ect of the prototype filter design is covered in Section 5.4. Synchronization and tracking methods are then discussed in Section 5.5. The topics of channel equalization and computational complexity are briefly discussed in Sections 5.6 and 5.7, respectively. Lastly, in Section 5.8, we discuss some potential applications of FBMC. 5.1.1 Notations: The presentations in this chapter follow a mix of continuous-time and discrete-time formu- lations, as appropriate. While x(t) refers to a continuous function of time t, x[n] is used to refer to its discrete-time version, with n denoting the time index. The notation f is used as frequency variable in X(f), the Fourier transform of the continuous-time signalx(t) and also as normalized frequency in X(ei2nf), the Fourier transform of the discrete-time signal x[n]. We use to denote linear convolution, and the superscript * to denote complex conjugate. Radio Access Network Slicing and Virtualization for 5G Vertical Industries, First Edition. Edited by Lei Zhang, Arman Farhang, Gang Feng, and Oluwakayode Onireti. © 2021 John Wiley & Sons Ltd. Published 2021 by John Wiley & Sons Ltd. 5 Filter Bank Multicarrier Modulation FBMC Methods FBMC communication techniques were first developed in the mid-1960s. Chang [3] presented the conditions required for signaling a parallel set of pulse amplitude modu- lated (PAM) symbol sequences through a bank of overlapping filters within a minimum bandwidth. To transmit PAM symbols in a bandwidth-efficient manner, Chang proposed vestigial sideband (VSB) signaling for subcarrier sequences. Saltzberg [4] extended the idea and showed how Chang's method could be modified for transmission of quadrature amplitude modulation (QAM) symbols in a double-sideband (DSB)-modulated format. In order to keep the bandwidth efficiency of this method similar to that of Chang's signaling, Saltzberg noted that the in-phase and quadrature components of each QAM symbol should be time staggered by half a symbol interval. Another key development appeared in [5], where th