Application of the Method of Conditional Expectations for Reduction of PAPR and Cubic Metric of OFDM Signals
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The OFDM waveform exhibits high fluctuation in the signal envelope, which causes the nonlinear power amplifier of the transmitter to produce distortion. Peak-to-Average Power Ratio (PAPR) and Cubic Metric (CM) are the most commonly used metrics to quantify the phenomenon. Originally proposed in the literature for PAPR reduction, the Sign Selection problem is an approach for minimizing the metric of interest by altering the signs of the data symbols, which implies an exponential complexity. In this paper, the Method of Conditional Expectations (CE Method) is proposed to obtain a competing suboptimal solution to the Sign Selection problem. For PAPR reduction, a surrogate metric is introduced which allows for a more efficient application of the CE Method compared to a direct application to the PAPR metric itself without considerable performance degradation. For CM reduction, the tractability of the definition of CM is exploited to efficiently apply the CE Method. The reduction performance is analyzed to obtain a constant upper bound on the reduced metric value for every realization of the data symbols. Simulations show a persistent reduction of the effective PAPR - the value at which the distribution function of PAPR equals 0.999 - to about 6.5dB for a wide range of 64 to 1024 subcarriers. The steady performance is observed for CM reduction as well with a reduction of roughly 3dB. A pruned version of the sign selection approach is made possible by the CE Method, such that it reduces the rate loss from log_2 M to 1/2log_2 M bits per symbol for M-ary modulation order with insignificant loss in performance
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