Optimization results for the parallel DF relaying with different number of nodes.
Abstract
In this study, we evaluate the performance of differential evolution (DE) and particle swarm optimization (PSO) algorithms in freespace optical (FSO) and mobile radio communications systems. In particular, we obtain the optimal transmission distances for multiplerelay nodes in FSO communication systems and optimal relay locations in mobile radio communications systems for the cooperativediversity networks, using both algorithms. We investigate the performance comparison of DE and PSO algorithms for the parallel decodeandforward (DF) relaying. Then, we analyze the cost functions. Furthermore, we present the execution time and the stability of the DE and PSO algorithms.
Keywords
 freespace optical communications
 cooperativediversity networks
 optimal distance
 differential evolution algorithm
 particle swarm optimization algorithm
1. Introduction
The aim of the optimization was to provide the bestsuited solution to a problem under the given constraints. The optimization algorithms have recently been much attention and gained significant importance in plenty of engineering problems [1–8]. In this study, we evaluate the performance analysis of differential evolution (DE) and particle swarm optimization (PSO) algorithms both in freespace optical (FSO) and in mobile radio communications systems.
FSO communications have been proposed as a solution for the various applications including fiber backup, and backhaul for wireless communications networks [9]. Despite the fact that the usage of FSO communications is widespread in major applications for wireless communications, the performance limitations for longrange links due to the atmospheric turbulenceinduced fading have had profound impacts in FSO communications systems. The method used for relayassisted FSO transmission links is one of the fading mitigation technique has attracted significant attentions recently in FSO communications networks [9–11]. In [9], the authors consider relayassisted FSO communications and investigate the outage performance under serial and parallel scheme with amplifyandforward (AF), and decodeandforward (DF) relaying models. The authors in [10] consider a cooperative FSO communications via optical AF relay and investigate the bit error probability performance. Bit error rate (BER) analysis of cooperative systems in FSO networks is presented in [11]. The outage performance analysis of FSO communications is presented in both [12] and [13]. Kashani et al. [14] consider the diversity gain analysis and determine the optimal relay locations for both the serial and the parallel relaying schemes. Although cooperative transmissions have greatly been considered in the above manuscripts, to the best of the authors’ knowledge, there has not been any notable research for the relayassisted FSO communications systems using the optimization algorithms. To fill the research gap, in this paper, we analyze the performance of both DE and PSO algorithms in terms of the transmission distances when applied for the parallel DF relaying in FSO systems. Moreover, we investigate the performance comparison of these two algorithms in respect to the execution time, cost, and stability analysis.
In our study, as a second part of this paper, we focus on dualhop cooperativediversity network to study the impact of the relay location between the source and the destination. Cooperativediversity relay networks provide a significant performance increment in the radio frequency power transmission and the spatial diversity. They are also shown to be a promising solution to mitigate the signal fading arising from the multipath propagation in wireless communications [15, 16]. In the cooperativediversity networks, relay terminals are employed between the transmitter and receiver nodes, over multiple communications routes, in which two main protocols are used as follows: (i) amplifyandforward and (ii) DF [15–21].
Most of the previous publications have studied the cooperativediversity performance over different fading channels [15–26]. In [15], the authors analyzed the cooperativediversity network using AF cooperation protocol, operating over independent, but not necessarily identically distributed Nakagamim fading channels. The paper in [17] addressed the multibranch adaptive DF scheme for cooperativediversity networks. The best relay selection scheme for cooperativediversity network is studied in [18]. Furthermore, [19] investigated the advantage of the diversity over direct transmission and conventional noncooperative relaying scheme. In all these papers, analytical framework for performance analysis of BER and the outage probability is provided [15, 17–19]. As far as we know, both DE and PSO algorithms have not been applied for obtaining the optimal location of the relaying terminal over Nakagamim fading channel.
To fill the research gaps in mobile radio communications using cooperativediversity relay network, in this paper, we provide an optimization algorithms results, indicating the optimal location of the relaying terminal in the parallelrelaying scheme.
In summary, for the first part of this paper, the key contributions are twofold:
First, the locations of each individual relay nodes and the transmission distances are optimized for the parallel DF relaying scheme in FSO systems. Second, and more importantly, none of the previous studies provide a comparison among optimization algorithms when applied for FSO systems. In this paper, we investigate the performance comparison of DE and PSO algorithms for the parallel DF relaying in respect to the execution time, cost, and stability analysis.
For the second part of this paper, there is a major contribution:
To fill the research gaps in cooperativediversity relay network, we provide a rigorous data for the optimal location of the relaying terminal over Nakagamim fading channel achieving the best error performance using both DE and PSO algorithms in the parallel relaying schemes.
The rest of this paper is organized as follows: The system model and performance analysis are discussed in Section 2 exploiting the DE and PSO algorithms. Section 3 provides the numerical results and simulations. Finally, the concluding remarks are given in Section 4.
2. System model and performance analysis using the optimization algorithms
2.1. FSO communications systems
This section presents the system model for FSO communications networks with parallel DF cooperative relaying protocol shown in Figure 1a. We consider that the FSO links between the sourcetorelay (
In [14], the outage probability for the parallel DF relaying is expressed as follows:
where
In the outage probability of the parallel DF relaying scheme, there are 2^{M} possibilities for decoding the signal between
For the optimization problem, a function is employed to minimize the outage probability for the parallel DF relaying, which can be written as
The flowcharts for the optimization of the transmission distance using DE and PSO algorithms are shown in Figures 2 and 3, successively.
2.2. Mobile radio communications systems using cooperativediversity relay networks
A system, consisting of a source terminal (
The source signal is transmitted with the energy of
where
where
3. Numerical results and simulations
In this section, numerical and simulation results are presented for both FSO and mobile radio communication systems.
3.1. FSO communications systems
In this section, numerical results are presented. For the optimization algorithms, the parameters
Figure 5 shows the optimal
It can be noticed from Figure 6 that the execution time for the PSO algorithm closely matches with the execution time of the DE algorithm for different number of relays.
Figure 7 shows the optimization results for the locations of each individual relay nodes. Accurate relay placements are obtained for
Finally, the impact of the varying
The detailed optimization results with the DE and PSO algorithms for DF parallel relaying scheme are given in Table 1. Here, the results for the optimal transmission distances and optimal relay locations are listed for various
(dB) 
2 Relays  3 Relays  

DE  PSO  DE  PSO  
Optimal 
Optimal 
Optimal 
Optimal 
Optimal 
Optimal 
Optimal 
Optimal 

0  0.6323  0.2608  0.6323  0.2608  0.4017  0.1464  0.4016  0.1463 
3  2.0304  0.8562  2.0304  0.8562  2.0453  0.7813  2.0453  0.7813 
6  3.5568  1.5653  3.5568  1.5653  3.8708  1.6044  3.8708  1.6044 
9  5.1021  2.3490  5.1021  2.3490  5.6697  2.5207  5.6697  2.5207 
12  6.6391  3.1868  6.6392  3.1868  7.4014  3.4801  7.4014  3.4801 
15  8.1326  4.0077  8.1326  4.0077  9.0656  4.4476  9.0656  4.4476 
0  0.2276  0.0756  0.2276  0.0756  0.2276  0.0756  0.2276  0.0756 
3  2.0541  0.7280  2.0541  0.7280  2.0541  0.7280  2.0541  0.7280 
6  4.0930  1.6114  4.0930  1.6114  4.0930  1.6114  4.0930  1.6114 
9  6.0547  2.6065  6.0547  2.6065  6.0547  2.6065  6.0547  2.6065 
12  7.9173  3.6665  7.9173  3.6665  7.9173  3.6665  7.9173  3.6665 
15  9.6952  4.7477  9.6952  4.7477  9.6952  4.7477  9.6952  4.7477 
3.2. Mobile radio communications systems
The error performance of the DF scheme for the cooperativediversity relay network is illustrated in Table 2 with varying path loss exponent for different values of
Figure 9 shows the best BER performance for the considered system versus
Figure 10 demonstrates the effect of ∈ on the distance between source and the relay terminal (
Table 3 shows that, the optimal
The best BER performance for the considered system is depicted in Figure 11 when
The variation of the optimal
Finally, the ROC (receiver operating characteristics) curves for ∈ = 4 are depicted in Figure 13. The fading parameters are set to be
4. Conclusions
In this paper, we present a comprehensive performance comparison of the DE and PSO algorithms both in FSO and in mobile radio communications systems. For the first part, we investigate the optimal transmission distances for different number of relay nodes and power margin values in the parallel DF relaying scheme. Moreover, we analyze the cost function and the execution time for the DE and PSO algorithms. As a second part of this paper, we consider the cooperativediversity relay network for the mobile radio communications systems operating over Nakagamim fading channel. We provide a rigorous data for the optimal locations of the relaying terminal in the parallel DF relaying scheme using DE and PSO algorithms. Then, we analyze the bit error probability with varying
We demonstrate that the cost functions are suitably minimized proving the accuracy of the employed optimization algorithms. We find out that both algorithms have similar execution time, besides PSO is more stable than the DE algorithm. Furthermore, the PSO algorithm outperforms DE algorithm with regard to the cost function. It should be emphasized that both optimization algorithms are reliable and can be used for the applications both in the FSO and mobile radio communications systems.
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