# Review of Channel Estimation for Candidate Waveforms of Next Generation Networks
## 2 Structure of Filter Bank Multi-Carrier Systems
### Basic Structure of FBMC Systems  
Digital filter bank multi-carrier based transceivers are made up of two filter banks: synthesis filter bank (SFB) and analysis filter bank (AFB) [22; 24]. The synthesis filter bank is positioned at the transmitter while the analysis filter bank is found at the receiver. It is designed with \(M\) digital filters arranged in a parallel configuration [22; 24]. The synthesis filter combines \(M\) signals at the transmitter into a single signal that is ready for transmission over a channel. This single signal can also be referred to as the reconstructed signal. In PR filter banks, the output signal is a delayed replica of the input signal [34]. In practical applications, the output signal is designed to achieve NPR. As in the design of decimation and interpolation filters discussed in Section 2.1, the synthesis filter bank is designed with an interpolation filter and an upsampler, while the analysis filter is designed with a decimation filter and a downsampler. This makes the multirate filters periodically linear time-varying systems because they are made up of linear filters and also perform time-varying linear operations such as decimation [35]. Figure 5 illustrates a basic structure of digital filter banks [10; 36]. Figure 4: Basic structure of polyphase filters. Figure 3: Time domain plot of signal decimation for \(M=2\). This structure is considered as an FBMC system because it is designed to offer multirate filtering where the sampling rate of the input symbols \(x[n,k]\) at the transmitter is increased using an interpolator. Subsequently, it is filtered with a low-pass anti-imaging filter \(g[\hat{n},k]\) so as to remove images of the input spectrum. In other words, this system is adopted to connect and transmit the input symbols \((x[n,k])\) over the fading channel by converting the symbols into higher rates using an SFB. This enhances efficient data transmission over the frequency selective multipath fading channel in comparison with single rate multi-carrier systems. The upsampling of the input symbols at the SFB is performed in order to ensure that the sampling rate of the signals at the receiver input is the same, which is subsequently decimated at the AFB by filtering the received signals with the aid of an anti-aliasing filter \((f[\hat{n},k])\). The anti-aliasing filter is adopted so as to combat aliasing. The signal is then appropriately downsampled to obtain \(\hat{x}[n,k]\) in order to ensure efficient demodulation/detection of the received symbols. The concepts in Figure 4a,b are combined via a communication channel to realise the general structure of FBMC systems shown in Figure 5. One effective way of implementing FBMC based schemes assuming NPR is by realising the system through the use of discrete Fourier transform (DFT) based polyphase filter bank model, where IFFT is used to transform the input signal from the frequency domain to the time domain. These concepts are combined for the design of the FBMC based transceivers shown in subsequent sections. Potential FBMC waveforms for 5G networks include filter bank OFDM-OQAM, UFMC [13], BFDM [15; 16], and GFDM [37]. These waveforms can be designed using FBMC structures, such as exponentially or cosine modulated filter banks. The aforementioned FBMC transmission waveforms are usually designed based on DFT. Hence, they are classified as DFT based FBMC systems. Other FBMC transmission technologies include discrete wavelet multitone (DWMT) [27; 28], filtered multitone (FMT) [9] and cosine modulated multitones [38]. The technologies in [9; 27; 28; 38] are designed based on discrete wavelet transforms (DWT). Accordingly, we classify the FBMC schemes based on the modulation type in Figure 6.  
Figure 5: Basic structure of FBMC based transceivers. Figure 6: Classification of FBMC schemes based on modulation. Unlike the DFT based FBMC systems, the DWT based FBMC systems employ the use of wavelet packet transforms (WPT).