Comparative Analysis of Different Modulation Schemes in Rician Fading Induced FSO Communication System

International Journal of Electronics Engineering Research. ISSN 975-645 Volume 9, Number 8 (17) 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 1, 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/N (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/N 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

116 Harmeet Singh and Amandeep Singh Sappal capable of transferring data, video and voice across the link length ranging from 1m to a few kilometres at frequency more than 3GHz and wavelength ranging from 785 to 15nm [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 [,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/N), 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/N (i.e. energy per bit per unit noise, better known as digital signal-tonoise 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 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/N 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.. 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.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]..1 Noise variance in terms of Eb/N 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* SF y x (1) h here noise and h are Gaussian random variables and SF is the scaling factor of modulated signal and fading induced by Rician Channel.

116 Harmeet Singh and Amandeep Singh Sappal ^ noise* SF y x X Y 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: ^ Random P SF Random W y x x Random ( X ) Random ( Y) Random ( X ) Random ( Y) LOS NLOS LOS NLOS () (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 V( X Y) V( X ) V( Y) (5) The value of Rician Fading Factor in scaling factor SF is 1 Eb N and standard deviation of random variable P is 1 [6]..1.1 Noise variance for BPSK and QPSK Substituting the value of modulation scaling factor [5] as Eb 1and Rician fading factor as 1 Eb N SF can be written as 1 SF. E N The overall variance of equation (3), after substituting above values in numerator and denominator, comes out to be b 1 1 E N 1E N b b (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]: W V V ( W ) V ( X Y) * V ( X )* V ( Y)* corr( W,( X Y)) X Y Here, corr( W,( X Y) is zero, thus above equation can be written as W 1 1 1 1 V X Y E b N ( K 1) E b N K 1 (7) (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: W 1 1 E N b V l X Y E b N 4 4 E b N (9).1. Noise variance for 16-QAM Substituting the value of modulation scaling factor [8] as Eb 5 fading factor as 1 Eb N, SF can be written as SF in Rician fading channel for 16-QAM becomes 5 E N b and Rician. The total variance V W 5 1 X Y 4 E N K 1 b (1) If value 3 is substituted in place of K, the equation (1) becomes W 5 E N b V l X Y 4 E b 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]: 1 ln I / I / l Pe Q I exp di (1) I l l Here, γ(i) represents the electrical SNR per bit and is given by, where RI. Substituting the values of parameters R and ξ from [9], we get I I / l. The equation (1) can be solved by Gauss-Hermite quadrature integration approximation [1] and the unconditional BER given in equation (1) can be reduced to the following form: n e i exp 1 l i l / i 1 1 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 n 1 P wq K sin / 4 exp x / (14) e i l i l i 1 and that of 16-QAM is given by n exp / 5 3 Pe wq i K lxi l 8 (15) i 1 4. BER FOR DIFFERENT MODULATION SCHEMES a. In case of BPSK Substituting equation 9 into equation 13, BER becomes n 1 Eb N Eb N Pe wq i K exp xi (16) i 1 Eb N 8Eb N

Comparative Analysis of Different Modulation Schemes in Rician Fading. 1165 b. In case of QPSK Substituting equation 9 into equation 14, BER becomes n 1 Eb N Eb N Pe wq i K sin exp xi (17) i 1 4 Eb N 8 Eb N c. In case of 16-QAM Substituting equation 11 into equation 15, BER becomes n 3 5Eb N 5Eb N Pe wq i K exp xi (18) 8 i 1 5 Eb N 8Eb N 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]: P P P I * out m (19) * where P out 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 ln l Pout Q m () l exp ln out l l m P (1)

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 and 1, we get 4Eb N 1 E N Pout Q ln m Eb N 4 Eb N b () Eb N Eb N m exp ln Pout 4Eb N 8Eb N (3) b. In case of 16-QAM Substituting equation 11 into equation and 1, we get 4Eb N 1 5 E N Pout Q ln m 5 Eb N 4Eb N b (4) 5Eb N 5E N m exp ln Pout 4Eb N 8Eb N b (5) 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.. As the values of Eb/No increases from -4dB to 1dB, 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 db, 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. 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 (σ ) 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 nonline 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 1dB values and it is least for values greater than 1 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.. 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 db 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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