  Mixed-numerology transmission is proposed to support a variety of
communication scenarios with diverse requirements. However, as the orthogonal
frequency division multiplexing (OFDM) remains as the basic waveform, the
peak-to average power ratio (PAPR) problem is still cumbersome. In this paper,
based on the iterative clipping and filtering (ICF) and optimization methods,
we investigate the PAPR reduction in the mixed-numerology systems. We first
illustrate that the direct extension of classical ICF brings about the
accumulation of inter-numerology interference (INI) due to the repeated
execution. By exploiting the clipping noise rather than the clipped signal, the
noise-shaped ICF (NS-ICF) method is then proposed without increasing the INI.
Next, we address the in-band distortion minimization problem subject to the
PAPR constraint. By reformulation, the resulting model is separable in both the
objective function and the constraints, and well suited for the alternating
direction method of multipliers (ADMM) approach. The ADMM-based algorithms are
then developed to split the original problem into several subproblems which can
be easily solved with closed-form solutions. Furthermore, the applications of
the proposed PAPR reduction methods combined with filtering and windowing
techniques are also shown to be effective.
