## 1 Introduction  
Ultra Wideband (UWB) technology has been deployed for broadband wired and wireless communications since in February 2002, the implementation of a regulation gave authorization on the use of UWB technology for telecommunications consumer in the United States by the Federal Communications Commission (FCC). Once the frequency band of 7.5 GHz not subject to licensing (FCC 02-48) has been allotted, the FCC welcomed the very high data rate (beyond Gbps) wireless communications. UWB was basically linked to waveforms without carriers (carrier-free) built from very short pulses [1,2]. In this way, a simple approved definition considered that these signals having a fractional bandwidth \(FB\geq 0.25\) with a frequency bandwidth \(\geq\)500 MHz can be considered UWB [2]. OFDM is a modulation technology that guarantees an orthogonality in the frequency domain since it uses the sinusoidal basis function [3]. Then, a cyclic prefix or zero padding is added to each symbol, which makes it possible to avoid the inter-symbol interference (ISI) due to the multipath channel. However, if the orthogonality between the sub-carriers is lost, it results in inter-carrier-interference (ICI), and thus OFDM system performances is degraded. In order to decrease the impact of these problems, a new Multi-band Orthogonal Frequency Division Modulation (MB-OFDM) system has been proposed in [4]. To make wireless connectivity possible between devices within the personal area network. At the same time, it is important to undergo the European Conformity (CE) and the multimedia industry current needs in the field of wireless personal area network (WPAN) with very high data-rates or for their use in future Wireless Universal Serial Bus (WUSB/IEEE 1394) [5], different standards have been implemented: Multi-band OFDM Alliance (MBOA), Wimedia and ECMA-368 [6]. In this paper, the ECMA-368 Standard is used. It points out the MB-OFDM scheme to transmit information for a wireless personal area network, however identically to all OFDM based communications systems, the ECMA-368 undergoes the large Peak to Average Power Ratio (PAPR), this drawback reduces the High Power Amplifier (HPA) efficiency at the transmitter. In the ECMA-368 system, very efficient amplifiers are used, mainly of two different types, namely, Traveling Wave Tube Amplifiers (TWTA) and Solid State Power Amplifiers (SSPA). Unfortunately, these amplifiers are highly non-linear and thus, in order to avoid the distortion of the signal, large back-offs are needed. As result, the efficiency is substantially reduced. This phenomenon leads to the in-band distortion, which increases the bit error rate (BER) [7] and the out-band spectral re-growthwhich also increases adjacent channel interference. Numerous methods have been proposed to overcome the high PAPR problem in OFDM signals [8; 9]. Among these techniques, the HPA pre-distorter [10] is one of the most promising ones because it avoids the increase on transmit energy, it does not need side information which reduces efficiency, it is only needed to be applied at the transmitter, which eases the implementation, and it does not increase the BER, among other advantages. It should be noted that most of the results and designing parameters in this paper can also be extended to other OFDM standards [11; 12; 13; 14]. TWTA and SSPA are the most efficient amplifiers, and are the two main amplifier choices for space-based RF communications. TWTA and SSPA are generally more advantageous for higher power and higher frequencies, at a reduced size, cost, and with improved thermal performance. Unfortunately, these amplifiers are highly non-linear [15], hence, a large back-off [16] is needed to mitigate the signal distortion. As outcome, the efficiency is substantially reduced. To run off a large back-off, several techniques were used to reduce the power envelope fluctuations (PAPR) [8; 17]. However, the non-linearity of HPA [18] still provoke a signal distortion, compromising the system performance.