ween transmitter and receiver can be transparent to each other, and is aligned with the 3GPP recommendations about 5G waveform candidates [16]. Fur- thermore, W-OFDM can provide a high robustness against timing and carrier frequency offset in the asynchronous systems [17]. A comparison of the power spectral density (PSD) of the transmit signals of the aforementioned waveforms is illustrated in Figure 3.1. It can be observed that all the new waveforms have much lower OoBE compared with OFDM. Owing to the aforementioned advantages, W-OFDM has become one of the most discussed candidate waveforms for the physical layer of 5G systems. Great efforts have been made to improve the performance of the W-OFDM system. For instance, a joint windowing scheme is proposed in [18] to eliminate adjacent channel interference (ACI) and reduce OoBE. In [19], a time-asymmetric windowing scheme is proposed to elimi- nate the inter-symbol interference (ISI) that is introduced due to the insufficient cyclic prefix (CP) length. Nevertheless, analytical investigations about the INI in W-OFDM are missing in the literature. In this chapter, we will introduce our research about W-OFDM [11] in an analytical way. Specifically, W-OFDM system model for single numerology and mixed-numerology scenarios are derived in Sections 3.2.1 and 3.2.2, respectively. Section 3.3 gives the detailed INI models, and the power of INI is investigated analytically 1 Also known as universal filtered OFDM (UF-OFDM). 3.2 W-OFDM System Model WOFDM FOFDM Normalized frequency (fs) Figure 3.1 Power spectral density comparison of the candidate 5G waveforms. for different numerologies. Simulation results are provided in Section 3.4 to verify the effectiveness of the derivations and analysis, and Section 3.5 concludes the chapter. The notations used in this chapter are illustrated as follows. {.}H and {.} stand for the conjugate transpose and transpose operation, respectively. diag{ {a} denotes the forming of a diagonal matrix A based on vector a. Blkdiag(A, N) is a block di