Research Article  Open Access
Antonio GarcíaZambrana, Carmen CastilloVázquez, Beatriz CastilloVázquez, "Improved BDF Relaying Scheme Using Time Diversity over Atmospheric Turbulence and Misalignment Fading Channels", The Scientific World Journal, vol. 2014, Article ID 213834, 7 pages, 2014. https://doi.org/10.1155/2014/213834
Improved BDF Relaying Scheme Using Time Diversity over Atmospheric Turbulence and Misalignment Fading Channels
Abstract
A novel bitdetectandforward (BDF) relaying scheme based on repetition coding with the relay is proposed, significantly improving the robustness to impairments proper to freespace optical (FSO) communications such as unsuitable alignment between transmitter and receiver as well as fluctuations in the irradiance of the transmitted optical beam due to the atmospheric turbulence. Closedform asymptotic biterrorrate (BER) expressions are derived for a 3way FSO communication setup. Fully exploiting the potential timediversity available in the relay turbulent channel, a relevant better performance is achieved, showing a greater robustness to the relay location since a high diversity gain is provided regardless of the sourcedestination link distance.
1. Introduction
Atmospheric freespace optical (FSO) transmission using intensity modulation and direct detection (IM/DD) can be considered as an important alternative to consider for next generation broadband in order to support large bandwidth, excellent security, and quick setup [1]. However, this technology is not without drawbacks. Atmospheric turbulence causes fluctuations in the irradiance of the transmitted optical beam, which is known as atmospheric scintillation, severely degrading the link performance [2]. Since FSO systems are usually installed on high buildings, building sway causes vibrations in the transmitted beam, leading to an unsuitable alignment between transmitter and receiver and, hence, a greater deterioration in performance. Cooperative transmission can significantly improve the performance by creating diversity using the transceivers available at the other nodes of the network. Recently, several works have investigated the adoption of this technique in the context of FSO systems [3–9], being recognized as a very promising solution for future adhoc optical wireless systems. In [4, 5] a 3way FSO communication setup is proposed to implement a cooperative protocol in order to improve spatial diversity without much increase in hardware. In [9], following the bitdetectandforward (BDF) cooperative protocol presented in [4], the analysis is extended to FSO communication systems using IM/DD over atmospheric turbulence and misalignment fading channels, considering cooperative communications with BDF relaying and equal gain combining (EGC) reception. In this paper, a novel BDF relaying scheme using timediversity in the relay channel is proposed. Closedform asymptotic bit errorrate (BER) expressions are obtained for a 3way FSO communication setup, showing a significant improvement in the robustness to impairments proper to these systems such as unsuitable alignment between transmitter and receiver as well as fluctuations in the irradiance of the transmitted optical beam due to the atmospheric turbulence. Fully exploiting the potential timediversity available in the relay turbulent channel, the superiority of the proposed scheme is corroborated if compared with the traditional BDF cooperative protocol [4, 9], since a greater robustness is provided to the relay location, maintaining a high diversity gain regardless of the sourcedestination link distance. In contrast to the traditional BDF, wherein the cooperative strategy works in two phases or transmission frames and the relay node detects each code bit of the cooperative signal individually and forwards it to the destination, the novel BDF relaying scheme here proposed is based on a new cooperative protocol working in three phases that implements timediversity in the relay turbulent channel by using repetition coding.
2. System and Channel Model
We adopt a threenode cooperative system based on three separate fullduplex FSO links, as shown in Figure 1, assuming intensitymodulated laser sources and ideal noncoherent (directdetection) receivers.
The cooperative strategy works in three phases or transmission frames, as shown in Table 1. In the first phase, the nodes and send their own data to each other and the destination node ; that is, the node () transmits the same information to the nodes () and . In the second transmission frame, the nodes and send again the same information to each other delayed by the expected fade duration and, hence, assuming that channel fades are independent and identically distributed (i.i.d.). In the third phase, the node (or ) sends the received data from its partner (or ) in previous frames to the node .

Following the BDF cooperative protocol, the relay node ( or ) detects each code bit to “0” or “1” based on repetition coding and sends the bit with the new power to the destination node . When repetition coding is used in the sourcerelay link transmission during the first and second phases, the information is detected during each transmission frame, combining with the same weight two noisy faded signals. In this way, a diversity gain of two is achieved for this link and, hence, a better performance compared with the traditional BDF cooperative protocol [4, 9]. It must be noted that the symmetry for nodes and assumed in this FSO communication setup and the fact that one transmission frame is overlapped imply that no rate reduction is applied; that is, the same information rate can be considered at the destination node compared to the direct transmission link without using any cooperative strategy. It is here assumed that all the bits detected at the relay are always resent regardless of these bits being detected correctly or incorrectly.
For each link of the three possible links in this threenode cooperative FSO system, the instantaneous current in the receiving photodetector corresponding to the information signal transmitted from the laser can be written as where is the detector responsivity, assumed hereinafter to be the unity, represents the optical power supplied by the source, is the equivalent realvalued fading gain (irradiance) through the optical channel between the laser and the receive aperture, and denotes the deterministic propagation loss. The atmospheric loss is determined by the exponential BeersLambert law as , where is the link distance and is the attenuation coefficient. It is given by , where is the visibility in kilometers, is the wavelength in nanometers, and is a parameter related to the visibility, with when . is assumed to include any frontend receiver thermal noise as well as shot noise caused by ambient light much stronger than the desired signal at the detector. It can usually be modeled to high accuracy as AWGN with zero mean and variance , that is, , independent of the on/off state of the received bit. We use , , , and to denote random variables and , , , and their corresponding realizations. The irradiance is susceptible to atmospheric turbulence and pointing error effects. It is considered to be a product of two independent random variables; that is, , and representing the attenuation due to atmospheric turbulence and the attenuation due to geometric spread and pointing errors, respectively. To consider a wide range of turbulence conditions, the gammagamma turbulence model proposed in [2] is here assumed. Regarding to the impact of pointing errors, we use the general model of misalignment fading given in [10] by Farid and Hranilovic, wherein the effect of beam width, detector size, and jitter variance are considered. A closedform expression of the combined probability density function (PDF) of was derived in [11] in terms of the Meijer’s function [12, equation (9.301)]. This PDF appears to be cumbersome to use in order to obtain simple closedform expressions in the analysis of FSO systems. To overcome this inconvenience, the PDF is approximated by a single polynomial term as , based on the fact that the asymptotic behavior of the system performance is dominated by the behavior of the PDF near the origin [9]. Different expressions for and , depending on the relation between the jitter variance and turbulence conditions, can be written aswhere is the wellknown Gamma function and and can be directly linked to physical parameters through the following expressions: with being the Rytov variance, which is a measure of optical turbulence strength. Here, is the optical wave number, is the wavelength, and is the link distance in meters. stands for the altitudedependent index of the refractive structure parameter and varies from for strong turbulence to for weak turbulence [2]. Assuming a Gaussian spatial intensity profile of beam waist radius, , on the receiver plane at distance from the transmitter and a circular receive aperture of radius , is the ratio between the equivalent beam radius at the receiver and the pointing error displacement standard deviation (jitter) at the receiver, , , , and is the error function. Hereinafter, the fading coefficient for the paths , , and  is indicated by , , and , respectively.
3. ErrorRate Performance Analysis
Here, it is assumed that the average optical power transmitted from each node is , being adopted an onoff keying (OOK) signaling. This scheme is based on a constellation of two equiprobable points in a onedimensional space with an Euclidean distance of . Here, the parameter is the bit period and represents the square of the increment in Euclidean distance due to the use of a pulse shape of high peaktoaverage optical power ratio (PAOPR) [9]. According to (1), the statistical channel model corresponding to the  link assuming repetition coding with EGC during the first and second frames can be written as with and . Assuming channel side information at the receiver, the conditional BER at the node is given by where represents the sum of variates , is the Gaussian function, and represents the received electrical SNR in absence of turbulence when the classical rectangular pulse shape is adopted for OOK formats. Since the variates and are independent, knowing that the resulting PDF of their sum can be determined by using the moment generating function of their corresponding PDFs, obtained via singlesided Laplace and its inverse transforms, approximate expression for the PDF, , of the combined variates can be easily derived as Hence, the average BER, , can be obtained by averaging over the previous PDF [12, equation (6.281)], obtaining the corresponding closedform asymptotic solution for the BER as can be seen in where the value of the parameters and depends on the relation between and as obtained in (2a) and (2b), corroborating not only that the diversity order corresponding to the sourcerelay link is independent of the pointing error when but also the fact that the diversity order has been increased twice if compared to the traditional BDF cooperative protocol [4, 9]. Once the error probability at the node is known, two cases can be considered to evaluate the BER corresponding to the BDF cooperative protocol here proposed depending on the fact that the bit from the relay  is detected correctly or incorrectly. In this way, the statistical channel model corresponding to the BDF cooperative protocol, that is, the bits received at directly from  link and from the relay , can be written as with and , where represents the random variable corresponding to the information detected at and, hence, when the bit has been detected correctly at and when the bit has been detected incorrectly. In a similar way to that in [9], but here considering the path loss, we can obtain the corresponding closedform asymptotic solution for the BER when the bit is correctly detected at , , and when the bit is incorrectly detected at , , as follows:
Once the error probability at the node is known and considering these two cases, the BER corresponding to the BDF cooperative protocol here proposed is given by
This expression can be simplified taking into account the asymptotic behavior previously obtained in (7) and (9) as follows: Taking into account these expressions, the adoption of the BDF cooperative protocol here analyzed translates into a diversity order gain, , relative to the noncooperative link  of
Comparing with [9, equation ], it must be noted that a factor of 2 is included in relation to the diversity order depending on the sourcerelay link because of repetition coding. The main aspect to consider in order to optimize the errorrate performance is the relation between and as obtained in (2b) for each link, corroborating that the diversity order is independent of the pointing error when . Once this condition is satisfied an optimization analysis about (13) is required, evaluating if the diversity order corresponding to the BDF cooperative protocol is determined by the sourcedestination and relaydestination links or by the sourcerelay link. For better understanding of the impact of the configuration of the threenode cooperative FSO system under study, the diversity order gain in (13) as a function of the horizontal displacement of the relay node, , is depicted in Figure 2 when a wide range of sourcedestination link distances and different relay locations are assumed. Here, the diversity order gain corresponding to the traditional BDF cooperative protocol [9] is also included in order to show the improvement in performance achieved when repetition coding is assumed in the sourcerelay link transmission. It is easy to deduce that the traditional BDF protocol only provides cooperative diversity for shorter sourcerelay distances since the performance is very related to the sourcerelay link quality, being strongly vulnerable to its turbulence conditions. However, the BDF protocol here proposed presents a greater robustness to the relay node location, allowing for choosing a potential relay node in a greater area while maintaining a high cooperative diversity regardless of the sourcedestination link distance.
(a)
(b)
(c)
(d)
Additionally, it can be deduced from (13) that the diversity order gain, , is lower as the value of is increased, presenting a maximum value wherein the two profiles related to the expressions and intersect. A numerical analysis of the location of the maximum value of is displayed in Figure 3 for different relay locations and sourcedestination link distances from 2 to 8 km.
In agreement with the results displayed in Figure 2, the location of the maximum value of is proportional to the sourcedestination link distance, , with an initially increasing value of as the value of is increased. It can be numerically shown that the location of the maximum value of is initially achieved at 56.2% of the sourcedestination link distance , later increasing this value as is increased until is 70.6% of . Next, as the value of is increased, the maximum value of is located at a value of lower than . In Figure 3, a similar performance for the BDF cooperative protocol here proposed is corroborated regardless the value of , presenting a more favorable relay location when is close to and , in excellent agreement with the results displayed in Figure 2 for values of of 3, 6, 9, and 12 km. Additionally, the performance corresponding to the traditional BDF cooperative protocol is also included in order to corroborate the greater vulnerability to the relay location, showing that its adoption is not advantageous for sourcerelay distances above 2 km. The improvement in performance can be easily corroborated by the fact that, even when the available diversity order is dependent on the relay location, this is now related to the expression , being twice as in the traditional BDF protocol, fully exploiting the potential timediversity available in the turbulent channel corresponding to the sourcerelay link. The results corresponding to this asymptotic analysis with rectangular pulse shapes and are illustrated in Figure 4, when different relay locations for sourcedestination link distances {3 km, 6 km} are assumed together with values of normalized beamwidth and normalized jitter of and . The parameters and are calculated from (3), and values of and are adopted. It must be commented that the impact of the deterministic propagation loss is here considered, assuming clear weather conditions with visibility of 16 km. Monte Carlo simulation results are furthermore included as a reference, confirming the accuracy and usefulness of the derived results. Due to the long simulation time involved, simulation results only up to are included. Simulation results corroborate that asymptotic expressions here obtained lead to simple bounds on the bit error probability that get tighter over a wider range of SNR as the turbulence strength increases. Additionally, we also consider the performance analysis for the direct path link (noncooperative link ) to establish the baseline performance as well as BER performance corresponding to the traditional BDF cooperative protocol [9]. It can be corroborated that these BER results are in excellent agreement with previous results shown in Figure 2 in relation to the diversity order gain achieved for this 3way FSO communication setup. In this way, diversity gains of 3.18 and 2.6 are achieved when km and relay locations of (km; km) and ( km; km), respectively, in contrast to the diversity gains of 1.84 and 1.3 are achieved by the traditional BDF cooperative protocol. Analogously, it can be seen that diversity gains of 2.07 and 2.18 are obtained when km and relay locations of ( km; km) and ( km; km), respectively, in contrast to the diversity gains of 1.31 and 1.09 are achieved by the traditional BDF cooperative protocol. It is corroborated that the traditional BDF protocol only provides cooperative diversity for shorter sourcerelay distances since its performance is very related to the sourcerelay link quality, especially when greater sourcedestination distances are considered. From previous results, it can be concluded that not only a significant improvement in performance has been obtained by increasing the diversity order but also that a greater robustness is now achieved regardless of the sourcedestination link distance.
(a)
(b)
4. Conclusions
In this paper, a novel bitdetectandforward relaying scheme using timediversity in the relay channel is proposed, significantly improving the robustness to impairments proper to these systems such as unsuitable alignment between transmitter and receiver as well as fluctuations in the irradiance of the transmitted optical beam due to the atmospheric turbulence. Closedform asymptotic BER expressions are derived for a 3way FSO communication setup when the irradiance of the transmitted optical beam is susceptible to either a wide range of turbulence conditions or pointing errors. Fully exploiting the potential timediversity available in the relay turbulent channel, a relevant better performance is achieved, compared with the traditional BDF cooperative protocol [4, 9], showing a greater robustness to the relay location since a high diversity gain is provided regardless of the sourcedestination link distance. Additionally, asymptotic expressions are used to determine a more favorable relay location.
Conflict of Interests
The authors declare that there is no conflict of interests regarding the publication of this paper.
Acknowledgment
The authors wish to acknowledge the financial support given by the Spanish MINECO Project TEC201232606.
References
 V. W. S. Chan, “Freespace optical communications,” Journal of Lightwave Technology, vol. 24, no. 12, pp. 4750–4762, 2006. View at: Publisher Site  Google Scholar
 L. Andrews, R. Phillips, and C. Hopen, Laser Beam Scintillation with Applications, Bellingham, Wash, USA, 2001.
 M. Safari and M. Uysal, “Relayassisted freespace optical communication,” IEEE Transactions on Wireless Communications, vol. 7, no. 12, pp. 5441–5449, 2008. View at: Publisher Site  Google Scholar
 M. Karimi and M. NasiriKenari, “BER analysis of cooperative systems in freespace optical networks,” Journal of Lightwave Technology, vol. 27, no. 24, pp. 5639–5647, 2009. View at: Google Scholar
 M. Karimi and M. NasiriKenari, “Outage analysis of relayassisted freespace optical communications,” IET Communications, vol. 4, no. 12, pp. 1423–1432, 2010. View at: Publisher Site  Google Scholar
 C. AbouRjeily and A. Slim, “Cooperative diversity for freespace optical communications: transceiver design and performance analysis,” IEEE Transactions on Communications, vol. 59, no. 3, pp. 658–663, 2011. View at: Publisher Site  Google Scholar
 C. AbouRjeily and S. Haddad, “Cooperative FSO systems: performance analysis and optimal power allocation,” Journal of Lightwave Technology, vol. 29, no. 7, Article ID 5713800, pp. 1058–1065, 2011. View at: Publisher Site  Google Scholar
 M. R. Bhatnagar, “Performance analysis of decodeandforward relaying in GammaGamma fading channels,” IEEE Photonics Technology Letters, vol. 24, no. 7, pp. 545–547, 2012. View at: Publisher Site  Google Scholar
 A. GarcíaZambrana, C. CastilloVázquez, B. CastilloVázquez, and R. BoludaRuiz, “Bit detect and forward relaying for FSO links using equal gain combining over gammagamma atmospheric turbulence channels with pointing errors,” Optics Expresss, vol. 20, no. 15, pp. 16394–16409, 2013. View at: Google Scholar
 A. A. Farid and S. Hranilovic, “Outage capacity optimization for freespace optical links with pointing errors,” Journal of Lightwave Technology, vol. 25, no. 7, pp. 1702–1710, 2007. View at: Publisher Site  Google Scholar
 H. G. Sandalidis, T. A. Tsiftsis, and G. K. Karagiannidis, “Optical wireless communications with heterodyne detection over turbulence channels with pointing errors,” Journal of Lightwave Technology, vol. 27, no. 20, pp. 4440–4445, 2009. View at: Publisher Site  Google Scholar
 I. S. Gradshteyn and I. M. Ryzhik, Table of Integrals, Series and Products, Academic Press, 7th edition, 2007.
Copyright
Copyright © 2014 Antonio GarcíaZambrana et al. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.