Performance analysis of packet layer FEC codes and interleaving in FSO channels
2017; Institution of Engineering and Technology; Volume: 11; Issue: 13 Linguagem: Inglês
10.1049/iet-com.2016.1320
ISSN1751-8636
AutoresJunnan Liu, Xingjun Zhang, Keith Blow, Scott Fowler,
Tópico(s)Advanced Optical Network Technologies
ResumoIET CommunicationsVolume 11, Issue 13 p. 2042-2048 Research ArticleFree Access Performance analysis of packet layer FEC codes and interleaving in FSO channels Junnan Liu, Junnan Liu Department of Computer Science and Technology, Xi'an Jiaotong University, Xi'an, 710049 People's Republic of ChinaSearch for more papers by this authorXingjun Zhang, Corresponding Author Xingjun Zhang xjzhang@mail.xjtu.edu.cn Department of Computer Science and Technology, Xi'an Jiaotong University, Xi'an, 710049 People's Republic of ChinaSearch for more papers by this authorKeith Blow, Keith Blow School of Engineering and Applied Science, Aston University, Birmingham, B4 7ET UKSearch for more papers by this authorScott Fowler, Scott Fowler Department of Science and Technology, Linköping University, Campus, Norrköping, SE-601 74 SwedenSearch for more papers by this author Junnan Liu, Junnan Liu Department of Computer Science and Technology, Xi'an Jiaotong University, Xi'an, 710049 People's Republic of ChinaSearch for more papers by this authorXingjun Zhang, Corresponding Author Xingjun Zhang xjzhang@mail.xjtu.edu.cn Department of Computer Science and Technology, Xi'an Jiaotong University, Xi'an, 710049 People's Republic of ChinaSearch for more papers by this authorKeith Blow, Keith Blow School of Engineering and Applied Science, Aston University, Birmingham, B4 7ET UKSearch for more papers by this authorScott Fowler, Scott Fowler Department of Science and Technology, Linköping University, Campus, Norrköping, SE-601 74 SwedenSearch for more papers by this author First published: 22 September 2017 https://doi.org/10.1049/iet-com.2016.1320Citations: 1AboutSectionsPDF ToolsRequest permissionExport citationAdd to favoritesTrack citation ShareShare Give accessShare full text accessShare full-text accessPlease review our Terms and Conditions of Use and check box below to share full-text version of article.I have read and accept the Wiley Online Library Terms and Conditions of UseShareable LinkUse the link below to share a full-text version of this article with your friends and colleagues. Learn more.Copy URL Share a linkShare onFacebookTwitterLinkedInRedditWechat Abstract The combination of forward error correction (FEC) and interleaving can be used to improve free-space optical communication systems. Recent research has optimised the codeword length and interleaving depth under the assumption of a fixed buffering size; however, how the buffering size influences the system performance remains unsolved. This study models the system performance as a function of buffering size and FEC recovery threshold, which allows system designers to determine optimum parameters in consideration of the overhead. The modelling is based on statistics of temporal features of correct data reception and burst error length through the measurement of the channel good time and outage time. The experimental results show good coherence with the theoretical values. This method can also be applied in other channels if a continuous-time-Markov-chain model of the channel can be derived. Nomenclature p the probability of transition from good state to bad state in DTMC model q the probability of transition from bad state to good state in DTMC model the correlation factor of the channel , , the p, q, after interleaving , the mean ON/OFF state holding time (ON/OFF time) the transmission time of one packet n FEC codeword length d interleaving depth S FEC buffering size near-perfect interleaving factor the smallest near-perfect interleaving depth k the number of information packets in an n-packet codeword the inefficiency factor of FEC the probability of event X happens the system performance factor (1 - packet loss ratio) the largest tolerable ratio of erasures in an FEC codeword r the ratio of OFF time over the total observing time the expected ratio of OFF time over the total time , the ON/OFF state holding time , the PDF of the ON/OFF state holding time N the number of pairs of ON and OFF transitions the PDF of r when observing N pairs of ON and OFF transitions the CDF of r when observing N pairs of ON and OFF transitions , the sum of the observed ON/OFF time within sampling size N , the value of , the required system performance the bandwidth efficiency C the overall overhead , , the overhead of buffering time, decoding time, and associated costs , , the factors of different kinds of overhead a, b, c parameters of curve fitting 1 Introduction As the demand of data traffic grows dramatically, the research of a high-bandwidth and economical approach of communication becomes more and more urgent and important. Radio frequency is limited in capacity and costly, since most sub-bands are exclusively licenced [1]. Optical communication has high bandwidth, but the fibre deployment is expensive, especially in extreme geographical conditions. Free-space optical (FSO) communication, which benefits from its high rate, flexible installation and licence-free spectrum, is widely discussed for its prominence when used in both backbone network and the 'last mile' problem [2]. FSO is mainly applied to convert military applications [3, 4] and space applications including inter-satellite and deep-space links. In the meantime, its terrestrial application, which provides high-speed connections for disaster recovery and temporary networks, kept being studied over the decades [5–7]. Recent successes of FSO researches [8–10] indicate that the technology is ready for practical application because the devices and techniques required have been developed rapidly. However, FSO communication systems are vulnerable to weather effects and atmospheric turbulence as well as pointing errors. As a result, adaptation methods and transmission protocols are being actively discussed [11–13]. For many scenarios such as real-time transmission and broadcasting, retransmission is either expensive or impossible to implement, so using forward error correction (FEC) is promising and has been widely studied [14–16]. Reviews [17, 18] give an overview of coding methods for optical transmission. An important aspect of FEC coding is the selection of the code rate and codeword length, and it is introduced in [19]. Some researchers studied the FEC performance according to probability [20, 21], but the formulae are computationally complex, which makes performance prediction more and more impractical as the size of the considered codeword increases. Interleaving is also necessary because in high-speed FSO transmission, an outage caused by atmospheric turbulence, which often lasts for several milliseconds, will cause a burst of packet erasures. The long burst error needs an extremely large codeword length or to be shuffled via interleaving, but the required interleaved FEC buffering size will be still very large, so optimisation between the FEC codeword length and interleaving depth is necessary. Since the performance depends on the buffering size [22], it is reasonable to make full use of the buffer memory and to reduce overhead under the limitation of a certain buffer size, which means the product of codeword length and interleaving depth is fixed. With the assumption of constant buffering size, optimisation between the codeword length and interleaving depth was first discussed with consideration of overhead [22]. Moreover, based on that, later work [23] proposed a near-perfect (NP) interleaving depth to define an upper bound of the effective interleaving depth when it is possible to select very large interleaving depth, and an interleaving-first algorithm to achieve better performance with lower complexity of coding and decoding. However, today memory devices are cheaper and cheaper, so that it is practical to use much larger buffering size, and therefore we have to consider how the buffering size influences the transmission performance, which has not been addressed in existing works. A specific and practically computable relationship between transmission performance and the flexible buffering size remains to be solved. Current studies are usually based on average features of errors such as the probability of bit or packet error and the correlation factor, instead of temporal features such as the error length or outage time distribution function, which is essential in buffering size and FEC recovery threshold determination. It is widely known that the performance of FSO transmission systems is affected by various factors. In [24, 25], Markov chains are used to model FSO channels, but do not give the required statistical features of errors. However, a definition of time share of fade has been proposed [19] to describe the probability distribution function (PDF) of the fading time. Similarly, there have been measurements of the statistics of channel good time [26]. Using these results, we can conclude the statistical features of channel good time and outage time, and based on that the distributions of burst error length and correct data length can be calculated with a given transmission time of the packet, according to which we can design channel-aware adaptation methods. This paper proposes a model of system performance as a function of buffering size and FEC code rate, based on a continuous-time-Markov-chain (CTMC) model of an FSO channel. Our model makes the performance prediction applicable to large and flexible buffering size with practical computational complexity. This approach allows us to optimise the FEC and interleaving strategy without fixing the product of FEC codeword length and interleaving depth. The model is verified through comparison with data from Monte Carlo simulations. This paper is organised as follows: Section 2 introduces the channel model we use. Section 3 proposes the system performance model and analyses the packet layer FEC codes and interleaving without fixed buffering size. Section 4 simulates the system and analyses the principle of the simulations we implement. Section 5 discusses the simulation results and the comparison of the calculated and simulated values of system performance. Finally, conclusions are drawn in Section 6. The notations used in this paper are listed in 'Nomenclature' section. 2 FSO channel model 2.1 Discrete-time-Markov-chain (DTMC) model We assume that FEC is used at the packet level, so that the channel can be considered as a binary erasure channel, which means the packet is either correctly received or discarded. Therefore, a general Gilbert–Elliot model [27], which is widely used when considering FEC coding and interleaving, is shown as Fig. 1. In the model, the channel condition is summarised by two states: good (or the channel is ON) and bad (or the channel is OFF). The channel good state is defined as: data transmitted in this state will all be received correctly. Similarly, the channel bad state is defined as: data transmitted in this state will be erased or discarded. Let p and q denote the transition probabilities from state G to state B and from state B to state G, respectively. The transition probability matrix is given by Figure 1Open in figure viewerPowerPoint DTMC model of the FSO channel Suppose is the probability matrix of the kth transmission state, where and denote the probability of being in the good state and bad state, respectively, then we have . The final steady state can be derived through solving and , where also indicates the overall packet loss ratio (PLR) of the basic channel, i.e. before adaptation methods are implemented. A correlation coefficient , defined as , describes the probability of remaining in the current state [22]. When interleaving is added with an interleaving depth of d, the distance between two formerly adjacent packets in an FEC frame will be d, so the new parameters in the DTMC model become (1) and the new correlation coefficient will be [23]. From the formulae above, we know that when is close to 1, the channel correlation is very small and hence the channel is almost memoryless, so adding interleaving will not give a large improvement. However, when is small, the channel is more likely to remain in the current state, which means the length of burst errors would be larger, so adding an interleaving strategy with a large d will decrease , and therefore decrease the average length of burst error, so that FEC decoding would be much easier. 2.2 Continuous-time-Markov-Chain (CTMC) model To design the adaptation system, the number of erasures that an FEC codeword can recover should be determined by the probability of recovering every burst error longer than a certain length, which in turn is determined by the system requirements. This value varies as a result of different distributions of burst error lengths even if the average error ratio is fixed, but the DTMC model gives only a fixed distribution. In the early research [20], the channel was modelled by a renewal process which can describe the different distributions by different PDFs of holding time. Measurements have been made of the temporal distribution of the fade time [19, 28], and experimental data in [26] gives the distributions of channel good time. These results allow us to make a CTMC model of the channel, so that we can derive the statistical features of the burst error lengths with a given packet transmission time. Then, we can make a CTMC model of the FSO channel, which can be described by an alternating renewal process as shown in Fig. 2. However, in practise the ON/OFF statistics should be systematically measured before a strategy of FEC coding and interleaving is adopted. Figure 2Open in figure viewerPowerPoint CTMC model of the FSO channel The correlation coefficient is important to the adaptation strategy, so we now calculate according to the CTMC model. Let be the packet transmission time, be the mean ON state holding time (ON time), and be the mean OFF state holding time (OFF time). In ON states, the average number of packets transmitted is . One of these packets is followed by an erasure and the other packets are followed by correctly received packets. Therefore, knowing the parameter p in the DTMC model denotes the probability of transition from state G to B, we now have and similarly . Thus, we have (2) Furthermore, we can conclude that the system is highly correlated when the mean ON or OFF time is much greater than the packet transmission time. 3 Analysis of packet layer FEC codes and interleaving without fixed buffering size When an adaptation strategy is evaluated, the performance of the system and the overhead are often considered. In this section, we first introduce the restrictions of FEC codeword length n and interleaving depth d and then propose the model of system performance as a function of FEC tolerable error ratio and the buffering size, and finally estimate the overhead. On the basis of these analyses, the system designer can compare the improvement of performance and the extra overhead to decide which pair of parameters are selected, according to the specific scenario. 3.1 Restrictions of interleaving depth Extending the codeword length of FEC and increasing the depth of interleaving are commonly known as effective ways to address burst errors. It is known experimentally that the performance of the transmission system is related to the buffering size [22]. When S is fixed, the final PLR of the system is essentially fixed. On the basis of this assumption, the parameters n and d are optimised to reduce the overhead under the condition that the system performance is similar [23]. In highly correlated channels, though the FEC tolerant error ratio is higher than the average channel error ratio, packet FEC still fails because erasures often appear in bursts. Moreover, highly correlated error bursts require an extremely large FEC codeword length which will cause an unacceptably large coding and decoding overheads. Consequently, the most efficient solution is interleaving because it scatters the burst errors into every codeword, so that the number of erasures in each codeword is averaged and thus tolerable. Also, because the complexity of FEC coding and decoding increases with the codeword length n, increasing the interleaving depth d is preferable. From (1) we know that approaches 0 as d increases. To describe this, we used experimental data from [19, 26] to plot as a function of interleaving depth, as shown in Fig. 3. Experimental work [19] measures the holding time when the receiving power is above and below the power threshold that the receiver can receive the data correctly, and gives the statistics of the OFF time. The power threshold is chosen based on the design decision [19] that the OFF probability is 0.3. The statistics of the ON time was measured in a different experiment [26], but this is not consistent with the average OFF probability in [19]. To ensure the consistency, we use the shape of the ON time distribution and adjust the mean and standard deviation proportionally to make the overall OFF probability 0.3. Assuming the information rate is 10 Gbps and the code rate is 0.65, the total transmission rate is 15.385 Gbps. Using 1046 B as the packet size [19], we can derive the packet transmission time is and . The channel is a typical highly correlated FSO transmission channel. Figure 3Open in figure viewerPowerPoint Correlation coefficient as a function of the interleaving depth From Fig. 3 we can see that the correlation coefficient asymptotically approaches zero for large d, thus increasing d becomes an increasingly inefficient way to reduce the channel correlation. To find a proper d, a threshold is defined in [23]: when , the channel is considered to be nearly uncorrelated and using a larger d will have little impact on system performance. The parameter is determined by the application scenario, and when approaches 1, the system performance approaches that of a perfectly interleaved system. The corresponding minimum interleaving depth is where denotes the smallest integer greater than or equal to x, and this result is referred to as the NP interleaving depth . According to (2), the NP interleaving depth, or the maximally efficient interleaving depth is derived as (3) 3.2 Restriction of FEC codeword length However, even if the interleaving depth is smaller than , the codeword length n cannot be too small because it leads to coding inefficiency [19]. For maximum distance separable (MDS) codes, the whole n-packet codeword that includes k information packets can be recovered if at least k packets are received. However, for non-MDS codes, the receiver has to receive more than k packets to recover the erased packets. This effect is called coding inefficiency, and the ratio of the extra part needed is called the inefficiency factor . is typically correlated with n when the type of FEC code is determined [29], denoted as , and specially, for LDPC codes, it is negatively correlated. As a result, increasing n appropriately could reduce the overhead of redundancy, and therefore increase the effective throughput when the total throughput is fixed. Some common examples of LDPC codes are shown in Table 1. Table 1. Examples of LDPC inefficiency and other parameters Code Codeword length Information bits Redundancy bits Code rate, % Overall efficiency, % Inefficiency long LDPC 16,200 14,400 1800 88.9 88.6 0.003 medium LDPC 5940 5040 900 84.8 84.2 0.006 short LDPC 1120 840 280 75 71.4 0.036 3.3 System performance model Following our discussion of the consequence of varying n and d and their restrictions, we now discuss how the system performance is related to S and FEC code rate. Note that represents the probability of event happens, the system performance can be derived according to the probability as (4) where is the largest tolerable ratio of erasures in an FEC codeword and implies the ratio of successfully received packet before adaptation methods. From [22] we know that the performance of different systems is very close if the buffering size is the same. Assume for now that the buffering size contains only one codeword, so that the system performance can be estimated by the probability of the error ratio in the buffering size being smaller than the tolerable error ratio . Since the burst error length is proportional to the OFF time and the correct data length is proportional to the ON time, with the same factor , we can use the ratio of OFF time over the total time to describe the error ratio. During the transitions between ON and OFF states in the CTMC channel model, determining the buffering size is like determining the sampling size to observe the OFF time ratio in the random process. Provided that the expected ratio of OFF time over the total time is , for a certain sampling size, the observed r from experiments should be close to , with a certain distribution called the sampling distribution, and its deviation should be smaller when the sampling size gets larger. An example is shown in Fig. 4, where the area of the shadow part of the figure denotes the probability that the erasures would not be recovered. If the sampling size is large enough, according to the central limit theorem, the distribution will be close to Gaussian. Figure 4Open in figure viewerPowerPoint PDF of the sampling distribution of the OFF ratio For the current problem, the sampling size equals the transmission time of S packets. If we have , there is 0.5 probability that the whole codeword can be recovered and another 0.5 probability that erasures are all discarded. As a result, the ratio of correct packets when would converge at according to (4). For a general CTMC model of the channel, let be the PDF of the ON time and be the PDF of the OFF time. If we observe N pairs of ON and OFF transitions, the PDF of r is denoted by , and its CDF is denoted by . Given , we can derive the system performance by (5) Moreover, using the definition of CDF, we can transform into (6) (7) where and denote the sum of the observed ON and OFF time within sampling size N, respectively. Since and are positive numbers, the formula (7) can be transformed into (8) Then knowing and are mutually independent, we can derive (9) where and are the PDFs of and , respectively. To calculate these distributions, can be derived as the PDF of the sampling distribution of , if the sum of N samples is taken as the statistic, whereas is matched similarly with . Particularly, if N is greater than 30, according to the central limit theorem, (or ) is close to Gaussian, with a mean value of (or ) and a deviation of (or ), where (or ) and (or ) denote the mean value and the deviation of (or ). Moreover, when N is large enough, we can estimate the sampling size by . Thus the system performance becomes (10) Thus, given the required system performance according to the particular deployment scenario, we can verify if and S can satisfy the requirement. 3.4 Bandwidth efficiency and overhead Let B be the total bandwidth of the channel, so that the effective throughput can be calculated by . The minimum FEC redundancy ratio should be . To ensure the effective throughput under the limitation of a certain bandwidth, we define the bandwidth efficiency by (11) Another factor the designer must consider is overhead. The overhead C can include buffering time , FEC coding and decoding time , and the associated costs including coding and decoding powers and the codec's price. Designers can weigh them according to the specific scenario with factors , , and (12) or add some other overhead they are concerned about. We can now adjust n and d and then compare the corresponding and C to decide which pair of coding/interleaving parameters should be adopted. If the system tolerable PLR and the FEC recovery threshold are given, we can derive the needed buffering size, and then adopt IF [23] or other algorithms to optimise the FEC codeword length and interleaving depth. Besides, we can also fix the interleaving depth to a NP value and list several FEC recovery thresholds, so that we can derive both system performance and overhead as functions of the FEC codeword length, after which the optimisation can be done. For example, we can first fix d to , so that and C can be calculated as a function of n, and then we select the n that results in the optimum and C. Specifically, suppose the system tolerable PLR is 0.03 and is fixed, we plotted three performance curves as a function of buffering size with in Fig. 5. The needed buffering sizes are marked in this figure. If it is not essential to reduce the bandwidth efficiency to such a small value in the current scenario, we will certainly choose the parameters with because it saves 1/3 of the buffering size in comparison to . If is so large that is too large, we can use or less and compare the corresponding and C to make a decision. Figure 5Open in figure viewerPowerPoint Different S are needed according to different and requirements 4 System simulation 4.1 Parameter selection Just as section Chapter 3.1 introduced, in our experiments, the probability of ON state is fixed by according to [19]. For the OFF time PDF, we use statistical features of the channel data taken directly from [19]. For the ON time PDF, we use data from [26] with its distribution shape, and adjust the mean and standard deviation parameters slightly and proportionally in order to achieve the condition . The packet transmission time is set to , and the correlation factor before adaptation is . 4.2 Implement Our model is implemented in MATLAB and the theoretical methods are verified using Monte Carlo simulations. The process of the simulation is designed and implemented as follows. First, the channel condition is simulated according to the CTMC model, by a 0–1 sequence that is able to be operated for packet erasures. To achieve this, a sequence of ON and OFF times in the CTMC model is generated according to the parameters as discussed in Section 4.1. This sequence of transition times then allows us to determine if a particular packet is fully received, erased or occurs over a transition boundary. In the latter case where only part of a packet is erased, we assume that inside the packet, an inner FEC can recover errors if more than 70% of the packet is received. The channel sequence is thus derived. The results confirmed that the overall ON time ratio is around 0.7. On the basis of the derived channel sequence, the next process in the simulation is coding, transmission, and decoding. Before the source data is sent, packet level FEC is applied and interleaving is performed. Then, the coded data sequence is modified according to the current channel condition to simulate the successful transmission or packet erasure. Finally, the received packets are de-interleaved and decoded, so that the system PLR can be calculated. 5 Results and analysis 5.1 FEC codeword length and interleaving depth In our numerical simulations, we first simulate the urban environment discussed in [22]. The parameters used are , , and . Second, we use the parameters introduced in Section 4.1 and . The results of these two simulations are shown in Fig. 6. The result corresponding to the higher value of is shifted to higher values of interleaving depth as expected from our previous discussion. Figure 6Open in figure viewerPowerPoint Interleaving causes different performances when is different We now consider the effect of changing the FEC codeword length n using values of 128, 10,000, 20,000, 50,000 and gradually increase the interleaving depth d, the system performance obtained is shown in Fig. 7a. A part of this figure is magnified to show the details. From both the overall and the magnified curves, we can conclude that the system performance is uniquely characterised by the buffering size , as predicted in [22]. Figure 7Open in figure viewerPowerPoint Analysis of simulation results (a) System performance depends on the buffering size, (b) Analysis of simulation results To evaluate the system performance at infinite buffering size in the simulation, we use curve fitting tools to derive the value numerically. We fit the system performance with the three parameter function . An example of quality of the fitting is shown in Fig. 7b, the excellent agreement gives us confidence in the derived asymptotic values. This procedure is then applied in several groups of experiments in which and the results are shown in Table 2. In the function where b is negative, when , will converge to c. From Table 2, we can see that when , c varies slightly around the theoretical value 0.85, and when , the theoretical value according to (4) is , and c is close to 0.9, as expected. Table 2. Results of curve fitting Codeword length (n) a b c 0.7 50,000 0.8545 0.7 20,000 0.8514 0.7 10,000 0.8568 0.8 50,000 0.8973 0.8 20,000 0.9049 5.2 Comparison between theoretical and simulated performances To verify the strategy, we compare the calculated system performance with the simulated one. The system performance can be calculated based on our theoretical considerations according to (5). In the function , we assume N is large enough and use a Gaussian distribution to predict . Also, because N is large enough, we have the following approximate relation between S with N, , and then plot the calculated system performance in the same figure with the simulated one, as shown in Fig. 8a. The agreement between the theoretical value and the simulation is worst at small S because the relation is invalid here and our OFF time distribution is not Gaussian. Specifically, the corresponding S should be greater than about 2,200,000 packets, if N is >30, to satisfy the basis of using the central limit theorem, and as can be seen from Fig. 8a, that the agreement is much better in this region of large buffering size. Figure 8Open in figure viewerPowerPoint Comparison of calculated and simulated values of system performance (a) When , (b) When and When we change to 0.33 and 0.314, a group of similar results are derived, as shown in Fig. 8b, from which we can see our mathematical prediction shows agreement with the simulated values. However, they are also restricted by the requirement of a large N, or a large N, which is not a problem since the needed buffering size is around 3 GB, which is not difficult to achieve now and such large block FEC is necessary and already widely used in highly correlated FSO transmission system. 6 Conclusion In this paper, we have proposed a theoretical model of system performance as a function of FEC buffering size and recovery threshold, based on a CTMC model of an FSO channel. It allows the designer to estimate the needed buffering size in a specific scenario or to determine the optimum parameters without fixing the buffering size first. We have designed a Monte Carlo simulation of FSO packet transmission including adaptation of the channel. The model is in very good agreement with the results of the numerical simulations. In the scenario where the raw channel good probability is 0.7, the overall system performance we have achieved is 0.97 using a buffer of packets and FEC recovery ratio of 0.33. This method is applicable in situations such as long-range or mobile transmissions, where the packet error rate before adaptation is significant. The CTMC model can be applied to any FSO channel provided the ON and OFF state statistical distribution functions are known. Our analysis of the interleaved FEC can also be applied in other (non-FSO) channels if a CTMC model of the channel can be derived. 7 Acknowledgments This work was supported by the project Designing Future Optical Wireless Communication Networks funded under the Marie Curie International Research Staff Exchange Scheme Actions of the European Union Seventh Framework Program [EU-FP7 contract no. 318906]; the National Key Research and Development Plan of China [grant no. 2016YFB0200902]; and the National Natural Science Foundation of China project [grant no. 61572394]. References 1Khalighi M.A., Uysal M.: 'Survey on free space optical communication: a communication theory perspective', IEEE Commun. Surv. Tutor., 2014, 16, (4), pp. 2231– 2258 2Leitgeb E., Plank T., Pezzei P. et al.: ' Integration of FSO in local area networks - combination of optical wireless with WLAN and DVB-T for last mile internet connections'. 2014 19th European Conf. 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