# A Survey of Candidate Waveforms for beyond 5G Systems
## 4 Performance Results and Discussion
### Further KPI Discussion  
In this subsection, other KPI for each waveform are compared and analyzed in further detail:  
* Processing delay and filtering/windowing: These KPI are directly related. GFDM relies on a CP insertion and performs the filtering operation by sub-carrier, after an upsample operation, requiring a long filter length (narrow bandwidth). Thus, the overall block processing delay will be high [4,6]. Both TIBWB-OFDM with and without WTO perform the filtering operating per sub-band, and thus, they use shorter filter length (wide bandwidth). However, the overall system delay is still high because the systems require that each one of the OFDM-based sub-symbol go through several operations. Besides, FFT modulation formats involving a relatively high duration multi-symbols are employed. Therefore, the overall block processing delay will be high for all these waveforms and they are not suitable for low latency applications. Additionally, F-OFDM schemes use shorter filter lengths and although including large CP lengths, the overall symbol duration remains low, compared to the previous waveforms. Thus, from the point of view of this KPI, the most suitable waveforms are OFDM and F-OFDM. * Robustness to frequency-selective channels: Overall, all the MC waveforms are robust to the frequency selectivity of the wireless channel. The OFDM principle is to divide the transmission channel's bandwidth into narrowband sub-carriers, by transforming a broadband frequency selective channel into multiple narrowband flat-fading sub-channels. Therefore, deep fadings will affect only a few sub-carriers. F-OFDM is based on OFDM schemes and GFDM can be seen as a generalization of OFDM [68], with both presenting the same robustness as OFDM, regarding multipath propagation. Both TIBWB-OFDM with and without WTO go beyond that and allow a deeper level of robustness against deep fading [46], due to the inclusion of the time interleave/deinterleave operations in their transceiver design, granting a higher degree of diversity in the frequency domain and robustness upon transmission under deep inband channel fades. Thus, from the point of view of this KPI, the most suitable waveforms are TIBWB-OFDM with and without WTO. * Robustness to time-selective channels: When the user mobility is taken into account, the changes of the transmission channel can cause ICI, affecting all the MC waveforms. F-OFDM is as robust as OFDM regarding this KPI. However, in [38,47] it is shown, respectively, that both GFDM and TIBWB-OFDM waveforms are MC schemes that are relatively robust regarding this impairment. In GFDM the use of very well localised pulse shapes in the frequency domain allows a certain degree of CFO resilience [38]. Additionally, in TIBWB-OFDM, the large multi-symbol length can also allow a more accurate estimation of the CFO or Doppler drift based on the IB-DFE principle [47]. This way, GFDM and TIBWB-OFDM with and without WTO are the most suitable waveforms to be considered in a mobile transmission/reception environment. * High flexibility and efficient MIMO implementation: All of the waveform contenders presented in this paper are flexible with the possibility of employing multiple numerology parameters since they are based on OFDM scheme. A friendly MIMO adaptation is directly related to the implementation complexity regarding the channel equalization techniques that are employed in the system [6]. In general, OFDM-based waveforms (F-OFDM and TIBWB-OFDM) allow an efficient MIMO implementation since the transceiver architecture allows a simplification in the FDE with only one equalization iteration per sub-carrier with simple channel estimation techniques. Also, in [63], it is shown that the TIBWB-OFDM waveform is also easily integrated in MIMO systems. GFDM is an exception since the sub-carrier superposition is performed in frequency domain causing ICI that must be dealt in the receiver, requiring a channel estimation in each sub-symbol [6].