Radio Resource Management in a Coordinated Cellular Distributed Antenna System By Using Particle Swarm Optimization

Transcription

1 Radio Resource Manageent in a Coordinated Cellular Distributed Antenna Syste By Using Particle Swar Optiization Oer Haliloglu (1), Cenk Toker (1), Gurhan Bulu (1), Hali Yanikoeroglu (2) (1) Departent of Electrical and Electronics Engineering, Hacettepe University, Ankara, Turkey (2) Departent of Systes and Coputer Engineering, Carleton University, Ottawa, Canada Eail: {oer, cenk.toker, bulu}@ee.hacettepe.edu.tr, hali@sce.carleton.ca Abstract In this paper, we consider a coordinated ulti-point transission (CoMP) schee used in a cellular syste where antenna ports are distributed throughout the cell, instead of using a single base station. Two schees are considered; either ports can be switched on and off (Binary Power Manageent, BPM) or their transission power can be adjusted (Continuous Power Manageent, ). The goal is to iize the iniu signal to interference plus noise ratio (SINR) in the network for both schees. The first proble is NP-hard and the second one is ultiodal. We propose to use particle swar optiization (PSO) as a solver for both probles. It is deonstrated that the proposed PSO based algoriths can efficiently solve both probles. Furtherore, through siulations, it is shown that for the sae total transit power per port, outperfors BPM. Index Ters - Distributed antenna systes, CoMP, port selection, radio resource anageent, particle swar optiization. I. INTRODUCTION The ever increasing user deand fro wireless counication systes in ters of both data rate and also coverage has been the underlying otivation of the search for advanced technologies. Traditional interference avoidance techniques which reuse frequency and tie resource blocks to itigate interference, utilize spectru inefficiently and can be inadequate to eet the deand for higher data rates. SINR degradation due to signal attenuation and interference fro other cells for cell edge users can be considered as a coverage issue. Furtherore, using transit power efficiently is iportant due to both syste perforance and environental aspects. It appears that all these issues cannot be siultaneously addressed and solved by the techniques which have been used in the last decades. Future developents will tend to be based on cooperative transission rather than interference avoidance, leading to coordinated ulti-point transission and reception (CoMP) [1]. CoMP is a proising technique for counication networks, especially in heterogeneous networks (HetNets) [2], due to the deployent of low power nodes, i.e., pico-, feto-cells and reote radio heads. CoMP offers self-optiization and self-configuration functionality for This work is supported by TUBITAK (The Scientific and Technological Research Council of Turkey), Turkey, under project no. 112E24. network operators and the direction of the future evolution of LTE-A sees to be guided by CoMP. In this paper, a downlink CoMP scenario is considered, and ports (reote radio heads in LTE-A terinology) are utilized to for a distributed antenna syste. It is assued that inter-user interference in a cell is eliinated by assigning the resource blocks (RBs) to the users of the cell in an orthogonal fashion, i.e., in each cell only one user equipent (UE) is allowed to use a specific RB. On the other hand, the transission of the ports using the sae RB in different cells can interfere each other. To siplify the forulation and deonstration, transission over a single RB is considered in this paper. Authors in [3] investigate a siilar scenario. The objective of the proble in [3] is to iize the iniu SINR aong all users by decreasing the best port settings. They handle this proble by setting the ports either on or off, i.e., a port can either transit at a fixed power or it is switched off. We call this schee as Binary Power Manageent (BPM). The proble is NP-hard [5] and need to be relaxed before it can be solved by an optiization tool, e.g., CVX [7]. Seidefinite relaxation (SDR) is a good way to tackle NP-hard probles [6], but it gives suboptiu results and can becoe not proising for ore coplex probles. In this paper, we allow ports to transit at a power level in the interval [,P ] rather than {,P } as in [3]. We call this schee as Continuous Power Manageent (). It can be shown that although the search space is continuous, the cost function is ulti-odal, i.e., there can be any local optiu solutions besides the global one. Therefore it is iportant to find the global optiu solution giving the best setup. In order to obtain the optiu solution, we offer to use particle swar optiization (PSO) which is an evolutionary optiization ethod first proposed in [8]. The ost iportant feature of PSO is, it distributes the particles (i.e., possible solutions) throughout the search space and perfors a global search. As in any other evolutionary optiization algoriths, PSO also does not suffer fro getting stuck at a local optiu, if it is set up correctly. If the peak power constraint for a port is considered, it is deonstrated that the solution to both the BPM and

2 Fig. 1: A seven cell distributed antenna syste with seven ports per cell. probles can be classified into two parts; a noise doinant region, and an interference-liited region. For a sall network of two cells, these regions are apparent. However as the network size, i.e., nuber of cells in the network increases, the solution gets interference-liited for physically eaningful scenarios. Through siulations it is shown that outperfors BPM for both a sall and also a relatively large network, especially in the interference-liited region. The paper is organized as follows; Section II describes the syste odel. Particle swar optiization is introduced in Section III. Coplexity analysis and siulation results are exained in Section IV and Section V. Section VI concludes the paper. II. SYSTEM MODEL Consider the scenario depicted in Figure 1, where there are M cells, and each cell contains L distributed single-antenna ports connected to each other via high speed counication links, giving M L ports in total. All ports in a cell transit the sae signal siultaneously. It is assued that the transit power of each port can be adjusted independently. The sae RB can be used throughout the network, however at ost one user is allowed to access the sae RB within a cell. A user can counicate with the ports in its dedicated cell, whereas the signals fro other cells are considered as interference. Resource anageent throughout the network is conducted by a central network entity. Let x be the inforation signal for the user in the - th cell, where E{x x n } = δ n and δ n = 1 when = n, and zero otherwise. The coplex-valued coefficients h ln represent the channel gain between the l-th port of the n-th cell and the UE in the -th cell for l = 1,...,L and = 1,..., M. The zero ean circularly syetric additive white Gaussian noise with variance σn 2 for the UE in the -th cell is denoted by n. Each port has its own peak power value given by P l (which can be taken as P network-wide for siplicity) and the transit power for the l-th port in the -th cell is controlled by the power coefficients α l {,1} for BPM, and α l [,1] for. Furtherore, let w l be the coplex beasteering coefficient for the l-th port in the -th cell. Then the received signal of the UE in the -th cell can be written as L y = α l Pl h l w l x + l=1 M n=1,n l=1 L α ln Pln h ln w ln x n +n,. (1) The expression in the first line provides the signal intended to the user in the -th cell whereas the second line contains the interference fro the other cells and also noise. Eventually, the corresponding SINR for the UE in the -th cell can be expressed as SINR (α,w) = L l=1 α l Pl h l w l 2 σn 2+ M n=1,n L l=1 α ln Pln h ln w ln 2, where the vectors α and w respectively represent the set of coefficients for the power coefficients α l and the bea steering coefficients w l. Transission strategy is based on iizing the iniu SINR over all users. This scenario can be forulated as an optiization proble with port power coefficients and beasteering coefficients as the optiization variables α,w s.t. in SINR (α,w) α {,1} LM for binary power anageent, and α,w s.t. in SINR (α,w) α [,1] LM for continuous power anageent. Both probles are nonconvex and it can be difficult to solve on the search space (α,w) as the nuber of cells increase. Since a port utilizes a single antenna, its bea steering coefficient is coposed of a coplex-valued scalar. In order to siplify the above optiization proble, it is assued that bea steering coefficients are chosen to atch the phases of the channel between the ports and their intended UEs (2) w l e j h l l,. (3) Although under this assuption the solution becoes suboptial, it has been shown that this approach iizes the SINR when the interference power is assued to be fixed [4].

3 In the new forulation, the proble is reduced to port selection for BPM and adjusting the power levels of the ports for, i.e., α in (α), s.t. α {,1} LM, for BPM (4a) α in (α), s.t. α [,1] LM, for. (4b) Clearly, proble (4a) is a non-linear binary-integer prograing proble and proble (4b) can be shown to have a ulti-odal cost surface. By using conventional optiization algoriths, i.e., convex optiization, the first proble can only be solved by using integer-relaxation which will possibly yield a suboptial solution. Furtherore, since the second proble is ulti-odal, a conventional solver ay get stuck at a local optiu solution. In order to overcoe these probles we propose to use Particle Swar Optiization (PSO) as a solver. III. PARTICLE SWARM OPTIMIZATION PSO [8] is a stochastic evolutionary optiization algorith which iics the behavior of swars (e.g., bees). Soe of the proinent features of PSO are ease of ipleentation, low coputational coplexity, and ability to find the global solution in a ultiodel proble. These features akes PSO a good candidate to solve the probles at hand. The PSO algorith is initialized with a population of rando candidate solutions, x i, naely particles. PSO finds optial regions of coplex search spaces through the interaction of individuals in the population of these particles. Each particle is initially assigned a randoized velocity, v i, and is iteratively oved through the proble space. It is attracted towards the location of the best fitness achieved so far by the particle itself, p i, and by the location of the best fitness achieved so far across the whole population, g [9]. The paraeters, c l,c g - called acceleration coefficients - control the behavior and efficacy of the algorith and are chosen heuristically. The variables r l and r g are rando positive nubers, drawn fro a unifor distribution. The pseudocode of the algorith is given below: Initialize population Repeat for i=1 to population size pick rando nubers, r l,r g U(,1) for d=1 to diension size update particle s velocity: v i,d wv i,d +c l r l (p i,d x i,d )+c g r g (g d x i,d ) update particle s position: x i x i +v i if f(x i ) > f(p i ) update particle s best known position: p i x i if f(p i ) > f(g) update the population best known position: g p i Until stopping criterion is satisfied In our optiization probles, we use binary PSO [1] for binary power anageent whereas traditional PSO is used for continuous power anageent. We use 6 swars and 1 swars for population size in two-cell cluster and seven-cell cluster, respectively. We take the inertia coefficient as w = 1, and acceleration coefficients as c l =.85 and c g = 2. IV. COMPLEXITY ANALYSIS In this Section, coplexity of the proposed ethods will be analyzed. In the case of binary power anageent, exhaustive search is done by searching all possible port states and has a coputational coplexity O(2 LM ), hence for large L and M this ethod is inefficient. By considering the algorith in Section III, particle swar optiization has a coputational coplexity in the order of O(SLMN) where S, L, M and N denote the population size, nuber of ports in each cell, nuber of cells and nuber of iterations done until stopping criterion is satisfied, respectively. For the stopping criterion, in, iterations continue until all SINR values are contained in a neighbourhood of.5 db, whereas in BPM, iterations continue until no change in the particle positions is observed for 2 consecutive iterations. However, it should be noted that the coplexity of BPM is higher than since the nuber of iterations and coputational coplexity of the update equation in BPM is higher. When there is one swar, update equation has 6 ultiplications in whereas there are 7 ultiplications and 1 exponentiation (coes fro the sigoud function in probabilistic update equation [1]) in BPM, which increases coputational coplexity. For the case of two-cell network, it is found that the average nuber of iterations for BPM and are 53 and 21, respectively, whereas for the seven-cell cluster, the average nuber of iterations for BPM and are 97 and 27, respectively. V. PERFORMANCE EVALUATION We analyze the perforance of the proposed ethod for a network of M hexagonal cells and L = 7 ports per cell through Monte Carlo siulations. One of the ports is located at the center of the cell, and others are located uniforly at a distance of 2/3 of the circuradius (r c ) fro the center, in order to increase the coverage of the cell. Ports can either be set off, or they can transit at a fixed power level of P for BPM, or they can transit at an adjustable power level in the interval [,P ] for the. For the siulations we consider a single RB throughout the network. As it is stated above, at ost one UE can use this RB in a cell, therefore M UEs are considered network-wide, and these UEs are located randoly in each cell for each channel realization. For the port-to-ue link, a Rayleigh fading channel with log-noral shadowing and path loss coponents as in [11] are considered. The coplex channel gains are h ln = ρ(dln )s ln h ln, whereρ( ) is the path loss function given below, d ln is the distance between the l-th port of the n-th

4 cell and the user in the -th cell, s ln represents log-noral shadowing with db ean and 8 db standard deviation, and h ln denotes the fading effect and has a coplex Gaussian distribution with zero ean and unit variance. For the suburban scenario described in [11], the distance between base stations is 1299, and the noise power is -114 db. The path loss function considered here is ρ(d ln ) = 1 ( log 1 (d ln)) where carrier frequency is taken as 2 GHz, antenna ports are at a height of 15, and each UE is assued to have 1.5 elevation. In order to assess the optiality of the proposed algorith based on PSO, we first consider a two-cell sub-urban acrocell scenario. One UE is randoly dropped in each cell. Each cell has L = 7 ports. Miniu SINR in the cluster is iized by the PSO based algorith for both binary and continuous power anageent scenarios given respectively by the probles (4a) and (4b). For coparison purposes, exhaustive search is also perfored for binary power anageent, which searches the best result out of 2 14 port state vectors. The results depicted in Fig.s 2 and 3 are averaged over 3 realizations. Fig. 2 copares the resulting SINR levels with respect to the iu port power liit P for both the BPM and schees. It can be seen that for lower P values, both the BPM and results yield alost the sae perforance. This is the noise-liited region in which one does not gain uch with power anageent due to negligible interference fro other cells. As power liit increases, e.g., higher than 3 db, becoes to outperfor BPM, and after approxiately P = 55 db a noise floor effect is observed liiting the perforance of BPM. The region P 3 db can be considered as the interference liited region, in which interference fro other users doinate the AWGN in the channel. In this region, rather than just switching the ports on and off (BPM), adjusting the transission power of the () appears to perfor better. As it can be seen fro Fig. 2 at P = 4 db, the UE with iniu SINR gains 5 db by. Fro Fig. 2, it should be noted that for the BPM schee, PSO perfors alost the sae as exhaustive search, verifying the optiality of the PSO algorith. This is an iportant aspect of PSO since PSO can optiize coplex probles with lower coputation tie. Obtaining to the optiu solution of the scenario is difficult by evaluating with exhaustive search, and it is not possible to find the global optiu by using a conventional optiization algorith. Therefore we cannot copare the result with PSO to that of an global optiizer. In Fig. 3, the average transit power per port vs. the iu port power liitp is copared for both the BPM and schees. According to the figure, both schees perfor siilar, and they both require siilar total transit power per port for the sae P values. In other words, for the (5) iniu SINR (db) BPM (port selection) BPM (exhaustive search) P (db) Fig. 2: Largest iniu SINR achieved by binary power anageent and continuous power anageent for a two-cell cluster. Solid, dashed and dotdashed line represents BPM (port selection), and BPM (exhaustive search), respectively. sae total transit power per port levels, yields higher iniu SINR values as copared to BPM. This result deonstrates the advantage of using in the interference liited region. For exaple, for P = 6 db, although requires the sae average transit power per port, it results in ore than 15 db gain in SINR as copared to BPM. Siilar to Fig. 2, Fig. 3 also deonstrates that PSO perfors alost the sae as exhaustive search for the BPM schee, verifying the optiality of solution of the PSO algorith. When we increase the scale of the proble, the advantage of over BPM becoes ore apparent. In the next set of siulations we consider a sub-urban acro-cell scenario with 7 cells and 7 ports per cell with the sae settings as in the above study. Fig. 4 depicts that the curve for and BPM are separated for alost all P values. Furtherore, Fig. 5 shows that for all P values even though and BPM require the sae P level to obtain the sae total transit power per port, outperfors BPM in ters of the iniu SINR in the network. Considering a range for P fro -1 db to 3 db as a typical operation condition, one can deduce that for a typical cellular counications scenario with oderate nuber of cells, is ore advantageous than BPM. VI. CONCLUSION In this paper, a coordinated ulti-cell distributed antenna syste is considered. In order to increase the coverage and throughput of the network, instead of eploying a single base station in a cell, a nuber of ports are distributed throughout the cell which transit the sae signal. Two transission schees are investigated; either the ports are switched on and off (Binary Power Manageent, BPM)

5 6 4 average transit power per port (db) BPM (port selection) BPM (exhaustive search) average transit power per port (db) BPM P (db) Fig. 3: Average transit power per port achieved by binary power anageent and continuous power anageent for a two-cell cluster. Solid, dashed and dotdashed line represents BPM (port selection), and BPM (exhaustive search), respectively P (db) Fig. 5: Average transit power per port achieved by binary power anageent and continuous power anageent for a seven-cell cluster. Solid and dashed line represents BPM and, respectively. iniu SINR (db) BPM P (db) Fig. 4: Largest iniu SINR achieved by binary power anageent and continuous power anageent for a seven-cell cluster. Solid and dashed line represents BPM and, respectively. with a iu transit power liit per port or they are allowed to transit with variable power (Continuous Power Manageent, ). It has been deonstrated that for a sall sized network, outperfors BPM especially in the interference-liited region, where interference to a user originates fro the ports of other cells. It is also shown that, for a ore coplex network with a higher nuber of cells, perfors better than BPM under practically eaningful conditions. Proper power anageent introduces an iportant gain to syste perforance, which can be considered very proising for next generation networks. It is observed that the ipleentation coplexity of when using PSO is lower than that of BPM, aking ore advantageous than BPM in both perforance and also coplexity aspects. REFERENCES [1] S. Venkatesan A. Lozano, and R. Valenzuela, Network MIMO: overcoing intercell interference in indoor wireless systes, Proc. 41st Asiloar Conf. Signals, Systes and Coputers, pp , Nov. 27. [2] R. Bendlin, V. Chandrasekhar, R. Chen, A. Ekpenyong, and E. Onggosanusi, Fro hoogeneous to heterogeneous networks: a 3GPP long ter evolution rel. 8/9 case study, Proc. 45th Annu. Conf. Inforation Sciences and Systes (CISS), pp. 1-5, Mar [3] T. Ahad, R. H. Gohary, H. Yanikoeroglu, S. Al-Ahadi, and G. Boudreau, Coordinated port selection and bea steering optiization in a ulti-cell distributed antenna syste using seidefinite relaxation, IEEE Trans. Wireless Coun., vol. 11, no. 5, pp , May 212. [4] W. Choi and J. Andrews, Downlink perforance and capacity of distributed antenna systes in a ulticell environent, IEEE Trans. Wireless Coun., vol. 6, no. 1, pp , Jan. 27. [5] L. Vanderberghe and S. Boyd, Seidefinite prograing, SIAM Rev., vol. 38, pp , Mar [6] Z. Q. Luo, W. K. Ma, A. C. So, Y. Ye, and S. Zhang, Seidefinite relaxation of quadratic optiization probles, IEEE Signal Process. Mag., vol. 27, pp. 2-34, May 21. [7] M. Grant and S. Boyd, CVX: Matlab software for disciplined convex prograing, version 1.21, Jan Available: [8] J. Kennedy and R. Eberhart, Particle swar optiization, Proc. IEEE Int. Conf. Neural Networks, Piscataway, NJ, USA, vol. 4, pp , [9] I. C. Trelea, The particle swar optiization algorith: convergence analysis and paraeter selection, Inforation Processing Letters 85, pp , 23. [1] F. V. D. Bergh, An analysis of particle swar optiizers, Ph.D. dissertation, University of Pretoria etd, Pretoria, South Africa, 21. [11] International Telecounication Union (ITU), Guidelines for evaluation of radio interface technologies for IMT-Advanced, TR M , ITU-R, Dec. 29. Available: