1. Introduction
Free-space optical (FSO) communication systems with high data rates, high security, and robustness to electromagnetic interference have gained much attention as a promising candidate to overcome the spectrum scarcity in wireless communications systems [
1,
2]. Nevertheless, the FSO link performance can deteriorate due to atmospheric turbulence, leading to the degradation of the intensity and phase of the estimated optical signal [
3,
4]. Under various statistical channel models for the FSO channel, a variety of important system performance characteristics such as the outage probability, ergodic capacity, and bit error rate (BER) have been analyzed in recent studies.
On the other hand, power line communication (PLC) has been usually regarded as a low-cost and energy-saving communication technology since it utilizes the existing cables for data transmission [
5]. Compared with other methods of communication, PLC has the characteristics of wide coverage, convenient connection, and no need to be rewired, which enables it to be used in both indoor and outdoor communication. However, due to the variations in location and time, it is a challenge to model PLC channels. Furthermore, the random fluctuation of attenuation, noise, and channel impedance in PLC systems makes it very hard to analyze the PLC channel [
6].
In the literature, various communication systems have considered integrating either PLC or FSO into either outdoor or indoor broadcasting communication. In [
6], the performance of a mixed cooperative communication system between PLC and visible light communication [
7,
8] was evaluated, while a dual hop wireless-PLC mixed cooperative system. Furthermore, a mixed FSO-radio frequency relaying (RF) system was considered in [
9] by using decoding and forwarding (DF) technique. Also, the authors of [
10] focused on the impact of pointing error on the performance of a dual-hop relay transmission system composed of asymmetric RF/FSO links and provided exact closed-form expressions for a variety of system key performance metrics. On the other hand, many practical scenarios can benefit from the integration of PLC with FSO using relaying techniques. To transmit information signals from an indoor source to an outdoor destination using an FSO link, there are various solutions such as implementing fiber optic or Wi-Fi signal links [
11]. With the former approach, the cost of implementation and maintenance can be high in some scenarios, while in the latter option, due to the presence of large obstacles and dead zones the signal fluctuations are a hindrance. However, currently, no research focuses on the cooperative transmission of the PLC-FSO relaying system. With its advantages such as cost-efficient and high rate communication, the combined deployment of the readily available PLC infrastructure with the FSO link has potential practical implementations and thus warrants investigation.
In this paper, due to the potential for simple implementations and high energy efficiency, we consider DF relaying systems that combine PLC and FSO integration. The proposed mixed system can support wireless networks to reach remote geographical area through the ubiquitous indoor power line infrastructure. More specifically, the analytical results are provided considering the effects of both pointing errors and various types of turbulence in the FSO link, as well as the impulsive-background noise in the PLC link. We derive the probability density function (PDF) and the cumulative distribution function (CDF) for the end-to-end SNR of the proposed system. Consequently, in compilation with the Gamma-Gamma distribution of the FSO link, the log-normal distribution of the PLC link is approximated using a Gamma distribution, thereby obtaining a tractable closed-form expression of the analytical BER performance and the outage probability of the proposed system. The results demonstrate that the analytical derivation exactly matched with the Monte-Carlo simulations, providing insights into the proposed system under various channel conditions.
The remainder of this paper is organized as follows. In
Section 2, we present the descriptions of the communication system and the channel model, include the PLC and FSO channel models. In
Section 3, we provide the derivation the CDF and PDF of the end-to-end SNR of proposed system. The mathematical expressions of the outage probability, the average BER, in
Section 4. The diversity order of the proposed system is presented in
Section 5 using asymptotic analysis at high SNR regime based on the derived outage probability. Consequently, some simulation results using Monte-Carlo simulation are presented in
Section 6 to validate the mathematical correctness of the derived mathematical results. Finally, some concluding remarks are provided in
Section 6.
6. Simulation Results
In this section, the numerical results from the Monte Carlo simulations with samples are provided to show the validity of the analytical results and provide some insights into how different parameters affect the proposed system performance. More specifically, we show the impacts of various impulsive noise, turbulence conditions, and pointing errors on the performance of the proposed system under two detection techniques, heterodyne and direct detection, which are denoted by and , respectively. For the FSO link, we set as , , and , corresponding to weak, moderate, and strong turbulence, respectively. Similarly, for the PLC link, the impulsive noise frequency and intensity vary from weak to strong levels in terms of and the ratio . Also, we have while , , and . The values of , and are (1,1,1) and (1,1,1/2) when BPSK and QPSK modulations are used, respectively. Additionally, in all figures, the theoretical results perfectly match the Monte-Carlo simulation results, demonstrating the accuracy of the analytical derivation.
In
Figure 2, we show the outage probability versus
for both cases of
and
under weak, moderate, and strong turbulence conditions. For a fixed average SNR of the PLC link, we can see that the outage probability significantly depends on the parameters of the FSO link. It can be observed that with the direct detection technique, the outage probability of the proposed system is higher than when the heterodyne detection is employed. Additionally, stronger turbulence leads to a higher outage probability.
In
Figure 3, we show the impacts of various PLC link parameters on the outage probability of the proposed system when the average SNR of the FSO link is fixed at 50 dB. More specifically, three scenarios are considered, where the strong, moderate, and weak impulsive noise conditions are given as
and
, respectively. The outage probability of the system increases with the stronger impulsive noise level, while weak impulsive noise achieves lower outage probability. On the other hand, the higher the impulsive noise is compared with the background noise, the higher the outage probability is, as
changes from a low value of 0.2 to 0.5.
Furthermore, the BER of the proposed system is given in
Figure 4 with the average SNR of the FSO link versus different values for the turbulence conditions and two modulation schemes such as quadrature phase-shift keying (QPSK) and binary phase-shift keying (BPSK). It is observed that the average BER performance provides a perfect match to the closed-form expression of our analytical derivation. As expected, the BPSK modulation achieves better performance in comparison with the QPSK modulation. Meanwhile, as the turbulence of the FSO link raises, the BER performance becomes worse.
In
Figure 5, we present the BER of the proposed system versus the average SNR of the PLC link under various channel conditions, in which the impulsive noise change from weak to strong, described by the values of
and
, respectively. Moreover, the average SNR value of the FSO link is fixed at 40 dB while the modulation type is BPSK. From
Figure 5, it is clear that both FSO and PLC links have significant impact on the overall performance and an increasing in the quality of individual link can result in an improvement of the BER result. Moreover, high values of impulse noise probability and power of noise lead to higher error probability. Also, the with the fixed SNR value of the FSO link, when the SNR of PLC link approach relatively high values, the FSO link become dominant factor and the BER performance can only achieve a value of
.
Finally, in
Figure 6, the impact of pointing error versus the average SNR of the FSO link is shown in the medium turbulence condition. Also, similar to
Figure 2,
and
are used to observe the persistence of different detectors on the outage performance for various pointing error conditions. It can be seen that when
, the proposed system can achieve the best outage performance while a decrease from
to
can dramatically degrade the system performance due to severe impact of pointing error at
.
7. Conclusions
In this paper, we analyze the performance of a mixed PLC-FSO communication system operating over a turbulence channel in the presence of pointing errors at the FSO link and impulsive-background noise at the PLC link. Under different system parameters, the results demonstrate that the outage probability and BER performance improve as the effects of pointing error, turbulence, or impulsive-background noise decrease. More specifically, results on various system parameters show that severe pointing error and turbulence condition on the FSO link can lead to degradation of the outage probability and average BER performance. Similarly, high values of impulse noise probability and noise power in PLC link also leads to poor performance. Also, the diversity order of the proposed system only depends on the values of , and . Our study also shows that the simulation results coincide with the analytical curves at various SNR values. From the derived analytical results, the performance of proposed system can be thoroughly investigated to show the impact of various critical system parameters. Consequently, from the trends of the simulation and analytical results, the PLC transmission link is shown to be a promising backhaul solution for the FSO link and integration of both PLC and FSO links can provide an efficient indoor to outdoor transmission technique.