# A Survey of Candidate Waveforms for beyond 5G Systems
## 4 Performance Results and Discussion
### BER Performance  
Figure 7 compare the BER performances of TIBWB-OFDM waveforms with and without WTO, GFDM, F-OFDM and with conventional CP-OFDM. In order to provide a fair comparison in a realistic scenario, the same amount of CP, considered in Section 4.2, is employed in CP-OFDM and F-OFDM transmissions. The four receiver embodiments proposed in [64] are employed for the TIBWB-OFDM with WTO waveform. Furthermore, the conventional TIBWB-OFDM results are presented for the linear MMSE and IB-DFE receivers, as in [47]. Regarding OFDM, F-OFDM and GFDM a FDE MMSE algorithm is employed at the early stage of the receiver. However four different interference cancellation methods are considered in the GFDM receiver. The MF, ZF and DSSIC detectors mentioned in the previous section are included, along with the simpler version of the DSSIC detector (the GFDM SIC detector) which subtracts the ICI presented in the signal at \(k\)th sub-carrier and caused only by the \((k+1)\)th sub-carrier [43; 53]. Perfect synchronization and channel estimation is assumed at reception. The channel code employed is a (128,64) LDPC code and bit-interleaving is applied over 21 consecutive coded words for the TIBWB-OFDM and OFDM cases. For GFDM and F-OFDM, since the number of time-slots is higher the bit-interleave operation is applied over 32 consecutive coded words. For a fair comparison results are also presented as function of the ratio energy per information bit to noise spectral density \(\frac{E_{k}}{N_{0}}\) added to the required amount of back-off taking as reference PAPR at \(CCDF=10^{-4}\). Additionally, the CP power penalty is also considered.  
Figure 6: PSD of CP-OFDM, GFDM, F-OFDM and TIBWB-OFDM with and without WTO.  
More specifically, Figure 7 includes the performance for the different techniques for \(\beta=0.5\), with results for the iterative receivers being presented for the 5 th iteration. Clearly, by analyzing this figure, we can conclude that the TIBWB-OFDM receiver D has the best performance when back-off associated to the PAPR is considered, with almost no added complexity when compared to receiver B. Also, we can conclude that the GFDM detectors SIC, but mainly, DSSIC can really improve the BER performance of GFDM standard MF and ZF receivers, while exhibiting a similar performance when compared to standard TIBWB-OFDM case with receiver A. It is worth stating that the SIC algorithms were applied only for 1 iteration. Furthermore, although the TIBWB-OFDM with WTO (regarding receivers B and D) is a waveform that have interference levels that must be dealt in the receiver, they present better BER performances than standard OFDM and TIBWB-OFDM (regarding receiver B) cases, due to its much lower PAPR owing to the windowing and packing with overlap operation. Finally, we can also conclude that F-OFDM presents a slightly better performance (less than 1 dB) than CP-OFDM due to the large ZP that is added in the last stage of the transmitter.  
To sum up, with the employing of more efficient and complex receiver equalization techniques, the TIBWB-OFDM and TIBWB-OFDM with WTO are able to provide a satisfactory performance, outperforming OFDM and F-OFDM in terms of reliability. GFDM presents the overall worst BER performance, however it is possible to enhance the receiver's interference cancellation algorithms in order to provide a more acceptable performance.