# An Improved GreenOFDM Scheme for PAPR Reduction
## 1 Introduction  
Orthogonal Frequency Division Multiplexing (OFDM) is a widely used modulation technique for wireless communication systems thanks to its high spectral efficiency and robustness against frequency-selective channel. However, a well-known limitation of OFDM (as well as other multi-carrier schemes) is its high Peak-to-Average Power Ratio (PAPR) [1]. In addition, the PAPR in OFDM is a random variable. These characteristics of the PAPR in OFDM are troublesome for many reasons:  
1. the PAPR of OFDM signals needs to be correctly estimated in order to take its dynamic range into consideration for the Digital-to-Analog Converters specification [2, 3]. 2. in order to correctly estimate the PAPR of OFDM signals in the digital domain, the computational complexity of the digital modulator is increased due to oversampling [4]. 3. the high PAPR of these signals generally increases the Power Amplifier's (PA's) power dissipation as its linear region has to be extended to be able to accommodate signals with wide amplitude excursions. Not doing so results in non-linear distortions and out-of-band radiations that degrade the system performances [5]. To counteract the above-mentioned limitations, several PAPR reduction schemes have been proposed in the literature (with well documented surveys like [6, 7, 8] that outline the most important schemes that have been proposed during the last couple of decades). These schemes could be classified like proposed by [7, 8] into different but not exhaustive categories as follows:Signal distortion techniques: Clipping and Filtering [9, 10], Compounding [11]. * Multiple signaling and probabilistic techniques: SeLected Mapping OFDM (SLM-OFDM) [12, 13], Tone Injection [14], Tone Reservation [15, 16], Active Constellation Extension [17], and Partial Transmit Sequence (PTS) [18]. * Pre-coding techniques: Single Carrier Frequency Division Multiple Access (SC-FDMA) [19] and Carrier Interferometry [20, 21]. Among these schemes, the SLM-OFDM is a well known one and has very recently been improved into the so-called GreenOFDM technique [22, 23]. The underlying idea of SLM-OFDM is to generate a number of different OFDM symbol waveform candidates from the same data and to select the waveform with the lowest PAPR for transmission. For SLM-OFDM, the PAPR reduction depends on the number of waveform candidates; the more the number of candidates, the lesser the PAPR of OFDM. Essentially, GreenOFDM is a SLM-OFDM variant that increases the number of candidates in a square-scale while using the same number of Inverse Fast Fourier Transforms (IFFT) as in conventional SLM-OFDM. Thus, for a given number of computed IFFTs, a better PAPR reduction for GreenOFDM is attained as compared to SLM-OFDM. GreenOFDM receives attention in the literature [24, 25, 26, 27]. Some works compare the original GreenOFDM scheme with PTS variants but without using the same scheme [26, 27]. Other works aim to improve the PAPR reduction capabilities as in [24], but the results seem to come from a not so exhaustive simulation study. Finally, other works like [25] reducing the complexity by relaxing the PAPR reduction capability as it has been also proposed in other works [28]. In contrast to previous studies, we propose, in this paper, a simple yet efficient improvement of the GreenOFDM that allows us to obtain a higher number of candidates without increasing the number of IFFTs. As shall become apparent, this extension of the original GreenOFDM technique relies on the linearity of the IFFT that allows for simplifications in the initial GreenOFDM and permits a reduction by a factor of 2 of the number of IFFTs for a same PAPR performance, providing a relevant gain in terms of performance/complexity trade-off. The proposed idea results in PAPR reductions that are statistically similar to those obtained independently in [29]. However, in this work we provide analytical expressions to predict the PAPR in a given configuration, which aids the design of the analog front-end [2, 3, 5], and suggest further complexity reductions.