Elsevier

Optical Fiber Technology

Volume 60, December 2020, 102383
Optical Fiber Technology

A novel bio-inspired optimization algorithm for solving peak-to-average power ratio problem in DC-biased optical systems

https://doi.org/10.1016/j.yofte.2020.102383Get rights and content

Highlights

  • We introduce a novel nature-inspired optimization algorithm, called tree growth optimization (TGO) algorithm to overcome the search complexity of the partial transmit sequence.

  • We apply the proposed algorithm to the DC-biased optical signals to reduce the high peak-to-average power ratio.

  • The proposed TGO algorithm is a multi-agent algorithm that simulates the effort of trees to grow and survive in nature.

  • The TGO helps to find a near-optimal set of phase factors among a large set of phase factors in solution space.

  • The performance of the proposed algorithm is evaluated using a set of benchmarks and compared with several counterpart methods. The results reveal that the proposed algorithm outperforms its counterparts.

Abstract

In this paper, a tree growth optimization (TGO) algorithm is introduced to diminish the computational complexity of the partial transmit sequence in exploring the optimal phase factors. The proposed TGO algorithm is an efficient method for reducing the high peak-to-average power ratio of optical orthogonal frequency division multiplexing signals. The problem of the peak-to-average power ratio causes inter-modulation between sub-carriers due to the non-linearity of the fiber optics and some devices such as power amplifiers and analog-to-digital converter. The performance of the proposed algorithm is evaluated using a set of benchmarks and compared with several counterpart methods. The results reveal that the TGO outperforms its counterparts in terms of solution quality and computational complexity.

Introduction

Optical communication has attracted the attention of many researchers due to its high security and bandwidth. The proliferation of communication devices and increasing network traffic has made the improvement of network capacity inevitable. This development is facilitated using orthogonal frequency division multiplexing (OFDM) [1]. OFDM technology is widely used in wireless and wired communications. The OFDM has several advantages such as high spectral efficiency, stability against inter-symbol interference, and resistance to the frequency selective fading of channels [2]. Optical OFDM systems are a promising technology for ultra-high-speed data transmission. In contrast to original radio-frequency OFDM systems, in optical communications, the light intensity is controlled for data transmission. Thus, the baseband signals are real and positive [3]. Asymmetrically-clipped optical OFDM (ACO-OFDM) and DC-biased optical OFDM (DCO-OFDM) are the most well-known optical schemes. In these schemes, Hermitian symmetry is employed to produce real optical OFDM signals. In the ACO-OFDM, only the odd subcarriers carry the information, and the even subcarriers are set as zeros. In this scheme, the signal is clipped to zero for making the unipolar signal. In the DCO-OFDM, positive signals are generated by applying a DC bias to the signal [4]. The ACO-OFDM scheme suffers from the reduced spectral efficiency since only 25% of the subcarriers carry the information, and the DCO-OFDM scheme suffers from low power efficiency because of using a large DC-bias to compensate for the negative peak. Both the original and optical OFDM systems often face high amplitude variations of the transmitted signal, named peak-to-average power ratio (PAPR). The high PAPR decreases the performance of power amplifiers and creates out-of-band radiation with bit error rate (BER) performance degradation [5].

To decrease the high signal fluctuations of optical and original OFDM systems, several solutions have been reported such as clipping and filtering [6], block coding [7], non-linear companding [8], tone injection [9], peak windowing [10], precoding [11], selected mapping (SLM) [12], and partial transmit sequence (PTS) [13]. Among these solutions, the PTS is more well-known due to its high performance in reducing the PAPR. However, the PTS technique suffers from a fundamental issue, high computational complexity due to an exhaustive search to find an optimal permutation of phase weighting factors.

An interesting idea to decrease the computational complexity of the PTS is to combine the PTS with meta-heuristic optimization algorithms. Meta-heuristic algorithms mainly model natural phenomena or intelligence behavior of creatures to solve complex and non-linear problems. Fig. 1 shows a big picture of a meta-heuristic algorithm. As shown in the figure, a meta-heuristic algorithm can be considered as a black-box optimizer system that takes as input a set of problems’ variables and even some constraints in the form of limitations. The optimizer modifies the variables to reach a desired output until some termination conditions are satisfied. The output is a near-optimal solution and a cost or fitness value, which shows the quality of the generated solution.

Meta-heuristic algorithms can be grouped into several classes based on their source of inspiration. Two branches of meta-heuristics are evolutionary and swarm intelligence algorithms. A well-known example of evolutionary algorithms is the genetic algorithm (GA). The main idea behind the GA is based on Darwin’s theory of evolution. In solving an optimization problem, the GA algorithm begins its optimization process with a set of encoded solutions known as chromosomes. Each chromosome shows a potential solution to the given optimization problem. After evaluating the fitness of chromosomes, the fittest ones are selected to take part in the recombination phase to form the next generation. This process performs for several iterations until attaining a near-optimal solution for the given problem. Two examples of evolutionary algorithms that merged with the PTS scheme are hybrid GA (HGA) [14] and backtracking search algorithm (BSA) [15].

The other line of work is swarm intelligence algorithms. These algorithms simulate the social and intelligent behavior of animals or humans to create a black-box optimizer. A popular example that falls in this category is particle swarm optimization (PSO) [16]. This algorithm models the cooperation among a set of birds in the foraging process. Several swarm intelligence algorithms that are combined with PTS are flower pollination optimization (FPO) [4], artificial bee colony (ABC) [17], whale optimization (WO) algorithm [18], firework optimization (FWO) [19], firefly algorithm (FA) [20], and gray wolf optimization (GWO) [21].

The nature-inspired meta-heuristics are simple but very powerful in solving optimization problems. In this paper, we introduce an innovative bio-inspired swarm intelligence algorithm, called tree growth optimization (TGO) algorithm to overcome the high PAPR of DCO-OFDM signals with low search complexity and more simple implementation. The TGO is motivated by the growth of trees in nature. It involves three main operators that are competition, root spreading, and seed scattering. These operators are powerful enough to update a population of solutions in finding a near-optimal solution for the given optimization problem. It is shown that the proposed TGO-PTS approach dramatically degrades the PAPR of DCO-OFDM signals and outperforms the previous optimization meta-heuristics in terms of solution quality and convergence rate. In summary, our contributions are listed as follows:

  • We introduce a new nature-inspired algorithm called tree growth optimization (TGO) algorithm to decrease the computational complexity of the PTS scheme and to search the optimal permutation of phase factors.

  • We combine the TGO algorithm with PTS to develop the TGO-PTS method.

  • We evaluate the TGO-PTS on several benchmarks. The numerical results show the superiority of the TGO-PTS compared with the other methods.

The rest parts of the paper are prepared as follows. Section 2 is devoted to the problem definition. Section 3 explains the working principle of the proposed TGO algorithm. Section 4 describes the TGO-PTS method. Sections 5 presents and discusses the computer simulation results. Finally, Section 6 gives some conclusions.

Section snippets

Problem definition

The OFDM system is composed of several sub-carriers modulated by constellation mapping. We use the M-ary QAM modulator to map the input binary stream to QAM symbols. Then, the inverse FFT (IFFT) procedure is applied to the modulated symbols to form the time-domain OFDM signals. In an optical communication system, an LED converts the electrical signal to the intensity of an optical signal. So, the optical signals have to be both real and unipolar. The Hermitian symmetry operation is employed to

Tree growth optimization algorithm

TGO algorithm is a new bio-inspired strategy motivated by the growth of trees in nature. Trees use water, nutrients, and sunlight to grow and evolve [22]. In the growth process, trees have to compete with each other on natural shared resources [23]. Some trees to survive and expand their territory, scatter some seeds around the environment. The seeds move around the environment with the help of wind, birds, or animals. In addition to the seed scattering mechanism, some new seedlings can produce

TGO-PTS

By combining the TGO and PTS scheme, we propose a novel TGO-PTS method to find a near-optimal phase factor permutation to diminish the PAPR with minimum computational complexity. Fig. 10 shows the proposed TGO-PTS method. To apply the TGO for the PAPR reduction problem, just two changes need to be made in the algorithm including solution formulation and fitness calculation.

Simulation results

Computer simulations are performed to confirm the performance of the PTS scheme in the DCO-OFDM system when using the TGO algorithm to explore the optimal permutation of phase factors for PAPR reduction. In this section, we use K={63,255} sub-carriers, 10,000 random OFDM symbols, and 16-QAM modulation. The oversampling factor is set as =4 and the phase factors bv(v=1,2,,V) are chosen as {+1,-1}(w=2). The sub-blocks’ numbers V=21 is chosen for K = 63, and V={15,17} for K = 255. For all

Conclusions

In this paper, we optimized the PTS technique using a new bio-inspired algorithm, namely tree growth optimization (TGO) algorithm, for PAPR reduction of DC-biased optical OFDM (DCO-OFDM) signals. The proposed TGO is a multi-agent algorithm that simulates the effort of trees to grow and survive in nature. The TGO helps the PTS to find a near-optimal set of phase factors among a large set of phase factors in solution space. The proposed TGO-PTS scheme starts its work with a collection of

Declaration of Competing Interest

The authors declare that they have no known competing financial interests or personal relationships that could have appeared to influence the work reported in this paper.

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