# A Survey of Candidate Waveforms for beyond 5G Systems
## 1 Introduction  
Over the past recent years, the fifth generation (5G) of wireless communication systems and networks has been researched, engineered and deployed. This introduces a new paradigm that will change and define the future generations of telecommunication standards, revolutionizing the way people interact, work and live [1, 2]. The continuous growth of mobile devices and applications, with increasing bandwidth demands, will force the 5G and beyond technology to be able to support enormous volume of data, while being more energy efficient than the previous generation [3]. Therefore, 5G and beyond generations are envisioned to improve major key performance indicators (KPIs), including data rates, spectral efficiency, power consumption, transceiver complexity, connection density, latency, and mobility [4, 5]. This can be done by exploring different methods for achieving a higher capacity of exchanging information with enhanced coverage potential, reliability and availability [2, 6]. In general, three different types of services are to be supported in 5G: Enhanced Mobile Broadband (eMBB), massive machine-type communication (mMTC) which includes massive Internet of Things (IoT), and Ultra-Reliable and Low-Latency Communication(URLLC). Regarding eMBB, the KPIs driven from [7] include peak data rates of 20 Gb/s for the downlink (DL) and 10 Gb/s for the uplink (UL), spectral efficiencies of DL 30 bits/Hz and UL 15 bits/Hz, mobility up to 500 km/h and system bandwidth support up to 1 GHz. Regarding mMTC, the number of devices to be connected is enormous, requiring relaxed synchronization and low-cost devices [8]. Therefore, the KPIs include a density of 1 million devices per km\({}^{2}\), an area traffic capacity of about 10 Mbits/s/m\({}^{2}\), coverage of 164 dB and user equipment (UE) battery life up to 15 years. The URLLC implies a high reliability upon the transmission of a packet from the transmitter to the receiver, i.e., with a low probability of error (1 packet loss out of 100 million packet), no mobility interruption time and less than 1 ms latency [9]. In order to accomplish such ambitious requirements, the 5G and beyond networks will rely on an intelligent combination of several complementary factors and integration of advanced technologies [10] which includes:  
* More flexible and efficient use of the current spectrum available in sub-6 Ghz bands, which may include the aggregation of non-contiguous and fragmented under-utilized spectrum bands for different network deployment scenarios [11];
* Expand the operation of 5G and beyond mobile network to consider also carrier frequencies above 6 GHz, enabling high capacity and high throughput services with low latency [12];
* The use of milli-meter (mm)-wave systems [13; 14] to deliver an unprecedented level of service to the end user while dealing with new challenges, especially regarding high penetration loss, strong Doppler effects, sparsity and directionality [6; 12];
* Enhanced higher-order modulations, frame structure, multiple access and coding schemes;
* The concept of network slicing, which uses resources when and where needed, that are after released [15]. Another way of improving the efficiency of the wireless 5G and beyond networks consists on densification by either increasing the number of antennas per site or by adding more base stations (BSs) and access points (APs) allowing for better spatial reuse of the spectrum. However, the network efficiency can also be improved by using more spectrum or by improving the spectral efficiency, i.e., the number of bits that can be transmitted per second in each unit of bandwidth [16]. One viable approach of grating a considerable increase in the network spectral efficiency consists into the use of multiple antennas at the transmitter and the receiver, also known as multiple-input-multiple-output (MIMO).