 Figure 3.10b. However, no apparent SIR gain can be found for numerology 2 when Max is increasing, which is probably because of the two following factors. Firstly, although the increase of MTX (1) may decrease the sidelobes of numerology 1, it also generates larger overlapping of adjacent symbols, which leads to extra INI from previous LCM symbol for numerology 2 (as shown in Figure 3.6). Secondly, for numerology 2, the smooth transition edges of overlapping windows are mostly inherited from the roll-off parts of the victim's receive window. 3.5 Conclusions To conclude, a promising low OoBE radiation waveform, i.e. W-OFDM, is discussed ana- lytically in this chapter. Specifically, the INI model of W-OFDM system is investigated in the scenario of mixed numerologies transmission. Analytical expressions of the INI power are derived, which explains how the transmitter and receiver windows affect the INI level. Simulations are performed to verify the effectiveness of the derivations. According to the analysis in this chapter, it can be observed that the INI level in a mixed numerologies sys- tem depends on the spectral distance between the numerologies, the CFR of interferer, and the overlapping windows generated by the aggressor's transmitter windows and victim's receiver window. Compared to the normal OFDM, significant SIR gain can be achieved for the subcarriers with relatively large spectral distance by applying W-OFDM. The analytical expressions in this chapter can be easily extended to other OFDM-based systems and can be considered as the guideline for the design and waveform optimization of systems of 5G and beyond. 3.A Appendix 3.A.1 Derivation of (3.9) Substitute (3.3) and (3.1) into (3.5) and assume that the transmitter window and the receiver window satisfy conditions (3.6) and (3.7); we have w(1)(k). (3.A.1) 3 Windowed OFDM for Mixed-Numerology 5G and Beyond Systems Then, (3.9) can be obtained by substituting (3.8) in (3.A.1). In addition, y;(q,n,e,d) is defined as LSYM-1 12=0 r=l1-l2 (3.A.2) r=l1-12 where