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Calculations of Signal to Noise Ratio (SNR) for Free Space Optical

Communication Systems

Article in Baghdad Science Journal · March 2008

DOI: 10.21123/bsj.2008.5.1.95-100

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 Um-Salama Science Journal Vol.5(1)2008

Calculations of Signal to Noise Ratio (SNR) for Free Space

Optical Communication Systems
Hani j. Kbashi* Mohammed A. Hameed * Saba A. Shykre**

Date of acceptance 13/6/2007

Abstract
In this paper, we calculate and measure the SNR theoretically and experimental for
digital full duplex optical communication systems for different ranges in free space, the
system consists of transmitter and receiver in each side. The semiconductor laser (pointer)
was used as a carrier wave in free space with the specification is 5mW power and 650nm
wavelength. The type of optical detector was used a PIN with area 1mm2 and responsively
0.4A/W for this wavelength. The results show a high quality optical communication system
for different range from (300-1300)m with different bit rat (60-140)kbit/sec is achieved with
best values of the signal to noise ratio (SNR).

Introduction
Optical Signal to Noise Ratio However, the optical background (noise)
(SNR) is the measure of the ratio of signal that accompanies the desired optical signal
power to noise power in an optical will be amplified along with the signal;
channel. For a typical optical consequently, the SNR will tend to
communication system for which the SNR degrade as it passes through the
is relevant, the signal consists usually of transmission system. The optical noise
nearly monochromatic modulated light near the signal wavelength can impair the
superimposed on a background comprised receiver's ability to properly decode the
of (mostly unmodulated) optical power signal because of optical interference
distributed over a broad wavelength range between the optical signal and optical
- a range including the signal wavelength noise. This impairment can be a bigger
[1]
. contributor to the BER than the power
This noise arises typically in optical fluctuations in the optical noise, especially
amplification and it is better thought of as when an optical filter centered on the
a power density rather than a total power. signal wavelength is placed ahead of the
When the optical signal is carried by an receiver.
optical transmission system that includes This "free space" technique
optical amplifiers. The detection of the requires only a clear line-of-sight path
signal is typically affected by attenuation between the transmitter and the distant
and dispersion. With the use of amplifiers, receiver to form an information link. The
there is the additional impairment because availability of a coherent, monochromatic
of noise seen in the receiver due to the optical communication which, due to the
presence of ASE (Amplified Spontaneous very high frequency of the carrier (1014
Emission) noise. In practice, the use of an Hz), would allow a very large amount of
amplifier will help improve the signal information to be transmitted. Figure (1)
because the increase in the signal shows a block schematic of a typical
amplitude will help overcome noise digital optical communication system,
generated in the receiver's front end.
*Collage of Science University of Baghdad,
**Collage of Engineering University of Deyla. 95
 Um-Salama Science Journal Vol.5(1)2008

initially the input digital signal decoded to give the original digital
from the information source is suitably information [2].
encoded for optical transmission. The laser The full duplex optical
drive circuit directly modulates the communication system consists of a
intensity of semiconductor laser with the transceiver unit which consist mainly of
encoded digital signal. The photodetector the transmitter unit and receiver unit, The
is followed by a preamplifier to provide signal could be sent and received in a free
gain. Finally, the obtained signal is space between two which are terminal 1
and 2 [3].

Optical
Channel
Laser
Signal Driver Laser
In Modulator

Signal Amplifier and Optical

out signal Demodulator Detector
recovery

Figure (1) Schematic block of a typical optical communication system

The system of pulses modulated The Johnson noise voltage is

should be driven to the laser source by expressed in terms of the mean square
using driver circuit. Circuit applies the voltage developed across a load resistance
needed current to the laser in order to of RL (in Ohms) at a temperature T (in
control of the output power of the laser. Kelvin) in a frequency (Δ f ) [5, 6] :-
While the output pulse was detected using Where k is Botzmann's constant,
optical detector must be amplified using k= 1.38066 × 10-23 J/K
high speed operational amplifier. The
4 k T Δf
amplifier was designed to get a gain equal ith= ‫ـــ‬ …(2)
to 10k by selection the feedback resistance RL
equal to 10k and input resistance equal
to 1k.
Therefore the total current noise is:-
Measurement and Calculations in = ith + id ... (3)
The signal to noise ratio of the
system could be calculated as follows [4]:- Where id is the dark current.
S/N =20 log10 (is/ in) in dB (using The system work at the room
voltage or current ratio)............. (1) temperature (i.e. T=300 K), RL=22kΩ is
Where the symbol S represents the optical load resistor, and the signal bandwidth
signal power and the symbol N is the Δf=(60,80,100,120,140)kb/s, while id=4
optical noise power, in generated current nA by substitute these values in
noise in optical detector and is generated equation(2) and (3), the results of the
signal current. thermal noise current ith and the total
The two main sources of noise in current noise in are listed in the table(1) :
optical detector without internal gain are
thermal noise (Johnson noise) and dark
current.
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 Um-Salama Science Journal Vol.5(1)2008

Table 1: The thermal noise current and the At bit rate 60 kb/s
total current noise as a function of bit rate Table 3: The theoretical and experimental
Δf(kb/s) ith (nA) in (nA) values of the S/N at bit rate 60 kb/s
60 21.2 25.2 is μA S/N is μA S/N
(theoretical) (dB)(theoretical) (experimental) (dB)(experimental)
80 24.5 28.5 106.8 72.54 59.2 67.41
38.4 63.65 31.2 61.85
100 27.4 31.4 22.8 59.13 14.8 55.37
120 30.0 34 19.6 57.81 10.4 52.31
9.6 51.61 2.4 39.5
140 32.45 36.45 5.6 46.93 0.36 23.09

At bit rate 80 kb/s

The amount of the generated
current in the photodiode (is) depends on Table 4: The theoretical and experimental
the incident optical power on the values of the S/N at bit rate 80 kb/s
is(theoretical) S/N is(experimental) S/N
photodiode Pr (μW), and the responsivity μA
106.8
dB(theoretical)
71.47
μA
59.2
dB(experimental)
66.34
Rλ =0.4 (A/W) [7]. 38.4
22.8
62.58
58.06
31.2
14.8
60.78
54.3
is = Pr × Rλ ……….. (4) 19.6 56.74 10.4 51.24
9.6 50.54 2.4 38.5
The total power of the received signal 5.6 38.86 0.36 22

through the earth’s atmosphere can be At bit rate 100 kb/s

calculated by:
Table 5: The theoretical and experimental
Areceiver values of the S/N at bit rate 100 kb/s
P receiver = P transmit × ‫ × ــــــــــــــــــــــ‬exp (-μ *Range)... (5) is(theoretical)
μA
S/N
dB(theoretical)
is(experimental)
μA
S/N
dB(experimental)
(Div *Range) 2 106.8 70.63 59.2 65.5

38.4 61.74 31.2 59.94

A receiver = л ×(D2 / 4) ……………… (6)
22.8 57.22 14.8 53.46
The theoretical calculation of the 19.6 55.9 10.4 50.4
received optical signal power of the system 9.6 49.7 2.4 37.66
can be calculated, the maximum output 5.6 45.02 0.36 21.18

power Ptransmitted of the optical transmitter At bit rate 120 kb/s

for laser diode pointer is 5mW and laser
beam divergence 0.6 mrad, Areceiver of the Table 6: The theoretical and experimental
optical receiver 0.0028cm2, the values of the S/N at bit rate 120 kb/s
is(theoretical) S/N is(experimental) S/N
μA μA
atmospheric transmittance Ta of laser 106.8
dB(theoretical)
69.94 59.2
dB(experimental)
64.81
wavelength 650nm is about 62% and the 38.4
22.8
61.05
56.53
31.2
14.8
59.25
52.77
range R= [300,500,650,700,1000,1300]. 19.6 55.24 10.4 49.71
9.6 49 2.4 36.97
by substitute these values in equation (4) 5.6 44.33 0.36 20.49

and (5) we obtain the table (2) below: At bit rate 140 kb/s
Table 2: The received power (theoretical and Table 7: The theoretical and experimental
experimental) as a function of range values of the S/N at bit rate 140 kb/s
Pr Pr is(theoretical) S/N is(experimental) S/N
Range is(theoretical) is(experimental)
(theoretical) (experimental) μA dB(theoretical) μA dB(experimental)
(m) μA μA
μW μW 106.8 69.33 59.2 64.2
300 267 106.8 148 59.2 38.4 60.45 31.2 58.65
22.8 55.92 14.8 52.17
500 96 38.4 78 31.2 19.6 54.6 10.4 49.1
9.6 48.41 2.4 36.37
650 57 22.8 37 14.8
5.6 43.73 0.36 19.89
700 49 19.6 26 10.4
1000 24 9.6 1.2 2.4
1300 14 5.6 0.9 0.36
The variation of the S/N with the
power received which is represented by the
When substitute the values in the table (2)
generated signal current in optical detector
in equation (1) we obtain:-
are shown in figures 1,2,3,4,5 at different
b.t rats.

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Um-Salama Science Journal Vol.5(1)2008

80

S/N (dB) 76
h1
h2
S/N (dB) 80
72 76 h1
72 h2
68
64
68
64
60
60
56
56
52
52
48 48
44 44
40 40
36 36
32 32
28 28
24
24
20
20
16
16
12
12
8
8 4
4 0
0
0 20 40 60 80 100
0 20 40 60 80 100

is(μA) is(μA)
Figure (1) Figure (2)
The SNR as a function of signal current The SNR as a function of signal current
at in=25.2 (nA) & frequency carrier 60KHz at in=28.5 (nA) & frequency carrier
80KHz

76
80 h1
72
76 h1 h2
68
72 h2
64
S/N (dB) 68 S/N (dB) 60
64
60 56
56 52
52 48
48 44
44
40
40
36
36
32 32
28 28
24 24
20 20
16
16
12
12
8
4 8
0 4
0 20 40 60 80 100 0
0 20 40 60 80 100

is(μA) is(μA)
Figure (3) Figure (4)
The SNR as a function of signal current The SNR as a function of signal current
at in=31.4 (nA) & frequency carrier atin=34 (nA) & frequency carrier
100KHz 120KHz
76
72 Series1
68 H8
64
60
56
52
S/N (dB) 48
44
40
36
32
28
24
20
16
12
8
4
0
0 20 40 60 80 100

is(μA)
Figure (5)
The SNR as a function of signal current at
in=36.4 (nA) & frequency carrier 140KHz
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 Um-Salama Science Journal Vol.5(1)2008

It can be seen from above figures this region to obtain a good quality signal
when the range is increase the generated and less noise.
signal current decreases due to decreasing
of the received power which is led to Conclusions
decreases of the S/N.  Since the system is thermal noise
While the relationship between the limited, increasing the load resistance
signals current (is) generated in optical leads to reduce the thermal noise and then
detector, noise current and S/N is shown as increases SNR, in addition to decreasing
in figure (6). the minimum detectable power and
increasing the system power margin.
S/N dB
 We can see the optimum value of SNR
achivied at the carrier frequency is
(100kb/s), because of this value of carrier
frequency gives as minimum value of the
thermal noise.
 By increasing the bandwidth Δf of
transmitted signal of the system, the
thermal noise will increase in accordance
to with the equation (2), which leads to
decreases in SNR.

References
is*10 μA in*10 nA 1. Johnson. D. A, 2000 “Optical Through
the Air Communications“, Handbook.
Figure (6)
http://www.imagineeringezine.com/air-
The relationship between the S/N, is& in bk2. html
2. Senior. J. M, 1996 “Optical Fiber
From an above figure the Communications Principles and
increasing of the signal current generated Practice“, 2nd ed., Prentice Hall.
in optical detector due to the incident of 3. Gowar. J, 1984 “Optical Communication
the power received on the optical detector System“, Prentice Hall.
leads to increasing of the SNR quality of 4. Optical Components & Communication,
the system because of dependence on the 2001. Private communication.
power received which is a directly 5. Manor. H, & Arnon. S, “Performance of
proportional with the signal current an Optical Wireless Communication
generated in optical detector. While the System as a Function of Wavelength“,
SNR is decreasing with increasing of the Applied Optics, Vol.42, No.21, July
noise current generated due to attenuation 2003.
6. Johnson. D. A, 2003 “Johnson Noise
in optical detector.
And Shot Noise”, University of Brown,
It can be observed from the figure
College of Science, Department of
(6) that S/N is directly proportional with is Physics.
and in the same time it is inversely 7. Kbashi. H. J, 2005 "Optical
proportional with in. Communication System Based on Full
The above figure shows the Duplex Wavelength Division
optimized value of the is in the range Multiplexing Technique", PhD Theses
between (40-50)μA and frequency carrier University of Baghdad, College of
range between (90-110)kb/s. This would Science, Department of Physics.
allow a wide selected frequency range in

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 ‫‪Um-Salama Science Journal‬‬ ‫‪Vol.5(1)2008‬‬

‫حساب نسبة أالشارة الى الضوضاء لمنظومة أتصال ضوئٌة فً الفراغ‬

‫صبا اسعد شكري***‬ ‫محمد عبدهللا حمٌد**‬ ‫هانً جاسم كباشً*‬

‫*مدرس‪/‬كلية العلوم ‪/‬جامعة بغداد‪.‬‬
‫**مدرس مساعد‪/‬كلية العلوم ‪/‬جامعة بغداد‪.‬‬
‫***مدرس مساعد‪/‬كلية الهندسة ‪/‬جامعة ديالى‪.‬‬

‫الخالصة‪:‬‬
‫تم في هدا البحث حساب وقياس نسبة االشارة الى الضوضاا ‪ )SNR‬نظرياا وعملياا لمساافاخ مفتلواة وبمعاد‬
‫نق ا بياناااخ مفتلوااة بعااد اب تاام حساااب القاادرة المسااتلمة لك ا مسااافة لمنظومااة اتساااالخ ضااو ية رقميااة متعاكسااة االتجااا‬
‫لمسافاخ مفتلوة في الجو‪ ,‬تتكوب المنظومة مب مرسلة ومستلمة في ك جانب تم اساتفدام الليا ر كوساا ناقا وفساا‬
‫الليا ر المسااتفدم فااي هااو المنظومااة هااو نااول ليا ر اشاابا الموسا خ مر ااي ‪ )pointer‬بقاادرة مقاادارها ‪ 5mW‬وباااو‬
‫موجي ‪ 650nm‬والكاشف الضو ي المستفدم نول فوتاوني ساليكوني ‪ PIN‬وبمسااحة ‪ 1mm2‬وبأساتجابية ‪ 0.4A/W‬لهاوا‬
‫‪(60-‬‬ ‫ا لاو الموجي‪ .‬اثبتخ النتا ج اب منظومة االتساالخ الضو ية المسممة واخ كوا ة عالية لعادة نقا بيانااخ‬
‫‪ 140)kbit/sec‬ولعااادة مساااافاخ مفتلواااة ‪ (300-1300)m‬ماااب فااا الحساااو علاااى افضااا قااايم لنسااابة االشاااارة الاااى‬
‫الضوضا ‪.‬‬

‫‪100‬‬

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