Impact of Drectonal Recevng Antennas on Wreless Networks Jean-Marc Kelf and Olver Smon Orange Labs 38-40 rue du Général Leclerc, 92130 Issy-Les-Moulneaux, France {jeanmarc.kelf, olver.smon}@orange.com arxv:1405.3137v1 [cs.it] 13 May 2014 Abstract We are nterested n hgh data rates nternet access, by the mean of LTE based wreless networks. In the am to mprove performance of wreless networks, we propose an approach focused on the use of UE equpped by drectonal recevng antennas. Indeed, these antennas allow to mtgate the nterference and to mprove the lnk budget. Therefore, the Sgnal to Interference plus Nose Rato (SINR) can be mproved, and consequently the performance and qualty of servce (QoS), too. We establsh the analytcal expresson of the SINR reached by a user wth drectonal antenna, whatever ts locaton. Ths expresson shows that drectonal antennas allow an mprovement of the SINR, and to quantfy t. We develop dfferent scenaros to compare the use of drectonal antennas nstead of omndrectonal ones. They allow to quantfy the mpact of drectonal antennas n terms of performance and QoS. Index Terms Wreless, LTE, drectonal antennas, performance, qualty of servce, throughput and coverage analyss I. INTRODUCTION Wth the development of nternet servces and the explodng traffc demand, one of the great challenges for telecommuncatons operators s to offer hgh data rates servces wherever the user s. Indeed, the deployment of broadband nternet access n rural areas s costly snce t usually requres buldng or upgradng a large area wred access networks for very few people. A soluton to decrease ths cost conssts n offerng nternet hgh data rates servces by usng wreless access. In ths case, rural area users are connected to the network by usng a rado access mean,.e. a rado base staton, connected to the nternet, transmttng and recevng data. Wth smlar data rates as ADSL, LTE s partcularly nterestng to be used for fxed rural nternet access. Unfortunately, LTE s hghly senstve to nterferences. The challenge conssts n decreasng the nterferences n order to ncrease the SINR and capacty. Dfferent solutons are possble to mtgate nterferences and they are to a large extent complementary: Antenna parameters plannng, Inter- Cell Interferences Coordnaton (ICIC), Coordnated multpont (CoMP), Hgh-order Multple Input Multple Output (MIMO), Advanced recevers such as Interference Rejecton Combnng (IRC) etc... Another soluton s proposed n ths paper: usng termnals wth drectonal antennas. Ths soluton requres statc poston of the termnal and s obvously specfc to fxed rado servces. Drectonal antennas should allow mnmzng the nterferences and, at the same tme, sgnfcantly mprovng the lnk budget, thus allowng large cells deployment and hgher network capacty. Inter-Cell Interferences Coordnaton (ICIC) [1] [2] [3] s another technque allowng the lmtaton of nterferences mpact. The effcency of ths technque depends on the coordnatons between cells that can be done. Coordnated Mult-Pont (CoMP) transmsson technques [4] [5] allow to lmt the nterferences or have lmted capablty of nterferences suppresson. CoMP requres the transmtters to share channel-state nformaton (CSI). Multple Input Multple Output (MIMO) technques [6] [7] allow to mprove the SINR. Ths technque s based on the deployment of multple transmttng antennas and mutple recevng antennas. Our Contrbuton: In ths artcle, we develop an analytcal approach whch allows to easly calculate the SINR achevable n a gven area, by users equpped wth drectonal recevng antennas or omndrectonal recevng antennas. It allows the calculaton of the CDF (Cumulatve Dstrbuted Functon) of the SINR of user equpments (UE). Snce ths CDF characterzes the performance and the QoS, t becomes easy to do an evaluaton of the mpact of the ntegraton of drectonal recevng antennas on UE. The paper s organzed as follows. In Secton II, we present the system model. In partcular, we establsh the analytcal expresson of the SINR of a UE equpped wth a drectonal or an omndrectonal antenna. In Secton III, the scenaros are descrbed. Secton IV presents the results obtaned. Secton V concludes the paper. II. SYSTEM MODEL We consder a wreless network composed of S geographcal stes, composed by 3 base statons (BS). Each BS covers a sectored cell. We focus our analyss on the downlnk, n the context of an OFDMA based wreless network (e.g. WMax, LTE). Let us consder: S = {1,..., S} the set of geographc stes, unformly and regularly dstrbuted over the two-dmensonal plane. N = {1,..., N} the set of BS, unformly and regularly dstrbuted over the two-dmensonal plane. The BS are equpped by drectonal antennas (fg. 1): N= 3 S. H sub-channels h H = {1,..., H} where we denote W the bandwdth of each sub-channel. Each sub-channel conssts n a fxed number of subcarrers.
(u) the transmtted power assgned by base staton k to sub-carrer f n sub-channel h towards user u. (u) the propagaton gan between transmtter k and user u n sub-carrer f and sub-channel h. P (k) g (k) We assume that tme s dvded nto slots. Each slot conssts n a gven sequence of OFDMA symbols. Snce the tme s slotted, transmssons wthn each cell do not nterfere one wth each other. We assume that there s no nterference between sub-carrers. The total amount of power receved by an UE u connected to a BS k 0, on sub-carrer f of sub-channel h s gven by the sum of : useful sgnal P (k0) ference due to the other transmtters and thermal nose N th. We consder the SINR γ (u) defned by: γ (u) = P (k0) (u)g(k0) (u), nter- P (k) (u)gk (u) k N,k k 0 (u)g(k0) (u) k N,k k 0 P (k) (u)gk (u) + N th as the crteron of rado qualty. As we nvestgate the qualty of servce and performance ssues of a network composed of omndrectonal recevng antennas and drectonal ones, the scenaros analyzed consder that all the subcarrers are allocated to UEs. Consequently, each sub-carrer f of the sub-channel h of any BS s used and can be an nterferer of the ones of other BS. So we can drop the ndexes f and h. A. Propagaton Let us consder a path gan g = Kr η X, where K s a constant, r s the dstance between a transmtter t and a recever u, and η > 2 s the path loss exponent. The parameter X characterzes the shadowng expressed as a lognormal random varable. Let us consder a user M connected at the BS, located at dstance r from t and angle θ wth the drecton of ths antenna (Fg. 2). 1) Omndrectonal recevers: Equpped wth an omndrectonal antenna, ths UE receves a useful power P o expressed as P o (r, θ ) = G T (θ )X (2) where P t the transmtted power, G T (θ ) s the antenna gan of the transmttng antenna of the BS, and X represents the shadowng. 2) Drectonal recevers: When ths user s equpped by a drectonal antenna, he receves a power P d expressed as (1) P d (r, θ ) = G T (θ )G R (φ )X (3) where G R (φ ) s the antenna gan of the drectonal recevng antenna and φ represents the angle between the drectonal recevng antenna and the drecton of the transmttng antenna (Fg. 1 and 2). B. Expresson of the SINR The expresson (1) of the SINR can be expressed, for each sub-carrer (droppng the ndexes f and h): γ(r, θ ) = j N,j G T (θ )G R (φ )X. (4) j G T (θ j )G R (φ j )X j + N th We notce that the antenna gan G R = 1 for omndrectonal recevng antennas. The angle φ j s the angle between the drectonal recevng antenna of the UE (red arrows drected toward the BS n the central cell n Fg. 1) and the transmttng antenna j. So we have φ j = θ j θ (Fg. 2). Therefore, as drectonal antennas are drected toward the BS, on the numerator of (4) we have φ = 0 and G R (φ )= 1 (by usng expresson (13) of the antenna gan G R ). We can express (4) as: γ(r, θ ) = j N,j G T (θ )X (5) j G T (θ j )G R (φ j )X j + N th In the am to analyze the specfc mpact of the use of drectonal recevng antennas nstead of omndrectonal ones, t s nterestng to establsh the SINR wthout shadowng. Indeed, n ths way, t s more easy to propose an nterpretaton of ths mpact, snce t s not coupled to the nfluence of a lognormal random varable. Consderng a densty ρ S of stes S and followng the approach developed n [9] [12], let us consder a UE located at (r, θ ) n the area covered by the BS. The denomnator of (5) can be expressed as: I = + P t ρ S Kr η G T (θ)g R (θ θ )rdrdθ G a T (θ a )G R (θ j θ a ) + N th (6) where the ntegral represents the nterference due to all the other stes of the network, and the dscrete sum represents the nterference due to the 2 base statons co-localzed wth the base staton. The ndex a holds for these 2 BS. Let notce that θ j θ a = 0. So we have G R (θ j θ a ) = 1. Moreover, consderng the three sectors of a ste S, we have for any angle θ G T (θ) = G 1 T (θ) = G2 T (θ + 2π/3) = G3 T (θ 2π/3), Snce each ste s equpped by 3 antennas we can express (6) as:
I = P t ρ S Kr η G T (θ)g R (θ θ )rdrdθ = G a T (θ a ) + N th P t ρ S Kr η rdr G a T (θ )G R (θ θ )dθ a=1 G a T (θ a ) + N th = P t ρ S Kr η rdr 3 G T (θ)g R (θ θ )dθ Fg. 1. Hexagonal network wth drectonal recevng UE (red arrow toward the BS). G a T (θ a ) + N th (7) I = P t ρ S Kr η rdr G a T (θ )G R (θ θ )dθ a=1 G a T (θ a ) + N th = P t ρ S Kr η rdr 3 G T (θ)g R (θ θ )dθ G a T (θ a ) + N th (8) The approach developed n [9] [12] allows to express Pt ρ S Kr η rdr as 2πρ SP tk(2r c r) 2 η η 2, where 2R c represents the nterste dstance. We refer the reader to [9] [12] for the detaled explanaton and valdaton through Monte Carlo smulatons. Therefore, (8) can be expressed: 2π I = 6πP t(2r c r) 2 η ρ S K G T (θ)g R (θ θ )dθ η 2 0 G a T (θ a ) + N th (9) 1 γ(r, θ ) The SINR (5) γ(r, θ ) s fnally gven by the expresson: 2π G 0 T (θ)g R (θ θ )dθ G T (θ ) = 6πρ S(2R c r ) 2 η (η 2)r η 3 + Ga T (θ a) + G T (θ ) C. Interest of the analytcal formula N th G T (θ ) (10) The classcal way to compute SINR gven by (4) needs to take nto account all the dstances between the UE and the base statons. Moreover, the formula s ntractable. Therefore, t s needed to approxmate or to do smulatons, even f the shadowng s not taken nto account. Conversely, the formula (10) expresses the SINR by only consderng the dstance between the UE and the servng BS. Ths formula s tractable and a smple numercal calculaton s Fg. 2. User equpment M located at (r, θ ). It receves a useful power from antenna and nterference power from antenna j. The drectonal antenna of UE s drected toward the antenna. needed to calculate t. Another advantage of ths formula s that t focuses on the mportant parameters of the system, such as nterste dstance, propagaton parameter, transmttng antenna gan. It also hghlghts on the mpact of drectonal antennas, through the recevng antenna gan, and shows how ther use can decrease the nterferences and consequently ncrease the SINR. D. Throughput calculaton The SINR allows to calculate the reachable throughput D u of an UE u, by usng Shannon expresson. For a bandwdth W, t can be wrtten: D u = W log 2 (1 + γ u ) (11) Expresson (11) enables to calculate the theoretcal maxmum achevable throughputs. Remarks: Let notce that the mappng between the receved SINR and the acheved throughput are establshed by the mean of lnk curves n the case of realstc network systems. A. Scenaros III. SCENARIOS AND ASSUMPTIONS Our am conssts n analyzng the nterest to deploy UE equpped wth Drectonal Recevng Antennas nstead of Omndrectonal Recevng Antennas. Varous parameters may have an mpact on the SINR, the throughput and the coverage
of BSs. We present herenafter the parameters we chose n our analyss. We analyze dfferent scenaros correspondng to the stuatons whch may happen n a real network: sub-urban envronment: ISD = 2000m rural envronment: ISD = 5000m rural envronment: ISD = 10000m For each scenaro, we consder two knds of drectonal recevng antennas: aperture of 35 aperture of 17.5 B. Assumptons Let us consder: Hexagonal network composed of sectored stes Three base statons per ste Antenna gan of transmttng BS s gven by (n db) [ ( ) ] 2 θ G T (θ) = mn 12, A m, (12) θ 3dB Fg. 3. CDF of the SINR for suburban envronment (ISD= 2000m), omndrectonal recever compared to drectonal one wth aperture 17.5 (left) and 35 (rght) where θ 3dB = 70 and A m =25 db Antenna gan of drectonal recevng antennas s gven by (n db) [ ( ) ] 2 φ G R (φ) = mn 12, A m, (13) φ 3dB where (φ 3dB,A m ) = (35, 23 db) or (17.5, 21 db) downlnk OFDM LTE, carrer frequency 2.6 GHz, channel bandwdth 10MHz, the transmttng power: we set t at 46 dbm, as n a realstc transmsson envronment. standard devaton of the shadowng σ = 8dB. IV. RESULTS The analyss s focused on the analyss of the qualty of servce, performance and coverage. The establshement of the cumulatve dstrbuted functons (CDF) of the SINR represents an mportant characterstc of the system. Indeed, they frst allow to characterze the coverage and the outage probablty. They also characterze the performance dstrbuton, and the qualty of servce that can be reached by the system. A. Impact of the nterste dstance on SINR dstrbuton Ths analyss conssts n determnng the nterest to deploy drectonal antennas accordng to the knd of envronment: rural or sem-urban. Fgures 3, 4 and 5 show the cumulatve densty functon (CDF) of the SINR offered to the UE, n all scenaros consdered. These curves show that, when the nterste dstance ncreases, the SINR reached by UEs equpped wth omndrectonal antennas decrease. For example, consderng an outage probablty of 0.1, the decrease of the SINR may reach 9 db. Indeed, for an ISD of 2000 m the SINR reaches -1 db (Fg. 3 left) and for an ISD of 10000 m the outage probablty decreases untl -10 db (Fg. 5 left). There s also a decrease for UEs equpped by drectonal recevng antennas. However, ths decrease s very low. In partcular, t Fg. 4. CDF of the SINR for rural envronment (ISD= 5000m), omndrectonal recever compared to drectonal one wth aperture 17.5 (left) and 35 (rght) Fg. 5. CDF of the SINR for rural envronment (ISD= 10000m), omndrectonal recever compared to drectonal one wth aperture 17.5 (left) and 35 (rght)
only reaches 0.7 db n the same case as before. Ths result can be explaned as follows. The nterference due to the other base statons of the network s larger by usng omndrectonal antennas than by usng drectonal ones (cf. (10)). When the ISD ncreases, the mpact of thermal nose becomes more and more mportant. However, the relatve mpact s much larger n the case of omndrectonal antennas than n the case of drectonal antennas. We can thus conclude that () whatever the scenaro consdered, a deployment of UE equpped wth drectonal antennas allows to mprove the CDF of the SINR (compared to the case where UE are equpped wth omndrectonal antennas). Therefore the outage probablty decreases, and the performance and QoS ncrease, () snce the coverage of a BS s an ncreasng functon of the SINR, the use of drectonal antennas mproves the coverage of a BS, too. () the performance and QoS of UE equpped by drectonal antennas are much less senstve to the nterste dstance, and thus to the type of envronment (rural or sem-urban). B. Impact of the aperture angle on SINR dstrbuton Let us consder the same curves as before. Fgures 3 and 5 show that an aperture of 17.5 allows to reach hgher SINR than an aperture of 35. For example, consderng an outage probablty of 0.1, the decrease of the SINR reaches 1 db by the use of an antenna wth aperture of 35 nstead of 17.5 (Fg. 3 left compared to rght wth ISD=2000 m). Ths decrease reaches about 1.5 db for an ISD of 10000 m (Fg. 5 left compared to rght). Therefore, a low aperture allows a hgher mprove of the SINR than a wde one. It s due to the expresson of the nterference (9) whch depends on G R. Wth a low aperture, the mpact of the nterference due to the other base statons of the network decreases. Let us however notce that the maxmum dfference observed on these curves reaches 2 db. It s relatvely low. C. Impact on the SINR of each UE The CDF observed n Fg. 3, 4 and 5 show that the use of drectonal recevng antennas mproves the qualty of servce and the performance, and that t allows to decrease the outage probablty n all cases. We could conclude that t s nterestng, n all cases, to use a drectonal recevng antenna than an omndrectonal one. However, these curves do not focus of the mpact of the use of drectonal antennas on each pont of the system. Therefore, t seems nterestng to analyze ths pont of vew: () by calculatng for each UE, the dfference between the SINR reached when ths UE s equpped by a drectonal antenna, and the SINR reached f t s equpped by an omndrectonal one, () and by drawng the CDF of that dfference of SINR. Ths curve s represented n Fg. 6. It can be observed a very nterestng result: that dfference may be postv, negatv, or null. Ths result means that for some UEs of the system, t s not nterestng to replace omndrectonal recevers by drectonal ones. It seems to be n contradcton wth the other observatons (Fg. 3, 4 and 5), whch showed that the use of drectonal antennas mproved the system n all cases. In fact, these last curves are the expresson of the global behavour of the whole system. They do not provde nformaton for each ndvdual UE. It means that, though globally ncrease by usng drectonal antennas, the SINR may locally decrease. Fg. 6 also shows that, n the 2000 m ISD case, for about 20% of the UE, the use of drectonal antennas decrease the SINR (0 CDF 0.2). For a proporton of 20% of the UE the use of drectonal antennas nether ncrease nor degrade the SINR (0.2 CDF 0.4). And for 60% drectonal antennas ncrease the SINR. Another nterestng result of ths curve conssts n the observaton of the ampltude of the mprovement. Indeed, Fg. 3 shows that the dfference between omn drectonal SINR and drectonal one reaches a maxmum of about 5 db. In contrast, Fg. 6 shows that that dfference may reach 20 db! Ths result can be nterpreted as follows. The UEs whch have low SINR by usng omndrectonal antennas may have a large mprove of SINR by usng drectonal antennas. However, the use of drectonal antennas may degrade the SINR of some UEs, and ths degradaton may reach 15 db. Fg. 6. CDF of the dfference at each pont of the SINR drectonal (aperture 17.5 ) and the SINR omndrectonal for sem-urban envronment (ISD= 2000m) D. Impact of the shadowng on SINR dstrbuton Snce we establshed a formula of the SINR wthout consderng the shadowng, t appears nterestng to analyze the mpact of the shadowng, too. In ths am, we compare smulatons by consderng shadowng and smulatons wthout shadowng. Let us remnd that UE are connected to the BS whch offers the hghest useful power. Fg.7 shows that the mpact of shadowng on the dstrbuton of the SINR s relatvely low. It can be observed that for omndrectonal antennas, the dstrbutons wth and wthout shadowng are dentcal except for low values of SINR: the dfference reaches about 1 db for an outage of 2%. In the case of drectonal antennas, the curves are very close: the maxmum dfference observed s about 1 db. Therefore, t seems justfed to develop an analyss model wthout consderng the shadowng. Moreover that analyss
allows to establsh a smple analytcal expresson of the SINR. Ths one allows to establsh performance and qualty of servce n a smple way. Remark : Ths result s due to the fact that UE are connected to ther best servng staton,.e. the BS whch offers the hghest useful sgnal. [8] S. Kaser, Spatal Transmt Dversty Technques for Broadband OFDM Systems, Proc. of Globecom, 2000. [9] J.-M. Kelf, M. Coupechoux and P. Godlewsk, Spatal Outage Probablty for Cellular Networks, Proc. of GLOBECOM, 2007. [10] Report ITU-R M.2135-1, Gudelnes for evaluaton of rado nterface technologes for IMT-Advanced, 12/2009 [11] 3GPP TSG-RAN1 WG1, LTE Downlnk Performance, Conference Call, Apr 24th 2007. R1-071978. [12] J-M. Kelf, M. Coupechoux and P. Godlewsk, On the Dmensonng of Cellular OFDMA Networks, Physcal Communcaton Journal, Ref : PHYCOM118, onlne October 2011, DOI : 10.1016/j.phycom.2011.09.008. Fg. 7. CDF of the SINR for suburban envronment (ISD= 2000m), omndrectonal recever compared to drectonal one wth aperture 17.5 (left) and 35 (rght) V. CONCLUSION We propose an approach, based on the use of drectonal recevng antennas on UEs, to mtgate nterferences n wreless networks. We show that soluton allows an mprovement of the CDF of the SINR, therefore an mprovement of performance and qualty of servce, and we quantfy t. Although the SINR s degraded for some UEs, most of them have a hgh mprovement of ther SINR. Moreover, we establsh that ths soluton s very few senstve to the envronment, rural or semurban. And t s less complex to mplement and deploy than other solutons based on ICIC or CoMP. Ths soluton seems to perfectly ft wth hgh data rate Internet access. REFERENCES [1] Daewon Lee, Geoffrey Y. L and Suwen Tang Inter-Cell Interference Coordnaton for LTE Systems, Globecom 2012 [2] Chrysovalants Kosta, Bernard Hunt,Atta U. Quddus, Rahm Tafazoll Improved Inter-cell Interference Coordnaton (ICIC) for OFDMA multcell systems, European Wreless 2013 [3] D. Lopez-Perez, I. Guvenc, G. De La Roche, M. Kountours, T. Q. S. Quek and J. Zhang, Enhanced Intercell Interference Coordnaton Challenges n Heterogeneous Networks, IEEE Wreless Communcatons, June 2011. [4] Xnyu Zhang, Mohammad A. Khojastepour, Karthkeyan Sundaresan, Sampath Rangarajan, Kang G. Shn Explotng Interference Localty n Coordnated Mult-Pont Transmsson Systems, ICC 2012 [5] L.-H. Nguyen, R. Rhenschmtt, T. Wld, S. ten Brnk Lmts of Channel Estmaton and Sgnal Combnng for Multpont Cellular Rado (CoMP), Internatonal Symposum on Wreless Communcaton Systems, 2011 [6] Dorra Ben Chekh Battkh, Jean-Marc Kelf, Marceau Coupechoux and Phlppe Godlewsk Dynamc System Performance of SISO, MISO and MIMO Alamout Schemes, Sarnoff Symposum, 2011 [7] Stefan Schwarz, Mchal Smko and Markus Rupp, On Performance Bounds for MIMO OFDM Based Wreless Communcaton Systems, Internatonal Workshop on Sgnal Processng Advances n Wreless Communcatons, 2011