In this paper, we study the tone reservation method for reducing the peak-to-average power ratio (PAPR) in general orthonormal transmission systems. We prove that strong solvability, where the peak value of the transmit signal has to be bounded by a constant times the energy of the information symbols, is equivalent to weak solvability, where the peak value of the transmit signal has to be only bounded. Further, we show that in the case where the PAPR problem is not weakly solvable, almost all information sequences lead to an unbounded transmit signal.
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Boche et al. (2018) studied this question.
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