# A Survey of Candidate Waveforms for beyond 5G Systems
## 3 Candidate Waveforms
### Time Interleaved Block Windowed Burst Orthogonal Frequency Division Multiplexing
#### 3.4.2 TIBWB-OFDM Packing with WTO  
Although the TIBWB-OFDM technique already tackles some of the disadvantages inherent to the use of the OFDM, while being easily applied to MIMO and mMIMO systems [48; 63], it also brings interesting challenges. The promised spectral and power efficiency increases proposed by the method are limited by the growth of the windowed OFDM-based blocks and also due to their juxtaposition. Even though performing the windowing operation with higher roll-off improves the spectral confinement of the transmitted signal, when juxtaposing the component blocks, the overall length of the TIBWB-OFDM multi-symbol increases proportionally to \((1+\beta)\). Consequently, the achieved spectral efficiency of this technique is limited, by either:  
* improving spectral confinement by reducing OOB emission when using a larger roll-off. This however, results in greater multi-symbol length, which increases the required bandwidth, in order to keep transmission rate [49].
* by improving symbol rate when conventional rectangular window is used since a sole ZP is used per group of packed OFDM-based blocks. This results in very high OOB emissions, just like typical OFDM schemes [49].  
Furthermore, the windowing operation employed in the transmission is responsible for the decrease in the average signal power, due to the low amplitude of the window tails. As a consequence, the overall PAPR of the TIBWB-OFDM multi-symbol tends to grow as the window roll-off increases [50].  
Figure 4: TIBWB-OFDM with WTO transmitter (**a**) and receiver (**b**). Conventional TIBWB-OFDM is obtained by removing the WTO block in transmitter and WTO compensation in receivers A and B.  
Additionally, in Figure 4a, an alternative packing structure is also presented within the original art of TIBWB-OFDM block construction. It includes a partial overlap between the adjacent windowed OFDM symbols that form the TIBWB-OFDM multi-symbol, in time domain, to keep original transmission rate and spectrum occupancy [49; 50]. This constitutes the basis of the TIBWB-OFDM with WTO waveform, whose transmitter is based on the previously mentioned operations, followed by an overlapping procedure, as suggested by Figure 4a.  
The overlapping operation precedes the time interleaving block, and, therefore, instead of simply juxtaposing the OFDM symbols, they are partially tailed overlapped, in time domain, i.e., the last samples of the current symbol are added with the first samples of the next symbol, with the overlap signal samples being given by  
\[s_{wo}[n]=\sum_{i=1}^{N_{s}}s_{w,i}[n-(i-1)N]. \tag{15}\]  
The remaining steps that generate the WTO signal are the same that are included within the original transmitter, as in [46; 47]. The only difference is that, before ZP insertion, (13) now becomes  
\[\mathbf{s}_{\pi}=\mathbf{s}_{wo}\mathbf{\Pi}^{(\mathbf{N}_{s})} \tag{16}\]  
The number of overlapped samples can be regulated, as in [49]. However, the most interesting scenario is when the temporal expansion of the overall signal is mitigated, meaning that the overlapped windowed OFDM symbols maintain a total length of \(N\) samples (except for the first and last one). The total length of the TIBWB-OFDM with WTO multi-symbol is now \(N(N_{s}+\beta)\). It is clear that the temporal expansion of the overall signal is \(N\beta\), thus meaning that is negligible when compared to packing \(N_{s}\) conventional OFDM blocks with rectangular windowing. This way we can increase the spectral efficiency of the system [49]. This alternative packing also improves the power efficiency of the system by creating a flatter waveform with fewer transitions, increasing the average power of the transmitted signal, and thus reducing on the signal's PAPR [49; 50].