Zekeriyya+Esat+Ankaral?+Berker+Pek?z+and+Hüseyin+Arslan

Support of many different services， approximately 1000x increase of current data rates， ultra?low latency and energy/cost efficiency are among the expectations from the upcoming 5G standards. In order to meet these expectations， researchers investigate various potential technologies involving different network layers and discuss their tradeoffs for possible 5G scenarios. As one of the most critical components of communication systems， waveform design plays a vital role here to achieve the aforementioned goals. Basic features of the 5G waveform can be given in a nutshell as more flexibility， support of multiple access， the ability to co?exist with different waveforms， low latency and compatibility with promising future technologies such as massive MIMO and mmWave communications. Orthogonal frequency division multiplexing （OFDM） has been the dominant technology in many existing standards and is still considered as one of the favorites for broadband communications in 5G radio access network （RAN）. Considering the current interest of industry and academia on enhancing OFDM， this paper drafts the merits and shortcomings of OFDM for 5G RAN scenarios and discusses the various approaches for its improvement. What is addressed in this paper includes not only enhancing the waveform characteristics， out of band leakage and peak to average power ratio in particular， but also methods to reduce the time and frequency redundancies of OFDM such as cyclic prefix and pilot signals. We present how the requirements of different 5G RAN scenarios reflect on waveform parameters， and explore the motivations behind designing frames that include multiple waveforms with different parameters， referred to as numerologies by the 3GPP community， as well as the problems that arise with such coexistence. In addition， recently proposed OFDM?based signaling schemes will also be discussed along with a brief comparison.

5G waveform； 5G RAN； eMBB； multicarrier systems； OFDM

1 Introduction

xponential growth in the variety and the number of data?hungry applications along with mobile devices leads to an explosion in the need for higher data rates， and this is definitely the main driving factor in 5G [1]. Therefore， a wide range of data rates up to gigabits per second are targeted in 5G technologies which are expected to be deployed around 2020. In order to achieve these goals， academia has been in a great collaboration with industry as obviously seen in European Union projects as 5GNOW [2]， METIS [3]， MiWaveS [4] and FANTASTIC?5G [5]. Along with those， standardization has been started in 3GPP to deliver the demanded services timely.

One of the most challenging parts of achieving targeted high data rates is physical scarcity of the spectrum， and researchers have been putting an extensive effort to this challenge. One popular approach is to extend existing spectrum towards virgin higher frequencies up to 100 GHz [6]. Another approach is to increase spectral efficiency for a given spectral resource. Millimeter wave （mmWave） communications and massive multiple?input multiple?output （MIMO） are the representative concepts of these two approaches and very promising technologies for facilitating 5G goals， especially for enhanced mobile broadband （eMBB） services which constitutes one of the main service groups considered for 5G radio access network （RAN）.

Even though not considered as the revolutionary part of 5G， one of the most fundamental components of any communication system is the waveform design. Therefore， intensive discussions are being conducted in academia and industry， in order to select the proper waveform meeting 5G requirements. Among all the candidates， multicarrier techniques are prominent especially for broadband wireless communications due to several advantages such as immunity against frequency selectivity， multiuser diversity support and adaptive modulation/coding techniques. Orthogonal frequency division multiplexing （OFDM） has been the dominating technology so far and successfully deployed in many of the current standards such as Long Term Evolution （LTE） and Wi?Fi. In the transition from existing technologies （4G） to the next generation， waveform selection ramifies to two paths for 5G RAN. The first one is re?considering OFDM based methods by improving its characteristics and handling its drawbacks with proper solutions. The second one， on the other hand， is to implement alternative multicarrier technologies and redesign everything based on a different rationale. Fig. 1 shows transceiver block diagrams for OFDM and other popular multicarrier schemes including filtered multi?tone mode of filter bank multicarrier （FBMC）， universal filtered multicarrier （UFMC） and generalized frequency division multiplexing （GFDM）. Let us firstly provide the merits and challenges of the multicarrier technologies considered as an alternative to OFDM in the context of 5G expectations.

1.1 FBMC

FBMC is one of the most well?known multi?carrier modulation formats in wireless communications literature which is also discussed as a 5G waveform in [7]. It offers a great advantage of shaping each subcarrier and facilitating a flexible utilization of spectral resources along with meeting various system requirements， e.g.， low latency， multiple access， etc. This is also an advantage for making signal robust against channel effects， i.e.， dispersion in time and frequency domains. For example， rectangular filters are preferable for time dispersive channels while raised cosine filters are more robust against frequency dispersion. Many other pulse shaping filters are also investigated to cope with various effects of the channel and provide a reliable system design based on different scenarios [8].

Despite all the advantages of FBMC， the significantly long filter lengths resulting in colossal symbol durations not only become a problem if low latency applications or short bursts of machine type communications are in focus [9]， but also introduce an excessive computational complexity for MIMO detection as the channel coherence bandwidth would fall below the subcarrier bandwidth [10]， which would mean problems in all main applications of 5G.

1.2 UFMC

UFMC is a generalized version of filtered multicarrier techniques where groups of subcarriers， i.e.， sub?bands， are filtered rather than filtering each subcarrier individually [11]. By doing so， interference between neighboring sub?bands is decreased compared to conventional OFDM. Also， sub?band based filtering operation， when compared to the subcarrier filtering operation performed by FBMC， aims to increase the efficiency for short?burst type communications such as IoT scenarios or very low latency packets by reducing the filtered symbol duration and outperforms both cyclic prefix （CP）? OFDM and FBMC for such use cases [9]. A similar scheme is also presented as resource block （RB）?filtered OFDM in [12]. On the other hand， while UFMC aims to solve the problems of FBMC while maintaining its advantages， the increased fast Fourier transformation （FFT） length introduces complexity issues at the transmitter and receiver operations.

1.3 GFDM

GFDM is a block?based multicarrier filtered modulation scheme， designed to address the challenges in the vast usage scenarios of the fifth generation by providing a flexible waveform [9]. GFDM allows reuse of techniques that were originally developed for OFDM， as circular convolution is employed to filter the individual subcarriers， making the GFDM frame self?contained in a block structure. For tactile internet scenarios， GFDM can be distinguished from other multicarrier waveforms by how it achieves robustness over highly mobile channels. This is accomplished via taking the advantage of the transmit diversity provided by the easy generation of impulse responses simply obtained with circularly shifting the single prototype filter in time and frequency. To improve the reliability and latency characteristics even further， the GFDM waveform can be combined with the Walsh?Hadamard transform for increased performance in single?shot transmission scenarios. When combined with offset quadrature amplitude modulation mapping， GFDM avoids self?generated interference if non?orthogonal filters are employed for next generation multiple accessing.

In a different point of view， GFDM can be considered as a highly parameterizable waveform that is flexible across frames rather than a single waveform. By choosing the parameters of the GFDM waveform appropriately， one can obtain different waveforms such as OFDM， single carrier?frequency domain equalization （SC?FDE）， FBMC and Faster?Than?Nyquist at the output， as demonstrated in [9]. In spite of these type of interesting flexibilities， GFDM is a computationally extensive scheme mainly because FFT/inverse FFT （IFFT） could not immediately be employed at the GFDM based transceiver [13]. Furthermore， the circular convolution used in the filtering process， referred to as tail?biting in [14]， introduces non?orthogonality across subcarriers as explained in [8]. Therefore， a successive interference cancellation at the receiver side is required so as to remove inter?carrier interference （ICI） [15].

Unlike the aforementioned technologies， OFDM has been widely and successfully used in wireless digital communication systems such as LTE and Wi?Fi due to its numerous advantages such as low?complexity implementation with FFT and the robustness against multipath channels with single?tap FDE. However， plain OFDM signals suffer from the distortions due to the non?linear characteristics of power amplifier （PA）. At the same time， the block nature of OFDM symbols may result in a high out?of?band （OOB） leakage and cause severe adjacent channel interference. Considering these issues， alternative schemes， GFDM， UFMC and FBMC definitely offer some advantages over OFDM. However， backward compatibility of OFDM with the existing technologies along with the other advantages makes enhancement of OFDM more appealing for the industry rather than going for a new waveform， as far as seen in the current standard discussions [16]-[18]. Therefore， in this paper， we draft various approaches addressing the shortcomings of OFDM and discuss how OFDM fits the envisioned 5G concepts and technologies.

Organized into the following five sections， this paper first presents the methods that enhance the spectral compactness， robustness against nonlinear effects of radio frequency （RF） front?end and spectral efficiency of OFDM. We provide examples of transmitter algorithms that lower peak?to?average power ratio （PAPR） and OOB leakage of OFDM without requiring major modifications at the receiver side. Secondly， considering newly introduced 5G RAN applications such as massive MIMO， we discuss the methods that address reducing the redundancies of OFDM in time （CP duration） and frequency （pilots） in order to increase spectral efficiency. Following that， we describe one of the main goals of 5G， which is to make all the diverse applications requiring different waveforms co?exist in the same frame， as addressed by 3GPP community within numerology contributions. The motivations and challenges of this concept are briefly investigated. Finally， new OFDM?derived approaches that aim to overcome the drawbacks of OFDM are provided along with the issues they encounter.

2 Improvements in Waveform

Characteristics

In a general sense， the key terms characterizing a basic OFDM waveform are multicarrier modulation and rectangular pulse shape1， and the majority of the advantages and disadvantages of OFDM are stemming from these features. In this section， we discuss how to improve characteristics of OFDM and make it a more convenient waveform for 5G RAN in terms of high PAPR， OOB leakage and redundancy introduced by CP.

2.1 OOB Leakage Suppression

High OOB leakage is a major issue in OFDM due to the inherent rectangular shape of OFDM symbols. In the frequency domain， subcarriers are shaped by sinc functions and addition of their sidelobes results in a considerable energy leakage on the neighboring channels as shown in Fig. 2. Although there are well?known filters emitting less energy on side bands， e.g.， raised cosine and Gaussian filters， OFDM does not allow pulse shaping unlike FBMC and GFDM， and therefore， a severe interference might be inevitable for users operating on the neighboring frequencies， especially for asynchronous scenarios. Leaving sufficient guard bands between the users might be considered as a practical solution， but this would not be an efficient way of utilizing spectral resources. In 5G scenarios， as far as envisioned so far， a huge number of asynchronous and data?hungry users should co?exist within a limited spectrum. Therefore， OFDM signals should be more localized in the frequency domain by handling OOB leakage problem in a practical way to adapt OFDM to such scenarios.

For the aforementioned purpose， OOB leakage of OFDM signals has been extensively addressed with numerous techniques in the literature as reviewed and compared in [19]. For instance， a time domain windowing approach is proposed in [20]， which can make the transitions between the OFDM symbols smoother and avoid signal components at higher frequencies. Hence， the OOB leakage of OFDM symbols is significantly reduced. This approach became very popular due to its simplicity， effectiveness and requirement of no modification at the receiver side. However， the introduction of an extra redundancy as much as the windowing duration remained a problem. In [21]， while the total duration for CP and windowing is kept constant for all subcarriers， windowing is mostly applied to the edge subcarriers since the leakage of edge subcarriers causes more interference on the adjacent frequencies. In a practical multiuser scenario where users need different CP sizes， this approach can decrease the windowing redundancy compared to the classical approach via a convenient user scheduling. Users with low time?dispersive channels are assigned to the edge subcarriers and users having highly time?dispersive channels are assigned to the inner subcarriers. Thus， the total duration required for CP and windowing could be shorter without causing any problem. In [22]-[25]， the OOB leakage is addressed from frequency domain perspective. A set of subcarriers， named as cancellation carriers， are allocated for canceling the sidelobes in [22]， [23]. However， such approaches also introduce redundancy in the frequency domain and degrade spectral efficiency similar to classical windowing approach. In [24]， sidelobe suppression is done by weighting subcarriers in such a way that sidelobes are combined on adjacent frequencies as destructively as possible. However， weighting leads to a pre?distortion of subcarriers and bit?error rate （BER） performance naturally reduces. In order to limit this distortion， a frequency domain precoder is proposed in [25]， which only maintains the spectrum of OFDM signals under the prescribed mask rather than forcing OOB leakage to zero. By doing so， interference on the adjacent frequencies is kept on a reasonable level at the expense of a smaller degradation BER performance.

2.2 PAPR Mitigation

As a consequence of multicarrier transmission， i.e.， transmitting multiple signals in parallel， high PAPR is inevitable for OFDM signals due to the probable constructive combination of signals in time domain. In Fig. 3， a comparison between SC signals having various modulation orders up to 256?QAM， and OFDM signals having a different number of subcarriers （N） is provided. Obviously， there is a huge difference in PAPR even when the number of subcarriers is as low as 32. It could be ignored for users requiring low power transmission. However， in many scenarios such as the mobile users on cell edges， a reliable transmission requires high power and high PAPR of the signal for this scenario makes the signal vulnerable to non?linear effects of RF front?end components. These components typically have a limited linear range， and any part of the signal exceeding the linear range is non?linearly scaled. Non?linear scaling of a signal can also be referred as multiplying a part of signal components with various coefficients. This makes a time?varying channel effect on the signal， and the signal is distorted as if it is exposed to a Doppler spread effect at the transmitter. As a result， non?linearity of RF components may lead to severe interference not only in the users band but also for the others operating on neighboring frequencies due to the spectral regrowth. At this point， one may notice that the OOB leakage is not only the function of the waveform itself but also the spectral regrowth of the ideal waveform signals due to the high PAPR in practice. Then， even if the OOB suppression performance of the related studies in the literature is quite satisfactory， a good scheme needs to address PAPR and OOB leakage jointly for fixing these two shortcomings， practically.

PAPR suppression techniques are surveyed well in [26]， however， many of them tackle with PAPR individually without considering OOB. On the other hand， some existing studies use PAPR reduction concepts for suppressing OOB. This is achieved by actively selecting some predesigned sequences， i.e.， selected mapping （SLM） sequences in [27]. Another well?known PAPR reduction method， partial transmit sequences are applied on OFDM signals partitioned into contiguous blocks in the frequency domain in [28]. Additionally， the optimized phase rotations are multiplied by each sub?block to provide a contiguous transition between the OFDM symbols to suppress OOB leakage along with PAPR. Another joint suppression method is presented in [29]， where the constellation points are dynamically extended. For the similar purpose， a method called CP alignment is proposed in [30] similar to the interference alignment method presented in [31]. The key idea in this method is to add a perturbation signal， called alignment signal （AS）， to the plain OFDM symbols in order to reduce the PAPR and OOB leakage such that the AS aligns with the CP duration of the OFDM symbols after passing through the channel. However， this method completely relies on the perfect channel estimation and any error might result in an interference on the data part. In order to fix this problem， a recent method called static CP alignment is proposed in [32] where the AS is designed according to a pre?determined filter independent of the channel. These methods also provide physical layer security to some extent by using additional signals that confuse the unauthorized users [33].

Joint PAPR and OOB leakage suppression techniques are definitely offering a comprehensive solution in enhancing characteristics of OFDM signals. However， they require symbol based active optimization， which introduces complexity issues at the transmitter side. Therefore， simpler solutions such as windowing are still needed in this field.

3 Reducing Redundancies of OFDM

Classical CP?OFDM is known as one of the most spectrally efficient transmission schemes and sufficiently satisfying the requirements of LTE?Advanced Pro and currently used IEEE 802.11 systems. However， it still suffers from redundancies， in both time and frequency domains. The redundancy in time comes from the use of CP while the redundancy in frequency domain comes from the use of pilot subcarriers and guard bands. In order to adopt OFDM for future radio access technologies and to achieve the aforementioned goals in data rate， these redundancies should be reduced， significantly.

3.1 CP Reduction

In communication channels with multipath delay spread， a guard interval （GI） is required to prevent leakage in time between the successive symbols. CP is a smart way to utilize the guard interval by copying the samples from the end of a symbol and pasting them to its beginning. Thus， the linear convolution of the channel becomes a circular convolution， which makes the channel matrix diagonalizable only by taking its Fourier transform and enables a simple equalization in the frequency domain. The length of the CP is chosen to be larger than the expected delay spread to avoid any inter?symbol interference （ISI） and ICI. Also， in order to maintain orthogonal coexistence of neighboring transmission blocks， predefined values have been used for the length of the CP and applied to all the blocks. For example， two CP rates are defined in LTE where the normal CP duration in terms of symbol duration is given as while the extended CP duration is .

Recent works have shown that extending the CP duration might not be the best approach to combat against long delay spreads [34]-[36]. The newly proposed 5G scenarios have introduced their own methods for ISI mitigation. An example is mmWave MIMO systems that employ highly directional transmission using beamforming. For such systems， beam switching reference signals are broadcasted so that the receivers can determine which predefined beam is directed to their way， resulting in higher signal to interference plus noise ratio for all receivers. Inventors have shown in [34] that such signals not only provide support for beam switching but can also be used to estimate delay spread exceeding CP duration. Then， ISI could be canceled from received symbols， which reduces the required CP. In [35]， authors claim that MIMO receivers can identify the presence of any residual interference after equalization by evaluating the channel matrix. It was shown that decreasing the modulation and coding index instead of extending the CP length， would increase the throughput. In addition to these methods， advanced signal processing techniques can be employed to mitigate the interference. A good example of that is the bi?directional M?algorithm based equalizer proposed in [36]. It has shown that a system which experiences a delay spread six times longer than the CP duration exhibits the same performance of a conventional system with sufficient CP. It is achieved at only the expense of performing two iterations of the proposed algorithm referred to as trellis?based interference detection and mitigation.

In some scenarios， the maximum excess delay might be much less than the duration of normal CP which makes the minimum CP overhead of 7% a pointless guard for LTE systems. To reduce this overhead， the authors of [37] present the idea of a flexible frame design. A wider range of options in terms of subcarrier spacing and CP length are used for the OFDM symbols inside the proposed frame structure. Then， the users experiencing similar channel dispersions are grouped and the proper symbol parameters are determined for each group within the frame. Thus， overall efficiency is enhanced by avoiding inconvenient parameter selection. An extension of this approach to mmWave single user MIMO systems can also be found in [34]， where the use of additional subframe configurations is presented independently for each user. Increasing the number of options for the CP duration is also recommended in the 3GPP standard contributions [38]， [39].

CP overhead also constitutes a disadvantage for the low latency required applications as it introduces delays in the transmission which might cause drawbacks for 5G services such as ultra reliable low latency communications （URLLC）. In the algorithm proposed in [40]， the author removed the CPs entirely from all symbols except the first one for reducing total transmission delay. In the proposed method， the CP used by the first symbol is utilized to obtain a detailed estimation of the channel time and frequency characteristics. Afterwards， the subcarrier spacing is reduced to ， where denotes the subcarrier spacing used in the first symbol anddenotes the total number of symbols including the first one. All symbols sent later are combined to fit in the same bandwidth used by the first symbol using an IFFT size of ， and sent as a single symbol without CP. Thus， the total transmission time is reduced by ， where is the CP duration.

3.2 Pilot Decontamination

Another redundancy that has been with OFDM since it became practical is the use of pilots within the subcarriers. In time domain duplexing （TDD） systems， inside a cell， the mobile stations transmit mutually orthogonal pilot sequences to the base station （BS） so that the BS can estimate the channel in the uplink （UL）， and assuming channel reciprocity， precode accordingly for the downlink （DL）. In the case of frequency domain duplexing （FDD） systems， because the channel state for the UL and DL is different， a two?stage procedure is required. The BS first transmits pilot symbols and then， the users feedback their channel state information to the BS. For the massive MIMO concept with the TDD case， many beams are established for a vast number of users compared to the past. Each beam requires a different mutually orthogonal sequence， which increases the length of the sequences immensely and decreases the resources available to transmit data symbols. For the FDD case， the same situation happens as the number of transmit antennas at the BS goes to infinity. A proposed method to reduce this overhead is reusing pilot sequences of nearby cells， which introduces inter?cell?interference and gives rise to the “pilot contamination” effect [41]. The high number of lengthy pilots also increases the latency and makes Internet of Things （IoT）?type sporadic and short messages inefficient.

Some researchers allow the use of the pilots but try to reduce the overhead， which can be referred to as soft pilot mitigation. In [42]， the authors propose using only the amplitudes of the subcarriers as the pilots， and the phase of the same subcarriers can be used to transmit information in an effort to increase the data rate. In [43]， the author proposes many techniques to mitigate pilot contamination for the TDD case. The terminals are suggested to match the DL reference signal powers in the UL， in order to reduce both the overall pilot interference in the neighboring cells and the pilot overhead required for closed loop power control. Another suggestion is reusing pilots softly to avoid inter?cell?interference. Some pilot sequences are proposed to be assigned for use only at the cell edge whereas the same groups of pilot sequences can be transmitted with less power near the BSs. Even further， the author suggests that the angular resolution provided by the massive number of antennas can be used to coordinate pilot allocation between cells and safely reuse the pilot sequences for spatially separated terminals. In [44]， the authors have aligned the Power Delay Profiles （PDPs） of the users served by the same BS to orthogonalize the pilots sent within the common OFDM symbol. By aligning the PDPs for the same number of users that can be sounded within the same symbol， it has been shown that the average signal?to?noise ratio （SNR） can increase by half.

Another group of researchers has proposed blind channel estimation or signal detection techniques to remove pilots completely， which would be appropriately called hard pilot mitigation. In [45]， the authors have shown that pilots can completely be removed as the singular value decomposition of the received signal matrix projects the received signal onto an interference?free subspace governed by an easily predictable non?linear compound. The authors have demonstrated that the proposed subspace projection method outperforms linear channel estimation if a power margin between the users of interest and interfering users are provided， especially when the base station antennas outnumber the coherence time （in number of symbol durations）. In [46]， the authors have treated the detected UL data as pilot symbols to obtain the least squares estimate of the channel. Also， by estimating the channels of all users sequentially， they obtained extracting vectors that accurately extract the desired data from the mixture signal.

4 Numerology

Wireless users have different requirements in waveform based on the service that they get or channel conditions that they experience. Therefore， there is not any one?size?fits?all solution for waveform design. The ongoing discussions on the usage of different numerologies also confirm this argument and consequently， one crucial expectation from future standards is the allowance to use multiple waveforms in one frame. This would definitely constitute a great relaxation in selecting the most proper waveform based on user needs. However， managing their coexistence is a critical issue. Especially， inter?user interference management for uplink/downlink， synchronous and asynchronous scenarios should be carefully investigated to utilize spectral resources efficiently.

In the context of 3GPP 5G standardization contributions， the term numerology refers to the configuration of waveform parameters， and different numerologies are considered as OFDM?based sub?frames having different parameters such as subcarrier spacing/symbol time， CP size， etc. [47]. By designing such numerologies based on user requirements， industry targets to meet the aforementioned user?specific demands to some extent. A general illustration of such numerologies is provided in Fig. 4. Here， numerology?I would be properly assigned to highly mobile users having more time?variant channels and the ones with low latency requirement. On the other hand， numerology?II offers more robustness against frequency selectivity and includes less redundancy due to low CP rate.

Let us give more details on the parameters and the importance of their selection for designing different numerologies：

1） CP length： The basic function of CP is to avoid inter?symbol interference and in?band interference. In order to achieve that， CP length should be specified as longer than the maximum excess delay of the channel impulse response. Therefore， users experiencing a wireless channel causing high dispersion in time （or more selectivity in frequency） should have longer CP lengths compared to the users with low dispersive channels. In addition， CP makes the signal robust against time synchronization errors. This might be very critical especially for asynchronous UL scenarios and low latency demanding services.

2） Subcarrier spacing： It can also be referred to as subcarrier bandwidth and is directly related to the duration of an OFDM symbol. When the CP size is determined on the basis of the channel conditions and application requirements， decreasing subcarrier spacing increases spectral efficiency as the CP rate decreases. However， for highly mobile users， channel responses might vary within a symbol duration which leads to ICI. Therefore， symbol time should be kept smaller by increasing subcarrier spacing in order to make the transmission robust against time?varying， i.e.， frequency dispersive channels. Additionally， a proper choice of subcarrier spacing is very critical for immunity against phase noise， which is specifically important for users operating on high frequencies such as mmWave frequencies.