# A Survey of Candidate Waveforms for beyond 5G Systems
## 3 Candidate Waveforms
### Orthogonal Frequency Division Multiplexing  
In order to fulfill the 5G and beyond KPI requirements [28], a new radio interface has been suggested by 3 rd Generation Partnership Project (3 GPP) for 5G systems [29]. The choice of the waveform for 5G New Radio culminated in the adoption of Orthogonal Frequency Division Multiplexing (OFDM) [27] added by a cyclic prefix (CP) for the underlying PHY technology in mobile broadband systems, regarding DL transmissions, as in 4G LTE systems. OFDM is a MC modulation technique that can be implemented based on the numerology parametrization (number of sub-carriers, sub-carrier spacing and CP length) [10]. An OFDM signal consists on a group of \(N\) adjacent and orthogonal sub-carriers spaced, at frequency domain. The sub-carrier spacing depends on aspects such as radio-channel frequency selectivity, rate of channel variations, phase noise and Doppler effect [12; 30]. Figure 1 represents the scheme of an OFDM transceiver. The bitstream \(\mathbf{b}\) is bit-interleaved and channel coded before mapping the resulting bitstream into constellation symbols. These symbols are drawn from a \(M\)-ary constellation, \(S_{k},k=0,\cdots N-1\) are mapped into each sub-carriers and simultaneously transmitted in an overlapping and parallel approach, with the transmitted signal being given by  
\[s[n]=s_{n}=\sum_{k=0}^{N-1}S_{k}w[n]e^{\frac{2 mk}{N}},n=0,...,N-1, \tag{1}\]  
where \(w[n]\) is a unitary rectangular pulse, allowing a considerable gain in spectral efficiency, saving up to 50% of the used spectrum [27]. The sub-carries spacing grants a degree of orthogonality, allowing an efficient demodulation free from interference from other sub-carriers [31] and exhibiting robustness against ICI. OFDM presents other interesting advantages, such as, the easy implementation of the transmitters based on inverse fast Fourier transform (IFFT) algorithm, as can be perceived from (1). The receivers include the CP removal, followed by a frequency domain equalization (FDE) procedure, resulting in \(\tilde{S}_{k}\) (denoting the estimated symbol sequence) Finally, the demapper, bit-deinterleaver and channel decoding operations are applied to the symbol sequence, resulting in the estimated bitstream, \(\bar{\mathbf{b}}\). e based on its inverse transform, i.e., the fast Fourier transform (FFT), allowing an efficient and low complexity FDE. It also enables the possibility of adapting the transmitted power and the modulation cardinality and an easy integration with MIMO technology, both at the transmitter and receiver, and a simple channel estimation [32; 33]. Figure 1: OFDM transmitter (**a**) and receiver (**b**). Since the individual user's channel delay spread is not taken into consideration [4] and due to different time delays upon reception of an OFDM symbol, ISI can occur, where the last part of the current symbol adds with the first part of the time delayed symbol. In order to avoid ISI, associated with multipath fading, in each OFDM symbol, it is necessary to add a cyclic extension of the symbol itself, called a CP, which is a copy of the tail of a symbol placed at its beginning [24], resulting in \(x_{n}\). Its duration is required to be greater than the impulse response of the transmission channel, which, in turn, is related to the channel delay spread. This also allows transforming the linear convolution that occurs in the transmission channel, in a cyclic convolution at the level of the individual processing of each OFDM symbol, enabling the implementation of a simple receiver based on the FFT. However the use of a CP per OFDM symbol increases the transmission overhead, by adding redundancy since the same content is transmitted twice as the CP. This lowers the effective throughput of the CP-OFDM system as well as its spectral efficiency, since the duration of the CP often represents a considerable percentage of the period of the symbol(which can reach up to 7-33%) [24]. Another aspect is related to the power wasted to transmit the CP, which reduces the power efficiency of OFDM transceivers.