Improvement of Ground to Satellite FSO Link Performance Using Transmit Diversity in Weak

Atmospheric Turbulence Hemani Kaushal, V.K.Jain1, Subrat Kar

Department of Electrical Engineering, I.I.T Delhi, New Delhi, 110 016, India 1Dept of Electr. & Electronics Engn, Universiti Teknologi PETRONAS (UTP), Malaysia E-mail: himaniz@yahoo.com, drvirander_jain@petronas.com.my, subrat@ee.iitd.ac.in

Abstract – The performance of ground to satellite Free Space Optical (FSO) communication link is degraded due to the presence of atmospheric turbulence that causes fluctuations in both intensity and phase of the received optical signal. In this paper, bit error rate (BER) performance of FSO link using transmit diversity is investigated for coherent (sub-carrier BPSK and sub-carrier QPSK) and non-coherent (OOK and Q-PPM) modulation schemes in weak atmospheric turbulence channel. It is seen that multiple transmitting antennae help to overcome the turbulence induced fading effect. It is observed that sub-carrier BPSK modulation outperforms the other modulation schemes in terms of minimum SNR requirement for a given BER. Among non-coherent modulation schemes, Q-PPM performs better than OOK. However, as the level of Q in Q-PPM increases, its performance degrades and it becomes worse than OOK for certain values of atmospheric turbulence. Also, the effect of correlation among different transmitting antennae beams is analysed on the link performance.

Index Terms - Free Space Optical (FSO) communication, log normal channel, atmospheric turbulence, modulation, diversity, Bit Error Rate (BER).

I. INTRODUCTION

With the increasing demand of communication requirement all over the world, there is a need to switch to higher carrier frequencies. Thus, laser communication seems to be an attractive alternative to microwave links for free space communication owing to the fact that the frequency of operation of laser links are almost four to five orders of magnitude higher than microwave links. This gives laser communication various advantages over microwave system in terms of greater bandwidth, narrow spatial beam width and smaller antennae size (which is crucial factor in satellite communication). In addition, FSO system is easily deployable, cost effective, requires lower transmitter power levels [1-3]. However, it requires propagation of laser beam through the atmosphere which is severely affected by the

presence of clouds, rain, snow and fog leading to beam attenuation and aerosol scattering. Further, the random changes in the refractive index of the atmosphere caused due to inhomogeneties of temperature and pressure in the air leads to intensity and phase fluctuations in the received optical signal. These fluctuations or turbulence in the atmosphere deteriorate the signal intensity at the receiver and degrade the BER performance.

Various techniques have been used to mitigate the effect of turbulence induced fading: (i) increasing receiver diameter [4] i.e., aperture averaging, (ii) employing multiple transmitters/receivers [5, 6, 7] i.e., spatial diversity and (iii) compensate the condition of turbulence [8] i.e., adaptive optics before transmission. In this paper, we propose to use transmit diversity technique for uplink transmission to satellite to average out the deleterious effects of atmospheric turbulence. The likelihood that all the beams simultaneously being directed off axis will be substantially reduced relative to the likelihood of the same result for a single beam as the beams will pass through the portion of atmosphere that is largely uncorrelated. Further, employment of multiple transmitting beams will limit the transmit power density within the allowable safe laser power to support ground to satellite communication.

The rest of the paper is organized as follows: Section II describes the system and channel models used for analysis of ground to satellite communication link. In section III, we present the BER analysis and results of FSO link using coherent and non-coherent modulation schemes with transmit diversity. The comprehensive discussions and conclusions of analysis are presented in sections IV and V, respectively.

II. SYSTEM AND CHANNEL MODELS

A FSO communication system consists of three main functional elements: transmitter, atmospheric channel and receiver. The system model considered in this paper comprises of multiple transmit antennae at the ground station and single

receiver placed on distant space borne satellite. In this case, the signal arriving at the detector is

∑ (1)

where M is the number of independent beams and I the received signal irradiance at a point receiver. We assume that total uplink power remains constant and thus, each beam has 1/M th of the total power.

The receiver area is normalized to unity so that the received optical power becomes same as the optical intensity. The generated photocurrent by the photodetector of responsivity R is given as

(2)

where ~ 0, is additive white Gaussian noise. Considering the weak atmospheric turbulence and assuming the log irradiance l of laser light traversing through the turbulent atmosphere is normally distributed (i.e.,

, is the signal irradiance without turbulence), its probability density function (pdf) is given as

(3)

In the above equation, is the mean value of l given by 2⁄ and the variance of log irradiance [9, 10]. Hence, the pdf of irradiance I is log normal as given below / ⁄ (4)

The modelling of the atmospheric channel is often characterized by the refractive index structure constant Cn

2(h) which gives the measure of variance of the index of refraction due to inhomogeneties in the atmosphere. Therefore for uplink laser communication, Cn

2(h) profile model describes the varying strength of optical turbulence as a function of altitude h. Several models are proposed to describe the strength of the atmospheric turbulence as a function of height Cn

2(h) [11]. The most commonly used model for atmospheric turbulence in ground to satellite optical communication link analysis is Hufnagel-Valley Boundary (HVB) [12] and is given as

2.72 10 3 . (m-2/3) (5)

where is the mean square value of the wind speed in m/s and h altitude in km. For our analysis, we have used the HVB model with V=21 m/s.

The multiple uplink laser beams used to mitigate the effect of turbulence should be at least uncorrelated and separated by a distance greater than the atmospheric coherence diameter, r0 which is determined by the atmospheric structure constant Cn

2(h) and optical wavelength as given below

0.45 (6)

where 2 ⁄ is the optical wave number, H the altitude of the receiver and the zenith angle (angle between the local zenith and line of sight to satellite).

The spatial correlation matrix used to model the correlation among the M transmit laser beams is given as

1 1 1 (7)

where dij is the separation between the ith and jth transmit antennae and b(d) the normalized log irradiance covariance function [13] between two positions in the transmitting plane perpendicular to the direction of propagation and is defined by

(8)

The spatial covariance matrix Γ can be obtained from and is given by Γ .

III. BER ANALYSIS AND RESULTS FOR COHERENT AND NON-COHERENT MODULATION SCHEMES

In this section, BER expressions for FSO link using transmit diversity is evaluated. Error probability analysis for coherent and non-coherent modulation schemes is first carried out using single input and single output (SISO) system and it is then used as a benchmark for transmit diversity system. The BER without turbulence is given by

√ (9)

where Q(.) is the Gaussian function defined as

√ ⁄ (10)

In the presence of turbulence, averaging in fading environment is carried out and the above BER expression will get modified and is given by

(11)

where the parameter I as defined earlier is the received irradiance. Since I is a random variable, the average BER will be

∞ (12)

Substitution of fI (I) from (4) gives / ⁄∞ (13)

The SNR without turbulence is given by S 2⁄ where I is the received irradiance, R the photodetector responsivity and A the photodetector area which is taken as unity.

A closed form solution of (13) does not exist. However by using an alternative representation of Q-function together with the Gauss Hermite quadrature integration [14], the above equation can be approximated as

√ √ ⁄√∞∞ (14)

where / ⁄√ . This equation can be solved using Gauss Hermite quadrature integration [15] as given below ∑∞

∞ (15)

where xi and wi represent the zeros and weights of the mth order Hermite polynomials.

For transmit diversity (also referred as MISO array system), M laser array are sufficiently separated so that fading experienced between source-detector pairs are statistically independent. In this case, the effective variance in (14) is scaled by the number of transmit antennae i.e., ⁄ and that results in the reduction of effective log normal variance of the diversity channel. It may be mentioned that this linear scaling sometimes does not hold if there is a correlation among the transmitting antennae as it reduces the achievable diversity gain. In that case, the effective variance [16] is given by

∑ Γ (16)

where Γ , p,l=1,2.......M, are the correlation coefficients.

A. Performance Analysis for Coherent Modulation Schemes: Sub-carrier BPSK and QPSK

In a coherent sub-carrier modulation scheme, RF signal (sub-carrier) is pre-modulated with the information signal and is then used to modulate the intensity of the optical carrier. Based on the analysis given above, the performance of sub-carrier BPSK and QPSK is analyzed in weak atmospheric turbulence and is shown in Figs.1 and 2, respectively. It is seen from the below figures that degradation in the

performance due to turbulence is more in sub-carrier QPSK than in sub-carrier BPSK modulation scheme. However, in both the cases, there is an improvement in the performance with the increase in the number of transmitting antennae.

Fig.1 BER versus SNR in weak turbulence ( 0.1 and 0. 3 for sub-carrier BPSK for uncorrelated beams (i.e., 0) with and without transmit diversity.

Fig.2 BER versus SNR in weak turbulence ( 0.1 and 0. 3 for sub-carrier QPSK for uncorrelated beams (i.e., 0) with and without transmit diversity.

The improvement becomes more significant when the turbulence level is high. An improvement of more than 2 dB in SNR is observed when the transmitting antennae are increased from 1 to 3 for both the modulation schemes. Further increase in the number of transmitting antennae causes improvement in the link performance, but the level of improvement is not much. Figs. 3(a) and 3(b) demonstrate the effect of spatial correlation on the link performance for sub-carrier BPSK and QPSK, respectively. The results are plotted for a correlation value of b(d) = 0.3, where d is the separation between the transmitting antennae. It is seen that the degradation in performance of sub-carrier QPSK is more than in sub-carrier BPSK at the same diversity level with the increase of correlation value.

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Fig.3. (a) Sub-carrier BPSK and (b) sub-carrier QPSK performance with correlation coefficient 0.3 in weak atmospheric turbulence ( 0.1 and 0. 3 .

B. Performance Analysis for Non-Coherent Modulation Schemes: OOK and Q-PPM

In OOK, the data bit is transmitted by pulsing the light source either ‘on’ or ‘off’ during each bit interval. At the detector side, a careful adjustment of threshold has to be done to detect the incoming data bit without an error. In case of Q-PPM, an optical pulse is placed in one of the Q adjacent time slots to represent a data word i.e., each PPM symbol having the signalling interval of length Ts is subdivided into Q slots each of length T=Ts /Q and there are log2(Q) bits associated with each pulse in these slots. The interval Ts is known as PPM symbol duration. Hence the location of pulse determines the word and not the bit. Therefore Q-PPM is more power efficient than OOK and does not require threshold adjustment to make an optimal decision. BER performance of OOK and Q-PPM (Q=4) schemes with M =1, 3 and 7 transmitting antennae for uncorrelated beams are shown in Figs. 4(a) and 4(b), respectively.

It is observed that degradation in the performance of OOK is

more than in Q-PPM with the increase in turbulence level as the required SNR to maintain same BER performance is higher for OOK modulation scheme. The performance improves significantly as the transmit diversity order is increased due to the fact that it effectively reduces the log irradiance variance of the diversity channel by the factor of M. The improvement is more pronounced when the turbulence level is high and it is true for both the modulation schemes.

The BER performance of Q-PPM modulation scheme for a typical case of three uncorrelated transmitting antennae beams and 0.3 is shown in Fig. 5. It is observed from this figure that there is degradation in the link performance as the value of Q increases. It implies that the link performance for Q=2 is better than that of Q=4, 8, 16.....256. Further, there is marginal difference in the performance for Q=2 and 4.

Fig.4 BER versus SNR for (a) OOK and (b) 4-PPM in weak turbulence ( 0.1 and 0. 3) for uncorrelatead beams (i.e., 0) with and without diversity.

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Fig.5 Performance of Q-PPM system for uncorrelated beams (i.e., 0) in weak atmospheric turbulence for different levels of Q.

The BER performance for OOK and 4-PPM modulation schemes with transmit diversity for a correlation of 0.3 is shown in Figs. 6 and 7, respectively. For a typical three transmitting antennae beams, the performance of Q-PPM (Q=2, 8, 32 and 256) for a correlation of 0.3 is shown in Fig.8.

Fig.6 Performance of OOK system with correlation coefficient 0.3 in weak atmospheric turbulence .

IV. COMPREHENSIVE DISCUSSIONS

It is observed from Figs. 1 to 8 and Tables I and II that sub-carrier BPSK requires least SNR for a given performance in weak atmospheric turbulence due to its increased sensitivity. Among non-coherent modulation schemes, Q-PPM gives better performance than OOK in terms of required SNR. A comparative study of coherent (sub-carrier BPSK and QPSK) and non-coherent (OOK and Q-PPM) modulation schemes for a typical case of three transmitting antennae with correlation

Fig.7 Performance of 4-PPM system with correlation coefficient 0.3 in weak atmospheric turbulence.

Fig.8 Performance of Q-PPM system with correlation coefficient 0.3 in weak atmospheric turbulence.

coefficient 0.3 in weak atmospheric turbulence ( 0.3) is shown in Fig. 9.

In all the modulation schemes, the performance improvement with transmit diversity is observed. Also, a significant improvement is seen when the number of transmitting antenna, M is increased from 1 to 3 especially at higher values of atmospheric turbulence for all the modulation schemes. Further increasing the value of M (say M=7) causes improvement in the performance, but level of improvement is marginal. Hence we cannot increase the number of transmitting antennae indefinitely as it leads to saturation of the diversity gain after a certain value of M. Also, with the increase in the correlation coefficient, degradation in the system performance is observed. This brings the need for sufficient separation between transmitting antennae to achieve promised diversity gain from multiple transmitters.

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Fig 9. Comparative study of coherent and non-coherent modulation schemes for three transmitting antennae with correlation coefficient 0.3 in weak

atmospheric turbulence ( 0.3 .

TABLE I

Minimum SNR requirement for sub-carrier BPSK ($) and QPSK (#) modulation schemes at BER=10-6.

Correlation Coefficient

Turbulence level

Number of Transmitting Antennae

M=1 M=3 M=7

0.0 0.1 14.44$ 17.75#

13.82$ 16.87#

13.65$ 16.68#

0.3 19.52$ 22.53#

15.91$ 18.97#

14.67$ 17.69#

0.7 33.93$ 36.93#

22.99$ 26.01#

18.39$ 21.43#

0.3 0.1 14.44$ 17.45#

14.20$ 17.22#

14.12$ 17.13#

0.3 19.52$ 22.53#

18.10$ 21.21#

17.69$ 20.70#

0.7 33.93$ 36.93#

30.05$ 33.06#

28.50$ 31.51#

TABLE II

Minimum SNR requirement for OOK and Q-PPM modulation schemes at BER=10-6.

Corr Coeff

Turb level

Mod Type

Number of Transmitting Antennae

M=1 M=3 M=7

0.0 0.1 OOK 19.73 19.19 19.03 4-PPM 14.74 14.12 13.98

16-PPM 15.29 14.61 14.41 0.3 OOK 24.28 21.11 19.96

4-PPM 20.24 16.32 14.98 16-PPM 21.00 17.02 15.56

0.7 OOK 36.89 27.33 23.24 4-PPM 34.80 23.60 18.86

16-PPM 37.18 24.73 19.78 0.3 0.1 OOK 19.73 19.40 19.24

4-PPM 14.74 14.49 14.41 16-PPM 15.29 15.02 14.93

0.3 OOK 24.28 22.17 21.46 4-PPM 19.96 18.66 18.12

16-PPM 21.00 19.53 18.96 0.7 OOK 36.89 30.72 28.52

4-PPM 34.80 30.79 29.21 16-PPM 37.25 32.56 30.76

V. CONCLUSIONS

The performance of coherent and non-coherent modulation schemes in ground to satellite link has been analyzed using transmit diversity in weak atmospheric turbulence. It is observed that transmit diversity helps to mitigate the turbulence induced fading for all the modulation schemes. It is also observed that diversity plays a major role as the strength of turbulence increases. This improvement becomes lesser due to spatial correlation and that brings the need for efficient separation among the transmitters. Sub-carrier BPSK outperforms all the modulation schemes in terms of required SNR.

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