# A Survey of Candidate Waveforms for beyond 5G Systems
## 2 Waveform Key Performance Indicators for 5G and beyond Communications  
A candidate waveform that defines physical shape of the signal that carries the modulated information through a wireless communication channel, should fulfill the following KPIs [22]:  
1. High Spectral Efficiency: Spectral efficiency is an important parameter since it indicates the achievable amount of bits that can be transmitted per second and per unit of bandwidth (bits/s/Hz), thus defining the maximum attainable bit rate given the available bandwidth. It is crucial to transmit the maximum amount data, using the minimum bandwidth that is possible, due to both licensing requirements and the spectrum scarcity resulting from the increasing transmission bandwidth requirement with demand for any time. Low spectral efficiency waveform formats can lead to high spectral amplitude outside the allocated bandwidth. This is known as out of band (OOB) radiation, which causes multiplexed services being transmitted on adjacent frequency channels to interfere with each other, a phenomena known as inter-channel interference (ICI) [6]. 2. Peak-to-average-power-ratio: The PAPR indicates the ratio between the maximum peak and the average transmitted power of the signal. A high PAPR results from the large fluctuations of the signal's envelope and it is associated to a high power consumption at the base station's terminals front-end, decreasing transmission energy efficiency. This is mainly due to the need of using linear power amplifiers, that are poorly efficient and is even lower when they are operated with some amount of back-off in order to avoid amplifier's saturation and signal distortion (which can lead to spectral regrowth and higher bit error rates (BERs)) [24; 25]. 3. Processing delay: Directly related to the URLLC 5G requirement, a waveform format with high complexity and large block processing delays increases the overall latency. The processing delay can be controlled by reducing the symbol temporal duration or period or increasing the sub-carrier spacing, which can be performed by efficient algorithms and signal processing techniques [4; 6]. 4. Robustness to frequency-selective channels: When the transmitted signal travels through a wireless channel, it travels trough several paths with varied length, with multiple echos of the signal reaching the receiver. This causes an effect denoted as multipath fading [26]. The several copies of the waves that carry the transmitted signal arrive at the receiver with random amplitudes, frequencies and phases and can be combined constructively and destructively, interfering with one another. This leads to a temporal dispersion of the signal which can induce inter-symbol interference (ISI),impacting severely the transmission. Therefore, waveforms must be designed in order to be robust to this impairment. 5. Robustness to time-selective channels: In wireless environments, transmitter and receiver mobility and, consequently, time-varying channels are still an open issue. The waveform transceiver system must be design in order to be robust to time-selective channels, by taking into account the channel coherence time, related to changes in the amplitudes, delays and the number of multipath components are observed. In fact, larger transmitted blocks can lead to higher sensibility to both carrier frequency offset (CFO) and Doppler effects [6]. 6. Massive Asynchronous Transmission: In 5G and beyond systems, a high number of communicating nodes will be communicating at a given time. In order to efficiently utilize network resources, asynchronous multiple access is essential. Thus, waveforms designs that are well localized in a multiplexed domain by allowing asymmetric and dynamic allocation of both time and frequency resources, as in frequency division duplex (FDD) and time division duplex (TDD), can achieve higher throughput through more efficient channel utilization [6]. 7. Complexity: The hardware and computation complexity represent a critical metric.