The Generalized Definition of the Waveform
The main components of a waveform are defined in this section to understand concept of the waveform design in a better way. Basically, waveform is a physical signal that contains information. Data bits are mapped to the physical signal through a proper waveform. Also, additional symbols (e.g., redundancy, preconditioning like precoding and guard utilization, noise, etc.) are the parts of the physical signal. These signals occupy physical resources (like bandwidth, time, space, code, power, etc.) in multi-dimensional hyperspace.
Figure 1 shows the main components of a waveform design including lattice structure, pulse shape and frame structure.
Lattice structure is a multi-dimensional resource mapping and each point show a location of one resource element [19]. The resource element is the smallest discrete part that contains physical signal on a lattice structure. For example, the resource element is one symbol and one subcarrier for fifth generation (5G) New Radio (NR) in time-frequency planes, respectively. The possible spacings between lattice points give numerology structures for a waveform. Lattice structure can be uniform or non-uniform. If the lattice structure is uniform, it means that lattice spacings are fixed and there is a single-numerology waveform.
For example, the spacings between Long Term Evolution (LTE) lattice points are fixed and LTE employs a single-numerology waveform. However, 5G NR uses a flexible nonuniform lattice structure that indicates multiple numerologies. Additionally, both of LTE and 5G NR use a multi-dimensional lattice on time-frequency planes. More dimensions can be possible in the future communications systems.
Pulse shape (also known as filter) gives the main characteristic to a waveform by deciding how to transmit the symbols on lattice points [19]. As a result, waveform defines the physical shapes that contains energy in the hyperspace. The variances of energy in the hyperspace give the localization of a pulse shape. Moreover, correlation between the lattice points is determined by the pulse shapes. This correlation and the localization show the orthogonality of a waveform design.
In the literature, the following filters are utilized while designing waveforms: Rectangular, hanning (raised-cosine), exact hamming, exact blackman, tapered-cosine-in-time, tapered-cosine-in-frequency, root-raisedcosine, Mirabbasi-Martin, prolate, optimal finite duration pulses, Kaiser, modified Kaiser, Gaussian, IOTA, Hermite, and extended Gaussian. These pulse shapes have different localization characteristics.
Frame structure can be defined as a packaging (formation) of multiple user information because waveform is the process of generating the collective pysical signal corresponding to multiple users (and/or multiple information data) that occupies the hyperspace. Waveform characterizes the multiple-access scheme using the frame structure. The multiple-access scheme controls the sharing of resources by multiple users and multiple shapes in the hyperspace. Individual pulse shapes are combined under a frame structure to form a waveform. The frame controls the interaction between the pulse shapes by utilizing waveform processing.
For example, lattice points can be used as guard intervals if it is beneficial for the overall performance of a waveform design. The lattice points do not need to carry data and they are controlled by the frame structure. The waveform frame is constituted by the scheduling units in a communications systems. Within this context, numerology assignment, waveform processing (pulse shape processing and guard utilization), orthogonal multiple access (OMA), non-orthogonal multiple access (NOMA) and duplexing decisions are applied via frame structure of a waveform design.
Waveform Relationships of Channel and RF Impairments
Example interactions between several requirements, communications layers, channel structure and core technologies are shown in Figure 2. They are all con-nected to each other strongly with important relationships. If the waveform can be related with the other parts of communications, then the overall system can be designed properly. For the relationships, effects of wireless channel and RF hard-ware impairments are discussed in this section. Application requirements and impacts of the waveform design on RATs are investigated in the next sections.
There are several relationships of MAC and network layers with the waveform design as shown in Figure 2. MAC layer decides distribution of resources among the users. It controls the resource allocation and scheduling mechanisms together with the waveform frames. As an example relation for the network layer, if there are overlapping in any lattice domain of a waveform design, synchronization can be di cult in this domain. Overlapping can cause an interference if there is a misalignment in anyway. Therefore, synchronous networks have problems with the waveform designs that have overlapping in any lattice domain.
User requirements are other important aspects for the system designs in 5G and beyond. The user requirements include various constraints which can be described as wireless channel conditions and RF-hardware impairments. Some of these e ects can be given as 1) Doppler spread, 2) multipath e ects, 3) path loss, phase noise, 5) frequency o set, 6) power ampli er (PA) non-linearity. This list may be improved to include other impairments in the future. We assumed that all these impairments are provided as feedbacks via channel quality information and other similar systems.
The waveform design has strong relations with the wireless channel. First of all, single-carrier and multi-carrier waveform designs have di erent impacts on the channel. Single-carrier waveforms use whole bandwidth (BW) for one carrier. If transmission BW is larger than coherence BW, the channel becomes frequency-selective. In multi-carrier waveforms, transmission BW are divided into subcarri-ers. If narrow bands are less than coherence BW, a at response is received from each portion of the BW.
Additionally, the lower limit of subcarrier spacing is generally determined with the coherence time to handle inter-carrier interferene (ICI). Single-carrier waveforms are better with respect to Doppler spread. Hence, it is better to prefer single-carrier waveforms for a time-selective channel (dispersive in frequency domain). On the other hand, multi-carrier waveforms can be used for frequency-selective channels (dispersive in time domain).
For example, if there is a selectivity in frequency, localized pulses in frequency domain need to be used for the waveform design. If there is a selectivity in time, then localized pulses in time domain need to be used. As a last example, if there is a selectivity in space, the waveform design needs localized beams in angular domain. Depending on the channel requirements, a proper trade-o has to be done to design a suitable waveform.
If the channel impairments are to be addressed, then a larger subcarrier spacing is needed to be used for the high Doppler spread which is a result of mobility, multipath, and angular spread. Furthermore, a longer CP duration is a need for the scenarios with long delay spreads. Additionally, the low number of subcarriers is needed for high path loss scenarios because the high number of subcarriers results in high PAPR values which is not a good condition for PA usage. Basically, the key necessities of the channel impairments can be achieved in this way.
Understanding the relation between RF impairments and waveform is crit-ical for the design of proper waveforms. Within this context, single-carrier and multi-carrier waveform designs have di erent signi cant e ects on the RF impair-ments. For multi-carrier waveforms, the increasing number of subcarriers results with more power ampli er (PA) non-linearities. PAs are not linear in nature, they show non-linearities after speci c thresholds for the input powers. PA non-linearities cause in-band interference (IBI) and interference with neighboring band that constitutes out-of-band emission (OOBE). For single-carrier waveforms, PA non-linearities increase as roll-o factor decreases or modulation order increases.
As another RF impairment, phase noise a ect the single-carrier waveforms with time varying and correlated noise. Besides, phase noise causes ICI for the multi-carrier waveforms. It is an important problem especially in high frequencies. Moreover, the e ect of sample timing o set (STO) is di erent on single-carrier waveforms and multi-carrier waveforms. Loss of the optimal sampling phase is the problem caused by STO in single-carrier waveforms.
For multi-carrier waveforms, STO causes ICI. In, di erent waveforms are compared from the carrier frequency o set (CFO) together with the in-phase and quadrature (IQ) imbalance perspectives. Non-identical amplitudes and not xed 90 degree phase di erence between I-branch and Q-branch lead to IQ imbalance. Ideally, I and Q should be orthogonal. Single-carrier waveforms are generally more robust against the IQ imbalance problems because of the ability of better spectrum controlling.
For the RF-hardware impairments, a larger subcarrier spacing is a necessity for the high phase noise and frequency o set. Moreover, the low number of sub-carriers is a solution for high PA non-linearity to restrain high PAPR values like in the high path loss scenario. For the necessity of the low number of subcarriers, larger subcarrier spacings can be preferred.
There are various wireless communications scenarios, and service requirements according to ETSI 3GPP documents. These scenarios include 1) indoor hotspot, 2) dense urban, 3) rural, 4)urban macro, 5) high speed, 6) extreme long distance coverage in low density areas, 7) urban coverage for massive connection, 8) highway, 9) urban grid for connected car, 10) commercial air to ground, 11) light aircraft, 12) satellite extension to terrestrial.
In, the given scenarios are discussed and some detailed scenario parameters are provided for 5G systems. These parameters are also used in the remaining part of this thesis when needed. Di erent scenarios change the weights of di erent requirement parameters related to the services and users in the coverage area of a system.
Waveform Relationships of Application Requirements
A detailed analysis is presented for the requirements of use cases and standards for wireless communications in this section. Cellular and Wi-Fi, namely IEEE 802.11 family of standards, communications are discussed. Applications are mapped to the requirements for the standards of cellular and Wi-Fi communications.
In LTE, i.e., fourth generation (4G), and other previous generations, di er-ent requirements were not grouped and there was only a single service type in a single standard for cellular communications. However, di erent application requirements are grouped under various service types in one standard starting from 5G NR. Thus, the requirements of cellular communications are investigated considering three main service types of 5G NR: eMBB, URLLC and mMTC.
For Wi-Fi communications, di erent application requirements are grouped un-der several standards rather than the service types in one standard. Requirements are analyzed under several Wi-Fi standards that include IEEE 802.11ay, 802.11ad, 802.11be, 802.11ax, 802.11ac, and 802.11ah. In light of these standards, one can state that a set of new requirements generally brings a new Wi-Fi standard.
It can be expected to see more sophisticated service types for beyond 5G and a higher number of standards for Wi-Fi because diversity requirement continues to increase. Additionally, di erent standards might have similar set of system requirements. As an example, mMTC service type in 5G has almost the same set of requirements with IEEE 802.11ah standard.
