Journal of Electrical and Computer Engineering

Volume 2018, Article ID 3075890, 11 pages

https://doi.org/10.1155/2018/3075890

## PAPR Reduction Using Fireworks Search Optimization Algorithm in MIMO-OFDM Systems

^{1}Optics & Photonics Team, Faculty of Sciences, Abdelmalek Essaadi University, Tétouan, Morocco^{2}Information Technology and Systems Modeling Team, Faculty of Sciences, Abdelmalek Essaadi University, Tétouan, Morocco

Correspondence should be addressed to Lahcen Amhaimar; am.ca.eau@ramiahmal

Received 2 March 2018; Revised 6 July 2018; Accepted 25 July 2018; Published 3 September 2018

Academic Editor: Tho Le-Ngoc

Copyright © 2018 Lahcen Amhaimar et al. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

#### Abstract

The transceiver combination technology, of orthogonal frequency division multiplexing (OFDM) with multiple-input multiple-output (MIMO), provides a viable alternative to enhance the quality of service and simultaneously to achieve high spectral efficiency and data rate for wireless mobile communication systems. However, the high peak-to-average power ratio (PAPR) is the main concern that should be taken into consideration in the MIMO-OFDM system. Partial transmit sequences (PTSs) is a promising scheme and straightforward method, able to achieve an effective PAPR reduction performance, but it requires an exhaustive search to find the optimum phase factors, which causes high computational complexity increased with the number of subblocks. In this paper, a reduced computational complexity PTS scheme is proposed, based on a novel swarm intelligence algorithm, called fireworks algorithm (FWA). Simulation results confirmed the adequacy and the effectiveness of the proposed method which can effectively reduce the computation complexity while keeping good PAPR reduction. Moreover, it turns out from the results that the proposed PTS scheme-based FWA clearly outperforms the hottest and most important evolutionary algorithm in the literature like simulated annealing (SA), particle swarm optimization (PSO), and genetic algorithm (GA).

#### 1. Introduction

The transmission data through the use of multicarrier modulation techniques like orthogonal frequency division multiplexing (OFDM) has been considered as a good choice for data transmission over single carrier systems. The OFDM technique has various advantages and now being used in a number of wireless communication systems. Meanwhile, the multiple-input multiple-output (MIMO) with OFDM system, has recently attracted a great deal of attention due to its various advantages such as high data rate, spectral efficiency, diversity in a fading environment, and robustness to channel fading [1]. Hence, a system with OFDM modulation and multiple transmit and multiple receive antennas (MIMO-OFDM) is now becoming adopted by several applications such as digital audio broadcasting (DAB), Worldwide Interoperability for Microwave Access (WiMAX), the fourth generation of telecommunication systems (4G), digital video broadcasting (DVB), high speed WLAN standards, and many others application areas of MIMO-OFDM [2]. But besides these useful advantages, it still suffers from the high envelope fluctuations of the transmitted signal called the peak-to-average power ratio (PAPR), which decreases the efficiency of high power amplifiers (HPA), improves the complexity of nonlinear elements, and causes out-of-band radiation with degradation of bit error rate (BER).

To deal with this problem, several solutions have been proposed to mitigate the high PAPR of OFDM [3, 4] and MIMO-OFDM signals [5, 6], as clipping [7], clipping and filtering [8], coding [9], tone injection [10], peak windowing [11], selected mapping [12], and partial transmit sequence (PTS) [13–15]. All these methods have their own advantages and disadvantages, but the PTS technique is still the most attractive one due to its efficiency in PAPR reduction. However, the exhaustive search complexity of finding the optimal phase combination for PTS increases exponentially with number of subblocks and to reduce the computational complexity, many evolutionary algorithms for optimization-based PTS schemes have been proposed such as genetic algorithm (GA) [16, 17], ant colony optimization (ACO) [18], simulated annealing algorithm (SA) [19], and the most well-known algorithm of particle swarm optimization (PSO) [20, 21]. In this paper, we propose a novel swarm intelligence algorithm called fireworks algorithm (FWA) [22], to reduce the PAPR with less complexity and more easy implementation, and this developed search optimization algorithm is based on the explosion process simulation of fireworks. It turns out from the results that the proposed method FWA-PTS effectively reduces PAPR of MIMO-OFDM signal and clearly outperforms the old algorithms in both global high precision of calculated solution and convergence speed.

This manuscript is organized as follows. In Section 2, MIMO-OFDM system model and the PAPR problem is formulated, and then the principles of PTS techniques are introduced. Section 3 describes the framework of the FWA-based PTS and mechanisms of the algorithm with some improved version, while Sections 4 and 5 are devoted to the analysis of simulation results and conclusions successively.

#### 2. MIMO-OFDM System and PTS Approach

##### 2.1. PAPR of the MIMO-OFDM Signal

The transmission of signal through the use of transceiver based on orthogonal frequency division multiplexing (OFDM) system is a typical technique which divides the effective spectrum channel to a number of orthogonal subchannels, and with equal bandwidth, each subchannel handles independently with its own data using individual subcarrier, and the OFDM signal is the sum of all independent subcarriers. In transmission systems with multicarrier signal, the input data of binary sequences are mapped into symbols by a modulator (PSK, QPSK, QAM, etc.). Then, the N symbols are inserted into the IFFT block to modulate each subcarrier independently and to obtain the OFDM signal in time domain .

The complex envelope of OFDM signal in the discrete time domain with oversampled factor *L* (usually used ) can be mathematically written aswhere is the number of subcarriers and is the *n*th complex symbol carried and transmitted by the subcarrier.

From equation (1), the signal in time domain generated by IFFT operation consists *N* number of independently modulated and orthogonal subcarriers with large peak values (PAPR) when added up at the output of IDFT block. The PAPR of the OFDM signal in discrete time is defined as the ratio between the maximum power and the average power of the complex OFDM signal, and it can be defined aswhere is given by (1) and denotes the expected value (average power).

MIMO-OFDM is a generalized case of OFDM systems based on space time block code (STBC) [23–25] for two, three, and four antennas. The encoder signal with two transmitting antennas, using Alamouti code and an input signal is written as

The signals and are transmitted by antennas 1 and 2, respectively.

At each antenna of MIMO-OFDM system, the peak-to-average power ratio is defined aswhere number of transmitted antennas. The time domain signal at each transmit antennas can be presented as

The expression characterized the peak power variation of MIMO-OFDM systems is defined as

##### 2.2. PAPR Reduction by Partial Transmit Sequence

The probabilistic distortionless technique of partial transmit sequence presented in Figure 1, divided an input data block into *V* disjoint subblocks, represented by the vector , such that . The partition of subblocks was performed with a simple method, where all the used subcarriers by another block must be zero so that the sum of all the disjoint subblocks constitutes the original signal. Then, the subblocks are oversampled and transformed to time domain by LN-point IFFT (inverse fast Fourier transform) and using an optimization algorithm or conventional searching method, each subblock is multiplied by a phase factor as follows:where is the time domain signal of each subblock . The complex phase factor , rotates the sequences independently to obtain the OFDM signals with the lowest PAPR possible. The phase vector is chosen within interval, and the optimum one can be presented as