Full length articleOptimizing cubic metric in orthogonal frequency division multiplexing systems using chaotic differential search algorithm
Introduction
Cubic metric (CM) [1] has been recently approved as a more accurate indicator than the peak-to-average power ratio (PAPR) for envelope fluctuations and estimation of the non-linear distortion in orthogonal frequency division multiplexing (OFDM) systems [2], [3]. In wireless applications, several PAPR and CM reduction approaches have been reported [4], [5]. These approaches are non-linear companding [6], clipping [7], precoding [8], partial transmit sequence (PTS) [9], tone injection and reservation [10], and selected mapping [11]. In the companding approach, a non-linear compander is applied at the transmitter side and a decompanding procedure is utilized at the receiver end to retrieve the primary signal. The clipping approach diminishes the CM of signals by clipping to a preset level. In the precoding scheme, first, a precoder matrix is applied to the frequency-domain signals. Afterward, an inverse fast Fourier transform (IFFT) is performed. In the tone injection and reservation approaches, several additional sub-carriers are employed for CM reduction. In the selected mapping, the input frames are multiplied to the some phase factor streams, and then each frame is passed to an IFFT operation. Finally, the PAPRs of all time-domain signals are calculated and the signal with minimum PAPR is selected for transmission. Using the PTS scheme, the input frame is split into several disjoint sub-frames. To make a single data frame from sub-frames three operations should be done: multiplying the sub-frames with their corresponding phase factors, applying the IFFT operation, and finally merging the sub-frames. For the data frame, to have the least amount of PAPR, the phase factors must be in optimal order. It needs to explore all combinations of phase factors to achieve an optimal permutation of phase factors. The PTS scheme is regarded as the most efficient approach due to its robust CM reduction capability [12], [13], and [14]. The original PTS usually suffers from the high computational complexity derived from the exploring of optimal phase factors and a huge number of IFFT procedures.
The original PTS is often combined with an optimization technique to overcome the search complexity issue. Recently, several evolutionary and swarm intelligence algorithms have been incorporated with the PTS technique to explore the optimal phase factors and reduce the high PAPR or CM of OFDM signals. Some of the well-known evolutionary algorithms are genetic algorithm (GA) [15], hybrid genetic algorithm (HGA) [16], backtracking search algorithm (BSA) [17], shuffled frog leaping algorithm [18], and adaptive differential evolution (ADE) algorithm [19]. In [15], the authors proposed the GA-PTS method, in which sub-optimal phase factors are modeled as a population of chromosomes. This population updates using three operators including cross-over, mutation, and selection. In [16], a hybrid version of GA is proposed to enhance the performance of the GA-PTS method. A local search strategy is embedded in HGA to efficiently find the sub-optimal permutation of phase factors. In [17], the BSA is employed to solve the search complexity shortcoming of the PTS scheme. The BSA is a powerful extension of the standard GA, which is equipped with an improved crossover and a memory to use experiences obtained in previous iterations. Some of the most popular swarm intelligence algorithms used in PTS scheme are particle swarm optimization (PSO) [20], artificial bee colony (ABC) [21], harmony search (HS) [22], tabu search (TS) [23], firefly algorithm (FF) [24], grey wolf optimization (GWO) [25], and ant colony optimization (ACO) [26]. These algorithms are multi-agent strategies, in which several agents explore the search space through cooperating or competing with each other. The existing optimization algorithms achieved encouraging results in minimizing the search complexity of the standard PTS, but their performance is far from ideal state and more improvements are required.
We propose an efficient evolutionary algorithm named chaotic differential search algorithm (CDSA). The proposed CDSA is a powerful extension of the differential search algorithm (DSA) [27]. We combine the CDSA with PTS to solve the search complexity issue of the conventional PTS approach and decrease the CM of OFDM signals. The CDSA–PTS is a fast convergence algorithm and needs a few control parameters and explores an optimal set of phase factors. The CDSA–PTS approach is compared with the optimal PTS (OPTS), standard OFDM system, and several state-of-the-art methods including GA-PTS [15], PSO-PTS [20], ABC-PTS [21], TS-PTS [23], GWO-PTS [25]. The achieved results verify that the CDSA–PTS is a more efficient approach than its counterparts in terms of CM mitigation performance.
The rest of the paper is arranged as follows: Section 2 discusses the basic concepts and background theoretical foundation. The suggested CDSA–PTS approach is explained in Section 3. Simulation results are exhibited in Section 4. Eventually, conclusions are given in the latest section.
Section snippets
Theoretical foundation
The CM for OFDM signals is calculated as follows [3]: where is the reference signal’s raw CM (RCM), is an empirical constant. Following the long term evolution (LTE), and are respectively 1.52dB and 1.56 [28]. The parameter is calculated as follows [2]: were is the root mean square operation. is an element of the time-domain OFDM symbols , which is calculated as
CDSA-PTS technique for CM reduction
Differential search algorithm (DSA) [27] is one of the most superior population-based evolutionary methods developed for solving multi-variable and complex optimization problems. The inspiration source of DSA is the Brownian-like random walk process used by living beings in migration. In the DSA, the search space is modeled as a food area, and each point in the space shows a super-organism migration. The objective is to find more fruitful regions over the food area, which corresponds to the
Simulation results
In this part, an OFDM system is implemented for simulation. The modulation type is 16-QAM and the number of sub-carriers is chosen as . We use the RCM to exhibit the envelope fluctuations of OFDM systems rather than the CM. In the PTS technique, the complementary cumulative distribution function (CCDF) is used to evaluate the RCM reduction ability of different algorithms. The CCDF is the probability that the RCM of a frame is bigger than the preset threshold . To generate the CCDF, 10,000
Conclusion
In this work, the PTS is optimized to reduce the cubic metric (CM) of OFDM signals with a novel chaotic differential search algorithm (CDSA). The CDSA–PTS is compared with several baseline and state-of-the-art algorithms in terms of convergence rate and CM reduction ability. The acquired numerical results justified that the CDSA–PTS algorithm has low computational complexity and outperforms its counterparts in terms of CM reduction performance and convergence speed. There are several directions
CRediT authorship contribution statement
Hojjat Emami: Presented the idea of CDSA algorithm, Implemented the CDSA algorithm and apply it on PTS scheme, Carried out and supervised the experiment, Writing the manuscript. Abbas Ali Sharifi: Developed the theoretical formalism, Performed the analytic calculations and performed the numerical simulations, Interpretation of the results.
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.
Acknowledgments
Both H. Emami and A. A. Sharifi authors contributed to the final version of the manuscript. They provided critical feedback and helped shape the research, analysis and manuscript.
Hojjat Emami is an assistant professor at the University of Bonab, Iran. He received the Ph.D. degree in artificial intelligence from Malek-Ashtar University of technology in 2016. Before that, he received a Masters degree in artificial intelligence from the University of Tabriz in 2012. His research areas are artificial intelligence, agent-based systems, automated negotiation, expert systems, natural language processing, decision support systems, business intelligence, and data mining.
References (29)
- et al.
An improved backtracking search optimization algorithm for cubic metric reduction of OFDM signals
ICT Express
(2020) - et al.
Imperialist competitive algorithm combined with chaos for global optimization
Commun. Nonlinear Sci. Numer. Simul.
(2012) - S. Afrasiabi-Gorgani, G. Wunder, The method of conditional expectations for cubic metric reduction in OFDM, in: 2019...
- et al.
Partial transmit sequence scheme for envelope fluctuation reduction in OFDMA uplink systems
IEEE Commun. Lett.
(2018) OFDM for Wireless Communications Systems
(2004)- et al.
Peak-to-average power ratio reduction in ofdm systems: A survey and taxonomy
IEEE commun. Surv. Tutor.
(2013) - et al.
Hybrid peak-to-average power ratio reduction techniques: Review and performance comparison
IEEE Access
(2017) - et al.
A novel criterion for designing of nonlinear companding functions for peak-to-average power ratio reduction in multicarrier transmission systems
Wirel. Netw.
(2018) - et al.
On the optimization of iterative clipping and filtering for PAPR reduction in ofdm systems
IEEE Access
(2017) Discrete hartley matrix transform precoding-based OFDM system to reduce the high PAPR
ICT Express
(2019)
A review of partial transmit sequence for PAPR reduction in the OFDM systems
IEEE Access
OFDM PAPR reduction by switching null subcarriers and data-subcarriers
Electron. Lett.
Low-complexity selected mapping schemes for peak-to-average power ratio reduction in ofdm systems
IEEE Trans. Signal Process.
Complexity reduction of PTS technique to reduce PAPR of OFDM signal used in a wireless communication system
IET Commun.
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Hojjat Emami is an assistant professor at the University of Bonab, Iran. He received the Ph.D. degree in artificial intelligence from Malek-Ashtar University of technology in 2016. Before that, he received a Masters degree in artificial intelligence from the University of Tabriz in 2012. His research areas are artificial intelligence, agent-based systems, automated negotiation, expert systems, natural language processing, decision support systems, business intelligence, and data mining.
Abbas Ali Sharifi received the Ph.D. degree in telecommunication engineering from University of Tabriz, Iran, in 2015. Now he is an assistant professor in the department of electrical engineering at the University of Bonab. His current research interests include wireless communication, signal processing, and cognitive radio networks.