5 G Numerology

arXiv:1805.02842v2[eess.SP]13Jun2019
Fundamentals of Multi-Numerology 5G New Radio
Ahmet Yazar∗, Berker Peköz† and Hüseyin Arslan∗†
∗Department of Electrical and Electronics Engineering, Istanbul Medipol University, Istanbul, 34810 Turkey
Email: {ayazar,huseyinarslan}@medipol.edu.tr
†Department of Electrical Engineering, University of South Florida, Tampa, FL 33620 USA
Email: {pekoz,arslan}@usf.edu
Abstract—The physical layer of 5G cellular communications
systems is designed to achieve better flexibility in an effort to
support diverse services and user requirements. OFDM wave-
form parameters are enriched with flexible multi-numerology
structures. This paper describes the differences between Long
Term Evolution (LTE) systems and new radio (NR) from the flex-
ibility perspective. Research opportunities for multi-numerology
systems are presented in a structured manner. Finally, inter-
numerology interference (INI) results as a function of guard al-
location and multi-numerology parameters are obtained through
simulation.
Index Terms—3GPP, 5G, adaptive scheduling, multi-
numerology, new radio, OFDM, waveform.
I. INTRODUCTION
Long Term Evolution (LTE) waveform has a fixed structure
that is optimized to serve high data rate applications. There
is only limited support for other applications due to the
inflexibility of the waveform. An example for the limited
flexibility is the extended cyclic prefix (CP) configuration uti-
lized by macrocell base stations (BSs) at all times to keep the
system operating at larger delay spreads at the cost of reduced
spectral efficiency [2]. This adaptation is rather limited as the
configuration is static; even when not needed by any user
equipment (UE), the system is configured to operate with these
parameters and does not have the flexibility to improve the
efficiency by utilizing normal CP. Other than delay spread, any
degradation in signal to interference plus noise ratio (SINR),
regardless of the cause, is addressed solely using adaptive
modulation and coding (AMC) by reducing the throughput
until a fixed reliability threshold is achieved [3]. For instance,
if SINR degrades due to inter-carrier interference (ICI) in high
mobilities, this issue can only be addressed using AMC in
LTE, reducing throughput and under-utilizing the bandwidth
(BW). As can be seen from the above examples, LTE has
limited flexibility and cannot support the rich application and
user requirements of 5G services [4].
5G is designed to provide a wide variety of services by
rendering waveform parameters flexibly [5]. The new design
paradigms make an enhanced-mobile broadband (eMBB) ex-
perience possible everywhere, including highly mobile UE
connected to macrocells. The flexibilities introduced to the
waveform enable reduced latencies and improved reliability,
empowering ultra reliable and low latency communications
The extended and updated version of this work was published in River Pub-
lishers Journal of Mobile Multimedia [1]. https://doi.org/10.13052/jmm1550-
4646.1442
(uRLLC) rather than high data rate applications. In addition,
massive machine type communications (mMTC) is enabled
for suitable scenarios with new radio (NR).
This flexibility was provided by coexisting of numerolo-
gies, where each numerology consists of a set of parameters
defining the frame and lattice structure of the waveform.
In contrast to the single-numerology utilization in LTE, NR
allows simultaneous multi-numerology utilization [6]. One of
the first studies that incorporated multi-numerology or mixed-
numerology systems and designed a framework that provides
numerous services simultaneously in a unified frame was [7].
Multi-numerology structures that were included in the Third
Generation Partnership Project (3GPP) NR standardization
were also studied in literature [8]–[12].
In this paper, three main contributions have been made as
listed below:
1) LTE and NR were compared from the flexibility per-
spective regard to 3GPP 38-series documents.
2) Research opportunities for multi-numerology systems
are presented in a structured manner.
3) Through simulation, inter-numerology interference
(INI) results as a function of guard allocation and multi-
numerology parameters are obtained.
The rest of the paper is organized as follows: Section II
presents the comparison between LTE and NR systems from
the flexibility perspective. New concepts introduced in NR
are also described in this section regarding to 3GPP 38-series
documents. Research opportunities for potential improvements
of multi-numerology systems are explained in Section III.
Section IV shows simulation results for multi-numerology
structures. Finally, the conclusion is given in Section V.
II. FLEXIBILITY OF NR COMPARED TO LTE
New concepts are introduced and building blocks are
defined to provide more flexible radio access technologies
(RATs) in [13] and [14]. In this section, concepts that were
introduced in NR are defined and their differences with LTE
are distinguished. Release 15 was taken as the reference for
both NR and LTE.
In 3GPP Release 15, standalone (SA) operation according
to [15], [16] and non-SA (NSA) operation coexisting with
other technologies according to [17] are defined. NSA oper-
ation was finalized in Release 15, but some issues regarding
SA operation, along with details necessary to provide mMTC,
was left for further study to be finalized in Release 16.

Waveform defines how the resources are placed in the
time-frequency lattice and the structure (pulse shapes and
filters) that maps information symbols to these resources [7].
In the downlink (DL), NR uses CP-orthogonal frequency
division multiplexing (OFDM) with multi numerologies (a
mother waveform plus its derivatives). The mother waveform
is the same in LTE but there is only one numerology. In
the uplink (UL), there is an option to use either of CP-
OFDM and discrete Fourier transform (DFT)-spread-OFDM
(DFT-s-OFDM) with multi numerologies for NR [18]. How-
ever, the only option in LTE is DFT-s-OFDM with a single
numerology.
The time-frequency lattice is the grid of discrete resources
in the continuous time-frequency plane, where each “atom” on
the grid shows where the continuous plane has been sampled,
thus defining where/when information can be transmitted [7].
LTE used a fixed lattice in which the frequency (and corre-
sponding time) spacing between each point was always the
same throughout the whole transmission band [5]. However,
NR defines flexible time-frequency lattice enabling multi-
numerology structure. For the case of OFDM, numerology set
consists of number of subcarriers, subcarrier spacing (∆ f ), slot
duration and CP duration (TCP) [4]. The ∆ f , TCP, slot duration,
and maximum BW allocation options for NR numerologies
according to [6] and [19] are presented in Table I. These
numerologies can be used simultaneously in a cell. On the
contrary, LTE is a single-numerology system thus all these
parameters are fixed at all times for a BS.
A BW Part (BWP) is a new term that defines a fixed band
over which the communication taking place uses the same
numerology throughout the existence of the BWP [20]. It is a
bridge between the numerology and scheduling mechanisms.
BWPs are controlled at the BS based on UE needs and
network requirements. In contrast to LTE, 5G UEs need not
monitor the whole transmission BW; they only scan the BWPs
assigned to themselves. BWPs allow UEs to process only
part of the band that contain their symbols, reducing power
consumption and enabling longer battery lives. This is very
useful for the low-power communications systems, particu-
larly mMTC services. BWPs may overlap to facilitate low
latency services while providing data to noncritical services
to ensure efficient utilization of resources.
BS channel BW is another new term that refers to the
contiguous BW currently in use by the next generation node
B (gNB) for either transmission or reception [21]. In other
words, it refers to the total BW that is processed by the gNB.
Unlike LTE slots that consist of 7 OFDM symbols in case
of normal CP, NR slots can consist of 14 symbols for ∆ f s
up to 60 kHz [22]. Furthermore, LTE Resource Blocks (RBs)
cover 12 consecutive subcarriers over a subframe (i.e., two
slots) duration, whereas NR RBs are defined only using the
same BW definition; their durations are not fixed [6]. As
opposed to the fixed LTE Transmission Time Interval (TTI)
duration of one slot, NR TTI may be a mini-slot in the case of
uRLLC or beam-sweeping operation in frequency range-2, a
slot for regular operation, or multiple slots in the case of large
TABLE I
NUMEROLOGY STRUCTURES AND THE CORRESPONDING MAXIMUM BW
ALLOCATIONS FOR DATA CHANNELS IN 5G
Frequency ∆f TCP Slot Max. BW
Range (FR) (kHz) (µs) Duration (ms) (MHz)
FR-1
15 4.76 1 50
30 2.38 0.5 100
60 1.19 | 4.17 0.25 100
FR-2
60 1.19 | 4.17 0.25 200
120 0.60 0.125 400
number of eMBB packets; thus having a definition varying as a
function of the service [22]. NR re-uses the LTE radio frame
definition [23], however, the number of slots per sub-frame
depends on the ∆ f and is given by the multiplicative inverse
of the slot duration seen in Table I [6].
III. RESEARCH OPPORTUNITIES FOR
MULTI-NUMEROLOGY SYSTEMS
As it can be seen from the previous section, the main
flexibility causative for NR is mostly focused on the new
frame with multi-numerology structures. Different user and
service requirements can be met using multiple numerologies.
In other words, multiplexing numerologies provides the flex-
ibility needed by NR.
This section presents exemplary multi-numerology algo-
rithms that exploit the flexibilities in NR design pointed out in
Section II. 3GPP standards give the BS and UE manufacturers
the freedom to implement any additional algorithm they desire
as long as it is transparent to the receiver [24]. Examples
provided in this section also exploit this degree of freedom.
A. Non-Orthogonality of Multi Numerologies
Resource elements within the same numerology are orthog-
onal to each other, but resource elements of any two different
numerologies are non-orthogonal to each other and interfere
with one another [5]. Non-orthogonality can result either
from partially or completely overlapped numerologies, or non-
overlapping numerologies for synchronous communications.
As it can be seen from Fig. 1, non-orthogonality is originated
from overlapping subcarriers for the first case. However, the
reason of non-orthogonality is out-of-band (OOB) emission in
the second case. Optionally, guard bands can be employed to
reduce interference for the second case. Performance analysis
for the effects of guard bands between numerologies is given
in Section IV. Besides these, subcarriers are non-orthogonal
to each other for intra- or inter-numerology domains in
asynchronous communications [25].
In [26], authors proposed a numerology-domain non-
orthogonal multiple accessing (NOMA) system with overlap-
ping multi-numerology structures. NR allows overlapping of
BWPs using different numerologies in time-frequency grid
[13]. Numerology-domain NOMA system designs can be
developed to exploit this gap in 5G.

Fig. 1. Orthogonality and non-orthogonality for intra-numerology and inter-
numerologies cases.
B. Numerology Selection Methodologies
BWP is a useful tool for multi-numerology systems as
BWP defines a specific numerology. BS can modify UE
numerologies by changing it’s BWPs. Parameter configuration
process for the BWPs is employed by BW adaptation (BA)
tool on BS [27]. There can be up to four defined BWPs for
each UE but there is one active BWP for each user in Release
15. However, future NR releases are planned to allow multiple
(up to four per UE in Release 16) active BWP configurations.
Active BWPs and the corresponding numerologies can
be selected using different methodologies. Various trade-offs
between distinct performance metrics that include spectral
efficiency, INI, flexibility, and complexity can be considered
while deciding on active BWPs and so numerologies.
For one active BWP at a time case, an example numerol-
ogy selection methodology is proposed in [4] that uses a
heuristic algorithm to configure numerologies suitable for each
user. Fig. 2 illustrates this resource allocation optimization
methodology. The proposed method also provides an active
BWP switching mechanism. ∆ f , TCP, and spectral efficiency
requirements of all users in a cell are input to the algorithm.
It is possible to increase the number of numerologies
in beyond 5G. Offering more numerologies simultaneously
ensures that all user and service requirements are satisfied, but
this requires more sophisticated numerology selection mecha-
nisms. To reduce computational costs, BSs may use two-step
numerology selection methods in the future. The first step
decides on the most suitable numerology set between different
sets. Then, the second step determines the best numerologies
from the set that is selected in the first step. Additionally,
there can be many different numerology selection methods
for multiple BWPs active at a time case.
C. INI Estimation Models
INI can be simply defined as ICI between subcarriers of dif-
ferent numerology structures. The amount of INI can vary with
∆ f , BW, guards, TCP, the number of different numerologies,
alignment of different numerologies in frequency domain,
filtering/windowing usage, frequency bands, user powers, and
so on. All of these parameters need to be analyzed together
to form estimation models for INI.
INI estimation is very important topic because it can be
used as a feedback to all other adaptive systems that include
Fig. 2. Simple representation of numerology selection methodology in a cell
serving users with various necessities [4]. User necessities are gathered by
BS at different times but numerology decisions are made at the same time.
adaptive guards, numerology selection, filtering/windowing
decision, and optimization of the number of numerologies.
Interference models can be very useful for adaptive decision
on different algorithms for multi-numerology systems. For ex-
ample, an INI estimation method between different transmitter
and receiver windowed OFDM numerologies are provided in
[28], where the exact calculation of INI using the channel
impulse responses (CIRs) and data of all users, as well as
estimation techniques for practical cases such as unknown data
as well as unknown CIRs are provided.
D. Effects of Guard Bands Between Multi Numerologies
This subsection deals with the adjustment of frequency
domain guards with respect to estimated INI after numerolo-
gies are selected. In 3GPP standards, it is revealed that
there are minimum guard band requirements, a maximum
or an optimum value is not enforced, making guard bands
choices flexible with high granularity [21]. Adaptive guard
band concept for different numerologies becomes a crucial
research area at this point.
As it is well known, the OFDM signal is well localized
in the time domain with a rectangular pulse shape, which
corresponds to a sinc pulse in the frequency domain. Sincs
cause significant OOB emission and guard bands are needed
between two adjacent subbands with different numerologies
to handle the interference.
The OOB emission increases as the symbol duration de-
creases. Therefore, more guard band is required for the
numerologies with higher ∆ f . For the edge subcarriers of
two adjacent numerologies, SINR decrease is more signif-
icant compared to the remaining subcarriers. Most of the
interference comes from the edge subcarriers [29]. Grouping
services in BWPs reduces the amount of necessary guards
and eases scheduling when such fast numerology variations
become necessities. Moreover, passing OFDM signal through
power amplifiers causes non-linear distortions. The peak-to-
average power ratio (PAPR) and OOB emission increase as the
number of active subcarriers increases. As a result, more guard

Fig. 3. Block diagram for the simple implementation of multi numerologies. The scaling factor of ∆f s is chosen as 2k , where k is a positive integer.
band is needed for the transmissions with wider occupied
numerology BWs.
In Section IV, the effects of guard bands between multi
numerologies with the performance analysis results are shown
regarding to the implementation block diagram given in Fig. 3.
E. Effects of Guard Intervals for INI Elimination
In addition to guard bands between different numerologies,
the guards in time and frequency domains must be jointly
optimized to boost the spectral efficiency [30]. Various slot
configurations and UE scheduling guidelines reveal that few
restrictions exist regarding scheduling users in time domain.
This implies that the guard times can also be utilized flexibly,
similar to guard bands. Combining time-frequency guard
flexibility yields that empty resource elements can virtually be
placed anywhere. Interpreting this at a multi-user level reveals
that the UL slot of one UE and the DL slot of another UE can
be scheduled to consecutive time or frequency resources with
little guard time and band. This poses serious requirements
in pulse shaping, making localized pulses and interference
rejection techniques critical.
Also, the use case and power imbalance factors should be
considered on the guard allocation. The power control mech-
anism mitigates the interference problem in power imbalance
scenarios as well, but it prevents deployment of higher order
modulation for the users that experience higher SINR. Thus,
power control requires relaxation using an adaptive guard
design to increase the throughput. The potential of adaptive
guards can be increased further by utilizing an interference-
based scheduling algorithm [30].
F. Filtering and Windowing in NR
INI cannot only be handled using guards but also with
the filtering and windowing approaches that require additional
guards. Applying filters and windows methods are left for the
implementation in 3GPP standardization.
Allocating users optimal guards minimizes but not com-
pletely eliminates the interference on the received signal in
a non-orthogonal system. The receiver may also engage in
filtering and windowing to further eliminate the remaining
interference, but doing so using conventional methods requires
additional guards. The assigned optimum guards may not even
be sufficient if extreme latencies are required. The algorithm
presented in [28] deals with the minimization of aggregate
inter-symbol interference (ISI), ICI and adjacent channel in-
terference (ACI) by windowing each received subcarrier with
the window function that minimizes the aggregate interference
at that subcarrier. The optimal window lengths require perfect
knowledge of the interfering users’ data and channels. While
this can be known and applied at UL reception at the gNB in
a manner similar to successive interference cancellation (SIC)
or multi-user (MU) detection, this cannot be done at the UE.
Therefore, the algorithm presents methods to estimate optimal
subcarrier specific window durations if only the CIRs, power
delay profiles (PDPs) or the power offsets of the interferers
are known.
G. Optimization on the Number of Active Numerologies
Authors of [4] find the efficient number of active numerolo-
gies that should be simultaneously employed by users. The
algorithm aims to minimize various overheads to provide a
practical solution satisfying different service and user require-
ments using multi-numerology structures. All of the different
numerologies that are defined in standards do not need to be
used in every situation.
Basically, the amount of total guard band in the lattice
increases with increasing number of numerologies. Hence,
there is a trade-off between the spectral efficiency and multi-
numerology system flexibility. Although not imposed by the
standard [6], they allocate BWPs configured to use the same
numerologies consecutively in an effort to reduce guard bands
and computational complexity.

IV. SIMULATION RESULTS ON MULTI-NUMEROLOGY
In this section, INI results as a function of guard allocation
and multi-numerology parameters are provided based on the
block diagram in Fig. 3. It is assumed that BWPs with
different numerologies are not overlapped at a time and BWPs
with the same numerologies are grouped together in the
frequency domain. Also, user powers are taken as equal.
Random binary phase shift keying (BPSK) symbols are
generated separately for two-numerology structure. For the
first numerology, which has ∆fref kHz subcarrier spacing, N-
point inverse fast Fourier transform (IFFT) is employed. The
second numerology has 2k × ∆fref kHz subcarrier spacing and
uses N/(2k)-point IFFT, where 2k is the scaling factor and
k is a positive integer. Here, the second half of the IFFT
inputs for the first numerology and the first half of the IFFT
inputs for the second numerology are zero-padded to separate
two numerologies in frequency domain. After each IFFT
operation, CP samples are added with a ratio of CPR to every
OFDM symbol. There are 2k OFDM symbols with the second
numerology corresponding to one OFDM symbol with the first
numerology. Thus, the number of samples for each of the
numerologies are the same, and they can be added to form a
composite signal at the transmitter.
Wireless channel and noise are ignored to just focus on
the INI in the simulation results. At the receiver side, CP
samples are removed from each OFDM symbol. N-point fast
Fourier transform (FFT) is used for the first numerology over
full composite signal. However, only N/(2k) samples of the
composite signal to make them input into N/(2k)-point FFT
for the second numerology. 2k
subblocks are constituted by
dividing the composite signal into 2k parts and these subblocks
are processed one by one. The first half of the FFT output for
the first numerology and the second half of the FFT output for
the second numerology are taken to obtain received symbols.
Interference estimations are done for each of the used sub-
carriers separately. Monte Carlo method is applied to increase
the statistics in simulation results. The number of tests is 500
and different set of random data is used in each of these
tests. Thereafter, the average interference on the subcarriers
are estimated. There are four cases in the simulation results
presented in Fig. 4. Number of usable subcarriers are half of
the IFFT sizes in each case.
In Fig. 4, INI results are plotted like that there is not any
guard bands between the edge subcarriers of two numerologies
when there are actually guard bands. The reason of this
representation is to make a comparison with different amount
of guard bands easily. The below basic inferences are made
from the simulation results:
1) There is more INI at the edge subcarriers of different
numerologies.
2) INI present at each subcarrier decreases as the guard
band between different numerologies increases.
3) The effect of guard bands are more prominent for the
edge subcarriers.
4) CP addition causes additional interference for the nu-
merology with smaller ∆ f .
5) Subblocks of the second numerology are constituted by
dividing the composite signal. Hence, the symbols of
the first numerology causes an extra interference on the
second numerology at the receiver side.
6) INI on every (2k)th subcarrier is less than that of the
other subcarriers for the numerology with smaller ∆ f .
Simulation results show that there are opportunities for the
adaptive algorithm designs in 5G as mentioned in Section III.
V. CONCLUSION
Next generation communications systems including NR are
evolving towards increased flexibility in different aspects.
Enhanced flexibility is the key to address diverse requirements.
Spectral guards and pulse shapes are critical part of this
flexibility. These are left for the implementation as long as
it is transparent to the counterpart of the communications.
NR flexibility can be exploited by finding optimal and prac-
tical solutions for implementation dependent parts of the 5G
standardization. The flexibility of NR brings too many open-
ended research opportunities compared to the previous cellular
communications generations.
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200 400 600 800 1000 1200 1400
Subcarrier Indices
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Inter-NumerologyInterference(dB)
INI Estimation for Multi Numerologies
0 SC of GB for Numerology-1
12 SCs of GB for Numerology-1
1000 1020 1040
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(a) Case 1: Numerology-1 has 15 kHz ∆f and Numerology-2 has
30 kHz ∆f . Guard bands are 0 kHz, 180 kHz and 360 kHz.
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(c) Case 3: Numerology-1 has 15 kHz ∆f and Numerology-2 has
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(d) Case 4: Numerology-1 has 15 kHz ∆f and Numerology-2 has
Fig. 4. Simulation results for four different cases with different guard band amounts between numerologies.
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