A Multi-objective Approach to Indoor Wirele Heterogeneou Networ Planning Sotirio K. Goudo 1, David Plet 2, Ning Liu 2, Luc Marten 2, Wout Joeph 2 1 Radiocommunication Laboratory, Department of Phyic, Aritotle Univerity of Thealonii, Thealonii, Greece 2 bwica, Ghent Univerity / imind, Dept. of Information Technology, Gaton Crommenlaan-8-box-201, B-9050 Ghent, Belgium Abtract We preent a multi-objective optimization approach for indoor wirele networ planning ubject to contraint for expoure minimization, coverage imization and power conumption minimization. We conider heterogeneou networ coniting of WiFi Acce Point (AP) and Long Term Evolution (LTE) femtocell. We propoe a deign framewor baed on Multi-objective Biogeography-baed Optimization (MOBBO). The reult of the propoed method indicate the advantage and applicability of the multi-objective approach. Index Term Indoor wirele networ planning, heterogeneou networ, expoure minimization, biogeographybaed optimization, Pareto optimization, multi-objective optimization. I. INTRODUCTION Wirele networ deign problem are in general multiobjective. Common deign objective include expoure minimization, coverage imization, power conumption minimization and cot reduction [1-6]. Multi-objective Evolutionary Algorithm (MOEA), which mimic behaviour of biological entitie, are uitable optimization technique for olving the above-decribed problem. Biogeography-baed optimization (BBO) [7] i a recently introduced evolutionary algorithm, which i baed on mathematical model that decribe how pecie migrate from one iland to another, how new pecie arie, and how pecie become extinct. The way the problem olution i found i analogou to nature way of ditributing pecie. In the BBO approach there i a way of haring information between olution [7], imilar to the other evolutionary algorithm. Additionally, BBO ha ome unique feature, which are different from thoe found in the other evolutionary algorithm. Thee difference can mae BBO outperform other algorithm [7]. In thi paper, we ue a multi-objective extenion of the BBO algorithm (MOBBO) combined with the concept of nondominated raning found in Nondominated Sorting Genetic Algorithm-II NSGA-II [8]. Therefore, we apply both the above-mentioned multi-objective evolutionary algorithm to the heterogeneou wirele networ planning problem. With heterogeneou, we mean a combination of different wirele technologie, namely WiFi AP and Long-Term Evolution (LTE) femtocell. We define thi problem a one with three objective function. We conider an objective function for expoure minimization, coverage imization, and power conumption minimization. The advantage of our approach are clearly hown for multi-objective networ planning problem. II. PROBLEM DEFINITION We conider the ground plan of an office building in Ghent, Belgium to which the networ planning optimization will be applied (Fig. 1). It i a 90 m (length) by 17 m (width) office environment. The red circle indicate point that do not require coverage (e.g. toilet, elevator haft and itchen). The wall material i layered drywall indicated in Fig.1 with brown line, while the gray line indicate concrete. Fig. 1. Map of the ground plan the office building where the networ planning i applied. WiFi (IEEE 802.11n) acce point at 2.4 GHz and LTE bae tation at 2.6 GHz will be intalled at a ubet of 425 poible location in the building. The aumed receiver antenna gain i 0 dbi and a received power of 68 dbm i required to obtain a capacity of 54 Mbp. There are alo 425 receiver location for which coverage and expoure level will be calculated. The PL will be modeled according to two-lope model propoed by the IEEE 802.11 TGn channel model group [9]. The networ-planning problem i to find the AP characteritic (poition and Equivalent Iotropically Radiated Power (EIRP)) in uch a way that the power conumption i minimized, the human expoure to electric field i minimized, and the coverage i imized. All the above objective are ubject to contraint regarding coverage and expoure. Furthermore, ince we conider a heterogeneou networ, at leat one LTE femtocell hould be preent. The coverage requirement depend on the capacity in Mbp and therefore on the receiver enitivity that i required in each cae.
Such a problem i inherently multi-objective. It can be defined by the minimization of the objective function given below: 1 ( ) on f x = N AP minimize power conumption (1) Col ( x ) f2 ( x ) = 100 Ctot ( x ) imize coverage (2) f3 ( x ) = Emedian ( x ) minimize expoure (3) ubject to: g ( x) = f 1 2( x) C coverage (4) g ( x) = f 2 3( x) E expoure (5) ( ) on g x = N 3 LTE 1 at leat one LTE femtocell i preent(6) on where N AP i the total number of bae tation (both LTE on and WiFi) that i turned on, N LTE the number of turned on LTE femtocell, C the coverage percentage required (0-100), E the deired electric-field imum median value (V/m), E median the calculated electric field median value (V/m), C ol i the number of reception point covered by the current olution in thi indoor environment, and C tot i the total number of all reception point in the building floor. The above-mentioned problem can be olved uing a multi-objective evolutionary algorithm. It i an integerprogramming problem, for which everal different olution exit. III. BIOGEOGRAPHY-BASED OPTIMIZATION (BBO) The mathematical model of Biogeography are baed on the wor of Robert MacArthur and Edward Wilon in the early 1960. Uing thi model, they have been able to predict the number of pecie in a habitat. The habitat i an area that i geographically iolated from other habitat. The geographical area that are well uited a reidence for biological pecie are aid to have a high habitat uitability index (HSI). Therefore, every habitat i characterized by the HSI which depend on factor lie rainfall, diverity of vegetation, diverity of topographic feature, land area, and temperature. Each of the feature that characterize habitability i nown a uitability index variable (SIV). The SIV are the independent variable while HSI i the dependent variable. Therefore, a olution to a D-dimenional problem can be repreented a a vector of SIV variable[ SIV1, SIV2,... SIV D ], which i a habitat or iland. The value of HSI of a habitat i the value of the objective function that correpond to that olution and it i found by ( ) 1 2 HSI = F habitat = F( SIV, SIV,... SIV D ) (7) Habitat with a high HSI are good olution of the objective function, while poor olution are thoe habitat with a low HSI. The habitat with high HSI are thoe that have large population and high emigration rate μ. For thee habitat, the immigration rate λ i low. The immigration and emigration rate are function of the number of pecie in the habitat. Thee are given by μ = E S λ = I 1 S where I i the imum poible immigration rate, E i the imum poible emigration rate, i the number of pecie of the -th individual, and S i imum number of pecie. BBO ue both mutation and migration operator. The application of thee operator to each SIV in each olution i decided probabilitically. The mutation rate m of a olution S i defined to be inverely proportional to the olution probability and it i given by 1 P ms ( ) = m P (8) (9) (10) where P i the probability that a habitat contain S pecie and m i a uer-defined parameter. More detail about the BBO algorithm can be found in [7, 10]. A. Multi-objective Biogeography-baed Optimization (MOBBO) Multi-objective BBO algorithm extend the original BBO algorithm for olving MOOP. The reult found by an evolutionary algorithm are alo called Pareto et approximation or approximation et. MOBBO i the hybridization between BBO and ue concept common in other MO algorithm lie NSGA-II. The MOBBO algorithm i outlined below: 1) Initialize the BBO control parameter. Map the problem olution to SIV and habitat. Set the habitat modification probability P mod, the imum immigration rate I, the imum emigration rate E, the imum migration rate m and the elitim parameter p (if elitim i deired). 2) Initialize a random population of NP habitat (olution) from a uniform ditribution. Set the number of generation G to one. 3) Evaluate objective function and contraint function value. 4) Apply non-dominated raning to NP habitat. Compute (HSI) for each habitat of the population baed on nondominated raning. 5) Map the HSI value to the number of pecie S, the immigration rate λ, the emigration rate μ for each olution of the population.
6) Generate a new child population of NP habitat, which i originally the ame a the parent population. 7) Apply the migration operator for each member of the child population baed on immigration and emigration rate uing (8) and (9). 8) Update the pecie count probability uing ( ) P 1P 1 1P 1 S S P λ μ μ + + λ = + + + < ( λ + μ) P + λ 1P 1 S = S (11) where P i the pecie count probability matrix. 9) Apply the mutation operator to each member of the child population according to (10). 10) Evaluate objective function and contraint function value. 11) Merge original parent population with new child population to form a population 2NP habitat. 12) Apply non-dominated raning to 2NP habitat. Select NP non-dominated habitat, which are the new parent population. The non-dominated raning refer to orting of the vector regarding non-domination. Thi orting approach i called Fat Non-dominated Sorting Approach and i decribed in detail in [8]. 13) Repeat tep 5 until the imum number of generation G i reached. To decreae the population bac to the original ize a orting technique i applied. Thi ue the concept of Crowding Ditance (CD), which approximate the crowdedne of a vector in it non-dominated et lie NSGA-II [8]. IV. NUMERICAL RESULTS We conider 425 different poible AP poition placed at a height 200 cm above ground level and the receiver i aumed at a height 100 cm above ground level (Fig. 1). WiFi Ap and LTE femtocell have different EIRP value. Therefore, the total number of the optimization variable i 850. The firt 425 variable could have a value of 0 (no AP turned on), 1 (WiFi AP turned on), or 2 (LTE femtocell turned on). The range of the poible EIRP value i from 0 to 20 dbm (100 mw) for both the WiFi and the LTE AP. We will compare the reult from three different networ planning deign cae. The cae will be for High Definition (HD) video coverage, and Standard Definition (SD) video coverage. We compare MOBBO with NSGA-II. The algorithm are executed 20 time. The bet reult are compared. Both algorithm are initialized with a population ize of 200 and run for 1000 iteration. In order to chooe the bet-compromied olution from the Pareto Front a uitable deciion maer ha to be ued. The fuzzy et theory ha been ued a a deciion maer in everal application in the literature lie tranportation planning, vendor election, etc. [11, 12]. The atifaction degree of each objective function i repreented by a linear fuzzy memberhip function expreed a μ 1 if z z min z z min = if z min < z < z z z 0 if z z (12) min where z the value of -th objective function, z, z are the minimum and imum value of the -th objective function repectively. The bet-compromied olution i found by uing n 1 obj = μ n (13) obj = 1 where n obj i the number of objective and i the degree of atifaction. For each Pareto Front point, we calculate the value of. The point with the imum value i the bet-compromied olution. The firt example i that of cae 1, which aume High Definition (HD) video coverage (receiver enitivity et to -68 dbm and -68.1 dbm for WiFi and LTE repectively) for all point with coverage C = 99%, E = 0.25 V / m. The expoure i low in order to tet the algorithm' performance on demanding cae. The 3D Pareto front for thi cae found by both algorithm are hown in Fig. 2 and Fig. 3 repectively. Each point of the Pareto front denote a feaible networ configuration. We notice that NSGA-II obtained Pareto front with a larger number of AP than MOBBO. The tradeoff for thi cae i the lower electric field value. Fig. 2. Pareto front for cae 1 found by MOBBO
Fig. 3. Pareto front for cae 1 found by NSGA-II (b) The final example preent a networ layout where 25Mpb video (SD) i required for all point. The receiver enitivity i et to -79 dbm and -77.1 dbm for WiFi and LTE repectively. The contraint for thi cae are C = 99%, E = 0.1 V / m. For thi cae we aume that a LTE femtocell i alway preent with EIRP=10 dbm at a pecific poition. The Pareto front found are hown in Fig. 4 and Fig.5. The AP range for MOBBO i from 3 to 7. The NSGA-II for the ame expoure and coverage range obtained olution that range from five to eight. Fig. 5. Algorithm TABLE I. Pareto front for cae 2 found by NSGA-II BEST COMPROMISED SOLUTIONS Cae 1:HD video coverage C = 99%, E = 0.25 V / m Numbe r of AP Coverag e (%) Emedian (V/m) Std. Dev. MOBBO 5 100 0.113 0.142 NSGA-II 13 100 0.037 0.045 Cae 2:SD video coverage C = 99%, = 0.1 / Fig. 4. Pareto front for cae 2 found by MOBBO Algorithm Numbe Coverag Emedian Std. Dev. r of AP e (%) (V/m) MOBBO 4 100 0.030 0.058 NSGA-II 6 100 0.024 0.043 Table I report the bet-compromied olution found by both algorithm in the two cae. We notice that for cae 1 MOBBO obtained the olution with the lowet number of AP. The olution found by NSGA-II i that with the lowet electric-field value. The reult for cae 2 differ. The number of AP i lower than that of the other cae. A could be expected, the lower martphone (Wifi and LTE) receiver enitivity reult in fewer AP needed. We notice that the olution obtained by MOBBO i the one with the lowet number of AP. The olution obtained by NSGA-II i the one with the lowet expoure value. We notice that the E-field tandard deviation value are lower for lower expoure. Thi implie that the E-field ditribution i more homogeneou for thee cae. We alo notice that the olution obtained by NSGA-II are the one with the lower tandard deviation value. The tradeoff for lower AP number (thu lower power conumption) i higher field expoure value and larger diperion of E-field value.
The networ layout and the E-field ditribution for the bet configuration obtained by MOBBO i hown in Fig 6a-6b. In cae 2 (Fig. 6b), the LTE femtocell (EIRP of 10 dbm) and the WiFi AP are indicated. It i evident that increaing the number of AP reult to lower expoure value and more homogeneou E-field ditribution. MOBBO produce better reult than NGSA-II for the ame population ize and for the ame number of generation. The numerical reult obtained by multi-objective algorithm allow the networ engineer the poibility of electing from a et of optimal olution. All the above algorithm can be eaily applied to different networ planning problem. In our future wor, we intend to examine different networ configuration uing different contraint. Fig. 6. Networ layout of bet-compromied olution found by MOBBO a) Cae 1 b) Cae 2. (WiFi AP = dot, LTE femtocell = hexagon, EIRP i indicated within dot or hexagon). V. CONCLUSION The problem of heterogeneou (LTE and WiFi) networ planning for optimal coverage with the lowet power conumption and the lowet expoure i addreed in thi paper. An application for a realitic office environment i invetigated leading to reduction of cot and expoure when multi-objective algorithm are applied. We propoed a multi-objective algorithm baed on BBO and the concept of non-dominated raning. MOBBO ha been compared againt NSGA-II for the networ planning problem. REFERENCES [1] J. Zhang, X. Jia, Z. Zheng, Y. Zhou, Minimizing cot of placement of multi-radio and multi-power-level acce point with rate adaptation in indoor environment, IEEE Tranaction on Wirele Communication, 10 (2011) 2186-2195. [2] W. Li, Y. Cui, X. Cheng, M.A. Al-Rodhaan, A. Al-Dhelaan, Achieving proportional fairne via AP power control in multi-rate WLAN, IEEE Tranaction on Wirele Communication, 10 (2011) 3784-3792. [3] I. Sohn, S.H. Lee, J.G. Andrew, Belief propagation for ditributed downlin beamforming in cooperative MIMO cellular networ, IEEE Tranaction on Wirele Communication, 10 (2011) 4140-4149. [4] D. Cao, S. Zhou, Z. Niu, Improving the energy efficiency of two-tier heterogeneou cellular networ through partial pectrum reue, IEEE Tranaction on Wirele Communication, 12 (2013) 4129-4141. [5] D. Cao, S. Zhou, Z. Niu, Optimal combination of bae tation denitie for energy-efficient two-tier heterogeneou cellular networ, IEEE Tranaction on Wirele Communication, 12 (2013) 4350-4362. [6] D. Plet, W. Joeph, K. Vanhece, L. Marten, Expoure optimization in indoor wirele networ by heuritic networ planning, Progre In Electromagnetic Reearch, 139 (2013) 445-478. [7] D. Simon, Biogeography-Baed Optimization, IEEE Tranaction on Evolutionary Computation, 12 (2008) 702-713. [8] K. Deb, A. Pratap, S. Agarwal, T. Meyarivan, A fat and elitit multiobjective genetic algorithm: NSGA-II, IEEE Tranaction on Evolutionary Computation, 6 (2002) 182-197. [9] V. Erceg, Schumacher, L., et al.. TGn Channel Model, IEEE p802. 11 Wirele LAN Doc. IEEE802.11-03/940r4., (2004). [10] H. Ma, D. Simon, M. Fei, Z. Chen, On the equivalence and difference of evolutionary algorithm, Engineering Application of Artificial Intelligence, 26 (2013) 2397-2407. [11] M. Farina, P. Amato, A fuzzy definition of "optimality" for manycriteria optimization problem, IEEE Tranaction on Sytem, Man, and Cybernetic Part A:Sytem and Human., 34 (2004) 315-326. [12] D. Peidro, P. Vaant, Tranportation planning with modified S-curve memberhip function uing an interactive fuzzy multi-objective approach, Appl. Soft Comput. J., 11 (2011) 2656-2663.