Multi-Numerology Multiplexing and Inter-Numerology Interference Analysis for 5G Abuu B

Multi-Numerology Multiplexing and Inter-Numerology Interference Analysis for 5G Abuu B. Kihero, Muhammad Sohaib J. Solaija, Student Member, IEEE, and Huseyin¨ Arslan, Fellow, IEEE

Abstract—Fifth generation (5G) radio access technology (RAT) rate, URLLC needs high reliability and low latency while is expected to flexibly serve multiple services with extremely mMTC necessitates low energy and bandwidth consumption diverse requirements. One of the steps taken toward fulfilling and high coverage density [2]. It is important to keep in this vision of the 5G-RAT is an introduction of the multi- numerology concept, where multiple frame structures with dif- mind that this division of services is by no means thorough, ferent subcarrier spacings coexist in one frequency band. Though and there are going to be various scenarios that do not fall efficient in providing the required flexibility, this approach completely within a single defined use-cases [3]. introduces a new kind of interference into the system known In order to meet these diverse requirements of 5G services, as inter numerology interference (INI). This study is geared there have been two primary candidate approaches proposed toward analyzing the INI problem considering a cyclic prefix orthogonal frequency domain multiplexing (CP-OFDM) system by researchers. First, proposition of new waveforms for 5G and exposing the factors contributing to it through mathematical New Radio (5G-NR) and second, using different numerologies analyses. In-depth discussion of various critical issues concerning of the same parent waveform, orthogonal frequency division multi-numerology system such as frequency domain multiplexing multiplexing (OFDM), where the term numerology refers to and time domain symbol alignment for mixed numerologies is the different configurations of subcarrier spacing and cyclic presented. Based on the findings of the conducted analyses, the paper highlights some approaches for minimizing INI in the prefix (CP) duration of an OFDM symbol [4]. The first system. The developed mathematical analysis is finally verified approach led to the proposition, analysis and comparison by Monte-Carlo simulations. of various waveforms like filter bank multi-carrier (FBMC), Index Terms—Interference analysis, inter-numerology Interfer- generalized frequency division multiplexing (GFDM), and ence, multi-service, mixed numerologies. universal filtered multi-carrier (UFMC). Several studies have compared these waveforms [5], [6] and it is the general consensus among the researchers that while each of these I.INTRODUCTION waveforms offers improvement over OFDM in some aspect, The vision for fifth generation (5G) of wireless technology none of them can claim to address all requirements of 5G. is much more than the mere evolution of broadband services. In addition to this, OFDM’s maturity and the immense effort It envisages a more diverse network with seamless cover- that is already put into its standardization for LTE led to age, higher data rates, various services, massive connectivity, it being selected as the waveform for 5G despite its CP and significantly higher reliability than any earlier generation overhead, frequency and time offset sensitivity, high peak-to- of mobile communication. As compared to the long-term average power ratio (PAPR) and spectral regrowth issues [7]. evolution (LTE), 5G advertises a thousand-fold increase in Therefore, for 5G-NR, 3GPP has opted for the second ap- data volume and number of connected devices per area, 100 proach i.e. use of multiple numerologies of OFDM waveform. times improvement in user data rates, reduction of energy Table I gives a brief summary of the different numerologies consumption by a factor of 10 and decrease in latency by present in the standard [8]. A total of five scalable numerology a factor of 5 [1]. These demands, when looked at simultane- options are provided with the conventional LTE numerology ously, seem improbable if not impossible to achieve, requiring (with subcarrier spacing of 15 kHz) chosen as the fundamental arXiv:1905.12748v1 [eess.SP] 29 May 2019 multiple magnitudes of improvement in current technology and numerology. By scalable we mean that all the standardized infrastructure. ∆f’s are 2µ multiples of the fundamental LTE numerology As an approach to address these diverse service require- (for µ = {0, 4}). One basic reason for choosing this set of ments, the standardization bodies, i.e., 3rd Generation Part- numerologies with scalable subcarrier spacing is to facilitate nership Project (3GPP) and International Telecommunication easy symbols alignment and clock synchronization in time Union Radiocommunication (ITU-R), have divided them into domain and thus simplifies the implementation [2], [9]. three different sets, one for each service, namely, enhanced It can be seen intuitively how different numerologies can mobile broadband (eMBB), ultra-reliable low latency commu- be used to meet the demands of each service class of 5G. For nication (URLLC), and massive machine type communication example, lower (in terms of subcarrier spacing) numerologies (mMTC). eMBB prioritizes large bandwidth and high data are more suitable for mMTC, since they can support higher Authors are with School of Engineering and Natural Science, Istan- number of simultaneously connected devices within the same bul Medipol University, Beykoz, 34810 Istanbul, TURKEY. H. Arslan bandwidth and require lower power, intermediate numerolo- is also with Department of Electrical Engineering, University of South gies are appropriate for eMBB which requires both, high data Florida, Tampa, 33620 Florida, USA (e-mail: [email protected]; [email protected]; [email protected]). rate and significant bandwidth, and higher numerologies are more suitable for delay-sensitive applications pertaining to the 2

TABLE I: Numerology structures for data channels in 5G [8]. a more generic mathematical analysis of INI for subband Numerology options (µ) Parameters filtered multi-carrier (SFMC) based systems, and proposes 0 1 2 3 4 Subcarrier Spacing some algorithms to minimize it. Zhang et. al. in [4] present 15 30 60 120 240 (kHz) a mathematical analysis of INI and describe factors such as OFDM Symbol 66.67 33.33 16.67 8.33 4.17 channel response, spectral distance between interfering and Duration (µs) victim numerology, and windowing operation at the transmitter CP Duration 4.69 2.34 4.17|1.17 0.58 0.29 (µs) and receiver to have great impact on the amount of INI Slot Duration 1 0.5 0.25 0.125 0.0625 suffered by the system. Though detailed, the focus of the (ms) presented analysis is limited to windowed-OFDM system, and only an approximate analytical model of INI for CP-OFDM is given. Apart from mere analysis of the INI, some studies [4], URLLC service due to shorter symbol duration. It is important [11], [18] have already gone further and proposed techniques to note that the selection of numerologies is not only dependent and algorithms to contain INI. For instance, [18] tries to on the service to be supported, other factors like the cell size, optimize the guard in time and frequency domains to minimize time variation of the channel, delay spread, carrier frequency INI while keeping in view the user requirements and their etc, also need to be taken into consideration in picking a power offset. The study in [19] discuses a power offset based numerology [10]. scheduling technique in multi-numerology systems to mini- While the use of multiple numerologies is essential in mize INI experienced by edge subcarriers of the multiplexed providing the necessary flexibility required for the diverse numerologies. services, it introduces non-orthogonality into the system which Regarding the fact that the standardization bodies have in turns causes interference between the multiplexed nu- selected CP-OFDM as a standard waveform for 5G-NR, an merologies [2], [4], [10], [11]. This new form of interference extensive INI analysis specific for this waveform is unar- is referred to as inter numerology interference (INI). Apart guably important in the literature. Our study, therefore, will from causing loss of orthogonality among subcarriers in fre- focus on the INI analysis for this core waveform of 5G. quency domain, mixed numerologies also bring up difficulty in The analysis not only provides better understanding of the achieving symbols alignment in time domain. With the same phenomenon, but also identifies areas where INI can be either sampling rate, an OFDM symbol of one numerology does controlled/minimized or even exploited to enhance perfor- not perfectly align with the symbol of another numerology mance of the system. The contribution of this paper can be which makes synchronization issues within the frame difficult. itemized as follows: However, with the scalable numerology design of 5G, symbol duration of one numerology is an integral multiple of the • A generic mathematical model for INI in multi- symbol duration of the other numerologies (see Fig. 2). numerology systems utilizing CP-OFDM is provided, Therefore, multi-numerology symbols can be perfectly aligned and analytical expressions for INI are calculated. The established INI models give clear insight on how dif- over the integral least common multiplier duration (TLCM ) as discussed in [9], [11]–[13]. Two different approaches of ferent parameters contribute to INI in the system. The developed INI expressions are verified with Monte Carlo achieving symbol alignment over TLCM duration are presented in [12], namely individual CP and common CP. The individual simulations. CP refers to the conventional CP configuration where a CP • A thorough investigation and comparison of the two sym- is attached to each OFDM symbol prior to transmission, as bols alignment techniques (i.e., individual and common standardized for LTE and 5G systems. Common CP, on the CP) presented in [12] are done from INI perspective. The other hand, is a new CP configuration technique where one INI mathematical analysis is done for both techniques. CP is used to protect multiple OFDM symbols against inter Along with these main contributions, a generic method of mul- symbol interference (ISI) [12], [14]–[17]. It is a promising tiplexing numerologies in a given spectrum band is described CP configuration technique for future wireless systems. It in detail from both frequency and time domains perspectives is briefly shown that these two approaches yield different and their mathematical expressions are also given. INI distribution among subcarriers of the victim numerology. The rest of this paper is organized as follows. Section II Proper understanding of the INI distribution is very crucial as discusses the downlink system model used for implementation it can open doors for developing better techniques of avoiding of multi-numerology system and its mathematical formulation or minimizing INI in the system. in both, frequency and time domains. Sections III and IV give In order to make an intelligent use of the multiple nu- detailed derivations of the INI expressions for individual and merologies concept introduced by 5G-NR, an in-depth analysis common CP configurations respectively. Numerical analysis and understanding of INI is inevitable. Researchers have and insights derived from the observed results are discussed already taken a step toward describing INI in details and in Section V. Section VI finally concludes the paper. identify various factors contributing to it. A more generic study of the factors affecting INI is conducted in [12], but its II.SYSTEM MODEL scope is limited to the identification and intuitive explanation A. Frequency Domain of the identified factors, supported by simulations without Let us consider a multi-numerology system with system providing any analytical verification. A study in [11] provides bandwidth B shared between two users. Active subcarriers 3

Fig. 1: Downlink multi-numerology implementation at the transmitter.

(a) (b)

Fig. 2: Multi-numerology symbol alignment over LCM symbol duration. (a) Individual CP case. (b) Common CP case. of the two users are assumed to utilize the bandwidth in to their specified portions of the spectrum. The SM blocks the ratio η1 and η2. For simplicity and numerical tractability implement the localized subcarrier mapping technique whose of the INI analysis, only two users utilizing numerology-1 output can be expressed as and numerology-2 are considered in this model. However, xnr(k) , 0 ≤ k ≤ η1N − 1 the analysis developed herein can be applied to any num- Xnr(k) = , (1) 0 , η1N ≤ k ≤ N − 1 ber of multiplexed numerologies by considering one pair of numerologies at a time. Let the two numerologies utilize and subcarrier spacing ∆f1 (narrow subcarrier spacing) and ∆f2 0 , 0 ≤ l ≤ (1 − η2)M − 1 Xw(l) = , (2) (wide subcarrier spacing) respectively. Throughout the paper xw(l) , (1 − η2)M ≤ l ≤ M − 1 we will refer to the first numerology with narrow subcarrier where, N and M are fast Fourier transform (FFT)/inverse fast spacing as NSN, and to the second with wide subcarrier Fourier transform (IFFT) sizes of NSN and WSN respectively, spacing as WSN. Abiding by the 5G standards, the ratio such that N = Q · M. Xnr(k) and Xw(l) are complex ∆f2/∆f1 = Q is always an integer power of 2. Note that modulated symbols on kth and lth subcarriers of NSN and Q = 1 refers to the case in which two users are using the WSN respectively, after SM. If we are to observe the WSN same numerology. subcarriers with the granularity of the NSN subcarriers, the Fig. 1 models the downlink implementation of the multi- l-indices of active subcarriers of WSN can be defined as numerology frequency-domain subcarriers multiplexing, time- l = η1M + k/Q for {0 ≤ k ≤ η2N − 1 : k/Q ∈ Z}. domain symbol alignment, and creation of the composite signal for the transmission. The model employs subcarrier B. Time Domain mapping (SM) blocks right after serial-to-parallel (S/P) blocks for properly arranging NSN and WSN subcarriers according The output of the IFFT blocks in Fig. 1 are time-domain symbols ynr and yw of NSN and WSN respectively, and they 4 are given by larger subcarrier spacing and larger CP duration simultaneously to overcome inter carrier interference (ICI) and ISI y (n) = IFFT {X }| nr nr N−points respectively. Common CP configuration provide a solution to η1N−1 1 X j2πnk/N this dilemma by allowing us to use larger subcarriers spacing = √ Xnr(k)e , (3) N and yet have larger CP duration to contain the ISI without com- k=0 promising the spectral efficiency and receiver complexity [16]. for 0 ≤ n ≤ N − 1, In another study, authors have used common CP configuration and to enhance performance of the multi-numerology based non- orthogonal multiple access (NOMA) systems [17]. Although yw(m) = IFFT {Xw}|M−points common CP configuration have exhibited better performance η2N−1 1 X j2π m(k+η N) compared to the conventional individual CP structure in some = √ X (η M + k/Q)e N 1 (4) w 1 scenarios, its INI performance is not yet well investigated. M k=0 It should be understood that, a modified frequency domain for 0 ≤ m ≤ M − 1, k/Q ∈ . Z equalizer has to be used at the receiver when common CP is As briefly explained in the introduction, the symbol align- used. Details concerning equalization with common CP can ment issue in the multi-numerology system is overcome when be found in [14] and [16]. the multiplexed numerologies are integral multiple of one Now, with the common CP, the Q-concatenated symbols of C another. For instance, subcarrier spacings ∆f2 = Q · ∆f1 y WSN (denoted by wc ) is given as imply that the symbol durations T1 and T2 are also related Q−1 by T1 = Q · T2, which means that Q-concatenated symbols C X y = yw (m − NCP − qM), (7) of WSN can be perfectly aligned with one symbol of NSN. wc q q=0 This gives rise to the concept of multi-numerology symbols alignment over TLCM duration as mentioned earlier. TLCM is and the transmitted signal y is given by usually equal to the symbol duration of the numerology with C y = ynr + y . (8) the smallest ∆f in a given system. With an exception of the wc extended CP option for the numerology with ∆f = 60 kHz, Let us assume that the transmitted signal passes through all standardized numerologies use the same CP-ratio, which a D-taps time varying multipath channel with its discrete guarantees that the multi-numerology symbols alignment over channel impulse response (CIR) given by TLCM duration holds even after CP addition to the symbols. D−1 As we have mentioned before, in this study individual CP X h(m) = γ (m)δ(m − τ ), (9) and common CP approaches of achieving multi-numerology d d d=0 symbols alignment are investigated. 1) Individual CP: The individual CP configuration is where τd and γd are propagation delays (in samples) and th shown in Fig. 2(a). It is a conventional approach where CP is complex amplitude associated with d tap, respectively. δ(·) added to each of the Q symbols of WSN before concatenating is the Dirac delta function that models the propagation delay of each tap. The received signal s is then expressed as them. Let NCP and MCP be the CP-sizes for NSN and WSN respectively, where N = Q · M . After CP addition to D−1 CP CP X each symbol, the ranges of indices n and m in (3) and (4) s(r) = h(r) ∗ y(r) = γd(r)y(r − τd), (10) respectively are redefined to −NCP ≤ n ≤ N − 1, and d=0 −MCP ≤ m ≤ M − 1. The Q-concatenated symbols of where additive channel noise is ignored. yI M WSN (denoted by wc ) can be modeled as an -point periodic In this analysis, we assume that a proper choice of numerol- extension of yw, given as ogy is made such that neither NSN nor WSN subcarriers are Q−1 affected by ICI. Furthermore, we consider that NCP > D and I X y = y (m − q(M + M )), MCP > D such that both numerologies are not affected by wc wq CP (5) q=0 ISI [20]. Therefore, only INI is expected in the system. where q is the WSN symbol index within TLCM duration. y yI III.INTER-NUMEROLOGY INTERFERENCE ANALYSIS FOR Now, nr and wc are summed up to form a composite signal y of the two numerologies for transmission [13], given as INDIVIDUAL CPCONFIGURATION A. INI from WSN to NSN y = y + yI . nr wc (6) At the receiver of the NSN user, NCP -sized CP is removed 2) Common CP: In this approach all Q concatenated WSN and then the time-domain received signal is transformed symbols are protected by only one CP of length Q × MCP (= to its frequency domain for the frequency domain channel NCP ) as shown in Fig. 2(b). This approach is motivated by the equalization and data detection processes. The N-point FFT concept of multi-symbols encapsulated OFDM (MSE-OFDM) of the received signal is taken as follows studied in [14]–[16]. As reported in Table I, CP size decreases S(v) = FFT {s(r)}| = HNSN (v) · Y (v), (11) with an increase in the subcarrier spacing. In case of a highly N−point doubly dispersive channel, we do not have flexibility to utilize 5

for 0 ≤ v ≤ η1 · N − 1, where v represents indices of where the desired subcarriers of NSN, and HNSN (v) denotes the 2 channel frequency response (CFR) at vth subcarrier, defined sin π 1 + (1 − Q)CP (k − v) Q R as D−1 Ψ(k, v) = 2 NSN X NSN − j2π vτ H (v) = γ (v)e N d . (12) d sin π (k − v + η N) N 1 d=0 Y is the FFT of the composite transmitted signal y, given as 2 sin π (1 + CP )(k − v) N+NCP −1 Q R 1 X − j2π rv Y (v) = √ y(r)e N . (13) + (Q − 1) · , N 2 r=NCP sin π (k − v + η N) N 1 Since y is composed of the signals of the two multiplexed numerologies, Y will then consist of the desired symbols WSN 2 ρ (k) = |Xw(η2M +k/Q)| is the WSN subcarrier power, (Ydes) of NSN as well as the interference YINI they receive from sidelobes of the WSN subcarriers. So, (11) becomes and CPR = NCP /N = MCP /M is the CP ratio employed by the the system. The term k − v + η1N is the spectral NSN S(v) = H (v) · [Ydes(v) + YINI (v)]. (14) distance between the interfering subcarrier at k +η1N and the victim subcarrier at v. Note that when Q = 1, i.e., the system Since we have considered the flat fading subchannel con- is comprised of a single numerology, the INI power in (17) dition each subcarrier, then, the channel effect in (14) can becomes zero as it would be expected. Signal-to-interference be completely compensated by using a conventional one-tap ratio (SIR) performance of the vth subcarrier of NSN due to frequency domain equalization. INSN (k, v) can be calculated as By using (13), (6), and (5), we can express the interference th η2N−1 YINI (v) from WSN to v subcarrier of NSN as NSN X SIRNSN (v) = ρ (v) INSN (k, v) M+M −1 Q−1 1 XCP X k=0 (18) NSN YINI (v) = √ ywq (r − q(M + MCP )) NM · ρ (v) N r=N q=0 = . CP Pη2N−1 ρWSN (k)Ψ(k, v) − j2π v(r−q(M+M )) k=0 · e N CP . (15) B. INI from NSN to WSN Note that, among the Q concatenated symbols of WSN, only Again, we consider s(r) in (10) as the received signal at th the first symbol (i.e., q = 0) overlaps with the CP portion WSN receiver. To demodulate a q symbol out of the Q- of the NSN symbol. Therefore, due to the CP removal at the concatenated symbols of WSN, the WSN receiver captures an NSN receiver, we can write s(r − q(M + MCP )) portion of the received signal, where 0 ≤ r ≤ M + MCP − 1, such that " M+MCP −1 1 X − j2π rv YINI (v) = √ yw (r)e N + s(r−q(M +MCP )) = yw (r)+ynr(r−q(M +MCP )), (19) N 0 q r=NCP where ynr(r − q(M + MCP )) is the portion of the NSN M+MCP −1 Q−1 # th X X − j2π v(r−q(M+M )) symbol added to the q symbol of WSN during creation of y (r − q(M + M ))e N CP wq CP the composite signal at the transmitter. M-point FFT process r=0 q=1 (16) at the WSN receiver results in S(v) = FFT {s(r − q(M + MCP ))}|M−point Further simplification of (16) is shown in Appendix A. Now, WSN (20) by substituting (32) and (33) from the Appendix A into (16), = H (v)[Ydes(v) + YINI (v)], th WSN th we find the INI power INSN (k, v) from k subcarrier of where H (v) is the CFR at the v subcarrier of WSN WSN to the vth subcarrier of NSN as user given as D−1 WSN X WSN − j2πvτd ρWSN (k) H (v) = γ (v)e M . (21) I (k, v) = |Y (v)|2 = Ψ(k, v), d NSN INIk N · M d=0 (17) for 0 ≤ v ≤ η1N − 1 and Recalling the localized subcarrier mapping technique imple- mented at the transmitter, the indices, v of the WSN subcarri- {0 ≤ k ≤ η2N − 1 : k/Q ∈ Z}, ers to be detected can be expressed as v = η2M +p/Q, where {0 ≤ p ≤ η2N − 1 : p/Q ∈ Z}. We can thus write (20) as WSN S(η1M + p/Q) =H (η1M + p/Q) Ydes(η1M + p/Q) + YINI (η1M + p/Q) . (22) 6

Again, considering perfect channel equalization at the receiver, power (i.e., ρNSN = ρWSN ), where SIR performance of both we can get rid of the channel effect HWSN in (22). numerologies becomes independent of their powers. These Now, we can find the interference YINI from NSN to WSN analytical relationships provide the basis of the heuristic multi- as numerology scheduling algorithms proposed in [18] and [19] where the authors suggest that numerologies with minimum YINI (η1M + p/Q) power offsets should be scheduled adjacent to each other. M+MCP −1 1 j2π X − r(η1M+p/Q) = √ ynr(r − q(M + MCP ))e M M NTER UMEROLOGY NTERFERENCE NALYSIS FOR r=MCP IV. I -N I A M−1 COMMON CPCONFIGURATION 1 X = √ ynr(r + MCP − q(M + MCP )) While following the same derivation steps as detailed in M r=0 Section III, here in this section we will only summarize the − j2π (r+M )(η M+p/Q) · e M CP 1 INI derivations for WSN and NSN. (23) (23) is simplified in Appendix B and (34) is obtained. Now, A. INI from WSN to NSN th by using (22) and (34) the INI power, IWSN (k, p) from k The N-points FFT processing at the NSN receiver yields th th subcarrier of NSN to the p subcarrier of WSN can be given the interference YINI (v) from WSN to v subcarrier of NSN as as NSN N+N −1 2 ρ (k) 2 CP I (k, p) = |Y (η M + p/Q)| = |ξ(k, p)| , 1 X C − j2π rv WSN INIk 1 Y (v) = √ y (r)e N N · M INI wc N r=N for 0 ≤ k ≤ η1N − 1 and CP (26) N−1 1 j2π {0 ≤ p ≤ η2N − 1 : p/Q ∈ Z}, X C − (r+NCP )v = √ y (r + NCP )e N . (24) wc N r=0 where By using (7) and (4) and adopting the same step as in π Appendix A and B, (26) can be simplified to sin Q (k − p) Q−1 η2N−1 ξ(k, p) = , 1 X X π YINI (v) =√ Xwq (η1M + k/Q) sin (k − p − η1N) N N · M q=0 k=0 − j2πq r(k−v+η N jπ NSN 2 Q 1 − N (M−1)(k−v+η1N) and ρ (k) = |Xnr(k)| is the NSN subcarrier power. · e e · ζ(k, v) Again, note that, when only one numerology occupies the (27) whole spectrum (i.e., Q = 1), the IWSN is zero as expected. where th The SIR of p subcarrier of WSN due to IWSN (k, p) is π given by sin Q (k − v) η1N−1 ζ(k, p) = . WSN X π SIRWSN (p) = ρ (p) IWSN (k, p) sin N (k − v + η1N) k=0 (25) WSN th NM · ρ (p) Now, the INI power INSN (k, v) from k subcarrier of WSN = . th Pη1N−1 NSN 2 to v subcarrier of NSN is given as k=0 ρ (k)|ξ(k, p)| WSN Remark 1: From the INI expressions obtained in (17) 2 ρ (k) 2 INSN (k, v) = |YINI (v)| = |ζ(k, v)| , and (24), we can deduce that power ρ of the interfering k M 2 (28) numerology, spectrum sharing factor η, as well as the ratio for 0 ≤ v ≤ η1N − 1 and ∆f2/∆f1 = N/M = Q of the multiplexed numerologies are {0 ≤ k ≤ η2N − 1 : k/Q ∈ Z}. the main factors affecting the amount of INI experienced by th each numerology. One can easily note that, if we increase Q The SIR of v subcarrier of NSN due to INSN (k, v) is given (i.e., decreasing M for a particular value of N) we minimize as the product N ·M in (17) and (24) resulting in a higher INI for η2N−1 NSN X both numerologies. This property was also observed by Zhang SIRNSN (v) = ρ INSN (k, v) in [4]. This suggests that, for a given set of numerologies, k=0 (29) M 2ρNSN (v) system INI can be minimized by scheduling numerologies with = . minimum Q adjacent to each other. Pη2N−1 WSN 2 k=0 ρ (k)|ζ(k, v)| Remark 2: The SIR expressions (18) and (25) show that any power offset between the two numerologies favor SIR performance of one numerology (with relatively higher power) and deteriorate the other (with low power). The fairer case is observed when the multiplexed numerologies have the same 7

B. INI from NSN to WSN 0.6 Individual CP: NSN-Analytic Contrary to the previous case of WSN with individual CP Individual CP: NSN-Simulation Individual CP: WSN-Analytic where equalization is done for each of the Q-concatenated 0.5 0.1 Individual CP: WSN-Simulation symbols, in this case, since all symbols share one CP, equal- Common CP: NSN-Simulation 0.08 Common CP: NSN-Analytic ization is therefore done over the whole block of Q WSN sym- 0.4 0.06 Common CP: WSN-Simulation Common CP: WSN-Analytic bols. The equalized frequency domain signal is then converted 0.04 back into the time domain where each symbol is demodulated 0.3 0.02 through M-points FFT process. As we have mentioned before, 0 further details concerning equalization with common CP can 50 55 60 65 70 75 be found in [14] and [16]. Again, by considering perfect INI power (linear) 0.2 equalization, we calculate the interference YINI from NSN to WSN as 0.1

YINI (η1M + p/Q) 0 M−1 0 20 40 60 80 100 120 1 j2π (30) X − (r−qM)(η1N+p) = √ ynr(r − qM)e N . Subcarrier index M r=0 Fig. 3: INI distribution on NSN and WSN subcarriers for individual and Substituting (3) into (30) and perform some simplifications common CP configurations through similar steps used in Appendix A and B, an expression for the INI power, I (k, p) from kth subcarrier of NSN WSN A. INI comparison for individual and common CP to pth subcarrier of WSN can be found as Illustrated in Fig. 3 is the INI power experienced by each I (k, p) = |Y (η M + p/Q)|2 WSN INIk 1 subcarrier of NSN and WSN for both, individual and common ρNSN (k) CP configurations. As one could expect, the edge subcarriers = |ξ(k, p)|2, N · M (31) of both numerologies are experiencing relatively higher INI for 0 ≤ k ≤ η1N − 1 and compared to the middle subcarriers. This is due to the higher sidelobes of the adjacent numerology, whose effect abates as {0 ≤ p ≤ η2N − 1 : p/Q ∈ Z}. one moves away from the edges. Again, as observed from One can notice from (24) and (31) that the INI power leaking the analytical expressions (24) and (31), the INI experienced from NSN to WSN for the individual and common CP cases by WSN is exactly the same for both CP configurations, are exactly the same. Therefore, their SIR performance are and that agrees well with the simulation results shown in also the same, given by (25). In this regard, we can conclude Fig. 3. The INI of NSN exhibits an interesting oscillatory that changing CP configuration affects INI distribution of the behavior from one subcarrier to another. This behavior is NSN only. due to the discontinuities created at the boundaries of the Q- One difference between the INI characteristics of the two concatenating symbols of WSN. That is why, as it can be investigated CP configurations is that, the INI experienced by observed from the next figure (i.e., Fig. 4), this oscillation NSN for the individual CP is a function of CPR, among other repeats itself after every Q subcarriers. The behavior is even factors, while that is not the case with the common CP. This more interesting when common CP configuration is used is intuitively plausible as in the common CP configuration no whereby one out of Q subcarriers suffers zero INI. The same CP portion of WSN concatenated symbols overlaps with the observation is reported in [11] for multi-numerology system symbol portion of the NSN (see Fig. 2). utilizing universal filtered multicarrier waveform. This peculiar INI distribution exhibited by NSN can be of great advantage in V. NUMERICAL RESULTS AND DISCUSSION some aspects. For instance, with common CP configuration, In this section we use Monte-Carlo simulations to evaluate pilot subcarriers for channel estimation or subcarries of the the accuracy of the analytically derived INI expressions. A reliability-sensitive application can be distributed to those multi-numerology system utilizing CP-OFDM waveform with locations with zero INI. Another critical thing to be noted NSN and WSN numerologies equally sharing the available from Fig. 3 is that, for NSN subcarriers with non zero INI bandwidth (i.e., η1 = η2 = 0.5) is considered. Throughout with common CP case, experiences higher INI compared to the analysis a CP ratio of 1/16, N = 128, and binary phase when individual CP configuration is used. Therefore, the fact shift keying (BPSK) modulated symbols with unit power are that common CP configuration has an advantage of having used, unless otherwise specified. As we have observed from number of INI-free subcarriers comes at a cost of increased the analytic expression in the previous sections, the amount of INI on the other subcarriers. INI experienced by each numerology in the system depends on the ratio Q of the subcarrier spacings of the multiplexed B. INI as a function of subcarrier spacing ratio (Q) numerologies instead of the actual values of their subcarrier Let us investigate the effect of the ratio of different subcar- spacing. Therefore, we also consider evaluating performance rier spacing for the two numerologies. Fig. 4 shows INI distri- of the system for different values of Q. bution on each subcarrier of NSN and WSN for different value of Q. Here, from the definition of Q (i.e., Q = ∆f2/∆f1), 8

5 NSN-Analytic: Q=2 1 NSN-Analytic: Q=2 NSN-Simulation: Q=2 NSN-Simulation: Q=2 WSN-Analytic: Q=2 0.9 WSN-Analytic: Q=2 WSN-Simulation: Q=2 0 WSN-Simulation: Q=2 NSN-Analytic: Q=4 0.3 NSN-Analytic: Q=4 NSN-Simulation: Q=4 0.8 NSN-Simulation: Q=4 WSN-Analytic: Q=4 0.25 WSN-Analytic: Q=4 WSN-Simulation: Q=4 0.7 -5 0.2 WSN-Simulation: Q=4 NSN-Analytic: Q=8 NSN-Analytic: Q=8 NSN-Simulation: Q=8 0.15 0.6 NSN-Simulation: Q=8 WSN-Analytic: Q=8 0.1 WSN-Analytic: Q=8 WSN-Simulation: Q=8 -10 0.5 WSN-Simulation: Q=8 0.05

0.4 0

INI power (dB) 50 55 60

-15 INI power (linear) 0.3

0.2 -20 0.1

-25 0 0 20 40 60 80 100 120 0 20 40 60 80 100 120 Subcarrier index Subcarrier index (a) Individual CP (b) Common CP

Fig. 4: INI as a function of Q

-10 32 NSN: Individual CP WSN: Individual CP 30 NSN: Common CP -12 WSN: Common CP 28

-14 26

24 -16

22 NSN: NSN > WSN -18 WSN: NSN > WSN 20 4 Average: NSN > WSN Average INI (dB) Average SIR (dB) WSN: NSN < WSN -20 18 NSN: NSN < WSN NSN WSN 16 Average: < -22 14 2 -24 12 2 4 6 8 10 12 14 16 18 20 22 24 26 28 30 32 0 1 2 3 4 5 6 7 Q Power Offset (linear) Fig. 5: Average INI experienced by each numerology with individual and Fig. 6: Average SIR of the multi-numerology system as a function of the common CP for different values of Q power offset

we fix ∆f1 at 15 kHz and change ∆f2 from 30 kHz, 60 kHz That is, the CP portion of each of the Q-concatenated WSN and 120 kHz. The INI each numerology receives seems to symbols contributes to the INI experienced by NSN. In Fig. increase with the increase in Q. This is quite expected since 5 we can see that the average INI of NSN with individual CP the higher the ∆f2 the larger the sidelobes of the WSN that is smaller than the rest when Q = 2, and larger when Q ≥ impart higher INI on NSN subcarriers. On the other hand, 4. The deviation is observed to be even more substantial with increasing ∆f2 widens the spectrum of the WSN and thus higher CPR and higher Q. collects more interference from NSN. As mentioned above, INI oscillation in NSN becomes C. Effect of power offset on INI more pronounced with increasing Q. For the common CP Depending on the channel conditions and application, users configuration, one Q-th of all NSN subcarriers are INI free. can have diverse power requirement, leading to power offsets Although the INI distribution among subcarriers of NSN and among them within the system. Power offset among the users WSN with common and individual CP configurations is quite utilizing the same numerology does not impose any threat NSN WSN diverse, it is observed that, for a given Q, if ρ = ρ on the performance of the system since the orthogonality (i.e., no power offset between the two numerologies), average is maintained. However, in the multi-numerology system, INI of NSN and WSN with common CP, and WSN with where INI exists, power offset between users utilizing different individual CP are exactly the same. The average INI of NSN numerologies highly affects the SIR performance of the system with individual CP is slightly different from the rest, as shown [12]. Fig. 6 presents SIR performance of the multi-numerology in Fig. 5. We count that this deviation is due to the dependency system utilizing individual CP configuration as a function of of the INI of NSN with individual CP on the CPR (see (17)). power offset. The investigation is done for Q = 2, and two 9

cases, ρNSN > ρWSN and ρWSN > ρNSN , are considered. APPENDIX A For each case, average SIR performance of each numerology SIMPLIFICATION OF (16) as well as average SIR of the whole system are observed. It Let us consider the first term of (16) is clear from Fig. 6 that power offset favors the numerology M+M −1 with higher power and degrades performance of the other XCP y (r)e−j2πrv/N numerology with relatively lower power. This is obvious since w0 r=N numerology with higher power has stronger sidelobes whose CP M+MCP −NCP −1 interference to the adjacent numerology is more severe. We X − j2π (r+N )v = y (r + N )e N CP note from Fig. 6 that, the amount by which SIR of NSN is w0 CP r=0 improved and that of WSN is degraded when ρNSN > ρWSN M+MCP −NCP −1 η2N−1 (a) 1 X X is exactly the same as the amount by which SIR of WSN is = √ X (η M + k/Q) WSN NSN w0 1 improved and that of NSN is degraded when ρ > ρ . M r=0 k=0 However, for a given power offset, performance of NSN is j2π (r+N )(k+η N) − j2π v(r+N ) · e N CP 1 e N CP slightly larger than that of WSN. This is only because of using η2N−1 Q = 2. As we have discussed earlier, when Q = 2, average INI 1 j2π X NCP (k−v+η1N) = √ Xw (η1M + k/Q)e N of NSN is slightly less compared to that of WSN (see Fig. 5). M 0 It is also observed from Fig. 6 that increasing power of one k=0 M+MCP −NCP −1 numerology relative to the other improves the overall average X − j2π r(k−v+η N) · e N 1 SIR of the system. However, this improvement is found to (32) r=0 depend on which numerology has higher power. The average η2N−1 NSN WSN (b) 1 j2π system SIR is higher for the case with ρ > ρ than X NCP (k−v+η1N) = √ Xw (η1M + k/Q)e N ρWSN > ρNSN . The reason is that, for a given bandwidth, 0 M k=0 NSN has more subcarriers that WSN, making its effect on the j2π (M+M −N )(k−v+η N) 1 − e N CP CP 1 average system SIR greater than that of WSN. Therefore, it · j2π (k−v+η N) is worth mentioning that, the observed trend of the average 1 − e N 1 system SIR is subjected to change when the two multiplexed η2N−1 (c) 1 X j2π N (k−v+η N) √ N CP 1 numerologies do not share the available bandwidth equally = Xw0 (η1M + k/Q)e M k=0 (i.e., η1 6= η2). We therefore understand that, the overall SIR jπ (M+M −N −1)(k−v+η N) performance of the system is simultaneously affected by both, · e N CP CP 1 power offset and bandwidth sharing factor, η. π From the above discussion it is evident that, even though sin N (M + MCP − NCP )(k − v) power offset among users of different numerologies may · , π improve the overall system performance, it however causes sin N (k − v + η1N) severe degradation in the performance of the numerology with relatively lower power. In order to favor both numerologies, it where the equality (a) is obtained by evaluating the term is more plausible to maintain the power offset between them yw0 (r + NCP ) by using (4). The equalities (b) and (c) follow as low as possible. after using the formula for the sum of a finite geometric series on the summation over r-indices, and the Euler’s formula, VI.CONCLUSION respectively. In this paper, a thorough investigation of INI for CP- By using (4) and following the same steps as above, the OFDM waveform is done through simulation and analytical second term of (16) can be expressed as derivations. The most critical factors affecting the amount of M+MCP −1 Q−1 X X −j2π N v(r−q(M+MCP )) INI suffered in the system are analyzed and some guidelines ywq (r − q(M + MCP ))e of minimizing their effects are highlighted. For instance an r=0 q=1 Q−1 η2N−1 intelligent scheduling of the multiplexed numerologies can be X 1 X used to minimize INI in the first place without adopting spec- = √ Xwq (η1M + k/Q) M trally inefficient techniques like guard band and windowing. q=1 k=0 − j2π (M+M )(k−v+η N) jπ (M+M −1)(k−v+η N) Placing numerologies with the minimum subcarrier spacing · e N CP 1 e N CP 1 ratio adjacent to each other, minimizing the power offset π between adjacent numerologies as well as making a proper sin N (M + MCP )(k − v) choice of mixed numerologies symbol alignment techniques · . (i.e., individual or common CP) in time domain are found to π sin N (k − v + η1N) be some of the inherent ways of controlling INI in the system. (33) 10

APPENDIX B [11] L. Zhang et al., “Subband ﬁltered multi-carrier systems for multi-service SIMPLIFICATION OF (23) wireless communications,” IEEE Trans. Wireless Commun., vol. 16, no. 3, pp. 1893–1907, 2017. Substituting (3) into (23), we have [12] A. B. Kihero et al., “Inter-numerology interference analysis for 5G and beyond,” IEEE Global Communications Conference (GLOBECOM) YINI (η1M + p/Q) Workshops, Dec. 2018. [13] L. Zhang, A. Ijaz, J. Mao, P. Xiao, and R. Tafazolli, “Multi-service signal M−1 η1N−1 1 j2π multiplexing and isolation for physical-layer network slicing (pns),” in X X k(r+MCP −q(M+MCP )) = √ Xnr(k)e N Vehicular Technology Conference (VTC-Fall), 2017 IEEE 86th. IEEE, M · N r=0 k=0 2017, pp. 1–6. j2π [14] X. Wang, Y. Wu, and J-YChouinard, “On the comparison between con- − (r+MCP )(η1M+p/Q) · e M ventional OFDM and MSE-OFDM systems,” in IEEE Global Telecom-

η1N−1 munications Conference (GLOBECOM), vol. 1. San Fransisco, CA: 1 j2π X − k(MCP −q(M+MCP )) IEEE, Dec. 2003, pp. 35–39. = √ Xnr(k)e N M · N [15] J.-Y. Chouinard, X. Wang, and Y. Wu, “MSE-OFDM: A new OFDM k=0 transmission technique with improved system performance,” in IEEE M−1 International Conference on Acoustics, Speech, Signal Processing − j2π (M (η M+p/Q)) X − j2π r(k−p−η N) · e M CP 1 e N 1 (ICASSP), vol. 3. Philadelphia, PA: IEEE, Mar. 2005, pp. 865–868. [16] M. Nemati and H. Arslan, “Low ICI symbol boundary alignment for r=0 5G numerology design,” IEEE Access, vol. 6, pp. 2356–2366, 2018. η1N−1 [17] A. T. Abusabah and H. Arslan, “NOMA for multinumerology OFDM (d) 1 j2π X − k(MCP −q(M+MCP )) = √ Xnr(k)e N systems,” Wireless Commun. Mobile Computing, May 2018. [18] A. F. Demir and H. Arslan, “The impact of adaptive guards for 5G and M · N k=0 j2π beyond,” in IEEE 28th Annual International Symposium on Personal, M(k−p−η1N) − j2π (M (η M+p/Q)) 1 − e N Indoor, Mobile Radio Communications (PIMRC), Montreal, Canada, · e M CP 1 · Oct. 2017, pp. 1–5. j2π (k−p−η N) 1 − e N 1 [19] A. Yazar and H. Arslan, “Flexible multi-numerology systems for 5G new η1N−1 radio,” J. mobile multimedia, vol. 14, no. 2, pp. 367–394, Oct. 2018. (e) 1 j2π X − k(MCP −q(M+MCP )) [20] T. Hwang, C. Yang, G. Wu, S. Li, and G. Y. Li, “OFDM and its wireless = √ Xnr(k)e N M · N applications: A survey,” IEEE Transactions on Vehicular Technology, k=0 vol. 58, no. 4, pp. 1673–1694, may 2009. − j2π (M (η M+p/Q)) − j2π (M−1)(k−p−η N) · e M CP 1 e N 1 π sin Q (k − p) · , π sin N (k − p − η1N) (34) where the equalities (d) and (e) again follow after employing the formula for the sum of a ﬁnite geometric series on the summation over r-indices, and Euler’s formula, respectively. Abuu B. Kihero received his B.S. degree in Elec- tronics engineering from Gebze Technical Univer- sity, Kocaeli, Turkey in 2015, and M.S. degree in in REFERENCES Electrical, Electronics and Cyber systems from Is- tanbul Medipol University, Istanbul, Turkey in 2018. [1] 5G Infrastructure PPP Association et al., “5G Vision - The 5G Infrastruc- He is currently working as a research assistant at ture Public Private Partnership: The Next Generation of Communication Communication, Signal Processing and Networking Networks and Services,” White Paper, February, 2015. Center (CoSiNC) while pursuing his Ph.D degree [2] A. A. Zaidi, R. Baldemair, H. Tullberg, H. Bjorkegren, L. Sundstrom, in wireless communication technologies at Istanbul J. Medbo, C. Kilinc, and I. Da Silva, “Waveform and numerology to Medipol University. support 5G services and requirements,” IEEE Commun. Mag., vol. 54, no. 11, pp. 90–98, 2016. [3] E. Dahlman, S. Parkvall, and J. Skold, 5G NR: The Next Generation Wireless Access Technology. Academic Press, 2018. [4] X. Zhang, L. Zhang, P. Xiao, D. Ma, J. Wei, and Y. Xin, “Mixed Numerologies Interference Analysis and Inter-Numerology Interference Cancellation for Windowed OFDM Systems,” IEEE Transactions on Vehicular Technology, 2018. [5] X. Zhang, L. Chen, J. Qiu, and J. Abdoli, “On the Waveform for 5G,” IEEE Communications Magazine, vol. 54, no. 11, pp. 74–80, 2016. [6] R. Gerzaguet et al., “The 5G candidate waveform race: a comparison of complexity and performance,” EURASIP J. Wireless Commun. Net- working, vol. 2017, no. 1, p. 13, 2017. [7] Rohde and Schwarz, “5G Waveform Candidates,” Application Note Muhammad Sohaib J. Solaija (S16) received his 1MA271-0e, June. 2016. B.E and M.Sc degrees in electrical engineering from [8] 3rd Generation Partnership Project (3GPP), “NR; Physical channels and National University of Science and Technology, Is- modulation (Release 15) ,” Technical speciﬁcation 38.211, ver 15.1.0, lamabad, Pakistan in 2014 and 2017, respectively. Apr. 2018. Currently he is pursuing his Ph.D. degree as a [9] J. e. a. Vihrial¨ a,¨ “Numerology and frame structure for 5G radio access,” member of the Communications, Signal Process- in Personal, Indoor, and Mobile Radio Communications (PIMRC), 2016 ing, and Networking Center (CoSiNC) at Istanbul IEEE 27th Annual International Symposium on. Valencia, Spain: IEEE, Medipol University, Turkey. His research focuses on Dec. 2016, pp. 1–5. interference modelling and coordinated multipoint [10] J. Sachs et al., “5G radio network design for ultra-reliable low-latency implementation for 5G and beyond wireless systems. communication,” IEEE Network, vol. 32, no. 2, pp. 24–31, 2018. 11

Huseyin¨ Arslan (S95-M98-SM04-F15) has received his BS degree from Middle East Technical Univer- sity (METU), Ankara, Turkey in 1992; MS and PhD. degrees in 1994 and 1998 from Southern Methodist University (SMU), Dallas, TX, USA. From January 1998 to August 2002, he was with the research group of Ericsson Inc., NC, USA, where he was involved with several project related to 2G and 3G wireless communication systems. Since August 2002, he has been with the Electrical Engineering Dept. of University of South Florida, Tampa, FL, USA. Also, he has been the dean of the College of Engineering and Natural Sciences of Istanbul Medipol University since 2014. In addition, he has worked as part time consultant for various companies and institutions including Anritsu Company (Morgan Hill, CA, USA), The Scientiﬁc and Technological Research Council of Turkey (TUBITAK). His current research interests are on physical layer security, mmWave communications, small cells, multi-carrier wireless technologies, co-existence issues on heterogeneous networks, aeronautical (high altitude platform) communications and in vivo channel modeling, and system design.