International Journal of Electronics Engineering Research.
ISSN 0975-6450 Volume 9, Number 8 (2017) pp. 1159-1169
© Research India Publications
http://www.ripublication.com
Comparative Analysis of Different Modulation
Schemes in Rician Fading Induced FSO
Communication System
Harmeet Singh1 and Amandeep Singh Sappal2
1,2Department of Electronics and Communication Engineering, Punjabi University, Patiala, Punjab, India.
Abstract
Free Space Optics is a optical communication technique which involves
atmosphere or free space as the communication medium. This atmosphere
may be turbulent in nature which causes fading of the signal. The channels
which introduce the fading of signal are said to be fading channels. In this
paper, Rician fading channel is considered, in which signal traverses through
multiple paths before reaching the receiver end. The fading strength of this
channel is derived in terms of noise variances for different modulation
schemes (BPSK, QPSK and 16-QAM) and are figured into Eb/N0 (energy per
bit per unit noise) form. The performance of this channel is analyzed for
BPSK, QPSK and 16-QAM modulation schemes with respect to channel
parameters viz. BER, Electrical SNR, Outage Probability and Power margin
for different Eb/N0 values. From the results, it is observed that for efficiently
transmitting signal in Rician channel with better BER performance, it should
be modulated with M-PSK modulation techniques rather than M-QAM.
Keywords: Rician fading channel, Free Space optics, BER, SNR, M-PSK,
M-QAM
1. INTRODUCTION
Free Space Optics (FSO) is a communication system that uses laser beams to transfer
data without the use of optical fiber. This technique involves free space or atmosphere
to transmit data via line of sight optical bandwidth from transmitter to receiver. It is
1160 Harmeet Singh and Amandeep Singh Sappal
capable of transferring data, video and voice across the link length ranging from 100m
to a few kilometres at frequency more than 300GHz and wavelength ranging from
785 to 1500nm [1]. The main advantages of this system include immunity from radio
frequency interference, licence free operation, high security level, backup system to
fiber optic communication, and easy installation. The applications of FSO system
comprises outdoor wireless access, storage area network, last mile access, enterprise
connectivity, metro network extensions, backhaul, service acceleration, bridging
WAN access and military access [2,3].
Outdoor FSO involves atmosphere as medium of transmission of optical signal. The
atmosphere may, at times, be turbulent in nature, due to which the optical signal may
get distorted. These distortions include absorption and scattering of the signal by the
particle that is present in turbulent atmosphere. These particles include that of fog,
dust, smoke, rain and many more. The strength of the signal decreases as it traverses
through such channels. This decrease in signal strength is known as fading and the
channels which introduce the fading of signal are said to be fading channels. Broadly,
fading channels are modelled into three categories, say, Additive White Gaussian
Noise (AWGN), Rayleigh and Rician fading channel.
To transmit the signal through a communication channel, it is very important to
modulate it at the transmitter end so as to increase the efficiency and decrease the cost
of communication. In FSO system, modulation of optical signal becomes even more
vital as it may help to reduce the effect of atmospheric turbulence (i.e. fading) on the
transmitted signal. To mitigate the effect of turbulence, a number of digital
modulation techniques, such as Binary Phase Shift Keying (BPSK), Quadrature Phase
Shift Keying (QPSK), Quadrature Amplitude Modulation (QAM) and many more, are
used [4].
To analyze the strength of the signal and the performance of the optical
communication system, a number of parameters come into picture. Among these
parameters, the most important are Bit Error Rate (i.e. BER), electrical Signal-to-
Noise Ratio (SNR), energy per bit per unit noise (Eb/N0), outage probability (i.e. the
probability of fading of signal more than the threshold level) and power margin (i.e.
amount of extra power required to achieve a particular BER).
This paper focuses on deriving the values of bit error rate for BPSK, QPSK and QAM
in terms of Eb/N0 (i.e. energy per bit per unit noise, better known as digital signal-to-
noise ratio) in Rician fading channel. Also, the three modulation schemes are analysed
and compared to find the suitable one among three for transmission through this
fading channel in free space optics. This comparison is validated by finding the
outage probability and power margin required for achieving the required bit error rate
in all the three modulation schemes in Rician fading channel.
Comparative Analysis of Different Modulation Schemes in Rician Fading…. 1161
The rest of the paper is organised as follows: Section 2 contains explanation of Rician
Fading Channel and relationship between fading strength and Eb/No for different
modulation schemes; Section 3 provides closed form solution for unconditional BER;
Section 4 gives relationship of BER vs. Eb/N0 in different modulation schemes;
Section 5 shows the significance of Eb/No in relationship between outage probability
and power margin, Section 6 gives the performance analysis followed by conclusion
in section 7.
2. RICIAN FADING CHANNEL
Rician fading channel is a channel model in which the signal reaches the receiver after
traversing through different paths, thus causing multipath interference. While passing
through this channel a signal segregates into multipath components among which the
dominant one is the line of sight component (i.e. specular component) and the rest are
termed as random or scatter components (i.e. non line of sight) [5,6].
Let the specular component be denoted by Gaussian random variable X and the
scattered component by random variable Y. According to the channel characteristics,
the X variable (LOS) should have non-zero mean, while Y (NLOS) should have zero
mean. However, the variances of both variables should be equal [6]. Due to the
difference of means of both components, Rician K factor comes into picture which is
defined as the ratio of power of LOS component to that of NLOS component. The
noise generated in Rician fading process is modelled by Gaussian random variable P
with zero mean and 0.5 variance. This fading occurs when one of the paths (mostly
line of sight) is stronger than the other paths (mostly non-line of sight). The total
fading in this model is a combination of fading occurring in both types of paths [6].
2.1 Noise variance in terms of Eb/N0 for different modulation schemes
Let us consider that the channel amplitude scaling factor (‘h’) estimate at receiver is
known and is accurate [6]. The transmitted symbols (‘x’) can be obtained from the
received signal (‘y’) by the process of equalization as given below. Considering the
normalised received signal as
*noise SFy x
h
(1)
here noise and h are Gaussian random variables and SF is the scaling factor of
modulated signal and fading induced by Rician Channel.
1162 Harmeet Singh and Amandeep Singh Sappal
^ *noise SFy x
X Y
(2)
Let noise be depicted by random variable P and h, a combination of line of sight
(LOS)and non-line of sight (NLOS) components, be depicted by random variables X
and Y respectively. SF is a combination of amplitude scaling of the signal induced by
Rician fading channel and the modulation technique used before transmission. This
creates scaling of amplitude of the signal as it passes through the channel and can be
given as
SF= Rician Fading factor * modulation scaling factor
If noise, X and Y are modelled as Gaussian random variables, Random(P), Random(X) and Random(Y) respectively, the equation (1) can be written as:
^
( ) ( ) ( ) ( )LOS NLOS LOS NLOS
Random P SF Random Wy x x
Random X Random Y Random X Random Y
(3)
Total variance of sum of two random variable X and Y becomes [7]:
V(X+Y)=V(X)+V(Y)+Covariance(X,Y) (4)
Since, X and Y are random and uncorrelated to each other, then
2 2 2( ) ( ) ( ) 2V X Y V X V Y (5)
The value of Rician Fading Factor in scaling factor SF is 01 bE N and standard
deviation of random variable P is 1 2 [6].
2.1.1 Noise variance for BPSK and QPSK
Substituting the value of modulation scaling factor [5] as 1bE and Rician fading
factor as 01 bE N SF can be written as
0
1
b
SFE N
.
The overall variance of equation (3), after substituting above values in numerator and
denominator, comes out to be
2 2
00
2 2
1 2 1 1 2
2 2
b bE N E N
(6)
Comparative Analysis of Different Modulation Schemes in Rician Fading…. 1163
The total variance of division of two Gaussian random variables in equation (3) is [7]:
( ) ( ) 2* ( )* ( )* ( , ( ))WV V W V X Y V X V Y corr W X Y
X Y
(7)
Here, ( ,( )corr W X Y is zero, thus above equation can be written as
2
0 0
1 1 1 12
2 2 12( 1)b b
WVX Y E N E N KK
(8)
The noise variance can be written in form of Rician K factor as mentioned in [6]. If
value 3 is substituted in place of K, the above equation becomes:
20
0 0
21 1
2 4 4
bl
b b
E NWVX Y E N E N
(9)
2.1.2 Noise variance for 16-QAM
Substituting the value of modulation scaling factor [8] as 5 2bE and Rician
fading factor as 01 bE N , SF can be written as 0
5
2 b
SFE N
. The total variance
in Rician fading channel for 16-QAM becomes
0
5 1
4 1b
WVX Y E N K
(10)
If value 3 is substituted in place of K, the equation (10) becomes
20
0
5
4
bl
b
E NWVX Y E N
(11)
1164 Harmeet Singh and Amandeep Singh Sappal
3. CLOSED FORM SOLUTION FOR UNCONDITIONAL BER
The unconditional probability of error Pe over log-normal irradiance fluctuation is
obtained from the following [9]:
2
2
0
220
ln / / 21exp
22
le
ll
I IP Q I dI
I
(12)
Here, γ(I) represents the electrical SNR per bit and is given by 2 22 , where
2RI . Substituting the values of parameters R and ξ from [9], we get
2 2/ 2 lI I .
The equation (12) can be solved by Gauss-Hermite quadrature integration
approximation [10] and the unconditional BER given in equation (12) can be reduced
to the following form:
2
0 1
1
1exp 2 / 2
n
e i l i li
P wQ K K x
(13)
where wi and xi are the weight factors and zeros of an nth-order Hermite polynomial.
Similarly for QPSK, unconditional BER is given by
2
0
1
12 sin / 4 exp 2 / 2
n
e i l i li
P wQ K x
(14)
and that of 16-QAM is given by
2
0
1
3 2exp 2 / 2
58
n
e i l i li
P wQ K x
(15)
4. BER FOR DIFFERENT MODULATION SCHEMES
a. In case of BPSK
Substituting equation 9 into equation 13, BER becomes
0 00
1 0 0
2 21exp
2 8
nb b
e i ii b b
E N E NP wQ K xE N E N
(16)
Comparative Analysis of Different Modulation Schemes in Rician Fading…. 1165
b. In case of QPSK
Substituting equation 9 into equation 14, BER becomes
0 00
1 0 0
2 212 sin exp
4 2 8
nb b
e i ii b b
E N E NP wQ K xE N E N
(17)
c. In case of 16-QAM
Substituting equation 11 into equation 15, BER becomes
0 00
1 0 0
5 53 2exp
5 2 88
nb b
e i ii b b
E N E NP wQ K xE N E N
(18)
5. OUTAGE PROBABILITY AND POWER MARGIN
Outage probability is another performance metric which is useful to determine the
probability of outage of signal in case of deep fading when average BER is more than
its threshold value and the signal is not able to reach at the receiver end. It can be
depicted in terms of SNR as follows [9]:
*
out mP P P I (19)
where outP depicts the probability of signal outage and * is average SNR for a given
noise channel with no atmospheric turbulence.
Power margin (m) is the extra power supplied to enhance the signal strength which
has had weakened due to turbulence induced fading. In other words, it is used to
determine the extra power required to be supplied to meet the threshold value of BER
and to avoid outaging of the signal. Mathematically, outage probability and power
margins are given as follows [9]:
1
ln2
lout
l
P Q m
(20)
2 2exp 2ln 2 2out l lm P (21)
1166 Harmeet Singh and Amandeep Singh Sappal
5.1 Outage probability and power margin w.r.t. Eb/No in Rician Channel
a. In case of BPSK and QPSK
Substituting equation 9 into equation 20 and 21, we get
0 0
0 0
4 21ln
2 2 4
b bout
b b
E N E NP Q mE N E N
(22)
0 0
0 0
2 2exp 2ln 2
4 8
b bout
b b
E N E Nm PE N E N
(23)
b. In case of 16-QAM
Substituting equation 11 into equation 20 and 21, we get
0 0
0 0
4 51ln
5 2 4
b bout
b b
E N E NP Q mE N E N
(24)
0 0
0 0
5 5exp 2ln 2
4 8
b bout
b b
E N E Nm PE N E N
(25)
6. ANALYSIS OF BER VS. SNR AND OUTAGE PROBABILITY VS.
POWER MARGIN GRAPHS
From figures 1 through 3, it is observed that
1. The BER performance of BPSK and QPSK are the same and is better than 16-
QAM.
2. As the values of Eb/No increases from -4dB to 12dB, the spread of curves in
graphs increases sharply in BPSK and QPSK, as compared to 16-QAM, which
implies that BER falls less significantly in 16-QAM than in other two.
3. For the range of 14 to 20dB, the curves of Eb/No are almost overlapping in all
the modulations and thus having least impact on BER of signal transmitted in
Rician channel.
Comparative Analysis of Different Modulation Schemes in Rician Fading…. 1167
Fig 1. BER vs SNR for different Eb/No in
case of BPSK
Fig 2. BER vs SNR for different
Eb/No in case of QPSK
Fig 3. BER vs SNR for different Eb/No in
case of 16-QAM
Fig 4. Outage Probability for
different Eb/No in case of BPSK and
QPSK
Fig 5. Outage Probability for different Eb/No in case of 16-QAM
1168 Harmeet Singh and Amandeep Singh Sappal
From above points of observations, it can be inferred that for efficiently transmitting
signal in Rician channel with better BER performance, it should be modulated with
M-PSK modulation techniques rather than M-QAM. The major reason supporting this
result is the low value of noise variance (σ2) in M-PSK modulation with relatively
high value in M-QAM schemes. In Rician channel, the transmission of signal is a
combination of line of sight and non-line of sight transmission components. In non-
line of sight transmission, the signal reaches the receiver end after reflecting from
different objects, which may absorb or scatter the signal, thus decreasing its strength.
Now, it is well known that in M-QAM, the information is encoded in amplitude and
phase of the signal. Therefore, as the signal follows the non-line of sight path, it loses
its amplitude and the signal strength decreases which ultimately results in rise of
BER. Hence, the noise variance factor in 16-QAM increases rapidly leading to its
worst performance among the three.
From the graphs in figure 4 and 5, it can be analyzed that:
1. For Eb/No ranging from -4dB to 4dB, the deviation in graphs is more
significant as compared to 4 to 10dB values and it is least for values greater than 10
dB. It signifies that power margin or the extra power required to supply to the signal
for achieving a sufficient signal strength at receiver end, in order to avoid outage, is
meaningful for higher values of Eb/No.
2. It can also be inferred that the amount of energy needed to supply in order to
achieve least power margin is maximum in 16-QAM as compared to BPSK and
QPSK for lower values of Eb/No. Therefore, 16-QAM should be least preferred over
other two modulation schemes. This justifies the points of observations inferred from
figures 1 to 3.
7. CONCLUSION
In this paper, the noise variances for different modulation schemes are derived in
terms of Eb/No in Rician fading channel. The graphs of BER vs. Electrical SNR and
Outage probability vs. Power margin are drawn for -4dB to 20dB range of Eb/No for
BPSK, QPSK and 16-QAM. It has been analyzed that BER decreases more sharply
for increasing values of Eb/No in M-PSK modulation as compared to M-QAM
technique. from the comparison of Outage probability vs. power margin graphs, it is
inferred that the amount of power required to achieve the threshold BER is more in
16-QAM than M-PSK. From both the observations, it can be concluded that M-PSK
modulated signal transmitted through Rician channel performs better than M-QAM in
terms of BER, outage probability and power margin and hence should be preferred.
Comparative Analysis of Different Modulation Schemes in Rician Fading…. 1169
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1170 Harmeet Singh and Amandeep Singh Sappal