. 1716-1724.
doi:10.1109/22.538964
[3] R. J. Green, “Secure Communications: The Infrared Al-
ternative,” In ICTON Mediterranean Winter Conference,
6-8 December 2007, pp. 1- 4.
doi:10.1109/ICTONMW.2007.4446906