Spectrum Management Methodology for WCDMA Systems Encompassing Uplink and Downlink

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1 Spectrum Management Methodology or WCMA Systems Encompassing plink and ownlink J. asreddine, J. Pérez-Romero, O. Sallent, R. Agustí ept. o Signal Theory and Communications, niversitat Politècnica de Catalunya (PC) Barcelona, Spain [nassred, sallent, orperez, ramon]@tsc.upc.edu Abstract In this paper a new spectrum management methodology or WCMA systems is proposed based on the concept o coupling matrix, which is able to capture inter-cell interactions. The proposed methodology takes into account the act that uplink and downlink requency carriers are ointly allocated and optimizes simultaneously the two link directions. Simulation results or symmetric and asymmetric services show the eiciency o the methodology in increasing capacity and reducing transmitted power. Keywords- Coupling matrix; Spectrum Management; WCMA I. ITROCTIO The tremendous increase in mobile user density and the pervasive non-homogeneity in both spatial and temporal traic distribution in cellular systems (e.g. urban hotspots and rural environment, daytime and nighttime traic distributions, etc.) require an evolution in the spectrum allocation vision or WCMA systems. Traic increase, together with nonhomogeneity, leads to the presence o islands o saturated cells although the overall system may not be congested rom a global point o view. This is due to the act that some cells have high interactions leading to high inter-cell intererence in addition to the dierence in cell loads. In the presence o several requencies (i.e. typically two or three), which is the case o currently deployed WCMA systems, requency carriers could be distributed in smart way in order to prevent such cells o sharing the same requency. Spatial non-homogeneity is currently aced by deploying micro-cells in high traic areas, leading to Hierarchical Cell Structures (HCS) [1]-[3]. In that sense, it is usual to operate the dierent cell layers (i.e. macro-cell and micro-cell layers) with dierent carrier requencies, although depending on the speciic intererence levels, this condition may be broken. For instance, scenarios breaking the HCS in WCMA systems were investigated in [4] and it has been shown that in some cases it is more suitable to share a requency by both layers. evertheless, the spectrum management problem neither has to be limited to HCS nor it has to be presumed that it has an a priori guide on a suitable solution, since it is strongly dependant on intererence and traic distribution along the deployed scenario. Thereore, spectrum management methodologies based on system characteristics can be o particular interest. In this context, we propose a heuristic spectrum management algorithm based on the concept o coupling matrix proposed in [5][6] or uplink and which is able to capture the interaction among the dierent cells rom both macroscopic and microscopic points o view. In addition to the ormulation o the coupling matrix or downlink, we propose in this paper a spectrum management methodology to distribute the available WCMA requency carriers among cells in a smart way. This paper assumes that the amount o traic per cell is such that only one WCMA carrier per cell is required, although the proposed methodology could be extended to the general case in which more than one carrier per cell is required. The paper is organized as ollows. In Section II, we introduce the coupling matrix or both uplink and downlink. In Section III, we present the spectrum management methodology. In Section IV, we describe the simulation model and provide some illustrative results in dierent scenarios. Finally, we conclude with relevant remarks and uture work. II. COPIG MATRIX et us consider a WCMA system with K base stations and F requencies. The set o all base stations is called Λ = {: [1, K]} and the set o all requencies is called Φ = {: [1, F]}. The number o users connected to base station is n. In the ollowing, two coupling matrices are developed or downlink and uplink respectively. A. ownlink In the downlink, the E b / 0 requirement or the i-th user o the -th cell, denoted as user i, can be expressed as: PTi, Θi Eb i, = (1) o P i T, PT, i 0, + χi + α i, where PTi, is the power devoted to the user i, χi represents the inter-cell intererence experienced by this user, Θi is the spreading actor including the modulation and code rate, i, is the pathloss between mobile i and base station, α is the orthogonality actor in downlink (α = 0 or perect orthogonality and 1 or non-orthogonality), 0, is the downlink background noise power, and P T, is the total

2 transmitted power by base station, which is given by n T, p, T, i i = 1 P = P + P (2) where P p, is the power devoted to common control channels in cell. It was shown in [7] that by using (1) and (2), we get where P T, P + + P S = 1 α S S l, p, 0, T, l, l l Λ {} =, (3) n i, 1 (4) i = 1 Θ i, l i + α = E b o i n i, (5) i 1 / = W Ri + α E The cell coupling existing in a WCMA cellular system is explicitly relected in the above equation, where the resulting transmitted power level by a given base station depends on all other base stations respective transmitted power levels. In matrix orm, the system o equations (3) is rewritten as b o i P = C P + P (6) T where P T = (P T,1, P T,2,, P T,K ) T is the total transmitted power vector, the -th element o P is deined by ( ) ( 1 ) P, = Pp, + 0, αs, and the coupling matrix C is a K K square matrix deined by 0 i l = C l, = S l, (7) otherwise 1 α S, From (3), we can iner that each element o coupling matrix C represents the impact o the total transmitted power by one base station on the transmitted power by another base station. B. plink In the ollowing, I stands or the total power received by base station and it is given by [7]: T I = χ + P + (8) R, 0, where χ and P R, are the inter-cell intererence and the total own-cell received by cell, and 0, is the uplink background noise power. In uplink, the E b / 0 requirement or the i-th user o the -th cell can be expressed as where Eb Pi, Θ i = P P + χ + 0 i R,, i 0, (9) P, i is the received power by base station rom user i. It was shown in [5] that, by using (9), we can write I + S I 0, l, l l Λ {} = Λ 1 S, (10) It is worth mentioning that the coupling between the -th cell and the l-th cell in the downlink is given by the term S,l in (3), which depends on how the users are distributed within the -th cell in relation to the l-th cell. On the contrary, the coupling in the uplink direction is given by the term S l, in (10) which depends on how the users are distributed in the l-th cell with respect to the -th cell. In matrix orm, the system o equations (10) can be rewritten as I = C I + P (11) where I = (I 1, I 2,, I K ) T is total received power vector, the - th element o P is deined by P, = 0, ( 1 S, ) and the coupling matrix C is a K K square matrix deined by 0 i l = C l, = Sl, (12) otherwise 1 S, From (10), we can iner that each element o coupling matrix C represents the impact o the total received power by one base station on the total received power by another base station. C. Generic Form Equations (3) and (10) can be written in the ollowing generic matrix orm: V = C V + P (13) where V is a Kx1 vector that replaces I in uplink and P T in downlink and is the link direction. III. SPECTRM MAAGEMET METHOOOGY It can be shown that, using the same reasoning as in [8], the coupling matrices are non-negative irreducible matrices. When representing a system by a non-negative irreducible matrix, spectral radius (i.e. the eigenvalue with the largest modulus) can be seen as a smart indicator that is able to capture overall system behavior. Indeed, a pervasive increase

3 in matrix elements (or an increase o any element) leads necessarily to an increase in the spectral radius o a nonnegative irreducible matrix [9]. Furthermore, it was shown in [10] that the spectral radius o non-negative irreducible matrices could be used as a congestion measure. Thereore, in this paper we use the spectral radius o the coupling matrix as a key element o the proposed spectrum management algorithm. A. Spectrum Management Algorithm We assume the usual case in currently deployed WCMA networks in which the operator has F requency carriers to be distributed among the dierent base stations. The traic level is such that only one carrier is required per base station, so the operator can take advantage o the availability o the F requencies by means o a smart requency-to-cell allocation in order to improve the intererence pattern with respect to a classical requency reuse-based approach. In this paper, we assume that the spectrum management algorithm is implemented in the initial planning phase. However, it would be easy to extend the proposed approach to a dynamic methodology that uses coupling matrix properties to detect relevant changes and optimize requency allocation as in the proposed approach or uplink in [11]. sing expected traic levels, the operator can estimate the coupling matrices C and C rom the reported values o pathlosses and E b / 0 or both uplink and downlink in a given coverage area. At each iteration o the algorithm, we derive 2F partial coupling matrices ( C,,,,,,, 1 C2 CF C1 C2 C F ) rom the total coupling matrices C and C. These matrices are the coupling matrices associated to the dierent requencies, that is, matrix C includes only the entries corresponding to cells associated to requency in link direction. In order to introduce the algorithm, we deine Λ as the set o cells operating with requency and λ as the spectral radius o matrix C. The algorithm is shown in Figure 1 and it starts by initiating Λ to empty sets. Basically, the idea o the algorithm is to allocate each cell to the requency in which the mutual interaction o this cell with the cells already allocated to this requency is minimal. B. Practical Considerations From a practical point o view, the operator can identiy dierent periods o time with dierent traic distributions and associate to each period a dierent requency allocation, based on the proposed methodology, so that the network coniguration can be changed to adapt to the traic variations. These periods are rather medium and long-term periods (i.e., at least several hours) and the elements o the matrix are estimated rom the expected averaged values o S l,. In this context, the ast luctuation (due to mobility, ast ading, etc.) is averaged and does not have important impact on the accuracy o the matrix. Moreover, all the needed inormation (E b / 0, long-term pathlosses, spreading actors) or the computation o the coupling matrices can be obtained using the measurements collected either by base stations or mobiles. Furthermore, the spectral radius can be computed using the power method [12]. The complexity o the spectrum management algorithm is a linear unction o the number o cells. Besides, the coverage o an operator could be divided into bunches, so that the algorithm can be applied separately to each bunch, in order to acilitate the spectrum management process. Thereore, the coupling matrix approach could be easily implemented in operational systems. 1. All matrices C are initiated to zero matrices: C = A vector T = {T 1, T 2,, T K } is computed. The value o T is computed using the sum o the corresponding rows and columns or each cell in matrices C and C : T = C + C + C + C l Λ {} ( ) l, l, l, l, Each element T combines the impact o cell on other cell and the impact o other cells on cell in both uplink and downlink 3. Cells are sorted using the sum T in order to take into account the impact o each cell on other cells and the latter on each cell. 4. Cell with the highest sum is associated to carrier 1 and set Λ 1 is updated. At this stage C will remain null. 5. pdate each sum T l o the remaining cells by eliminating the eect o the allocated cell : T = T C + C + C + C l l 1 ( ) l, l, l, l, 6. Sort the remaining cells using the new vector T and choose cell with the highest sum. 7. Estimate Ω = max λ by considering that cell is = {, } associated to all requencies. Ω capture the behavior o the worst link and should be minimized. 8. Choose requency with the lowest Ω and associate this requency to cell. 9. Add cell to set Λ. and repeat rom step 5 Figure 1. Spectrum Management Algorithm IV. SIMATIO A RESTS The perormance o the proposed methodology is compared to the perormance o the spectrum allocation in the classical HCS approach in a scenario with F=2 requencies using snapshot simulations. In the HCS, one requency is assigned to macro-cells and the second one is assigned to micro-cells. The considered scenario consists o three macrocell rings and seven hotspots with seven micro-cells in the center o the hotspots (Figure 2). Simulation parameters are introduced in Table I [13]. Three scenarios are considered. The irst scenario considers an asymmetric traic in which downlink spreading actor (SF) including the modulation and code rate is 20 db while uplink SF is 26 db, to account or the higher bit rate needed in downlink. On the contrary, the

4 second scenario considers a symmetric traic with the same SF=23 db in uplink and downlink. Finally, the third scenario considers the symmetric traic in macro-cells and the asymmetric traic in hotspots. Figure 2. ayout o the macro-cells, micro-cells and hotspots TABE I SIMATIO PARAMETERS Macro-cell layer BS pilot power 30 dbm Cell radius 1 km Orthogonality actor 0.4 BS maximum transmitted power 43 dbm Micro-cell layer Micro-cell BS pilot power 20 dbm Cell radius 0.2 Km Orthogonality actor 0.06 BS maximum transmitted power 33 dbm Common parameters ownlink BS power range 25 db Pathloss model log 10 d (Km) Background noise -98 dbm E max. power or macro-cell 30 dbm (20 or micro) (ownlink) E max. power (plink) 21 dbm Transmitted power range 25 db ownlink E b / 0 target 6 db plink E b / 0 target 3 db Shadowing actor deviation 7 db Shadowing actor cross-correlation 0.5 Macro-cell density (1 st sc.) mobiles/cell Micro-cell density (1 st sc.) 8.8:12.8 mobiles/cell (steps o 0.8 mobiles/cell) Macro-cell density (2 nd sc.) mobiles/cell Micro-cell density (2 nd sc.) mobiles/cell (steps o 0.8 mobiles/cell) Power control Perect power control In each snapshot a number o mobiles are randomly distributed in the scenario according to the spatial traic pattern. All results are averaged over 1000 snapshots. In Figure 3, we show the total downlink outage probability o the asymmetric scenario as a unction o average mobile density. The total outage probability is deined as the rate between the unsatisied users (i.e. those users measuring an E b / 0 below the target) and the total number o users in the system. Average mobile density is deined by the ratio between the total number o users in the system and the total surace. Figure 3 shows that the proposed Spectrum Management Methodology (SMM) outperorms the HCS especially or high mobile density. Furthermore, the capacity (i.e. user density when the outage probability is 0.02) is increased by 20% when the SMM is used (i.e. rom 10.7 to 12.9 mobiles/km 2 ). We highlight here that or these densities and asymmetric traic, uplink outage probability is very low (i.e. quasi-null) and thus the capacity o the system is limited by the downlink. In Figure 3 we also show the maximum outage probability among all cells as a new metric to detect islands o congested cells. Also rom the point o view o this metric, the SMM outperorms the spectrum allocation in the HCS and gives approximately the same capacity gain as in the case when the total outage in the scenario is considered. In Figure 4, we show the average transmitted power over all base stations as a unction o the average mobile density. As we can see, the SMM decreases signiicantly the transmitted power in the system thanks to the avoidance o high inter-cell intererence. Figure 3. ownlink outage probability as a unction o the average density in the asymmetric scenario In Figure 5, the total outage probability in the symmetric scenario is plotted. When using the HCS, it can be observed that the uplink perormance is better than the downlink one or low loads because the E b / 0 in downlink is higher than in uplink and the downlink orthogonality does not aect the inter-cell intererence, which is similar in both uplink and downlink. On the contrary, when the SMM is used, the uplink is the limiting transmission direction. This is due to the act that the SMM highly reduces the inter-cell intererence and thereore the system is limited by intra-cell intererence, which is higher in uplink than in downlink thanks to the orthogonality existing in the latter. Finally, we highlight the act that the proposed method increases the capacity by more than 21% (i.e. rom 25.7 to 31 mobiles/km 2 ). Furthermore, the outage probability is signiicantly reduced when the SMM is used instead o the HCS in both uplink and downlink. Moreover, other simulation results not shown here or the sake

5 o brevity reveal that also the average total transmitted power is reduced when the SMM is used instead o the HCS. uture work as well as the case where more than one requency carrier could be allocated to one base station. Figure 4. Average transmitted power as a unction o the average mobile density in the scenario with asymmetric traic Figure 6. Outage probability as a unction o average mobile density in the scenario with symmetric traic in macro-cells and asymmetric traic in hotspots ACKOWEGEMET This work was partially perormed in proect E2R II which has received research unding rom the Community's Sixth Framework program. This paper relects only the authors' views and the Community is not liable or any use that may be made o the inormation contained therein. The contributions o colleagues rom E2R II consortium are hereby acknowledged. This paper is also supported by the COSMOS grant (re. TEC , Spanish Ministry o Science and Education and European Regional evelopment Fund). Figure 5. Outage probability as a unction o average mobile density in the scenario with symmetric traic In Figure 6, we show the total outage probability o the third scenario. In this case also, the SMM increases the capacity by 14%. As in the symmetric scenario, the limiting link direction is uplink or the SMM and downlink or the HCS. V. COCSIOS A OPE ISSES In this paper, we proposed a coupling matrix that is able to capture inter-cell interaction in both uplink and downlink. Thereater, we introduced a practical spectrum management methodology based on this matrix. The proposed methodology takes into account the act that uplink and downlink requency carriers cannot be allocated independently. Simulation results or both symmetric and asymmetric services have shown that the proposed methodology outperorms the classical requency allocation in the HCS in terms o capacity and transmitted power. The proposed approach can be extended to a dynamic methodology that is able to detect relevant changes and ind the suitable requency allocation dynamically. This is let or REFERECES [1] MTS Forum Report 5, "Minimum spectrum demand per public terrestrial MTS operator in the initial phase", September [2] MTS Forum Report 6, "MTS/IMT-2000 spectrum", ec [3] "E Procedures in Idle Mode and Procedures or Cell", 3GPP Technical Speciication Group Radio Access etwork, TS V4.5.0, une 2002."TS [4] T. Rautiainen, Breaking the Hierarchical Cell Structure in WCMA etworks, IEEE VTC Spring 02. [5] J. asreddine, J. Pérez-Romero, O. Sallent, R. Agusti, and X. agrange, A Proposal on Frequency Management Methodologies or WCMA Systems using Cell Coupling Matrices, IEEE VTC Fall 06. [6] J. asreddine, J. Pérez-Romero, O. Sallent, R. Agusti, and X. agrange, A ovel Frequency Management Methodology or WCMA using Statistical Coupling Matrices, IEEE ISWCS 06. [7] J. Pérez-Romero,,O. Sallent, R. Agusti, and M. A. iaz-guerra, Radio Resource Management strategies in MTS, John Wiley & Sons, [8] S. A. Grandhi, R. Viayan,. J. Goodman, and J. Zander, "Centralized Power Control in Cellular Radio Systems," IEEE Transactions on Vehicular Technology, vol. 42, pp , [9] M. oob. Cvetkovic and H. Sachs. Spectra o Graphs: Theory and Application. Academic Press, [10] Hanly, S.V. "Congestion measures in S-CMA networks" IEEE Transactions on communications, pp , 1999, 47.

6 [11] J. asreddine, J. Pérez-Romero, O. Sallent, R. Agustí, "ynamic Spectrum Management Methodology or WCMA Systems Based on Inter-Cell Interaction Approach", IEEE WPMC 06. [12] emmel, J. W., Applied umerical inear Algebra, SIAM, [13] "RF System Scenarios", 3GPP, Technical Speciication Group Radio Access etwork, TS , V4.2, 2002.

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