tes the spectral distance between subcarrier k(k) and the u-th subcarrier of numerology 1, where k(k) = n2(k + AF(2) represents the subcarrier indexes of numerology 2 when its k-th subcarrier is observed with a granularity of Af(1). In addition,()ithe for the u-th subcarrier of numerology 1. Note that the interference from the (m - 1)-th transmitted symbol of numerology 1 is considered, which is shown as the dashed part in Figure 3.6. As shown in Figure 3.6, the first received numerology 2 symbol may be interfered by the numerology 1 transmitter window of the previous LCM symbol duration. Thus, for differ- ent receiver windows of numerology 2, the INI power within one LCM symbol might be slightly different. Hence, we define the average power of INI to measure the INI suffered by subcarrier k of numerology 2 as (k,m). (3.31) Likewise, the overlapping window in the CP-OFDM system is illustrated in Figure 3.7 for comparison. With (3.28) and (3.31), for the k-th subcarrier of numerology i, the component signal to interference ratio (SIR) caused by the u-th subcarrier of numerology j can be calculated as (3.32) where the power of the desired signal based on (3.20). Furthermore, the total of numerology i can be written as (3.33) 3 Windowed OFDM for Mixed-Numerology 5G and Beyond Systems Tx window numerology 1 N (Superscript((1) Rx window Rx window numerology 2 numerology 2 Overlapping Overlapping window window Figure 3.7 INI analysis for numerology 2 in CP-OFDM case. where (k)= is the entire INI power generated from numerology j. The quantitative comparison of SIRs between CP-OFDM and W-OFDM will be provided in Section 3.4. 3.4 Numerical Results and Discussion In this section, simulation results are provided to evaluate the effectiveness of the derived INI power for W-OFDM systems. In the simulations, we consider that two different numerologies are assigned to adjacent subbands as illustrated in Figure 3.3. The first numerology is with Af(1) = 15 kHz SCS and 1024-points DFT, while the second adopts Af(2)=3 30 kHz with 