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Wireless telecommunication systems are almost the most dominant field of the communication systems context nowadays especially the longterm evolution (LTE) system. Orthogonal frequency division multiplexing (OFDM), has become the base for current and future communication systems, because of its capability to combat multipath and fading channels and its competency for high data rate transmissions. However, coherent combination of subcarriers leads to large power peaks with respect to the average power level; this is the socalled peak power ratio (PPR). Various methodologies are available in the literature, the simple approach is the amplitude clipping. However, amplitude clipping causes inband distortion and outofbandradiation, thus, the bit error rate (BER) performance will degrades dramatically. Taher et al (2014) suggested a new amplitudeclipping algorithm, where the coreclipping function was replaced with a nondistorting function, but the proficiency of reducing the PPR was not in the good extent. In this paper, the new clipping function will be supported by frequencydomain randomization operation, such that the coherent combination of the OFDM subcarriers will not stay in the same order, leading to lower PPR at the output of the power amplifier. Results show that the hybrid combination of the randomization process with the new clipping function produces lower values of PPRs. Thus, the proposed approach has gotten 1.5 dB more reduction magnitude in the PPR with respect to Taher et al scheme. The complementary cumulative distribution function (CCDF) was the tool to monitor the PPR performance behavior.
Amplitude Clipping  CCDF  nonlinearity distortion  OFDM  PPR
Calculation of electric fields with the aid of an computer is now an inevitable tool in various electricityconcerned technology, in particular, for analyzing discharge phenomenon and designing high voltage equipments .The calculation of electric fields generally require higher accuracy, because the highest electric field stress on insulator is usually the most important and decisive value in insulation design or discharge study. This is one of reason why the boundarydividing methods are preferred to the regiondividing ones, such as finite difference method (FDM) or finite element method (FEM). The finite difference method is a powerful numerical method for solving partial differential equations. An FDM method divides the solution domain into finite discrete points and replaces the partial differential equations with a set of difference equations. Thus the solutions obtained by FDM are not exact but approximate. However, if the discretization is made very fine, the error in the solution can be minimized to an acceptable level. In this research grid of finite difference method divided (N by N), N represents number of nodes. In our calculation we take many cases, each case contains specific number of nodes such (7, 15, 25). Then we estimate electric field for different charges values and their locations. We depend on equation (AX = b) .Where A matrix represents node values (depend on boundary condition and operating nodes), X matrix represent electric potential, b matrix represents charges values. X estimation using gauss sideral method and successive over relaxation method .Then we calculate residual which calculated by equation (residual = b  AX). Then we estimated and plot Vx , and Vy. We approve accuracy of our calculation by less quantity of residual, which mean X reach to exact solution. Also we approve the residual value increased with number of nodes increase because we need to more calculations also the distance between charges increase.
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