  The advent of mixed-numerology multi-carrier (MN-MC) techniques adds
flexibilities in supporting heterogeneous services in fifth generation (5G)
communication systems and beyond. However, the coexistence of mixed
numerologies destroys the orthogonality principle defined for single-numerology
orthogonal frequency division multiplexing (SN-OFDM) systems with overlapping
subcarriers of uniform subcarrier spacing. Consequently, the loss of
orthogonality leads to inter-numerology interference (INI), which complicates
signal generation and impedes signal isolation. In this paper, the INI in
MN-OFDM systems is characterized through mathematical modeling and is shown to
primarily rely on system parameters with regard to the pulse shape, the
relative distance between subcarriers and the numerology scaling factor.
Reduced-form formulas for the INI in continuous-time and discrete-time MN
systems are derived. The derived mathematical framework facilitates the study
of the effect of discretization on the INI and partial orthogonality existing
in subsets of the subcarriers. The reduced-form formulas can also be used in
developing interference metrics and designing mitigation techniques.
