1. Introduction

FSO is a potential telecommunication platform that has achieved tremendous development on bit rate capacity, link distance, and integrated in multi-system [1-6]. It has attractive benefit such as free-licensed, low-cost, high-security, and high rate transmission [7]. It has major drawbacks that the SNR and BER performance is strongly influenced by noise modulation of atmospheric turbulence [8]. Some impacts as the results of atmospheric turbulence modulation on optical propagation are beam wander and spatial noise effects [9]. Those lead to fluctuation of amplitude and phase in optical propagation. Those also increase to scale-up with propagation path length and turbulence level on the atmosphere. Through these, signal intensity goes to fluctuation on focus spot of receiver lens randomly. Unfortunately, PD receives those impact in the form of fading, large noise bandwidth, and misalignment detection. It produces lower signal power which frequently falls below a the prescribed threshold level of PD and maximum noise as well. These lead to degradation of SNR. Hence, the lower SNR contributes to higher order of BER. Moreover, SNR and BER performance degrades in maximum by the presence of turbulence effects.

Recently, several methods have been developed to enhance SNR and BER performance on FSO under influenced of atmospheric turbulence. Spatial-diversity (SD), time-diversity (TD), cooperative-diversity (CD), photon detection technique (PDT), amplification method, and adaptive optics (AO) have been investigated so far in order to solve turbulence effects intensively [10-15]. Those methods pay great concern to minimize degradation SNR and BER performance. Generally, those aforementioned methods implement DD for retrieving a signal without an optical treatment previously in a receiver plane. Contrary to the benefit of FSO that has low-cost implementation, those aforementioned methods are quite complex and high-cost. SD offers enhancement SNR and BER performance with multiple system of transmitter and receiver that requires complex electronics of equal gain combiner [10]. TD provides method of signal transmission in multi-periode of time that also requires complex signal processing in the receiver system [11]. CD offers smart combination of spatial- and time-diversity that also requires complex algorythm as well [12]. PDT offers higher sensitivity for lower signal while noise does not taken into account to be suppressed optically [13]. Optical amplification that uses erbium-doped fiber amplifier commonly, also does not provide optical method to enhance signal intensity with minimum noise [14]. Moreover, AO offers enhancement of signal intensity with processing of optical propagation technique but beam wander does not taken into consideration as the serious problem to be suppressed [15]. By taking into consideration that beam wander and spatial noise effects can be suppressed optically at focus spot of receiver lens, the OSF can be implemented as a detection method before signal is received by PD. Thus, implementation of the OSF for suppressing noise that is caused by turbulence effects is the motivation of this work in order to enhance SNR and BER performance.

In this paper, the OSF is implemented on FSO of full-duplex transmission at wavelength of 1550 nm. It is a simple- and low-cost method for suppression of beam wander and spatial noise effects. It can be integrated with the aforementioned methods such as optical amplification or SD. It also has competitive benefit for bit rate capacity processing in comparison to TD. The characteristics of turbulence effects are random phenomena and independent process as well. Meanwhile, turbulence effects cannot be treated as a separate process in optical propagation. Thus, beam wander and spatial noise effects cannot be solved separately in order to enhance SNR and BER performance. Regarding those, the OSF is designed to suppress beam wander and spatial noise effects simultaneously. The OSF is composed of cone reflector and pinhole [16] that is installed on focus spot of receiver lens before PD. Cone reflector is designed to suppress beam wander that has random angle of focus spot through directed reflectance radially into pinhole diameter [17]. Pinhole is designed to suppress spatial noise through governing Fresnel diffraction on focus spot. Through suppression of beam wander and spatial noise effects simultaneously, fluctuation of signal intensity and noise reception into PD can be minimized. Thus, as the continuation work in [16, 17], SNR and BER performance enhancement using the OSF is reported through calculations ans experiment.

2. Noise Suppression to Enhance SNR and BER Performance Using the OSF

In Fig. 1, conceptually, the OSF [16, 17] has benefit among ideal of aperture averaging [18] and DD [19]. Technically, ideal of aperture averaging receives incident of optical propagation on receiver lens through multiple reception where . Statistically, it produces narrowest noise bandwidth with highest probability of signal intensity. DD that has a requirement for lower diameter of receiver lens than incident of optical propagation where produces wider noise bandwidth and lower probability of mean irradiance. In comparison to DD, the OSF that has reception of optical propagation also through suppression of beam wander and spatial noise effects produces competitive probability of signal intensity with minimum noise bandwidth. However in comparison to ideal of aperture averaging, the OSF has some advantages that are simplicity for reception of optical propagation as in DD, competitive probability of signal intensity, and narrow noise bandwidth.

Figure 1. The probability of mean irradiance and noise bandwidth for ideal of aperture averaging , direct detection , and the OSF on FSO

Figure 2. The optical system for suppression of beam wander and spatial noise effects in FSO under atmospheric turbulence. It is composed of a transmitter plane , a receiver lens plane , the OSF plane , PD plane , and is the origin where optical propagation from laser source directs from into [17]

In Fig. 2, The incident of optical propagation that modulates noise on receiver lens is focused onto pinhole radius of . Focus spot that coincidence on goes fading where fluctuation of signal intensity goes higher and falls below . Unfortunately, beam wander also leads misdetection into PD frequently. In order to suppress noise, The OSF governs Fresnel diffraction and reflectance of beam wander on focus spot before PD. The mean of signal intensity as the output of the OSF at under atmospheric turbulence is given below [17],

(1)

where brackets denotes mean value. In Eq. (1), , , , and are radius coordinate at , the effective aperture radius of receiver lens on , focus spot radius, reflectance beam wander angle from cone reflector into pinhole diameter with respect to optical axiz as shown in Fig. 2, Bessel function of the first kind, free-space irradiance of optical propagation that incident on receiver lens of , the effective of optical propagation that incident on receiver lens for path length , Sthrel ratio, spatial frequency at radius on as the function of spacing distance , Rytov variance for propagation path length , and wave number, respectively.

In Eq. (1), that is reflectance angle from cone reflector for incident beam wander angle has a range of to as stated below [17],

(2)

(3)

(4)

where , and are maximum angle of focus spot from receiver lens of that incident at for condition of non-turbulent atmosphere, hard diameter of receiver lens, pinhole diameter, tilt angle of cone reflector, reflectance angle with respect to tilt plane of cone reflector, and length of focus spot, respectively.

Turbulence effects that arise in optical propagation lead to fluctuation of signal intensity and maximum noise modulation. As shown in Eq. (1), Sthrel ratio characterizes beam wander and spatial noise on incident of optical propagation . Beam wander that arises also causes beam spreading where focus spot moves wider arround the optical axis randomly. Hence, focus spot experiences long-term beam spreading. Meanwhile, short-term beam spreading or spatial noise also arises as well. The signal intensity in focus spot goes lower as stated in Eq. (1) by term of . It means signal intensity goes fading where fluctuates randomly by the presence of beam wander and spatial noise. Hence, PD produces minimum of signal power and maximum noise. The OSF which consists of pinhole with radius of governs diffraction at . As shown by Eq. (1), pinhole produces near-field distribution of Fresnel diffraction at of . By those mechanism, signal intensity from pinhole is minimum of noise modulation.

By suppression of beam wander and spatial noise effects on focus spot, PD receives fundamental component of diffraction in optimum since and . It produces the mean of signal power as stated below [17],

(5)

where is the circular aperture function of pinhole that is given below [17],

(6)

where and is Bessel function of second kind. In comparison to DD [18, p.459], in Eq. (5) is increased by term of . The mean of signal power from the OSF is produced higher by PD. Term of in Eq. (5) works in optimum for noise suppression where . Term of in Eq. (5) also provides suppression of beam wander in order to minimize misalignment detection that is caused by random displacement of focus spot. It means, the OSF suppresses beam wander and spatial noise effects simultaneously. Thus, PD produces optimum of signal power with minimum noise.

Regarding enhancement of received signal power by PD in Eq. (5) as the compensation for confinement of signal intensity fluctuation in narrow region of pinhole through reflectance of cone reflector, degradation can be minimized by the OSF. is increased by suppression of signal power ratio, . The OSF minimizes those ratio in order to enhance as given below [20],

(7)

where and are optimum value of and signal power in the absence of atmospheric turbulence, respectively. In Eq. (7), the irradiance flux variance has range value of 0-1 for weak to strong turbulence level. Frequently, signal power falls below . The OSF enhances value of . Thus PD produces signal power beyond . Signal power ratio is decreased by the OSF as stated below,

(8)

The optimum suppression of produces that approximate to . In comparison to DD that [18, p. 460], this ratio is decreased into minimum value by the OSF as shown in Eq. (8). Thus, the OSF gives advantage to minimize signal power ratio by suppressing beam wander and spatial noise effects simultaneously.

Generally, probability density function uses gamma-gamma distribution as the channel model for FSO at atmospheric turbulence [18, p. 462]. is the probability of signal unit that is influenced by and as the representations of small- and large-scale of atmospheric turbulence, respectively. enhancement by the OSF minimizes the probability of . Based on [20], can be suppressed into lower order through enhancement. Furthermore, of OOK modulation method is derived from [20] with regards to integral solution in [21]. is stated below,

(9)

in Eq. (9) is determined by and . In order to achieve lower order of under turbulence effects, must be increased higher. Since the OSF suppresses noise, signal intensity increases higher than in DD. Hence, PD produces optimum of signal power rather than noise. It means the OSF decreases the signal power ratio of in order to enhance . Furthermore, by the improvement of , also decreases into lower order as well. In comparison to DD, is produced lower by the OSF, since is increased by suppression of as stated in Eq. (8).

3. Experimental Set-up

In Fig. 3, the experiment of FSO with full-duplex transmission implement wavelength, of . Bit rate transmission of 1 Gbps with OOK modulation is also used. Optical propagations are separated into box of turbulence simulator (BTS). For reference, optical propagation of backward-directed from beam collimator BC-1 into receiver lens-1 is conditioned with non-turbulent media. Optical propagation of forward-directed of from beam collimator BC-2 into receiver lens-2 is induced by turbulence media in BTS. The properties of optical propagation are of , of , and of . of is transmitted out from BC-2 into receiver lens-2. The properties of receiver lens are of and of . of is for PD-1 and PD-2. The optical power meter (OPM) and BER tester are used on experiment for and measurements, respectively.

Figure 3. FSO of full-duplex transmission using wavelength of that transmitting 1 Gbps of data rate on turbulence media of BTS while for measurement of performance, OPM (Optical Power Meter) and BER tester are used

In Fig. 4, BTS that provides turbulence media is designed for optical propagation of forward-directed in order to achieve beam wander and spatial noise modulation randomly.

For constant parameters of cone reflector and , the OSF is designed with various pinhole diameter that are , , , and for , , , and , respectively. Based on Eqs. (3) and (4) for and both contant values and , the range of beam wander that can be received by cone reflector is to . In order to produce optimum reflection at 1.55 µm, the OSF is made from material of silver [22]. Furthermore, in order to achieve Fresnel diffraction, the OSF is installed on focus spot of receiver lens where pinhole is at on and PD is placed on near to pinhole output of the OSF where spacing distance is at the order of .

Figure 4. Box of turbulence simulator (BTS) providing turbulence media to induce optical propagation of forward-directed. BTS is designed for volume dimension of where turbulence media is constituted by the mixing flows of high temperature-gradient. The steam at of with low-speed and cold air at of with wind-speed of are flowed altogether along the BTS volume. Furthermore, the flows are broken-up by ailerons that is installed along the path length inside BTS [17]

4. Results and Discussion

The calculations of and for DD and the OSF are shown in Figs. 6 and 7. is chosen as reference for analysis. The calculations are based on values of index structure, . The properties of optical propagation are set based on the experiment. Based on the , , and that are stated in Eqs. (3) and (4), , , and are chosen as beam wander angles. and are set constant for calculations. is chosen higher than , since it is dominant factor for SNR and BER performance degradation under atmospheric turbulence.

In Figs. 5 and 6, the performance of DD degrades in maximum by the presence of beam wander and spatial noise effects where and . The OSF improves degradation that presents in DD. increases linear as of the OSF goes lower for beam wander angles of , , and . The performance of FSO for is better than at and . Beam wander angle is at the range that is received by pinhole directly without reflectance of cone reflector. The range of beam wander angle for direct reception by pinhole is . While range of beam wander angle for reflectance by cone reflector is . However, for and SNR and BER performance is achieved better than DD. Recalled Eq. (8), determines value of . Thus, the OSF produces lower value of for lower . performance for the OSF is better than DD since goes lower as well. The OSF improves through suppression of beam wander and spatial noise effects simultaneously. It governs Fresnel diffraction as can be seen by the circular aperture function of pinhole that is stated in Eq. (6). Hence the OSF minimizes since goes lower. Even for larger pinhole diameter , is produced higher by the OSF than DD for , , and . The OSF also improves degradation as goes lower as well. It produces higher in order to achieve lower order of for , , and as well. Suppression of beam wander and spatial noise effects by the OSF is achieved through minimizing signal power ratio as shown by Eq. (8).

Figure 5. The calculation results where vs. is from the OSF for , , and , is from DD and

Figure 6. The calculation results where vs. is from the OSF method for , and , is from DD, and

In Fig. 7, experiment results of vs. for DD and the OSF are shown. of DD is 34.9 dB. Regarding , this performance quite degrades by the presence of beam wander and spatial noise modulation that arise randomly in BTS. The OSF improves those degradation in scale of 2.5 dB, 3.5 dB, 3.8 dB, and 4.2 dB for , , , and , respectively. improvement by the OSF is better than DD. But improvement by different of do not contribute to higher value. The OSF for each of tend to produce the same value of . For example, and do not produce high different value of . Only produces highest that approximates . However, the experiment result in Fig. 8 shows the same trend as the calculation in Fig. 6, that is increased by the OSF since goes lower.

In Fig. 8, experiment results of vs. for DD and the OSF method are shown. of DD is produced at 1.910^-5. Regarding = 1.010^-13 at , those performance quite degrades also. The OSF improves degradation in scale of 10^-2, 10^-4, 10^-6, and 10^-7 for , , , and , respectively. improvements by different of are significant. They achieve in scale range of 10^-1 to 10^-5 for to . produces that approximate to at . Moreover, Fig. 8 shows the same trend as Fig. 7, that is decreased to lower order by the OSF since goes lower as well.

Figure 7. The experiment results where vs. from the OSF, is from DD, and

Figure 8. The experiment results where vs. is from the OSF, is from DD, and

For long propagation path where beam wander and spatial noise are modulated higherly, the OSF is a potential detection method on FSO to overcome fading, noise, and misalignment of detection undergo randomly. In order to suppress noise optimally for long propagation path, the circular aperture function can be optimized by considering the ratio of pinhole diameter and spacing distance between the OSF and PD. Thus, term of in Eq. (2), leads to . Furthermore, for larger beam wander angle , the tilt angle of cone reflector also has significant contribution to reflect random displacement of focus spot. In order to fullfill this, parameters for cone reflector must consider term of of Eq. (2). Thus, maximum tilt angle of cone reflector is . Hence, wider range of to can be received by cone reflector largely. By considering those aforementioned conditions, the OSF brings some advantages such as noise suppression in optimum and fading in minimum. Moreover, misalignment of detection that is caused by larger beam wander angle can be minimized by cone reflector as well.

5. Conclusions

The OSF enhances SNR and BER performance on FSO as shown by results of calculation and experiment. In comparison to DD, SNR and BER performance by the OSF is produced better. Based on both calculations and experiment, increases higher and also decreases to lower order as pinhole diameter of the OSF goes lower. From the calculations, the range of beam wander angle that can be received by cone reflector of the OSF is while for is received by pinhole directly without reflectance. Thus, the OSF receives beam wander angle in the range of . From the experiment, increases from 2.5 to 4.2 and decreases from 10^-7 to 10^-12. The OSF suppresses noise in narrow area for minimizing fluctuation of signal intensity. Thus, PD produces optimum of signal power and minimum noise.

ACKNOWLEDGEMENTS

The authors acknowledge Mr. Surma in Opto-Electrotechnique and Laser Application of Universitas Indonesia for his contribution in Lab. facilities.