Wireless Communications and Mobile Computing

Volume 2017, Article ID 1421362, 17 pages

https://doi.org/10.1155/2017/1421362

## Transform Methods for the Reduction of the Peak to Average Power Ratio for the OFDM Signal

Department of Electrical Engineering, California State University, Long Beach, CA 90840, USA

Correspondence should be addressed to Rajendra Kumar; ude.blusc@ramuk.ardnejar

Received 26 July 2016; Revised 5 September 2016; Accepted 15 September 2016; Published 12 January 2017

Academic Editor: Michael McGuire

Copyright © 2017 Rajendra Kumar and Vuttipol Santitewagul. 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 paper presents multitransform OFDM-OP system for an effective PAPR (peak to average power ratio) reduction that has a reasonable computational requirement, does not introduce any distortion, needs relatively insignificant decrease in the bandwidth efficiency, and provides a PAPR very close to that for the single carrier modulation systems thus effectively eliminating any PAPR penalty incurred by the multicarrier OFDM system. The PAPR system consists of a bank of multiple orthonormal transforms and a minimum PAPR evaluation unit for finding the optimum transform index. The paper also presents a hybrid OFDM-OP-DSI system comprised of the multiple transforms and a novel dummy symbol insertion. The PAPR reduction performance of the presented systems is compared with those of the various other transform techniques of the literature. Various simulations on the presented systems show that these can achieve a PAPR that is very close to that of a single carrier system for QAM modulation with the order of modulation selected to be 16, 64, and 256.

#### 1. Introduction

Broadband wireless systems are in a rapidly evolutionary phase in terms of development of various technologies, development of various applications, deployment of various services, and generation of many important standards in the field [1–28]. Orthogonal Frequency Division Multiple Accessing (OFDM) techniques offer efficient bandwidth utilization and provide many other advantages such as some immunity against the distortion due to the multipath propagation environment. Therefore, the OFDM techniques have been adapted in many wireless communication and sensor standards, such as the Worldwide Interoperability for Microwave ACCESS (WiMAX), digital audio broadcasting (DAB), digital video broadcasting-terrestrial (DVB-T), and Long Term Evolution (LTE).

However, the use of a relatively large number of carriers used in the OFDM signal results in a relatively high peak to average power ratio resulting in a much reduced radio frequency (RF) power amplifier efficiency and distortion due to the amplifier nonlinearity. In order to keep the distortion to some specified limit, the output RF power is backed off from the maximum available power at the amplifier output. In addition to the reduced output power, the output backoff concurrently also results in the DC to RF power conversion efficiency. A detailed analysis of the distortion effects of the nonlinear power amplifier and some of the mitigating techniques are presented, for example, in [8, 9] and the references therein. Another problem arising due to distortion caused by the amplifier is the spreading of the spectrum of the OFDM signal outside the allocated band [10].

Thus there has been strong motivation to come up with techniques that can reduce the peak to average power ratio of the OFDM signal without causing any distortion in the process of transformation, or losing in terms of bandwidth or other efficiency measures. The paper presents multitransform OFDM-OP system for an effective PAPR (peak to average power ratio) reduction that has a reasonable computational requirement, does not introduce any distortion, needs relatively insignificant decrease in the bandwidth efficiency, and provides a PAPR very close to that for the single carrier modulation systems thus effectively eliminating any PAPR penalty incurred by the multicarrier OFDM system.

The contents of the paper are organized as follows. Section 2 of the paper presents a brief introduction to the OFDM system along with various notations used in the paper. Section 3 provides a brief review of the various peak to average power ratio (PAPR) reduction techniques in the published literature. Section 4 presents multitransform systems and methods recently invented by the first author of the paper and taught in US Patent 8,995,542, March 2015 [11], for an effective PAPR reduction which have a reasonable computational requirement, do not introduce any distortion, need relatively insignificant decrease in the bandwidth efficiency, and provide PAPR very close to that for the single carrier modulation systems thus effectively eliminating any PAPR penalty incurred by the multicarrier OFDM system. Section 5 presents simulation results on the performance of the various PAPR reduction techniques. Section 6 presents some concluding remarks.

#### 2. OFDM System

An OFDM-modulated signal consists of the parallel transmission of several signals that are modulated at different carrier frequencies evenly spaced by [1–7]. The complex valued input symbol sequence is split into subsequences with , , ; . The symbol subsequence modulates a corresponding subcarrier at frequency for . Thus the time sampled version of the complex envelope of the modulated signal is given by (1) wherein the sampling period with denoting the symbol period for the subsequence .The consecutive samples of constitute an OFDM symbol and according to (1) the samples during the th OFDM symbol may be obtained by an point IFFT (inverse fast Fourier transform) of the consecutive symbols in the symbol sequence or the th symbols in the symbol subsequences , . In the multiple access application of OFDM the symbol subsequence may be the symbol sequences generated for the multiple access users rather than subsequences of a single user symbol sequence. The OFDM signal has a guard interval of length for each OFDM symbol to mitigate the intersymbol interference. The sample values during any guard interval are obtained by the periodic extension of the subsequent sample values of . The transmitted radio frequency (RF) OFDM signal is given bywhere denotes the carrier frequency and denotes the continuous time signal obtained by interpolation of the sampled signal using, for example, 0th order hold. The signal may also be band limited by a band limiting filter such as the square root raised cosine filter in generating the analog signal .

Figure 1 shows the block diagram of the OFDM system. Referring to Figure 1, the data that may be a binary stream is inputted to the baseband modulator block that modulates the input data according to a modulation scheme that is selected to be the QAM modulation. The results of the paper will apply equally well to various other modulation techniques such as MPSK or MASK modulation schemes. The complex baseband signal , , is inputted to the serial to parallel converter with the output given by the OFDM modulation symbol vector where , or , ; ; . The inverse fast Fourier transform (IFFT) block provides the inverse Fourier transform of providing the OFDM modulated signal vector of dimension also referred to as the OFDM frame at the output that is inputted to the parallel to serial converter block. The parallel to serial converter block concatenates the components of the vector providing the baseband OFDM signal , given by (1). The complex baseband OFDM signal is inputted into the guard band insert block for extending the OFDM signal duration by the guard interval by a periodic extension of the signal . The OFDM baseband signal with a guard interval denoted by is inputted to a band limiting filter that may be, for example, a square root raised cosine filter and may include a digital to analog converter providing the filtered complex baseband OFDM signal that modulates a carrier signal providing the bandpass OFDM signal given by (2). This paper is focused upon the subsystem of the OFDM system that generates the complex baseband OFDM signal from the input data .