On the computation and reduction of the peak-to-average power ratio in multicarrier communications
For any code C defined over an equal energy constellation, it is first shown that at any time instance, the problem of determining codewords of C with high peak-to-average power ratios (PAPR) in a multicarrier communication system is intimately related to the problem of minimum-distance decoding of C. Subsequently, a method is proposed for computing the PAPR by minimum-distance decoding of C at many points of time. Moreover, an upper bound on the error between this computed value and the true one is derived. Analogous results are established for codes defined over arbitrary signal constellations. As an application of this computational method, an approach for reducing the PAPR of C proposed by Jones and Wilkinson is revisited. This approach is based on introducing a specific phase shift to each coordinate of all the codewords where phase shift are independent of the codewords and known both to the transmitter and the receiver. We optimize the phase shifts offline by applying our method for computing the PAPR for the coding scenario proposed by ETSI BRAN Standardization Committee. Reductions of order 4.5 dB can be freely obtained using the computed phase shifts. Examples are provided showing that most of the grain is preserved when the computed optimal phase shifts are rounded to quantenary phase-shift keying (PSK), 8-PSK, and 16-PSK type phase shifts.
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