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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 Singh 1 and Amandeep Singh Sappal 2 1,2 Department 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
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Page 1: Comparative Analysis of Different Modulation Schemes in ... · modulation techniques, such as Binary Phase Shift Keying (BPSK), Quadrature Phase Shift Keying (QPSK), Quadrature Amplitude

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

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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.

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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.

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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)

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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)

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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)

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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)

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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.

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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

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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.

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Comparative Analysis of Different Modulation Schemes in Rician Fading…. 1169

REFERENCES

[1] 4gon.co.uk, 'An Introduction of Free Space Optics (FSO) Technology',

[Online]. Available on http://www.4gon.co.uk/solutions/introduction

_to_free_space_optics.php. [Accessed on : 19 March 2017].

[2] A. Malik and P. Singh, “Free Space Optics: Current Applications and Future

Challenges,” International Journal of Optics, vol. 2015, 2015.

[3] H. A. Willebrand and B. S. Ghuman, “Fiber optics without fiber,”IEEE

Spectrum, vol. 40, no. 8, pp. 41–45, Aug. 2001.

[4] J. G. Proakis and M. Salehi, Digital Communications, McGraw-Hill,New

York, 5th edition, 2007.

[5] M. K. Simon, M. S. Alouini, "Digital Communication over Fading Channels -

A Unified Approach to Performance Analysis".

[6] M. Viswanathan, "Simulation of Digital Communication systems using

Matlab", Second edition

[7] A. Papoulis, "Probability, Random Variables, and Stochastic Processes", Third

Edition

[8] J. R. Barry, E.A. Lee, D.G. Masserschmitt, "Digital Communication", Third

Edition.

[9] Z. Ghassemlooy, W. Popoola and S. Rajbhandari, "Optical Wireless

Communications System and Channel Modelling with MATLAB".

[10] M. Abramowitz and I S Stegun, Handbook of Mathematical Functions with

Formulas, Graphs and Mathematical Tables, New York, USA: Dover, 1977.

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1170 Harmeet Singh and Amandeep Singh Sappal


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