Please Lower Small Cell Antenna Heights in 5G

Transcription

1 Please ower Small Cell Antenna Heights in 5G Ming Ding, Data61, Astralia David ópez Pérez, Nokia Bell abs, Irel Abstract In this paper, we present a new significant theoretical discovery If the absolte height difference between base station (BS antenna ser eqipment (UE antenna is larger than zero, then the network capacity performance in terms of the area spectral efficiency (ASE will continosly decrease as the BS density increases for ltra-dense (UD small cell networks (SCNs This performance behavior has a tremendos impact on the deployment of UD SCNs in the 5th-generation (5G era Network operators may invest large amonts of money in deploying more network infrastrctre to only obtain an even worse network performance Or stdy reslts reveal that it is a mst to lower the SCN BS antenna height to the UE antenna height to flly achieve the capacity gains of UD SCNs in 5G However, this reqires a revoltionized approach of BS architectre deployment, which is explored in this paper too I INTRODUCTION From 195 to 2, the wireless network capacity has increased arond 1 million fold, in which an astonding 27 gain was achieved throgh network densification sing smaller cells [1] After 28, network densification contines to fel the 3rd Generation Partnership oject (3GPP 4th-generation (4G ong Term Evoltion (TE networks, is expected to remain as one of the main forces to drive the 5th-generation (5G networks onward [2] Indeed, the orthogonal deployment of ltra-dense (UD small cell networks (SCNs within the existing macrocell network, ie, small cells macrocells operating on different freqency spectrm (3GPP Small Cell Scenario #2a [3], is envisaged as the workhorse for capacity enhancement in 5G de to its large spectrm rese its easy management; the latter one arising from its low interaction with the macrocell tier, eg, no inter-tier interference [2] In this paper, the focs is on the analysis of these UD SCNs with an orthogonal deployment with the macrocells Before 215, the common ndersting on SCNs was that the density of base stations (BSs wold not affect the per-bs coverage probability performance in interference-limited fllyloaded wireless networks, ths the area spectral efficiency (ASE performance in bps/hz/km 2 wold scale linearly with network densification [4] The implication of sch conclsion is hge: The BS density does NOT matter, since the increase in the interference power cased by a denser network wold be exactly compensated by the increase in the signal power de to the redced distance between transmitters receivers Fig 1 shows the theoretical ASE performance predicted in [4] However, it is important to note that this conclsion was obtained with considerable simplifications on the propagation environment, which shold be placed nder scrtiny when evalating dense UD SCNs, since they are fndamentally different from sparse ones in varios aspects [2] Fig 1 Theoretical comparison of the ASE performance in bps/hz/km 2 Note that all the reslts are obtained sing practical 3GPP channel models [5, 6], which will be explained in details later De to the practicality of the sed channel models, the reslts shown here accrately characterize realistic telecommnication systems both qalitatively qantitatively For example, considering a typical bwidth of 1 MHz~1 MHz for the state-of-theart TE network, the achievable area throghpt is in the order of several Gbps/km 2, becase the ASE for 4G is shown to be arond 1 bps/hz/km 2 In the last year, a few noteworthy stdies have been carried ot to revisit the network performance analysis for UD SCNs nder more practical propagation assmptions In [7], the athors considered a mlti-slope piece-wise path loss fnction, while in [8], the athors investigated line-of-sight (os non-line-of-sight (NoS transmission as a probabilistic event for a millimeter wave commnication scenario The most important finding in these two works was that the per-bs coverage probability performance starts to decrease when the BS density is sfficiently large Fortnately, sch decrease of coverage probability did not change the monotonic increase of the ASE as the BS density increases In or very recent work [9, 1], we took a step frther generalized the works in [7] [8] by considering both piece-wise path loss fnctions probabilistic NoS os transmissions Or new finding was not only qantitatively bt also qalitatively different from previos reslts in [4, 7, 8]: The ASE will sffer from a slow growth or even a small decrease on the jorney from 4G to 5G when the BS density is larger than a threshold Fig 1 shows these new theoretical reslts on the ASE performance, where sch threshold is arond 2 BSs/km 2 the slow/negative ASE growth is highlighted by a circled area This circled area is referred to as the ASE Crawl hereafter The intition of the ASE Crawl is that the interference power increases faster than the signal power de to the transition of a large nmber of interference /16/$ IEEE

2 paths from NoS to os with the network densification The implication is profond: The BS density DOES matter, since it affects the signal to interference relationship Ths, operators shold be carefl when deploying dense SCNs in order to avoid investing hge amonts of money end p obtaining an even worse network performance de to the ASE Crawl Fortnately, or reslts in [9, 1] also pointed ot that the ASE will again grow almost linearly as the network frther evolves to an UD one, ie, > 1 3 BSs/km 2 in Fig 1 According to or reslts considering a 3 MHz bwidth, if the BS density can go as high as 1 4 BSs/km 2, the problem of the ASE Crawl cased by the NoS to os transition can be overcome, an area throghpt of 1 3 Gbps/km 2 can be achieved, ths opening p an efficient way forward to 5G Unfortnately, the NoS to os transition is not the only obstacle to efficient UD SCNs in 5G, there are more challenges to overcome to get there In this paper, we present for the first time the serios problem posed by the absolte antenna height difference between SCN base stations (BSs ser eqipments (UEs, evalate its impact on UD SCNs by means of a three-dimensional (3D stochastic geometry analysis (SGA We made a new significant theoretical discovery: If the absolte antenna height difference between BSs UEs, denoted by, is larger than zero, then the ASE performance will continosly decrease as the SCN goes ltra-dense Fig 1 illstrates the significance of sch theoretical finding with =85 m [11]: After the ASE Crawl, the ASE performance only increases marginally (~14x from 191 bps/hz/km 2 to 1496 bps/hz/km 2 as the BS density goes from 2 BSs/km 2 to 1 3 BSs/km 2, which is then followed by a continos qick fall starting from arond 1 3 BSs/km 2 The implication of this reslt is even more profond than that of the ASE Crawl, since following a traditional deployment with UD SCN BSs deployed at lamp posts or similar heights may dramatically redce the network performance in 5G Sch decline of ASE in UD SCNs will be referred to as the ASE Crash hereafter, its fndamental reasons will be explained in details later in this paper In order to address this serios problem of the ASE Crash, we frther propose to change the traditional BS deployment, lower the 5G UD SCN BS antenna height to the UE antenna height, so that the ASE behavior of UD SCNs can roll back to or previos reslts in [1], ths avoiding the ASE Crash This reqires a revoltionized BS deployment approach, which will also be explored in this paper The rest of this paper is strctred as follows Section II describes the system model for the 3D SGA Section III presents or theoretical reslts on the coverage probability the ASE performance, while the nmerical reslts are discssed in Section IV, with remarks shedding new light on the revoltionized BS deployment with UE-height antennas Finally, the conclsions are drawn in Section V II SYSTEM MODE We consider a downlink (D celllar network with BSs deployed on a plane according to a homogeneos Poisson point process (HPPP Φ of intensity λ BSs/km 2 UEs are Poisson distribted in the considered network with an intensity of ρ UEs/km 2 Note that ρ is assmed to be sfficiently larger than λ so that each BS has at least one associated UE in its coverage [7 1] The two-dimensional (2D distance between a BS an a UE is denoted by r Moreover, the absolte antenna height difference between a BS a UE is denoted by Hence, the 3D distance between a BS a UE can be expressed as w = r (1 Following [9, 1], we adopt a very general practical path loss model, in which the path loss ζ (w associated with distance w is segmented into N pieces written as ζ 1 (w, when w d 1 ζ 2 (w, when d 1 <w d 2 ζ (w =, (2 ζ N (w, when w>d N 1 where each { piece ζ n (w,n {1, 2,,N} is modeled as ζn (w =A ζ n (w= nw α n, os: n (w ζn N (w =A N n w αn n, NoS: 1 n (w, (3 where ζn (w ζn N (w,n {1, 2,,N} are the n-th piece path loss fnctions for the os transmission the NoS transmission, respectively, A n A N n are the path losses at a reference distance w = 1 for the os the NoS cases, respectively, αn αn N are the path loss exponents for the os the NoS cases, respectively In practice, A n, A N n, αn αn N are constants obtainable from field tests [5, 6] Moreover, n (w is the n-th piece os probability fnction that a transmitter a receiver separated by a distance w has a os path, which is assmed to be a monotonically decreasing { fnction with regard to w For convenience, ζ n (w } { ζn N (w } are frther stacked into piece-wise fnctions written as ζ1 Path (w, when w d 1 ζ ζ Path 2 Path (w, when d 1 <w d 2 (w =, (4 ζn Path (w, when w>d N 1 where the string variable Path takes the vale of N for the os the NoS cases, respectively Besides, { n (w } is stacked into a piece-wise fnction as 1 (w, when w d 1 2 (w, when d 1 <w d 2 (w = N (w, when w>d N 1 (5 In this paper, we assme a practical ser association strategy (UAS, in which each UE shold be associated with the BS providing the smallest path loss (ie, with the largest ζ (w[8, 1] In addition, we assme that each BS/UE is eqipped with an isotropic antenna, that the mlti-path fading between a BS a UE is modeled as independently identical distribted

3 (iid Rayleigh fading [7 1] Note that a more practical Rician fading will also be considered in the simlation section to show its impact on or conclsions III MAIN RESUTS Using a 3D SGA based on the HPPP theory, we stdy the performance of the SCN by considering the performance of a typical UE located at the origin o We first investigate the coverage probability that this UE s signal-to-interference-pls-noise ratio (SINR is above a perdesignated threshold γ: p cov (λ, γ = [SINR >γ], (6 where the SINR is calclated as SINR = (w h, (7 I + N where h is the channel gain is modeled as an exponential rom variable (RV with the mean of one de to Rayleigh fading, P N are the transmission power of each BS the additive white Gassian noise (AWGN power at each UE, respectively, I is the cmlative interference given by I = Pβ i g i, (8 i: b i Φ b o where b o is the BS serving the typical UE located at distance w from the typical UE, b i, β i g i are the i-th interfering BS, the path loss associated with b i the mlti-path fading channel gain associated with b i, respectively Based on the path loss model in (2 with 3D distances the considered UAS, we present or maieslt on p cov (λ, γ in Theorem 1 shown on the top of the next page According to [9, 1], we also investigate the ASE in bps/hz/km 2 for a given λ, which can be compted as + A ASE (λ, γ =λ log 2 (1 + γ f Γ (λ, γ dγ, (18 γ where γ is the minimm working SINR for the considered SCN, f Γ (λ, γ is the probability density fnction (PDF of the SINR observed at the typical UE at a particlar vale of λ Based on the definition of p cov (λ, γ in (6, which is the complementary cmlative distribtion fnction (CCDF of SINR, f Γ (λ, γ can be expressed by f Γ (λ, γ = (1 pcov (λ, γ, (19 γ where p cov (λ, γ is obtained from Theorem 1 Considering the reslts of p cov (λ, γ A ASE (λ, γ respectively shown in (9 (18, we propose Theorem 2 to theoretically explain the fndamental reasons of the ASE Crash discssed in Section I Theorem 2 If > γ,γ < +, then lim λ + pcov (λ, γ = lim λ + AASE (λ, γ = oof: We omit the proof here de to the page limitation Instead, in the following, we describe the essence of theorem provide a toy example to clarify it We will provide the fll proof in the jornal version of this paper In essence, Theorem 2 states that when λ is extremely large, eg, in UD SCNs, both p cov (λ, γ A ASE (λ, γ will decrease towards zero with the network densification, UEs will experience service otage, ths creating the ASE Crash The fndamental reason for this phenomenon is revealed by the key point of the proof, ie, the signal power will lose its speriority over the interference power when λ +, even if the interference created by the BSs that are relatively far away is ignored This is becase the absolte antenna height difference introdces a cap on the signal-link distance ths on the signal power Theorem 2 is in stark contrast with the conclsion in [4, 7 1], which indicates that the increase in the interference power will be exactly conterbalanced by the increase in the signal power when λ + Since the proof of Theorem 2 is mathematically intense difficlt to digest, in the following we provide a toy example to shed some valable insights on the rationale behind Theorem 2 We consider a simple 2-BS SCN as illstrated in Fig 2, where the 2D distance between the serving BS the UE that between an arbitrary interfering BS the UE are denoted by r τr,(1 <τ<+, respectively In this example, when λ +, the, which can be intitively explained by the fact that the per-bs coverage area is roghly in the order of 1 λ, ths the typical 2D distance from the serving BS to the UE approaches zero when λ + Fig 2 Illstration of a toy example with a 2-BS SCN Considering that r is smaller than d 1 in practical SCNs [5, 6], we can assme that both the signal link the interference link shold be dominantly characterized by the first-piece os path loss fnction in (3, ie, ζ1 (w = A 1 r2 + 2 α 1 Ths, based on the 3D distances, we can obtain the signal-to-interference ratio (SIR as γ = A 1 r2 + 2 α 1 τ 2 r = 1 α 1 A 1 1+ τ r 2 α 1 (2 Note that γ is a monotonically decreasing fnction as r decreases when > Moreover, { it is easy to show that lim = lim λ + γ r γ = 1, (> τ α 1, ( = (21 Assming that τ =1 α 1 =2in (21, the limit of γ in UD SCNs will plnge from 2 db when =to db when >, which means that even a rather weak interferer, eg, with a power 2 db below the signal power, will become a real threat to the signal link when the absolte antenna height difference is non-zero in UD SCNs The drastic crash of γ

4 Theorem 1 Considering the path loss model in (2 the presented UAS, the probability of coverage p cov (λ, γ can be derived as N ( p cov (λ, γ = Tn + Tn N, (9 n=1 where Tn = [ ] d 2 n d h 2 n 1 2 I +N >γ fr,n (r dr, Tn N = [ ] d 2 n d 2 N h 2 n 1 2 I +N >γ fr,n N (r dr, d d N are defined as +, respectively Moreover, fr,n (r fr,n N (r d 2n 1 2 <r d 2 n 2, are represented by ( r1 fr,n (r =exp (1 ( ( r ( πλd exp πλd πrλ, (1 ( r2 ( ( fr,n N (r =exp πλd exp r (1 ( πλd ( 1 n r πrλ, (11 where r 1 r 2 are given implicitly by the following eqations as r 1 =arg {ζ r } N = ζn r2 + 2, (12 r 1 [ In addition, h I +N r 2 =arg {ζ r r 2 ] [ N >γ h I +N [ ] ( h >γ =exp I + N } = ζn N r2 + 2 (13 ] >γ are respectively compted by γn r2 + 2 n ( I n γ r2 + 2, (14 where I (s is the aplace transform of I for os signal transmission evalated at s, which can be frther written as ( + I ( + [ 1 (s =exp 2πλ r 1+ ( sp ζ d 2 + 2] exp 2πλ r 1 1+ ( sp ζ N d, (15 [ N ] ( ( h γn >γ =exp I + N r2 + 2 I N γ r2 + 2, (16 r 2 N n where I N (s is the aplace transform of I for NoS signal transmission evalated at s, which can be frther written as ( + I N ( + [ 1 (s =exp 2πλ 1+ ( sp ζ d 2 + 2] exp 2πλ r 1+ ( sp ζ N d (17 oof: We omit the proof here de to the page limitation We will provide the fll proof in the jornal version of this paper N n when > is de to the cap imposed on the signal power as the signal-link distance r in the nmerator of (2 cannot go below Sch cap on the signal-link distance the signal power leads to the ASE Crash, since other signalpower-comparable interferers also approach the UE from all directions as λ increases, which will eventally case service otage to the UE To sm p, in an UD SCN with conventional deployment (ie, >, both p cov (λ, γ A ASE (λ, γ will plnge toward zero as λ increases, casing the ASE Crash Its fndamental reason is the cap on the signal power becase of the minimm signal-link distance tied to, which cannot be overcome with the densification The only way to avoid the ASE Crash is to remove the signal power cap by setting to zero, which means lowering the BS antenna height, not jst by a few meters, bt straight to the UE antenna height Other applicable soltions may be the sage of very directive antennas /or the sage of sophisticated idle modes at the SCN BSs, which will be investigated in or ftre work IV SIMUATION AND DISCUSSION In this section, we investigate the network performance se nmerical reslts to establish the accracy of or analysis As a special case of Theorem 1, following [1], we consider a two-piece path loss a linear os probability fnctions defined by the 3GPP [5, 6] Specifically, in the path loss model presented in (2, we se N =2, ζ1 (w =ζ2 (w =A w α, ζ1 N (w = ζ2 N (w = A N w αn [5] And in the os probability model shown in (5, we se 1 (w =1 w d 1 2 (w =, where d 1 is a constant [6] For clarity, this 3GPP

5 Fig 3 p cov (λ, γ vs λ with γ =db Fig 4 A ASE (λ, γ vs λ with γ =db special case is referred to as 3GPP Case 1 As jstified in [1], we se 3GPP Case 1 for the case stdy becase it provides tractable reslts for (1-(17 in Theorem 1 The details are relegated to the jornal version of this paper Following [1], we adopt the following parameters for 3GPP Case 1: d 1 = 3 m, α =29, α N =375, A =1 138, A N =1 1454, P =24dBm, N = 95 dbm The BS antenna the UE antenna heights are set to 1 m 15 m, respectively [11], ths = 1 15 =85 m To check the impact of different path loss models on or conclsions, we have also investigated the reslts for a singleslope path loss model that does not differentiate os NoS transmissions [4], where only one path loss exponent α is defined, the vale of which is assmed to be α = α N =375 A Validation of Theorem 1 on the Coverage obability In Fig 3, we show the reslts of p cov (λ, γ with γ =db As can be observed from Fig 3, or analytical reslts given by Theorem 1 match the simlatioeslts very well, which validates the accracy of or theoretical analysis From Fig 3, we can draw the following observations which are inline with or discssion in Section I: For the single-slope path loss model with =m, the BS density does NOT matter, since the coverage probability approaches a constant for UD SCNs [4] For the 3GPP Case 1 path loss model with =m, the BS density DOES matter, since that coverage probability will decrease as λ increases when the network is dense enogh, eg, λ > 2 BSs/km 2, de to the transition of a large nmber of interference paths from NoS to os [1] When λ is tremendosly large, eg, λ 1 3 BSs/km 2, the coverage probability decreases at a slower pace becase both the interference the signal powers are os dominated, ths the coverage probability approaches a constant related to α [4, 1] For both path loss models, when =85m, the coverage probability shows a determined trajectory toward zero in UD SCNs de to the cap on the signal power introdced by the non-zero as explained in Theorem 2 In more detail, for the 3GPP Case 1 path loss model with λ = 1 4 BSs/km 2, the coverage probability decreases from 15 when =m to arond 1 5 when =85 m B The Theoretical Reslts of the ASE In Fig 4, we show the reslts of A ASE (λ, γ with γ = db Fig 4 is essentially the same as Fig 1 with the same marker styles, except that the reslts for the single-slope path loss model with =85m are also plotted From Fig 4, we can confirm the key observations presented in Section I: For the single-slope path loss model with =m, the ASE performance scales linearly with λ [4] The reslt is promising, bt it might not be the case ieality For the 3GPP Case 1 path loss model with =m, the ASE sffers from a slow growth or even a small decrease when λ [2, 2] BSs/km 2, ie, the ASE Crawl [1] After the ASE Crawl, the ASE grows almost linearly again as the network frther evolves to an UD one, eg, λ>1 3 BSs/km 2 [1] For both path loss models with =85m, the ASE sffers from severe performance loss in UD SCNs de to the ASE Crash, as explained in Theorem 2 In more detail, for the 3GPP Case 1 path loss model with λ =1 4 BSs/km 2, the ASE dramatically decreases from 3141 bps/hz/km 2 when =mto2bps/hz/km 2 when =85m C Factors that May Impact the ASE Crash There are several factors that may have large impacts on the existence/severity of the ASE Crash, eg, varios vales of α, Rician fading, etc In Fig 5, we investigate the performance of A ASE (λ, γ for 3GPP Case 1 nder the assmptions of =35m [3] or α =19 [1] or Rician fading [6] 1 De to the significant accracy of or analysis, we only show analytical reslts of A ASE (λ, γ in Fig 5 1 Note that here we adopt a practical model of Rician fading in [6], where the K factor in db scale (the ratio between the power in the direct path the power in the other scattered paths is modeled as K[dB] =13 3w, where w is the 3D distance in meter

6 2 Measrement campaigns for the UE-height channels Note that at sch height there is an nsal concentration of objects, sch as cars, foliage, etc 3 Implications of fast time-variant shadow fading de to rom movement of UE-height objects, eg, cars 4 Terrain-dependent network performance analysis 5 New inter-bs commnications based on grond waves 6 For macrocell BSs with a large, whose BS antenna height cannot be lowered to the UE antenna height, the existing network performance analysis for heterogeneos networks may need to be revisited, since the interference from the macrocell tier to the SCN tier may have been greatly over-estimated de to the common assmption of = Fig 5 A ASE (λ, γ vs λ with γ =db varios assmptions Or key conclsions are smmarized as follows: Decreasing from 85 m to 35 m (BS antenna height being 5 m helps to alleviate, bt cannot remove the ASE Crash nless =, as explained in Theorem 2 From Fig 5, the ASE with =35m peaks at arond λ = 3 BSs/km 2, bt it still sffers from a 6 % loss compared with the ASE with =m at that BS density Decreasing α helps to alleviate the ASE Crash becase it softens the SIR crash in (21 However, it ravates the ASE Crawl by showing an obvios ASE decrease when λ [2, 8] BSs/km 2 de to the drastic interference transition from NoS to stronger os with α =19 [1] From the simlatioeslts, we can see that Rician fading makes the ASE Crash worse, which takes effect early from arond λ = 4 BSs/km 2 The intition is that the romness in channel flctation associated with Rician fading is mch weaker than that associated with Rayleigh fading de to the large K factor in UD SCNs [6] With Rayleigh fading, some UE in otage might be opportnistically saved by favorable channel flctation of the signal power, while with Rician fading, sch otage case becomes more deterministic de to lack of channel variation, ths leading to a severer ASE Crash D A Novel BS Deployment with UE-Height Antennas Based on or thoght-provoking discovery, we make the following recommendation to vendors operators arond the world: The SCN BS antenna height mst be lowered to the UE antenna height in 5G UD SCNs, so that the ASE behavior of sch networks wold roll back to or previos reslts in [9, 1], ths avoiding the ASE Crash Sch proposed new BS deployment will allow to realize the potential gains of UD SCNs, bt needs a revoltion on BS architectres network deployment in 5G The new R&D challenges in this area are: 1 New BS architectres that are anti-valism/antitheft/anti-hacking at low-height positions V CONCUSION We presented a new significant theoretical discovery, ie, the serios problem of the ASE Crash If the absolte height difference between BS antenna UE antenna is larger than zero, then the ASE performance will continosly decrease with network densification for UD SCNs The only way to flly overcome the ASE Crash is to lower the SCN BS antenna height to the UE antenna height, which will revoltionize the approach of BS architectre deployment in 5G In or ftre work, we will also stdy how the sage of very directive antennas /or the sage of sophisticated idle modes at the small cell BSs can help to mitigate the ASE Crash REFERENCES [1] ArrayComm & William Webb, Ofcom, ondon, UK, 27 [2] D ópez-pérez, M Ding, H Classen, A Jafari, Towards 1 Gbps/UE in celllar systems: Understing ltra-dense small cell deployments, IEEE Commnications Srveys Ttorials, vol 17, no 4, pp , Jn 215 [3] 3GPP, TR 36872: Small cell enhancements for E-UTRA E- UTRAN - Physical layer aspects, Dec 213 [4] J Andrews, F Baccelli, R Ganti, A tractable approach to coverage rate in celllar networks, IEEE Transactions on Commnications, vol 59, no 11, pp , Nov 211 [5] 3GPP, TR 36828: Frther enhancements to TE Time Division Dplex (TDD for Downlink-Uplink (D-U interference management traffic adaptation, Jn 212 [6] Spatial Channel Model AHG, Sbsection 353, Spatial Channel Model Text Description V6, Apr 23 [7] X Zhang J Andrews, Downlink celllar network analysis with mlti-slope path loss models, IEEE Transactions on Commnications, vol 63, no 5, pp , May 215 [8] T Bai R Heath, Coverage rate analysis for millimeter-wave celllar networks, IEEE Transactions on Wireless Commnications, vol 14, no 2, pp , Feb 215 [9] M Ding, D ópez-pérez, G Mao, P Wang, Z in, Will the area spectral efficiency monotonically grow as small cells go dense? IEEE GOBECOM 215, pp 1 7, Dec 215 [1] M Ding, P Wang, D ópez-pérez, G Mao, Z in, Performance impact of os NoS transmissions in dense celllar networks, IEEE Transactions on Wireless Commnications, vol 15, no 3, pp , Mar 216 [11] 3GPP, TR 36814: Frther advancements for E-UTRA physical layer aspects (Release 9, Mar 21