y 2 numerology 2 N Superscript(1) Rx window numerology 1 Overlapping window Overlapping window Figure 3.4 INI analysis for subband when using numerology 1. 3 Windowed OFDM for Mixed-Numerology 5G and Beyond Systems Tx window Tx window numerology 2 numerology 2 N Superscript(1) Rx windowinumerology 1 Overlapping Overlapping window window Figure 3.5 INI analysis for numerology 1 in the CP-OFDM case. The difference between W-OFDM and CP-OFDM can be observed by comparing Figure 3.4 and 3.5, i.e. overlapping windows of CP-OFDM are rectangular windows with sharp transitions, while in W-OFDM system, the overlapping windows have smooth transition edges. As the level of INI depends on the discrete Fourier transform (DFT) magnitude of overlapping windows, the smooth time-domain transitions between symbols result in faster decay of the spectrum magnitude and hence a reduced INI. 3.3.2 Inter-numerology Interference Analysis for Numerology 2 By performing similar derivations as we did for numerology 1, the INI power level of numerology 2 can be expressed as (3.29) Consider that in the generalized synchronous scenario [4], one LCM symbol consists of samples. If we assume that the m-th received symbol of numerology 2 belongs to the m-th LCM symbol, it may be interfered by the m-th and (m - 1)-th transmitted symbol from numerology 1, where m=m.we = define m = mn2 + d, where d represents the relative position index for the m-th receiver window of numerology 2 within one LCM symbol, , N2 - 1. Again, we consider a channel with a smaller delay spread than the symbol duration. By substituting (3.2) and (3.4) into (3.29), the power of component INI can be calculated as (derivations are provided in Appendix C) (3.30) 3.3 Inter-numerology Interference Analysis Tx roff Tx window Numerology 1 Rx window Rx window numerology 2 numerology Rx_roff Overlapping Overlapping window window Figure 3.6 INI analysis for subband using numerology 2. where is the overlapping window generated by dN(2) (as illustrated in Figure 3.6). Ak ² = k k k - u deno