## 1 Introduction  
Recently, ultra wideband (UWB) has been used for radar or sensing in vehicular communications that play an essential role into operational areas in Smart Cities [1, 2]--in addition, in military communications and niche applications for its number of advantages that make it attractive for consumer communications applications (low cost, resistant to severe multipath and good time resolution) [3]. In vehicular communications [4], those advantages are especially relevant since transmissions must be reliable for safety applications. Moreover, the requirements are very strict in terms of power consumption and data rate due to the critical applications. In February 2002, the Federal Communications Commission (FCC) has implemented a regulation authorizing the use of UWB technology for telecommunications consumer in the United States by assigning a frequency band of 7.5 GHz not subject to licensing (FCC 02-48), the FCC opened the door for a very high data rate (beyond Gbps). The terminology UWB refers at first to waveforms without carriers (carrier-free) made of very short pulses [5]. In this context, a commonly accepted definition is that these signals have a fractional bandwidth (FB), greater than 0.25 with a frequency bandwidth greater than 500 MHz [6]. The calculation of fractional bandwidth is indicated in Equation (1)  
\[F_{B}=\frac{(F_{H}-F_{L})}{F_{C}}\ \ \text{with}\ \ F_{C}=\frac{(F_{H}+F_{L})}{2}, \tag{1}\]  
where \(F_{H}\) is the upper frequency, \(F_{L}\) is the Lower Frequency and \(F_{C}\) is the Center Frequency. Orthogonal Frequency Division Multiplexing (OFDM) technology is a modulation technique adopted in many broadcast standards. This is due to many advantages of OFDM: Robustness to frequency fading (very important in V2V - Vehicle to Vehicle communications) [7], resilient to intersymbol interference (ISI), spectrum efficiency and simple channel equalization. The ECMA(European Computer Manufacturers Association)-368 Standard also specifies a Multiband Orthogonal Frequency Division Modulation (MB-OFDM) scheme to transmit information for a wireless personal area network (WPAN). Despite the advantages of OFDM, however, it is characterized by large power envelope fluctuations, thereby a loss of power efficiency is obtained when signals go through the High Power Amplifier (HPA) due to the nonlinearity. This is particularly important in wireless sensor networks where the energy constraints are very strict. In the literature, there are many proposals to reduce or mitigate this problem in OFDM signals such as [8; 9; 10]. Active Constellation Extension (ACE) is one of the best choices to solve this drawback that is able to obtain a signal with an arbitrarily low Peak to Average Power Ratio (PAPR) with the adequate number of iterations. The ACE method modifies and expands the constellation points within an allowable region without affecting the demodulation slicer, and thus it does not need side information. In [10], different algorithms to achieve PAPR reduction through ACE are provided. The main problem with these algorithms is the complexity and convergence mainly due to high number of iterations, although arbitrarily low PAPR signals can be obtained. In [11], a neural network (NN) technique, referred to as Multilayer Perceptrons (MLPs), to obtain signals with low envelope fluctuations has been developed. Indeed, NN have been widely applied in solving optimization problems [12; 13; 14]. In the case of the PAPR proposal in [11], the NN were trained with the Approximate Gradient Projection (AGP) from ACE [10] and thus the result is an NN that generates from the original signal another one with similar characteristics as ACE but without its complexity and in one shot. The algorithm in [11] reduces the complexity, but, from the point of view of the implementation in a real system, only theoretical results are given.