# A Multi-Carrier Waveform Design for 5G and beyond Communication Systems
## 1 Introduction  
The fifth generation (5G) is a technology that will have a real and optimistic influence on our lives. In the past few years, many research teams across the globe have been exploring the myriad of possibilities that are offered by 5G networks. There are massive expectations for 5G networks and among them are three main application families that are going to have a huge impact. The first of these is the enhanced mobile broadband (eMBB). Due to the advent of Internet of Things (IoTs) and increasing connectivity of things, it is anticipated that 5G networks will support massive machine-type communications (MMTC). Last but not least, due to the real-time requirements of modern communication systems, the 5G network is also required to provide ultra-reliable and low latency communications (URLLC) [1; 2]. The abovementioned application poses stringent demands such as uninterrupted continuous connectivity, enormous system throughput, and improved spectral efficiency [3]. Such rigorous requirements have been inciting researchers to work on new multiple access (MA) and modulation techniques in order to satisfy these requirements in 5G networks and even beyond. It is because current technologies are not versatile and robust enough to satisfy the 5G and beyond mobile network constraints [4]. In the last few years, a significant amount of progress has been made and investigations have been carried out to determine the suitability of the universal filtered multi-carriers (UFMC) waveform for the 5G communication networks [5]. In this regard, a conceptual view of the UFMC waveform is pictorially demonstrated in Figure 1a. In this figure, the entire bandwidth is split into a number of sub-bands. Each sub-band contains a certain number of orthogonal sub-carriers. These sub-bands are filtered to reduce the out-of-band emissions (OBE). The filtering process also reduces the length of the filter significantly in comparison with the other 5G techniques proposed in the literature. Furthermore, sub-band filtering offers flexibility in design and reduces inter-symbol interference (ISI). Thus, the UFMC waveform is thought to be the most promising choice for short-burst communications [6]. The UFMC waveform achieves a good spectrum efficiency due to the lack of cyclic-prefix (CP), however, spectral inefficiency remains a silent major drawback of the standard UFMC waveform, making it infeasible for the future 5G communication networks and beyond [7; 8]. Therefore, the standard UFMC waveform requires more comprehensive study and improved design to cope with the problem of spectral inefficiency. The peak-to-average power ratio (PAPR) is yet another serious UFMC waveform problem due to its multicarrier nature. The presence of extremely large peaks in a signal ready for transmission causes a severe loss of performance, particularly when a signal is amplified by using a non-linear high-power amplifier (HPA). The HPA's non-linearity causes two main problems, one is the in-band distortion and the other is out-of-band (OOB) radiation. Furthermore, the in-band distortion causes a higher bit error rate (BER) and on the other hand, OOB radiations increases in adjacent channel interference. Figure 1: The universal filtered multi-carriers (UFMC) waveform vs. the power-domain UFMC waveform. Therefore, the low PAPR is one of the most desirable aspects of any communication waveform for its successful implementation. Hence, in this paper a new multicarrier waveform with low PAPR has been designed to improve the capacity and support the large number of 5G/5G++ users. The proposed waveform uses selective mapping (SLM)-based generalized chirp-like (GCL) precoding and power domain multiplexing to manage more mobile users using the same frequency spectrum. Figure 1b illustrates the basic concept of the proposed waveform, where \(k\) users can be multiplexed in the power domain, such as non-orthogonal multiple access (NOMA), to support a large number of users.