Tone Reservation´s Complexity Reduction Using Fast Calculation of Maximal IDFT Element

High peak to average power ratio (PAPR) is a main area of concern in multi-carrier signals like Orthogonal Frequency Division Multiplexing (OFDM) modulated signals and several techniques have been devised to reduce PAPR. One of these PAPR reduction techniques is ´Tone Reservation´ where PAPR is reduced by adding tones to the useful data tones to reduce the temporal signal´s peak. IDFT is performed to see the effect of the added tones on temporal signal´s peak and then the tones are adjusted in frequency domain accordingly to minimize this peak. Enormous use of IDFT operations to get optimized reserved tones makes Tone Reservation technique quite complex. During this optimization process, only the knowledge of maximal IDFT element is required though. Truncated IDFT algorithm calculates only this value and not the complete IDFT output and thus it makes the Tone Reservation´s IDFT complexity O(1.5N_itr.N) instead of O(N.N_itr.log₂(N)) where N and N_itr are size of IDFT and number of algorithm iterations respectively. This complexity reduction is achieved at the cost of less PAPR reduction. Afterwards, a combination of Truncated and classical IDFT algorithms is presented to be used for tone optimization which improves the PAPR reduction performance. It is observed that the complexity is reduced to half using this combination when compared to Tone Reservation classical IDFT complexity at the cost of 0.3 dB performance loss.