Theoretical Analysis of the Peak-to-Average Power Ratio and Optimal Pulse Shaping Filter Design for GFDM Systems

Generalized frequency division multiplexing (GFDM) has been regarded as a candidate for new multicarrier modulation schemes in future wireless communication systems (e.g., 5G systems). However, GFDM systems still suffer from the problem of high peak-to-average power ratio (PAPR). In this paper, theoretical analysis of the PAPR distribution for GFDM signals is performed. Exact closed-form expressions for the complementary cumulative distribution function (CCDF) of PAPR are firstly derived for critically sampled and oversampled GFDM signals, respectively, which tend to be sufficiently accurate as the number of subcarriers K is large enough (e.g., K ≥ 64). With aid of theoretical analysis results, an optimization criterion for the design of pulse shaping filters is obtained, which can nearly achieve the globally minimum CCDF results and is appropriate for practical applications. This criterion can also achieve the globally optimal result for minimizing the variance of instantaneous power. Based on this criterion, a measurement for the overall deviation of filter coefficients is proposed, which can help to roughly and efficiently evaluate the ability of PAPR reduction for pulse shaping filters. Although the PAPR reduction effect is limited with pulse shaping filters, it is found that large deviation may also lead to higher PAPR. Additionally, with the aid of closed-form CCDF expressions, PAPR characteristics of GFDM and other multicarrier systems (e.g., OFDM and FBMC/OQAM) are compared thoroughly. Simulation results verify the validity and accuracy of derived theoretical results, and demonstrate the effectiveness of the proposed optimization design criterion.