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Wireless communications of today is moving from cellular networks towards more distributed,self-configuring networks.Wireless had a huge growth over the passing years,first with cellular phones,then WiFi and so on. Orthogonal Frequency Division Multiplexing (OFDM) is the prominent candidate for the next generation of wireless communications physical layer standards.The Peak to Average Power Ratio (PAPR) is currently viewed as an important implementation issue in communication systems.Specifically,for wireless cellular systems the price of the mobile unit is required to remain low.High PAPR is one of the challenging issues for the Orthogonal Frequency Division Multiplexing. This thesis is about several PAPR reduction techniques and the related optimization problems.Many criteria involve in the selection of a PAPR reduction technique e.g.capacity, power increase,BER,complexity and throughput.A main consideration is that the cost of extra complexity for PAPR reduction is lower than the cost of power inefficiency.