Resource Allocation for OFDMA-Based Relay Assisted Two-Tier Fetocell Networks Aila Tharaperiya Gaage, Nandana Rajatheva, Marian Codreanu Telecounications Field of Study, School of Engineering and Technology, Asian Institute of Technology, Klong Luang, Pathuthani 0, Thailand,, Centre for Wireless Counications, University of Oulu, Finland,, ailapradheep@yahoo.co, rajath@ait.ac.th, rrajathe@ee.oulu.fi, arian.codreanu@ee.oulu.fi Abstract Co-channel interference (CCI is a ajor issue faced by efficient co-channel deployed orthogonal frequency division ultiple access (OFDMA based two-tier fetocell systes. There are several resource allocation echaniss proposed, such as, [] [4], to address this issue. However, none of these ethods have considered eploying relays in order to reduce transit power levels, and hence, reduce CCI with the added advantage of extended coverage. Thus, in this paper, a siple resource allocation echanis, which axiizes the su of the weighted rates (SWR, for relay assisted fetocell systes is proposed. Its ain advantage is the low coplexity achieved by exploiting the characteristics of Lagrangian and utilizing the Newton s ethod. I. INTRODUCTION Fetocell systes have attracted a significant attention due to their proised ability to cater for the high indoor capacity needs [6], [7]. Orthogonal frequency division ultiplexing (OFDM is one of the ost suitable candidates for the physical layer of these systes due its high flexibility. Co-channel deployed fetocell systes provide superior perforance copared to the deployents with dedicated channel assignents. However, co-channel deployents cause CCI between acrocell and fetocell as well as aong the fetocells coplicating the resource allocation for fetocell networks. Nevertheless, resource allocation protocols in these systes should be coputationally very efficient as feto access points (FAP are expected to be siple and cheap [6], [7]. CCI issue could be relaxed by eploying relays in the network with the added advantage of iproved coverage at inbuilding scenarios where frequently encountered walls significantly attenuate the transit signals. Specially, relays provide a considerable perforance boost when the high priority users have weak direct links to their destinations. In this scenario, higher transit power levels can also be used for achieving the sae weighted rate. However, increased CCI will severely degrade the signal to interference plus noise ratio (SINR levels of the coexisting acrocell network. Furtherore, as these self configurable FAPs are installed by the custoers to their own interest, setting the transit power levels to be low would be ore precautionary in order to protect the counication of the coexisting networks. Thus, eploying This research has been funded in part by the LOCON Project, TEKES, Finland and the Acadey of Finland grant 800. relays would be a better option copared to using higher transit power levels. Several resource allocation algoriths have already been proposed for OFDMA based two-tier fetocell systes, such as, [] [4]. CCI issue can be relaxed to a certain extent by eploying the open access schee proposed in []. However, the success of this echanis depends on the availability of sufficient backhaul capacities and the ability to synchronize the FAP with acrocell base station (BS over an IP backhaul. Authors of [3] have proposed a hybrid frequency assignent where the subcarriers are assigned depending on the location of the fetocell with respect to the acrocell BS. This ethod is less efficient as the fetocells near the acrocell BS are forced to use dedicated channel assignents. Resource allocation based on identifying the quietest bandwidths and the quietest subcarriers in order to assign the best subcarriers to fetocell users is proposed in [4]. Authors of [] have proposed a distributed resource allocation protocol for axiising the SWR subjected to the protection of acrocell users, and the ethod in [8] allocates subcarriers and power separately as it reduces the coplexity of the resource allocation protocol. To the best of our knowledge, there are no resource allocation ethods which have been proposed for relay assisted fetocell networks at the presence of CCI. Therefore, in this paper, we propose a siple resource allocation ethod for OFDMA based relay assisted fetocell systes. II. SYSTEM MODEL An OFDMA based down link (DL of a co-channel deployed fetocell network coexisting with a acrocell network as shown in Fig. is considered. M acro users and M feto users are in the OFDM band with N subcarriers. Macrocell and the fetocell allocate their resources individually as it reduces unnecessary signalling overheads. Furtherore, it is assued that the relay selection has already been done. Each counication link fro FAP to the th feto destination receiver (FD consists of a direct link over the subcarrier k d, and it ay be assisted by at ost one relay link, which uses the subcarrier k r, to transit the signal fro the relay (FR to FD. Each user is assued to use only one link for his counications. These relays are aplify and forward relays while their transit power levels are considered
Fig. : A fetocell syste coexisting with acrocell network. as variables. In this setup, FAP transits during st OFDM sybol period and then the relays forward the received signals to the destinations during next OFDM sybol period in order to avoid causing inter carrier interference due to the processing tie at the relay nodes. However, this protocol is still efficient as it utilizes all the subcarriers over every OFDM sybol period. Finally, FD uses axial ration cobining (MRC to cobine the received signals over these two links. The set of subcarriers allocated for the th user is Ω k d,,k r, and his axiu achievable error free data rate over the relayed link can be expressed as R Δf log + P d, SR P r, P d, α SR + P r, α + +P d, ( where Δf is the bandwidth of a OFDM subcarrier and, P d, and P r, are the transit power levels at FAP over subcarrier k d, and at FR over subcarrier k r, respectively. SR, and are given by α SR h SR + Q R k d,, α h + Q D k r, h (3 + Q D k d, where h SR and h are the channel gains of FAP FR and FAP FD links over the subcarrier k d, respectively, and h is the channel gain of FR FD link over subcarrier k r,. Q R k and QD k are the CCI received by FR and FD fro acrocell network over the k th subcarrier respectively. N 0 is the single sided power spectra density of additive white Gaussian noise. The objective of the resource allocation is to achieve the highest SWR. Thus, the resource allocation proble can be stated as follows, ax M ( w R (4 Subjected to b kd, P d, SU b kd, I kd,,,..., M (5 M b kr, P r, α RU b kr, I kr,,,..., M (6 M (P d, + P r, P T (7 P d, 0, P r, 0,,..., M (8 Ω,..., N, and Ω Ω n, n. (9 where w is the weight of th user, b k if k th subcarrier is occupied by the acrocell network, otherwise b k 0. SU and RU are defined as SU h SU k d, and RU h RU k r,. h SU k d, and h RU k r, are the channel gains between FAP and the acro user who receive signal over subcarrier k d,, and between FR and the acro user who receive signal over subcarrier k r, respectively. I k is the acro user s CCI threshold for k th subcarrier. P T is the total power budget available for the DL counications of the fetocell network. Since it is not possible to allocate a fraction of an OFDM subcarrier to a user, the feasible set is not convex. Furtherore, the objective function is also non-convex. Thus, the proble stated in (4 (9 is a non-convex optiization proble. Therefore, finding the optial solution requires an exhaustive search through all the possible allocations of the subcarriers (at least (M (M + N cobinations aong M users and their relays. Since that approach is not practical for an OFDM syste with a large nuber of subcarriers, we propose a suboptial approach where the optiization proble is divided into two sub-probles as follows, Sub proble : Subcarrier allocation Allocating subcarriers assuing an infinite aount of transit power and no interference constraints. Sub proble : Power allocation Power allocation for the given subcarrier distribution subjected to (5 (8. The power allocation sub-proble is solved first and then the heuristic algorith for allocating subcarriers is explained. III. POWER ALLOCATION SUB-PROBLEM Since P d, SR and P r, are the SINR s of FAP FR and FR FD links respectively, the rate given in ( can be approxiated at high SINR values as R log + P d, SR P r, P d, SR + P r, + P d,. (0 The factor Δf has been ignored as it is coon for all the users. Furtherore, due to the approxiation ade, (0 is not defined when siultaneously P d, 0and P r, 0. However, in this case, throughput ust be zero as well. Thus, R is redefined as log + P d,α SR Pr,α P d, + P α SR d, α +Pr,α R :(P d,,p r, (0, 0 0 : Otherwise (
Then, R and the objective function, U M w R, are concave functions. The proof is given in Appendix A. The Lagrangian for the power allocation sub-proble, axiizes U subjected to (5 (8, can be written as L(P, λ, γ,μ U +μ M M + M [ ] M Pd, + P r, + [ γkd, P d, + γ P ] kr, r, μpt b kr, λ kr, (P r, α RU I kr,. b kd, λ kd, (P d, α SU I kd, ( where λ, γ and μ are the dual variables. μ is a scalar while λ and γ are N vectors with λ k and γ k as the eleents of those two vectors respectively. P is a N vector with P d, and P r, as its eleents. Since the prial proble is convex, Karush-Kuhn-Tucker (KKT conditions guarantee the point (P, λ, γ, is a prial and dual optial point with zero duality gap when it is prial feasible and it satisfies the following conditions,..., M,[9] b kd, λ k d, SU γk d, + (Pd,,P r,(pd,,p r, (3 P r, b kr, λ k r, RU γk r, + (Pd,,P r,(pd,,p r, (4 b kd, λ k d, (Pd,α SU I kd, 0 (5 b kr, λ k r, (Pr,α RU I kr, 0 (6 γk d, Pd, 0, γk r, Pr, 0 (7 λ k 0, γk 0, k,..., N. (8 Furtherore, (3 and (4 can be rewritten as ( (Pd,,P r,(pd,,p r, (9 + b kd, λ k d, SU γk d, ( P r, (Pd,,P r,(pd,,p r, (0 + b kr, λ k r, RU γk r, Since R s are concave non-decreasing functions, ( and ( P r, are onotonically increasing functions of Pd, and P r, respectively. Furtherore, by (3 and (3, it is clear that these functions are correlated and their initial values are ( ( li (Pd,,P r,(0,0 P d, 0 Pr,0 w ( ( P r, Pr,0 A. Analysis on the Power Levels Case : ( ( : if Pd, 0 +P d, α w α (Pd,,P r,(0,0 Case : ( (Pd,,P r,(0,0 If Pd, 0, then b k d, λ k d, α SU : Otherwise ( onotonically increases with Pd,.IfPd, > 0, then b kd, λ k d, SU γk d, < 0 and γk d, 0. Thus, b kd, λ k d, < 0. However, b kd, λ k d, cannot be negative. Therefore, our assuption has resulted in a contradiction. Therefore, in this case, Pd, 0and, by ( and following the sae arguent ade for P d,, Pr, 0. < γk d, > 0 by (9 and λ k d, 0. However, this iplies γk d, < 0 and it contradicts with (8. Thus, Pd, > 0. Let Pd, be the required iniu power level to sat- ( isfy either (Pd,,P r,( P d,,0 b kd, Pd, SU I kd,. Therefore, by (3 P d, in arg in b kd, P d, SU I kd,, ( w P d, (3 Case.: ( (Pd, P r,,p r,( P d,,0 By following the sae set of arguents ade in Case, Pr, 0. Thus, Pd, P d, as well. Case.: ( (Pd, P r,,p r,( P d,,0 < Pr, > 0 based on the set of arguents ade under Case. In this scenario, Pd, and P r, should be jointly calculated such that, Pd, is the required iniu power level to satisfy either b kd, Pd, αsu I kd, ( or (Pd,,P r,(pd,,p r, μ, and Pr, is the required iniu power level to satisfy either b kr, Pr,α RU I kr, or ( P r, (Pd,,P r,(p d,,p r,. A bisection water filling algorith which changes the level of /μ can be used for allocating power based on the above cases. The lower bound of /μ is the iniu value of ( (Pd,,P r,(0,0 of all the users and its upper bound is set to the level of /μ resulted when the channel with axiu of ( (Pd,,P r,(0,0 of the users, i.e., worst channel, is filled with the axiu average aount of power. In Case., first Newton s ethod [5] is used for jointly calculating the power levels ignoring the interference constraints. Then the interference constraints are iposed on the calculated power levels. The algorith repeats changing the /μ level toward /. It terinates when the su of power levels allocated based on Case and Case satisfies (7 such that (P T Allocated power/p T P tol, where P tol is the tolerance of the power allocating error. IV. HEURISTIC SUBCARRIER ALLOCATION An infinite aount of DL power budget is assued. Thus, 0, and therefore, each subcarrier will be allocated power or
regardless of the link it is allocated. If a subcarrier is evaluated at a direct link, i.e. as k d,, the aount of power allocated for that subcarrier by Case. is P d, w μ (4 and the resulted weighted rate is w α r d, w log. (5 μ Based on Case. and (3, if a subcarrier is evaluated at FR FD link, i.e. as k r,, the aount of power allocated for that subcarrier, i.e. P r,, should satisfy Pd, (αsr DEN μ w. (6 If we assue the power level already allocated for the corresponding k d, subcarrier by (4 reains unchanged for the siplicity, P r, found by siultaneously solving (4 and (6 is given in (7 shown on top of the next page. Then the contribution to the SWR is r r, w log + P d, SR P r, P d, SR + P r, + P d, w w log μ (8 The evaluated subcarrier is allocated to the position where it results in the axiu weighted rate. Each subcarrier is allocated based on this algorith. V. SIMULATION RESULTS The key paraeters of the syste odel with their definitions are shown in Table I. All the siulations are carried out over Rayleigh faded channels with the path loss being proportional to d η, where d is the distance between BS and users. η is assued to be sae for indoor, indoor to outdoor and, outdoor to indoor counications. All the users are assued to be uniforly distributed. The weights of the feto users are uniforly distributed and noralised to have a unit su. Furtherore, each acro user occupies one subcarrier. TABLE I: Siulation Environent Paraeter Value (unit FFT Size (N 8 Fetocell user s targeted SNR, SNR TF 5 db Macrocell user s targeted SNR, 5 db Single sided power spectra density of noise, N 0-74 db/hz Interference threshold for acro users, It -50 db Path-loss exponent, η -4 Radius of the acro cell 000 Miniu distance to users fro acro BS 50 Radius of the feto cell 40 Miniu distance to users fro feto BS 3 Nuber of acro users, M 50 Nuber of feto users, M 30 P T for the fetocell network is set by P T 0log(M N 0 (d av η +SNR TF (9 Throughput (bps/hz 4 3.5 3.5.5 0.5 0 Su of weighted rates: (Prop. algo. Su of weighted rates: (Optiu 9.5 50 00 50 00 50 0 Interference threshold (db Fig. : Close-to-optiality of the proposed resource allocation algorith with N 4, M and M. Throughput (bps/hz 40 0 00 80 60 40 5,SNR TF 5 5,SNR TF 5 5,SNR TF 5 35,SNR TF 5 35,SNR TF 5 35,SNR TF 5 0 50 00 50 00 50 0 Interference threshold (db Fig. 3: Effect of It, SNR TF and on SWR. All the SNR s are in db. where d av is the average distance to a feto user fro the FAP (i.e..5. The transit power level of the acrocell BS over k th subcarrier (Pk M is the power level required to achieve at the corresponding acro user. Then, P M k 0log(N 0 (d ujk η + (30 where d ujk is the distance between the acrocell BS and the acrocell user who is receiving signal over the k th subcarrier. The optiu values of the SWR calculated through searching over all the possible subcarrier allocations and the values achieved by the proposed algorith in a sall syste are shown in Fig.. According to the siulation results, the SWR achieved by the proposed ethod is only.73% less than the optial value. Thus, in this scenario, proposed ethod has achieved results very close to the optiu case. Fig.3 shows the effect of It, SNR TF and on the SWR. SWR is increased with It as the axiu allowed transit power levels over the subcarriers occupied by the acro users are increased as It increases. In addition to that, when It is very high, the constraint on the interference levels is not active
P r, α P d, SR ( + P d, +(α SR P d, + α ( (α SR +4 ( ( P d, ( SR + + + (α SR ( α + SR +4P d, +α (7 + 4α over ost of the subcarriers, and thus, though It is further increased, SWR does not significantly increase. Furtherore, SWR increases as P T increases with SNR TF according to (9. When increases, P M k values increase according to (30. Thus, CCI introduced to feto users also increases and consequently SWR decreases. The coplexity of the proposed algorith ainly depends on the coplexity of the power allocation algorith as it requires the use of Newton s ethod when power is allocated according to Case.. As a easure of coplexity, we count the nuber of ties the /μ level is changed per resource allocation. This easure reflects the requireent of coputational power at the worst case scenario. According to the siulation results, the average nuber of changing /μ level is less than 4 and it does not significantly chang with It, SNT TF and SNT TM as well. VI. CONCLUSIONS The proposed resource allocation algorith axiizes the SWR of a relay assisted fetocell syste at the presence of cross-tier CCI constraints. This ethod uses a sub-optial approach in order to reduce the coplexity of the technique. Siulation results have verified that it provides results very close to the optial value in sall systes where finding the optiu value via exhaustive search is possible. The ain advantage of this ethod is the low coplexity achieved by exploiting the characteristics of the Lagrangian and utilizing the Newton s ethod to derive a siple power allocation algorith based on bisection water filling algoriths. Furtherore, its coplexity is essentially fixed and thus, the tie-varying nature of the channels and network paraeters do not ake the FAP to require an unexpected large aount of coputational power. Therefore, the proposed resource allocation protocol is an ideal candidate for the fetocell systes. APPENDIX A Let u w R, α SR, α, α 3, P P d, and P P r,. Then, u w (P αα 3 + P α(α + α 3 +P P α α α 3 P DEN (3 u P w P α α DEN, (3 Furtherore, it should be noted that u P r,. u P u P P and u P w P 4 DEN αα 4 3 + P 4 α(α 4 + α 3 +P 3 αα 3 +P P αα α 3 (5α +7α 3 +4P 3 P αα 3 α3 +P P 3 α α(α 3 +3α α 3 +α3+p P αα 3 (33 w P αα P DEN α α (α +α 3 +P α α +P P α(α + α 3 +P α (34 u P P w P α α DEN P P α α +P P α (α + α 3 +P α P 3 α α 3 (35 where DEN (P α + P α (P α + P α + P P α (α + α 3 +P α α 3 (36 Since the diagonal eleents of the Hessian of u are negative and the deterinant of the Hessian is positive ( u can be calculated by eqn.(33-(35, u s are concave functions. Therefore, the objective function, which is a su of concave functions, is also concave [9]. REFERENCES [] H. Claussen, Perforance of acro- and co-channel fetocells in a hierarchical cell structure, in In Proc. IEEE Syp. on Personal, Indoor and Mobile Radio Coun., PIMRC 007, 007, Sept. 007, pp. 5. [] J. Zhang, Z. Zhang, K. Wu, and A. Huang, Optial distributed subchannel, rate and power allocation algorith in OFDM-based twotier fetocell networks, in in Proc. IEEE Veh. Technology Conf. 00 (VTC 00-Spring, Taipei, May 00, pp. 5. [3] I. Guvenc, M.-R. Jeong, F. Watanabe, and H. Inaura, A hybrid frequency assignent for fetocells and coverage area analysis for cochannel operation, IEEE Coun. Lett., vol., no., pp. 880 88, Dec. 008. [4] G. Zhioua, P. Godlewski, S. Haouda, and S. Tabbane, A fetocells ressources allocation schee in OFDM based networks, in in Proc. IEEE nd Int. Conf. on Coun. and Networking (CoNet, Tozeur, Nov. 00, pp. 5. [5] C. Kelley, Solving Nonlinear Equations with Newton s Method. sia, 003, vol.. [6] S. Yeh, S. Talwar, S. Lee, and H. Ki, Wiax fetocells: a perspective on network architecture, capacity, and coverage, IEEE Coun. Mag., vol. 46, no. 0, pp. 58 65, Oct. 008. [7] V. Chandrasekhar and J. Andrews, Fetocell networks: A survey, IEEE Coun. Mag., vol. 46, no. 9, pp. 59 67, Sep. 008. [8] Z. Shen, J. Andrews, and B. Evans, Adaptive resource allocation in ultiuser OFDM systes with proportional rate constraints, IEEE Trans. on Wireless Coun., vol. 4, no. 6, Nov. 005. [9] S. Boyd and L. Vandenberghe, Convex Optiization. Cabridge University Press, 009.