# A Survey of Candidate Waveforms for beyond 5G Systems
## 3 Candidate Waveforms
### Time Interleaved Block Windowed Burst Orthogonal Frequency Division Multiplexing
#### 3.4.3 Receivers for TIBWB-OFDM with WTO  
In order to cope with both channel impairments and the additional interference introduced between adjacent OFDM component blocks of the TIBWB-OFDM multi-symbol, a different set of receivers must be developed. The TIBWB-OFDM with WTO receivers must be entail both channel equalization and inter-block interference cancellation (IBIC). Linear or iterative FDE can be applied to the received signal aiming to cancel out channel impairments, as for conventional TIBWB-OFDM without WTO. In order to mitigate inter-block interference, a two-way (i.e., simultaneously forward and backward) interference successive cancellation (ISC) is employed. While ISC can also be made iterative enabling better interference cancellation when combined with linear FDE, the IBIC procedure can be simplified after the initial iteration when this is combined with iterative FDE [64].  
The TIBWB-OFDM is also seen as an hybrid modulation technique [47], since in the receiver side, the signal can be interpreted as block-based SC-FDE and each data stream is equalized with a single tap equalizer, as shown in [46]. The basic block diagram of a TIBWB-OFDM receiver is given by receiver A (without the WTO compensation block) presented in Figure 4b. The received signal is converted to frequency domain by the means of a \(N_{x}\)-sized DFT, resulting in \(Y_{k},k=0,\cdots,N_{x}-1\), with \(N_{x}=N_{zp}+N_{b}N(1+\beta)\) for the TIBWB-OFDM original packing and \(N_{x}=N_{zp}+N(N_{s}+\beta)\) for the TIBWB-OFDM with WTO. The signal in the frequency domain can be written as in (9). In order to obtain an estimate of the transmitted signal, \(\tilde{X}_{k}\), linear FDE algorithms can be employed, such as the MMSE equalization [46] as in (10) (for this case, in both equations \(S_{k}\) and \(\tilde{S}_{k}\) are replaced with \(X_{k}\) and \(\tilde{X}_{k}\), respectively). Afterward, the estimated signal \(\tilde{\mathbf{X}}_{k}\) is then converted to time domain, \(\tilde{\mathbf{x}}_{n}\), through a \(N_{x}\)-sized IDFT, the ZP is removed and the block is deinterleaving resulting in the estimated BWB-OFDM block whose unformatting follows [47; 49; 62].  
The channel equalization can also include non-linear iterative FDEs, such as the iterative block decision feedback equalizer (IB-DFE) [65; 66], which was included in the TIBWB-OFDM receiver in [64] and is shown in Figure 4b.  
At this point, in order to cancel out the interfering resulting from the WTO operation, an IBIC algorithm must be employed. In [64], four different receiver embodiments are presented for a TIBWB-OFDM with WTO transmission, where iterative and non-iterative strategies can be used for both channel FDE and IBIC. They are all presented in Figure 4, depending on whether the links 1 and 2 are on or off. These receivers are divided as:  
* Receiver A (Link 1--off; Link 2--off): It consists on the linear MMSE FDE technique, presented in (10) to deal with channel impairments and an MMSE ISC algorithm to cancel WTO interference.
* Receiver B (Link 1--on; Link 2--off): It consists on the non-linear IB-DFE FDE [47] and MMSE ISC algorithms. Each iteration allows an improvement in BER performance since the ISC algorithm is applied iteratively.
* Receiver C (Link 1--off; Link 2--on): This receiver is similar to A since it includes the linear MMSE FDE scheme. However, instead of applying the MMSE ISC algorithm per iteration, an iterative IBIC algorithm is employed, assuming perfect reconstruction.
* Receiver D (Link 1--on; Link 2--on): This receiver is a combination of both receivers B and C, wherein the IB-DFE FDE technique and the iterative IBIC algorithm are employed.  
More details on the developed ISC algorithm can be found in [49; 64], while the iterative IBIC version along with the receivers are presented in [64].