# A Multi-Carrier Waveform Design for 5G and beyond Communication Systems
## 2 Related Work  
A significant new multi-carrier waveform for upcoming modern communication systems has been suggested in the literature [5; 11]. One of the most popular ones is the cyclic prefix-based orthogonal frequency division multiplexing (CP-OFDM) waveform [12]. It is being used in many fourth generation (4G) communication standards such as LTE-A, and the IEEE 802.11 family. The fundamental reason for its popularity is that this modulation scheme is capable of handling frequency selective fading channels. This is a capability that does not exist in all single-carrier-based schemes. In CP-OFDM, the data stream is divided in a parallel manner and each stream is modulated using narrow sub-carriers. Each sub-carrier's bandwidth is set in a way so that the transmission channels are non-coherent. This operation aids in the equalization of flat fading channels through a simple multiplication process. Moreover, the orthogonal overlap of sub-carriers in the OFDM waveform makes the frequency assignment very flexible and this in turn results in a very efficient usage of the frequency spectrum. The OFDM waveform can be easily implemented by using inverse fast Fourier transform (IFFT). The CP aspect of OFDM is introduced by copying the last part of IFFT and appending it to the start. This copy-append process gives the cyclic characteristic to the OFDM waveform and also acts as the interval guard. The length of the guard interval is determined through the length of cyclic part being appended. This process helps to reduce the inter-symbol interference (ISI). Apart from the advantages cited above, the CP-OFDM waveform has many drawbacks and shortcomings, such as high peak-to-average power ratio (PAPR), high out-of-band emissions (OBE), and higher sensitivity to synchronization errors, respectively. To counter and resolve the aforementioned disadvantages, several countermeasures have been proposed in the literature. These countermeasures include improved flexibility and better time-frequency localization. Additionally, the external guard interval in the CP-OFDM waveform is being proposed to be replaced with internal guard interval. This replacement will improve the flexibility and it will also enhance the spectral efficiency. Low implementation complexity, easy multiple input multiple output (MIMO) integration and backward compatibility still makes CP-OFDM one of the important players for new and upcoming standards; however, its rigid nature and poor coexistence with other standards further weaken its case along with the already mentioned drawbacks. Consequently, some new requirements, such as MMTC, which are unique to 5G networks, cannot be fulfilled with the existing CP-OFDM waveform [5]. The discrete Fourier transform spread OFDM (DFT-s-OFDM) is the most popular waveform employed in 4G LTE-A standard for its uplink communications due to low PAPR and robustness against multipath fading [13]. The DFT-s-OFDM waveform inherits many positive points from its predecessor CP-OFDM waveform, such as the reduced flexibility and excellent spectral efficiency. In the CP-OFDM waveform, the IDFT has high variance that can be reduced by introducing DFT operation before the IDFT. Moreover, the usage of cyclic prefix in DFT-s-OFDM enables the easy handling of the multipath channel effect. In addition to that, it has minimal implementation complexity, flexible spectrum assignment, and good MIMO adaptability. However, similar to the CP-OFDM waveform, the DFT-s-OFDM waveform also suffers from high OBE and cannot support the 5G requirements [14]. To resolve the abovementioned issues, several waveforms have been proposed in the literature. These waveforms are specifically proposed to handle the new challenges of 5G communication networks and beyond. Some of these waveforms related to the proposed work include filter bank multicarrier (FBMC) [15], multi-carrier non orthogonal multiple access (MC-NOMA) [16] and standard universal filtered multicarrier (UFMC) [17].