Impact of Inaccurate User and Base Station Positioning on Autonomous Coverage Estimation

Imact of Inaccurate User and Base Station Positioning on Autonomous Coverage Estimation Iman Akbari, Oluwakayode Onireti, Ali Imran, Muhammad Ali Imran and ahim Tafazolli Institute for Communication Systems ICS), University of Surrey, Guildford GU2 7XH, UK Telecommunications Engineering, University of Oklahoma, Tulsa, OK, USA Email: {i.akbari, o.s.onireti, m.imran, r.tafazolli}@surrey.ac.uk and ali.imran@ou.edu Abstract Autonomous monitoring of key erformance indicators, which are obtained from measurement reorts, is well established as a necessity for enabling self-organising networks. However, this reorts are usually tagged with geograhical location information which are obtained from ositioning techniques and are therefore rone to errors. In this aer, we investigate the imact osition estimation errors on the cell coverage robability that can be estimated from autonomous coverage estimation ACE). We derive novel and accurate exressions of the actual cell coverage robability of such scheme while considering: errors in user equiment UE) location and; errors in both UE and base station location. We resent generic exressions for channel modelled with ath-loss and shadowing, and much simlified exressions for the ath-loss dominant channel model. Our results reveal that the ACE scheme will be subotimal as long as there are errors in the reorted geograhical location information. Hence, aroriate coverage margins must be considered when utilising ACE. I. INTODUCTION ecently, extensive research and standardisation work has focused on the novel aradigm of self-organising network SON). SON aims at achieving a substantial reduction in caital and oerational exenditures CAPEX & OPEX) by reducing human involvement in network oerational tasks, while otimising the networks coverage, caacity and quality of service []. In general, SON concet involves the integration of self-configuration, self-otimisation and self-healing functionalities into an automated rocess requiring minimal manual intervention [] [3]. However, these autonomous features cannot be achieved with the current drive test based coverage assessment aroach, as it lacks automaticity and therefore results in huge delay and cost. In order to incororate SON features, system erformance metrics such as coverage, quality of service QoS), energy efficiency and sectral efficiency need to be monitored and otimised autonomously. This can be achieved by the measurement reorts rovided by the user equiment UE) to their serving node. These measurement reorts can then be exloited to determine a number of key erformance indicators KPIs), e.g. coverage and service mas, cell boundaries, hotsot locations, congestion indicators and energy consumtion indicators, at the base station BS) autonomously. This leads to a significant saving in time and labor cost on drive test based field measurements. Consequently, autonomous estimation of KPIs can substantially reduce the time frame and cost of the ost-deloyment otimisation cycle. These solutions require accurate geograhical location information for both the UEs and nodes which may be deloyed in an imromtu manner e.g Femto cells). Location information can be obtained by using ositioning techniques, such as observed time difference of arrival OTDOA) or assisted global ositioning system A-GPS) [4], [5]. For indoor environments, osition estimation techniques based on WLAN, radio frequency identification FID) and ultrasonic have been roosed [6] [9]. All these techniques are rone to errors. For examle, the accuracy of A-GPS has been evaluated as m, 2 m and m for rural, suburban and urban environments, resectively. On the other hand, the average accuracy of indoor techniques is about 2 m, however, they require installing secialised devices [6] [9]. By exloiting the measurement reorts gathered by the UEs and their location information, an autonomous coverage estimation ACE) can be develoed. In such a system, UEs measurement reort such as received signal strength SS) are tagged with their geograhical location information, which are obtained from the osition estimation techniques, and sent to their serving BS. The serving BS after retrieving the measurements, further aends its geograhical location information and forwards them to a trace collection entity TCE), which then generates the autonomous coverage ma. Since the osition estimation techniques are rone to errors, the measurement reorts may be tagged to a wrong location. In this aer, we investigate the imact of inaccurate osition estimation on the ACE scheme by deriving its cell coverage robability over the area of interest where the data are gathered from. We build on our earlier work in [] where we have considered the case with errors only in the reorted UE geograhical location. In this aer in addition to UE location error, we also consider the case with errors in the estimated location of the BS. We have considered the following channel roagation scenario in our analysis: ) ath-loss dominant channel model and 2) ath-loss and shadowing dominant channel model. The rest of this aer is organised as follows: In Section II, we resent the framework for ACE. In Section III, we derive the cell coverage robability of the ACE scheme for the channel model with both athloss and shadowing, while Section IV gives the derivation for the ath-loss dominant channel model. In Section V, we resent the numerical results which show that our analytical derivations are very accurate. Furthermore, our results show 978--4673-886-4/5/$3. 25 IEEE 4

that the imact of inaccurate osition estimation on the ACE coverage robability becomes more severe as the error in osition estimation increases. Finally, Section VI concludes the aer. II. AUTONOMOUS COVEAGE ESTIMATION FAMEWOK We consider an ACE scheme which exloits the measurement reorts gathered by the UEs. In such a system, UEs measurement reorts are tagged with their geograhical location information and sent to their serving BS. The serving BS after retrieving the measurements, further aends its geograhical location information and forwards them to a TCE, which can then generate the coverage ma. The reorted geograhical coordinates of the UEs and BSs are obtained from ositioning techniques, such as OTDOA or A-GPS [4], [5]. However, these techniques are rone to errors, and, hence the reorts may be tagged to a wrong location. In this aer, given a reorted UE osition, o, with coordinates c, d), we assume that its actual location is within a circular disc with radius r which is centered at o, as illustrated in Fig. a). Furthermore, we assume that errors in BS ositioning can be resolved such that its dislacement from its reorted osition, e, is known. For analytical tractability, we consider a single cell deloyment scenario where SS measurement reorts are gathered by the UE. The signal roagation model we emloy for obtaining the SS is as follows ) η P t P r ) = Φ, ) P l ) where P r ), P t and η denote SS at distance from the BS, transmit ower and ath-loss exonent, resectively. The arameter denotes the reference distance with a known ath-loss, P l ). The shadowing effect is modeled by the random variable, Φ, which follows a log-normal distribution such that log Φ follows a zero mean Gaussian distribution with standard deviation σ in db. The error in coverage estimation as a result of such autonomous scheme is evaluated by assessing the reliability of radio frequency F) coverage on the measurement based on the fundamental metric of cell coverage robability. ) Cell Coverage Probability: In general, the cell coverage robability can be defined as C = P [P r ) γ] da, 2) A and can be thought of equivalently as the average fraction of UEs who at any time achieve a target SS, γ, i.e., the average fraction of network area that is in coverage at any time. Hence, given a circular radial distance from the BS, we are interested in comuting the ercentage of area with SS greater or equal to γ. III. CELL COVEAGE POBABILITY WITH ACE Here we consider the scenario where both shadowing and ath-loss are the dominant factors in the channel roagation model. The robability that the reorted SS in db) at a a) Cell and user ositioning b) Calculating the angles Fig.. a) UE with reorted osition o, its actual osition lies within the circular disc with radius r centered o. b) shows the triangle created in a). distance from the BS will exceed the threshold γ, i.e., P[P r ) γ] can be obtained from [], [2] as P[P r ) γ] = 2 2 erf a + b ln ), 3) where a = γdbm) P t dbm)+p l )db)+η log σ 2 ), and b = η log e) /σ 2 when there are no errors in UE and BS location information. In the same way, cell coverage robability of the ACE scheme without error in location information can be exressed as C = 2 2 erf a+b ln ) d. 4) A. UE Geograhical Location Information Error Now we consider the case with errors in the geograhical location information reorted by the UEs to their serving BS. As stated earlier, the actual location of a UE lies within a circular disc centered at the reorted location. Consequently, its actual location with reference to its reorted location can be modeled as κ, φ) = 2 + κ 2 2κ cos φ, 5) where κ r and φ 2π. The PDF of the distance and direction of the UE s actual location with resect to its reorted osition are r and 2π, resectively. Therefore, the modified P[P r ) γ] as a result of the inaccuracies in the UE s location information can be obtained as P [P r ) γ] = E κ,φ {P [P r κ, φ)) γ]} 6) = 2πr r 2π P [P r κ, φ)) γ] dφdκ, where E is the exectation. This further simlifies as P[P r ) γ] = 2πr r 2π 2 2 erf a+ b +κ 2 )] 2κcos φ 2 ln2 2 dφdκ. 7) by substituting 3) into 6). Consequently, the actual ercentage of the area A in coverage due to the ACE scheme can be obtained as 5

In addition to the UE s osition error, we consider here the scenario where the geograhical location information reorted by the serving BS to the TCE is dislaced at a distance e from its actual location, as deicted in Fig 2. Hence, the measurement reorts stored in the TCE are also tagged with a wrong BS osition, thus resulting in the generation of a wrong coverage ma. In order to estimate the actual coverage robability of the ACE scheme over the area A circular area) centered at the reorted BS osition X, we estimate the fraction the reorts that will still be in coverage based on the actual BS osition X. Consider as the radius of the area of interest A centered at X, we can create a virtual reresentation of A centered at X such that both intersects at S and S 2, as shown in Fig. 2. The intersecting oints are characterized by the angle, α = π cos e 2). Hence, using this roerty, we define two regions, A and A 2, which are the shaded and unshaded areas in the area of interest, resectively, and we estimate the actual fraction of UE in coverage based on the actual BS osition, X. The distance between the reorted UE osition in region A and A 2 with resect to the actual BS ositions can be exressed as [ )] e sin θ A θ)= 2 +e 2 2ecos π θ sin 9) [ esinπ θ) A2 θ)= sin θ sin )][ ] sinπ θ), ) resectively, where π α θ 2π α and 2π α θ 3π α for A θ) and A2 θ), resectively. Consequently, the actual coverage robability of the ACE scheme over the area A can be exressed as Note that the sum of the areas of the two region is such that A +A 2 = A π 2 + A θ) α A2 θ) P[P r ) γ]ddθ P[P r ) γ]ddθ ), ) when there are errors in both the UE and BS geograhical location information. By substituting the exression of P[P r ) γ] in 7) into ), it is further exressed as 2) given at the to of the next age. IV. ACE COVEAGE POBABILITY: PATHLOSS ONLY CHANNEL MODEL Here we consider the scenario where the athloss is the redominant factor in the channel roagation model. We Fig. 2. BS with reorted osition at X has an actual location X, which is further assume that the ) cell coverage radius is such dislaced from x by e. that = γp l ) η. P t Hence for the case with no error in geograhical location information and no shadowing, C ACE = P [P r ) γ] =, while. Consequently from P[P r ) γ]da = 8) equation 2), the cell coverage robability over the circular A r 2π πr 2 2 2 erf a+ b +κ 2 )] radial distance,, C =, in this case. 2κ cos φ 2 ln2 2 dφdκd. A. UE Geograhical Location Information Error B. UE and BS Geograhical Location Information Error It can easily be shown that for the case without shadowing and with only UE ositioning error, P [P r ) γ] in 6) is equivalent to the fraction of the circular disc area that lies within the cell radius, as illustrated in Fig. By alying laws of trigonometry, we obtain P [P r ) γ] as follows P [P r ) γ] = β sin β + θ sin θ 2π [ 2π where β) = 2 cos 2 +r 2 2 ] 2r ) 2, 3) ] r, θ) = [ 2 cos 2 + 2 r 2 2 and. Hence, the cell coverage robability over the area A and as a result of the ACE scheme can be obtained according to 8) as C ACE = A = π 2 P [P r ) γ]da 4) β sin β + θ sin θ ) ) 2 d, 2π for the case without shadowing but with error in UE ositioning. B. UE and BS Geograhical Location Information Error Following a similar aroach with the shadowing case, we derive the cell coverage robability for the case with errors in both the UE and BS geograhical location information. The cell coverage robability of the ACE for the case with athloss as the dominant factor in the channel roagation model can also be exressed as in ), but with P[P r ) γ] defined in 3). We thus arrive at 5) given at the to of the next age. V. NUMEICAL ESULTS In this section, we resent numerical results in order to verify the accuracy of the roosed analytical methodology against simulations, as well as to show the imact of errors in reorted geograhical location information on the actual coverage estimated by the ACE scheme. We consider a single cell 6

π 2 π 2 + A θ) A θ) r 2π α A2 θ) r 2π 2 2 erf a+ b +κ 2 )] 2κcos φ 2 ln2 2 2 2 erf β sin β + θ sin θ ) ) 2 ddθ+ a+ b 2 ln2 +κ 2 2κcos φ 2 α A2 θ) dφdκddθ )] ) dφdκddθ. 2) β sin β + θ sin θ ) ) ) 2 ddθ. 5) TABLE I LIST OF PAAMETES Parameters Symbol Value unit) Standard Deviation σ 7, 9, 2 db Path Loss Exonent η 3.5 eference Distance m Path Loss at P l ) 34.5 db Power Transmitted P t 46 dbm Threshold γ 84.5 dbm UE osition error r m BS osition error e 2 m deloyment with the arameters secified in Table I and we estimate the cell coverage robability over a) circular coverage η region of area π 2, where = γp l ) P t 553.68 m. As far as simulations are concerned, we used the following methodology for the case with errors in geograhical location information reorted by the UE. ),, UE are distributed following a uniform distribution over the circular region of area π 2 and their ositions are taken as the reorted osition. 2) The actual osition of the i th UE with coordinates c i, d i ) is generated as c i + r u i cos2πv i ), d i + r u i sin2πv i ), where v i and u i are seudo random, seudo indeendent numbers uniformly distributed in [, ]. 3) The SS at the generated actual osition P r ), which is at the distance from the BS, is estimated according to ), where Φ = for the ath-loss dominant channel model. 4) The cell coverage robability achieved by the ACE scheme is then evaluated as the ercentage of UE with P r ˉ) γ. For the case with error in reorted BS geograhical location information, ste 3 is changed as follows to incororate this error. Given the BS with reorted coordinates x, y), its actual coordinates is obtained as x + e, y). The SS is estimated according to ) based on the distance between the actual BS and UT ositions, where Φ = for the ath-loss only channel model. In Figs. 3 and 4, we validate cell coverage robability exressions that were derived for the ACE scheme, for both the case with errors in reorted UE geograhical location information, and the case with errors in both reorted UE and BS geograhical location information. In Fig. 3, we comare our analytical results on the actual cell coverage robability of the ACE scheme with the simulated results, for the case when ath-loss and shadowing are the dominant factors in the signal roagation model. Whereas, a comarison for the case with ath-loss as the dominant factor is resented in Fig. 4. We note that in both figures, our analytical results closely matches with the simulation. The results in Figs. 3 and 4 further show that the estimated cell coverage robability as measured by the ACE scheme decreases as the UT osition error increases. Furthermore, having errors in BS location information further degrades the erformance of the ACE scheme. In Fig. 5, we lot the coverage estimation error as a result of using the ACE scheme, D A, against the UE osition error, for shadowing standard deviation σ = 7, 9, 2 db and BS osition error e =, 2 m. We define the coverage estimation error, D A, as D A = C ACE C %, 6) C where for the shadowing and ath-loss dominant channel model, C ACE is given in 8) and 2), for the case with errors in reorted UE geograhical location information and for the case with errors in both the reorted UE and BS geograhical location information, resectively, while C is given in 4) for the case without errors in reorted geograhical location information. In addition, C ACE for the ath-loss dominant channel model is given in 4) and 5) accordingly and C = in this case. Fig. 5 shows that the erformance of the ACE scheme in estimating the actual coverage dereciates as the error in UE osition increases. Furthermore, it can be observed that the erformance of the ACE scheme becomes more degraded as the shadowing standard deviation σ reduces. This imlies that errors in UE and BS osition estimation are less severe on the coverage as σ increases. The reason for this is that increasing σ introduces more randomness to the received signal; hence randomness created by the UE ositioning error would have more imact on a lower σ. VI. CONCLUSIONS In this aer, we have investigated the imact of inaccurate geograhical location information on the coverage robability 7

.99.98.97.96.95.94.93.92 2 3 4 5 6 7 8 9 -. -.2 -.3 -.4 -.5 -.6 -.7 2 4 6 8 Fig. 3. The coverage robability with ACE scheme as a function of UE osition error radius for the athloss dominant channel roagation model. BS osition error e = 2 m in 5)..7385.738.7375.737.7365.736.7355.735.7345.734 2 4 6 8 Fig. 4. The coverage robability with ACE scheme as a function of UE osition error radius when σ = 9dB. BS osition error e = 2 m in 2). estimation through an autonomous coverage estimation ACE) scheme. We have derived the exression of the actual cell coverage robability that can be obtained from such scheme while considering: errors in user equiment UE) geograhical location information and; errors in both UE and base station BS) geograhical location information. The accuracy of the derived exressions has been shown through numerical results for a range of UE and BS ositioning errors. The erformance of the ACE scheme will be subotimal as long as there are errors in the reorted geograhical location information. Hence, aroriate correction factors, that can be calculated using roosed model, must be used while utilising such ACE scheme. Fig. 5. Cell coverage degradation with ASE ACKNOWLEDGMENT This work was made ossible by NPP grant No. 5-47- 2-437 from the Qatar National esearch Fund a member of The Qatar Foundation). The statements made herein are solely the resonsibility of the authors. More information about this roject can be found at www.qson.org. We would like to acknowledge the suort of the University of Surrey 5GIC members for this work. EFEENCES [] J. L. Van den Berg,. Litjens, A. Eisenbltter, M. Amirijoo, O. Linnell, C. Blondia, T. Krner, N. Scully, J. Oszmianski and L. C. Schmelz, Self-Organisation in Future Mobile Communication Networks, in ICT Mobile Summit, Sweden, 28. [2]. Combes, Z. Altman, and E. Altman, Self-Organization in Wireless Networks: A Flow-Level Persective, in IEEE INFOCOM, Mar. 22,. 2946 295. [3] O. G. Aliu, A. Imran, M. A. Imran, and B. G. Evans, A Survey of Self Organisation in Future Cellular Networks, IEEE Commun. Surveys Tuts., vol. 5, no.,. 336 36, 23. [4] T. Kos, M. Grgic, and G. Sisul, Mobile User Positioning in GSM/UMTS Cellular Networks, in Proc. 48th International Symosium ELMA, Jun. 26,. 85 88. [5] 3rd Generation Partnershi Project 3GPP), Technical Secification Grou adio Access Network, Evolved Universal Terrestrial adio Access E-UTA); LTE Positioning Protocol LPP) elease ), 3GPP TS 36.355 V.3., 3GPP Std. Jun. 23. [6] F. Evvenov and F. Marx, Imroving Positioning Caabilities for Indoor Environment with WIFI, in IST Summit, 25. [7] J. Hightower, G. Borriello, and. Want, SPOTON: An Indoor 3D location Sensing Technology Based on F Signal Strength, in Uni. Washington CSE Tech eort, 2. [8] N. Priyantha, A. Chakraborty, and H. Blackrishnan, The Cricket Location Suort System, in MOBICOM, 2,. 32 43. [9]. Kaneto, Y. Nakashima, and N. Babaguchi, eal Time User Position Estimation in Indoor Environments Using Digital Watermarking for Audio Signals, in Pattern ecognition Conferece, 2. [] I. Akbari, O. Onireti, M. A. Imran, A. Imran, and. Tafazolli, Effect of Inaccurate Position Estimation on Self-Organising Coverage Estimation in Cellular Networks, in Euroean Wireless Conference, May 24. [] W. C. Jakes, Microwave Mobile Communications, 2nd ed. IEEE Press, 994. [2] T. S. aaort, Wireless Communications - Princiles and Practice, 2nd ed. Prentice Hall, 22. 8