Planning of Relay Station Locations in IEEE (WiMAX) Networks

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1 Ths full text paper was peer revewed at the drecton of IEEE Communcatons Socety subject matter experts for publcaton n the WCNC 010 proceedngs. Plannng of Relay Staton Locatons n IEEE 0.16 (WMAX) Networks Zakha Abchar, Ahmed E. Kamal and J. Morrs Chang Department of Electrcal and Computer Engneerng Iowa State Unversty, Ames, IA 0011, USA E-mal:abcharz, kamal, morrs}@astate.edu Abstract Broadband wreless access networks have receved a tremendous amount of research and development n the recent years. There have also been plot networks deployed n many ctes around the globe. In the IEEE 0.16j standard, Relay Statons (RS) play a promsng role of extendng the range of a Base Staton (BS). Ths archtecture s sutable to areas wth lmted nfrastructure, such as rural areas, snce t s dffcult to nstall many BSs, wth each havng a wred connecton. In ths paper, we present an optmzaton model that fnds the number of RSs and ther locatons to serve a customer base. We also show how our model can be adapted to make the plannng n real-lfe scenaros where there are obstacles, such as mountans and lakes, n the plannng area. I. INTRODUCTION Broadband wreless access networks have gathered a great momentum recently n terms of ndustry support, research and plot network deployment. The group of companes that support the development of the IEEE 0.16 famly of standards, commercally known as the WMAX, are members of the WMAX Forum. The forum oversees the promoton of WMAX through actvtes such as negotatng bandwdth lcensng polces and authorng requrements of nteroperablty tests between equpment from varous vendors. Research n wreless broadband networks has also pcked up actvely n many felds ncludng resource allocaton, relays placement, handover between cells, qualty of servce and others. Also, there are tens or even hundreds of plot networks deployed around the globe to test drve the WMAX technology. Ths paper consders the problem of plannng Relay Staton (RS) locatons n a wreless broadband access network, as n the archtecture proposed n the IEEE 0.16j document [1]. A relay s consdered as a strpped-down verson of a base staton (BS). Whle the BS has drect Internet connectvty, the RS does not. The RS s placed n the network to ncrease the connectvty between BSs and also to extend the coverage of a sngle BS. The RS does ts functons n a cost-effectve way snce t only requres a power source to run, so t could be deployed easly n vrtually any locaton. There are also systems that run relays (or base statons) on solar power [], whch makes the relays a good opton for rural areas. In ths paper, we consder the problem of plannng the locatons of relays to extend the coverage of a sngle BS, as shown n Fg. 1. The locaton of the BS s gven and t has wred connectvty. The RSs are used to extend the range of the BS wthout requrng further wred connectvty due to ts hgher expense especally n certan areas (such as rural areas) that are targeted by WMAX. We could easly put more relays beyond the BS snce they only requre a power source to operate. In our problem, the locaton of the BS s gven, whle the locatons of the RSs need to be determned to provde servce to a gven set of users wth gven demands n a gven area. The objectve of our work s to maxmze the capacty of the network to transport the hghest amount of data subject to meetng the demands of user s traffc, whle mnmzng the requred nfrastructure and coverng the requested area of servce. As a farly reasonable assumpton, we consder that the majorty of the traffc orgnates from, or s destned to the BS; so traffc wll be between the BS and the subscrber statons (SS) or moble statons (MS). Also, there s traffc n the uplnk and downlnk drectons and we consder that more traffc wll go from the BS, across the relays, to the SSs or MSs; that s, the downlnk traffc exceeds the uplnk traffc. Therefore, the down lnks are the bottleneck and ths s why we concentrate on them. Fg. 1. base staton relay staton S,0 r3 S,1 S1,0 r1 S0,0 r S1,1 S, S,3 BS wth relays tree. r are the rates of the lnks. We formulate the problem nto a mxed nteger lnear program (MILP). The optmzaton formulaton produces the locatons of the RSs and the rates on each lnk. The papers before us model the nterference extensvely. But they don t go nto detals on the capacty assgnment. We do the lnk rate allocaton that ensures the traffc wll fnd enough bandwdth. Fnally, we present numercal results that show the usefulness of our model. We also show how our model can do the RS plannng n a feld wth obstacles that would be present n real lfe scenaros. The rest of ths paper s organzed as follows. Secton II presents the related work and Secton III ntroduces the network model of ths paper. Secton IV presents the optmzaton /10/$ IEEE

2 Ths full text paper was peer revewed at the drecton of IEEE Communcatons Socety subject matter experts for publcaton n the WCNC 010 proceedngs. formulaton of the problem and Secton V gves some numercal results that llustrate the utlty of our model. Fnally, the paper concludes wth summarzng remarks n Secton VI. II. RELATED WORK A network plannng model s presented n [3] to fnd the locatons of BSs and RSs. The nput of the model s a set of BS an RS potental locatons and a set of Test Ponts (TPs) that represent the user data traffc. The plannng problem s solved by optmzaton. The man lmtaton of ths work s that the multhop lnks are lmted to at most hops from the BS. The consdered topology s the followng: the SS connects ether to the BS, or to a RS that s connected to the BS. Ths assumpton does not allow usng the RS to ts full potental n multhop lnks. In comparson, we allow RSs to be located several hops away from the BS, and be reachable through other RSs. The second lmtaton of ths work s that they do not consder the lnk rate allocaton and they do not consder users requrements. They seek to mnmze the power transmtted n the vcnty of a BS to reduce the nterference and, hence, the number of users connected to a BS. But, they do not consder the maxmum rate of BS-RS lnk and lmt the number of connectng statons to the RS; however, we model lnk rate allocaton n detal. The same authors of the work above present an extenson of ther work n [], where they consder a large coverage area that makes the computaton tme ntractable. Thus, they dvde the area nto clusters and apply the approach above to every cluster. Then, they solve the cases on the boundares of the clusters. The same lmtaton on the the maxmum use of hops n wreless stll remans. In [], the authors present an RS deployment problem. In ths problem, the SS s consdered to be a hotspot wth multple end users connected to t. An RS should be connected between the BS and the SS to mprove the performance. They consder a nomadc RS paradgm where the RS moves to serve multple SSs, one at a tme. A related problem s the BS plannng n UMTS systems. For example, a comparson of optmzaton solutons and algorthms for ths problem s presented n [6]. The optmzaton formulaton s mostly focused on modelng the nterference from the users and ams to fnd the plannng that reduces the nterference. Ths part of the work s smlar to [3], []. In addton, three heurstc-based algorthms are presented to fnd the BS stes. The results n ths paper show that the heurstc algorthms provde an optmal soluton n some cases (about half of the cases). Otherwse, they aren t far from the optmal solutons. Snce the problem s n the context of UMTS, some parameters do not apply to the case of WMAX. Also, n comparson, our model ncludes the rate allocaton of lnks that s not part of ths study. A plannng soluton for WMAX s presented n [7] where they allow the traffc of one SS to be allocated to several BSs. They also consder the capacty of the lnks and the requests of the TPs. However, only BS nstallaton s consdered and no RSs are ncluded. The soluton s a greedy algorthm that TABLE I OFDMA RATES (IN MBPS) FOR VARIOUS MODULATION SCHEMES USING 7MHZBANDWIDTH QPSK QPSK 16-QAM 16-QAM 6-QAM 6-QAM 1/ 3/ 1/ 3/ /3 3/ assgns the BS whch connects to SS wth lower degrees snce those SS do not have many choces of BS connectons. Other approaches nclude [], where the problem s deletng cells due to upgradng the network wth more powerful BSs, whch was solved by a heurstc-based algorthm. None of the works above consders the multhop nstallaton of RSs and modelng the capacty of the lnks at the same tme. In our paper, we consder these two aspects n our model. III. NETWORK MODEL Ths secton presents the network model that we consder. Frst, we explan what characterzes the capacty of a lnk. Then, we state our assumpton on channel assgnment. A. Lnk Capacty The capacty of a wreless lnk that s subject to addtve whte Gaussan nose can be modeled wth the Shannon- Hartley equaton [9]. The upperbound on the capacty s: C = B.log (1 S N ), where C s the capacty n bt/sec, B s the channel bandwdth n Hz, S s the receved sgnal power and N s the nose (S/N s the sgnal-to-nose rato or SNR). Ths equaton ndcates that the capacty changes wth the dstance snce the SNR degrades for long dstances due to path loss. The other factors that affect the achevable rate over a channel are the codng and modulaton schemes. Wth hgh SNR, the good channel qualty s leveraged to acheve a hgh rate. Wth low SNR, robust schemes are used to counter the bad channel and lmt the loss due to the hgh bt-error rate (BER). Hence, we express the maxmum rate between nodes and j by: m,j =Γ(SNR,j,β,modulaton), where β s the upperbound on the BER and Γ s the functon that maps all three parameters to the transmsson rate. The standard [10] lsts the achevable raw bt rates for the OFDMA physcal layer as shown n Table I. B. Channel Assgnment In the RS doman, we assume that two lnks nterferng wth each other are assgned dfferent channels. In ths way, the channel assgnment can be solved usng a tree colorng problem. Two nodes that are connected to each other have a lnk between them that s assgned a color. The lnk colors are re-used wthn the graph to save bandwdth resources. We choose ths assumpton snce t smplfes our work wthout loss of generalty. Another approach s to have all of the RSs transmt n one channel and use tme dvson multplexng. In ths paper, we do not address the schedulng scheme n detal snce t s out of scope of ths paper.

3 Ths full text paper was peer revewed at the drecton of IEEE Communcatons Socety subject matter experts for publcaton n the WCNC 010 proceedngs. IV. OPTIMIZATION In ths secton, we formulate the relay plannng as an optmzaton problem. We start wth the followng defntons. Let R = 1,..., n} be the set of canddate stes for RS, and let T = 1,..., m} be the set of Test Ponts (TP) that desgnate the user traffc. A TP represents one or multple users. In case of multple users, ther aggregated rates wll be added and t wll the rate of the TP. The TP can also be used to represent moble SSs. The average number of users n a locaton would be counted n the TP s traffc. In addton, the TPs can represent multple traffc classes, such as real-tme Pollng Servce (rtps), nonreal-tme Pollng Servce (nrtps), or Best Effort (BE). The requrements of the end users would be averaged and mapped to a certan locaton that s represented by a TP. In our work, we assume that the majorty of traffc s n the downlnk drecton. Hence, we present the soluton based on the downlnk only. Secondly, we assume that, for a lnk, the maxmum flow s based on the power budget, dstance, channel gan, and modulaton scheme. For a gven lnk length, multple rates can be assgned on t wth each one havng ts own bt-error-rate (BER). In ths paper, for a gven lnk length, we consder a rate wth a certan BER, say β, and for every dstance, we consder the correspondng rates that yelds a BER that s less or equal to β. In ths way, the multple hops on a path have a comparable value of BER along the path. A. Decson Varables The decson varables of the optmzaton problem are the followng: D R 1; an RS s deployed n ste, R = (1) 0; otherwse D BR 1; RS s connected to the BS, R = () D BT = D RR j = D RT j = 0; otherwse 1; TP s assgned to the BS, T 0; otherwse 1; RS s connected to RS j,, j R 0; otherwse 1; TP j s assgned to RS, R, j T 0; otherwse Secondly, for every lnk that s set n the problem, that s when D BR = D BT = Dj RR = Dj RT = 1, we need to fnd the correspondng flow values, f BR,f BT,fj RR,fj RT that have a postve real value. We defne the rate matrces f BR,f BT,f RR j (3) () (),f RT j to be the flow rate from the BS to RS, theratefrombstotp, the rate from RS to RS j and the rate from RS to TP j, respectvely. Ths makes our problem a mxed-nteger lnear problem (MILP). B. Topology Constrants The followng constrants are appled to our problem. Frst, when a lnk between the BS and RS s assgned, we have to make sure that RS s ndeed exstent, hence we have the constrant: D BR D R ; R (6) Smlarly, when a lnk between RS and RS j s assgned as exstent, both of these RSs should be exstent as well. Hence, we have: Dj RR DR Dj R (7) In addton, when RS s assgned to TP j, the RS should be exstent n the network. Hence, Dj RT D R ; R, j T () We also need to add a constrant that lmts the TP to connect to ether the BS or to a sngle RS. The constrant s the followng: j R C. Flow Constrants In addton to the constrants above, we add the flow conservaton constrants. These constrants ensure that (1) the total flow gong out of the BS s suffcent for all the TP s traffc, () the flow gong out of an RS s equal to all the flow gong nto the RS, and (3) the flow gong nto a TP s equal to the traffc of the TP. 1) Flow Constrant at the BS: Ths constrant makes sure that the BS s gvng out a total of capacty that s suffcent. f BR.D BR fj BT.Dj BT = r j (10) R j T j T D BT D RT j =1; T (9) To keep the system lnear, we use the followng transforms: X = f BR.D BR and, (11) Y j = f BT j.d BT j (1) Hence, Eq. (10) becomes, X Y j = r j (13) R j T j T whch can be solved by the followng constrants. Let Q be a large number such that Q>max(f BR,fj BT ), R, j T. X Q.D BR Q f BR R (1) X f BR R (1) X 0 R (16) X Q.D BR R (17) Y j Q.D BT j Q f BT j j T (1) Y j fj BT j T (19) Y j 0 j T (0) Y j Q.Dj BT j T (1)

4 Ths full text paper was peer revewed at the drecton of IEEE Communcatons Socety subject matter experts for publcaton n the WCNC 010 proceedngs. ) Flow Constrant at the RS: Ths constrant makes the ncomng total flow at an RS equal to the outgong total flow at the same RS, appled to all the RSs. f BR.D BR j R fj RR.Dj RR = j R f RR j.dj RR k T fk RT.Dk RT () Smlar to above, we replace Z j = fj RR.Dj RR,, j R and W j = fj RT.Dj RT, R, j T to make the system lnear. Then, Eq. becomes the followng. X j R Z j = j R We solve for Z j and W j as follows. Z j Q.D RR j Z j k T W k (3) Q f RR j, j R () Z j fj RR, j R () Z j 0, j R (6) Z j Dj RR.Q, j R (7) W j Q.Dj RT Q fj RT R, j T () W j fj RT R, j T (9) W j 0 R, j T (30) W j Q.D RT j R, j T (31) 3) Flow Constrant at the TP: Ths constrant ensures there s enough traffc flow for every TP. f BT.D BT j R fj RT.Dj RT = r (3) functon: mn V. NUMERICAL RESULTS D R (3) Ths secton presents examples that show how our model s used to plan a network. It also shows specal real-lfe cases n the plannng problem where there are obstacles n the coverage area. A. Solvng the Model We obtan numercal results from the model by solvng the CPLEX. In ths paper, snce we consder the applcaton as extendng the range of a BS, therefore the problem sze s lmted. There s a lmt on how many RSs can be used to extend the range of sngle BS. Wth a farly large problem, for example a grd of 10x10 potental RS locatons, the model s solvable n a far amount of tme. Therefore, we do not present an approxmaton algorthm n ths paper. B. Plannng We show a plannng example that uses our model. The example s shown n Fg.. We assume that RSs can be located on the corners of a square grd shown on the left sde of the fgure. We assume a square grd shape. Thus, the nput of the problem s the followng: the sde of the grd, the TPs, and the demand of TPs n Mbps. We place the TPs n the mddle of the unt square, as n the fgure. The soluton gves us the number and placement of the RSs, the used lnks, and the rates of the lnks. BS Potental RS ste TP (test pont) We use the transforms above to make the equaton lnear as follows RS1 10 Y j R W j = r (33) RS 6 RS7 D. Constrant on the Lnk Capacty The maxmum values of the flow f that can be transmtted on a lnk s lmted by the followng factors: the length of the dstance, the transmt power and the codng and modulaton schemes. We use the upperbound m that specfes the maxmum flow on a lnk. The constrants are as follows.: Topology and TP demands Soluton Fg.. Plannng Example f BR f BT fj RR fj RT E. Objectve Functon m BR ; R (3) m BT ; T (3) m RR j ;, j R (36) m RT j ; R, j T (37) We need to mnmze the total number of RSs that are used n the system such as to havng the followng objectve In real lfe, there s a grounds survey whch precedes a network deployment [11], [1], [13]. Based on the lnks characterstcs (ncludng SNR measurements and dstance between the nodes), the maxmum rates for every lnk are found,,k R, j T, from prevous secton). In our example, we use the rates that are summarzed n Table II. The unt dstance s the sde length of a square n the grd. The rates n ths example are based on the dstance. The soluton to ths plannng example s shown on the rght sde of Fg.. Three RSs are needed for ths problem whch are (m BR,m BT j,m RR,k,mRT,j

5 Ths full text paper was peer revewed at the drecton of IEEE Communcatons Socety subject matter experts for publcaton n the WCNC 010 proceedngs. TABLE II LINK RATES USED IN OUR EXAMPLES Dstance (unt) Lnk Rate (Mbps) f dstance <= 1 rate =10 else f dstance <= rate = else f dstance <= 3 rate = else f dstance <= rate =1 else rate =0 the hghlghted crcles. They are RS1, RS and RS7. The sold lne lnks are the BS-RS and RS-RS lnks. The dashed lnes are the BS-TP and RS-TP lnks. The underlned numbers are the lnk rates allocated by the soluton (subject to maxmum lnk rate n Table II). The rates of the dotted lnks are equal to the correspondng TPs rates, snce n our soluton the traffc of a TP s carred on a sngle lnk, ether to an RS or the BS. We note the followng observatons from ths example: The dstance from the TP to the BS doesn t necessarly ndcate a drect or relayed connecton. For example, the TP wth demand of s the farthest from the BS. However, ts demand s relatvely low whch can be satsfed by a sngle lnk. On the other hand, TPs whch are closer to the BS have hgher demands, and requre the use of relay statons. Secondly, the RS to RS lnks help n reducng the number of relays. In our example, there s more traffc to the rght ofthebs( = 1) than the left () and the mddle (6). Thus, n the soluton, the dagonal and horzontal lnks, both wth rate of Mbps, between RSs (1,7) and (,7), respectvely, relay the traffc from the rght sde to the less congested left sde. If ths was not the case, more relays would be needed on the rght sde. C. Obstacle Model In ths part, we consder the exstence of obstacles n the plannng area. In real lfe, obstacles could be natural such as a hll, a forest or a lake, or man-made structures such as buldngs, water towers or others. In ths subsecton, we consder two cases of obstacles as shown n Fg. 3. Frst, there mght be lakes or other smlar obstacles n the area. Ths type of obstacles does not allow deployng an RS n t. However, two adjacent RSs can transmt on a lnk that goes over ths types of obstacle, as shown n the fgure. In the model, the RS locaton over ths obstacle s canceled by settng the maxmum rate on such RS to null. In the model, these are the parameters for when RS s canceled: m BR =0as the rate to the BS, m RR j =0, j R as the rate to other RSs, and m RT k =0, k T as the rate to all TPs. The other type of obstacles that we consder doesn t allow a wreless lnk to penetrate t. For example, t could be a small hll n the area. We also consder that t mght be rough terran and t wouldn t allow deployng an RS on t. Ths type s also shown n Fg. 3. The same condtons that were for the frst type apply here to cancel the use of RSs that concde wth the obstacle. In addton, we need to cancel the lnks that traverse the obstacle too. So for every lnk that s blocked by the obstacle from the BS to RS, from the BS to TP j or from RS to RS k and from RS to TP j,wehavem BR = 0, m BT j =0, m RR k =0, mrt j =0. BS RS (relay staton)ste RS deployment not possble Vable lnk Lnk not possble Fg. 3. Lake Obstacle Model D. Plannng wth Lake-Type Obstacles Now we show how the plannng s solved by our model wth obstacles n the plannng area. We take the plannng case n Fg. and we nsert obstacles n t, once a lake and once a hll. Then we compare the plannng outcome due to the effect of the obstacles. Frst, we start by nsertng a lake n the plannng area as shown n Fg.. The lake covers the RS locatons of RS and RS6. Hence, t s no longer possble to deploy RSs at these stes. We note the followng observatons n comparson to Fg.. Fg.. RS1 7 RS9 Lake 6 RS 3 RS7 Plannng Result wth Lake Obstacle The number of RSs has changed from 3 to. Ths shows that an obstacle mght ncrease the number of RSs. Prevously, RS1, RS and RS7 were used. The obstacle makes RS no longer avalable. In the new plannng, the RSs used are RSs 1,, 7 and 9. As we desgnated n the model, the lnks can traverse a lake-type obstacle. Hence, n the plannng result, many lnks traversed the lake. Notably, from RS9, there are 3 lnks that go over the lake to RS1, the BS and RS. Hll

6 Ths full text paper was peer revewed at the drecton of IEEE Communcatons Socety subject matter experts for publcaton n the WCNC 010 proceedngs. Fnally, the lnks that were drect from TPs to BS reman unchanged snce the lake-type obstacle doesn t nterfere wth these lnks. E. Plannng wth Mountan-Type Obstacles In the followng case, we nsert a mountan-type obstacle n the plannng area. Ths type of obstacle, as the lake-type, cancels the overlappng RS poston. In addton, t cancels the lnks traversng t. Thus, the mountan-type obstacle s more restrctve than the lake-type. The result of the plannng s shown n Fg.. The result shows that here, RSs are now needed to support the TPs. Ths s ntutve snce ths obstacle has more restrctons than n the prevous case, whch requred RS, and compared to the ntal case wth no obstacles, whch requred 3 RSs. RS Fg.. RS9 Hll 9 6 RS RS11 RS7 Plannng Result wth Mountan Obstacle We note the followng observatons: The network used lnks that are dspersed around the mountan, snce t s not possble to go through t. Notce for TP (wth rate of Mbps), t was able to communcate drectly wth the BS n the case wth no obstacles and n the case wth lake obstacle. Now, t cannot do ths anymore, because of the mountan, and t goes through RS. Fnally, we saw that more restrctons n the plannng area on the RS locatons and the vable lnks wll lkely requre more RSs to satsfy the TPs. VI. CONCLUSION Ths paper presented a plannng model for Relay Statons (RS) deployment n WMAX networks accordng to the IEEE 0.16j standard. Our work s dfferent from other proposed work n the lterature n that t consders the conservaton of flow on all the nodes. Ths provdes enough bandwdth for all the connectons at every level of the RS grd. We formulated the problem nto a mxed nteger lnear program that solves for the RS locatons and the transmsson rates on the lnks. The model takes as nput the possble stes of RSs, the users demands for a number of TPs and mnmzes the number of RSs used. We showed how our model can be used to plan a network of RSs. We also consdered the exstence of two types of obstacles n the plannng area. The frst s the laketype obstacle, and the second s a more restrctve type called mountan-type obstacles. We showed how our model can be used wth each of the obstacle types. Fnally, we provded observatons and nsght on the effect of obstacles on the plannng results. VII. ACKNOWLEDGEMENT Ths work was supported n part by the Natonal Scence Foundaton under grant CNS-066. REFERENCES [1] Baselne Document for Draft Standard for Local and Metropoltan Area Networks Part 16: Ar Interface for Fxed and Moble Broadband Wreless Access Systems Multhop Relay Specfcaton, IEEE 0.16j- 06/06r, 006. [] A solar-powered wmax base staton soluton, Intel Applcaton Note, Intel Netstructure(r) WMax Baseband Card, [3] Y. Yu, S. Murphy, and L. Murphy, Plannng base staton and relay staton locatons n eee 0.16j mult-hop relay networks, Consumer Communcatons and Networkng Conference, 00. CCNC 00. th IEEE, pp. 9 96, Jan. 00. [], A clusterng approach to plannng base staton and relay staton locatons n eee 0.16j mult-hop relay networks, Communcatons, 00. ICC 0. IEEE Internatonal Conference on, pp. 6 91, May 00. [] B. Ln, P.-H. Ho, L.-L. Xe, and X. Shen, Optmal relay staton placement n eee 0.16j networks, n IWCMC 07: Proceedngs of the 007 nternatonal conference on Wreless communcatons and moble computng. New York, NY, USA: ACM, 007, pp. 30. [6] E. Amald, A. Capone, and F. Malucell, Plannng UMTS Base Staton Locaton: Optmzaton Models wth Power Control and Algorthms, IEEE Transactons on Wreless Communcatons, vol., no., pp , 003. [7] P.Ln,H.Ngo,C.Qao,X.Wang,T.Wang,andD.Qan, Mnmum cost wreless broadband overlay network plannng, n World of Wreless, Moble and Multmeda Networks, 006. WoWMoM 006. Internatonal Symposum on a, 006, pp. 7 pp. 36. [] D. Abusch-Magder, Novel algorthms for reducng cell stes durng a technology upgrade and network overlay, n Wreless Communcatons and Networkng Conference, 00 IEEE, 00. [9] W. Stallngs, Wreless Communcatons and Networks. Prentce Hall, 001. [10] IEEE Standard for Local and Metropoltan Area Networks Part 16: Ar Interface for Fxed Broadband Wreless Access Systems, IEEE Std (Revson of IEEE Std ), pp. 1 7, 00. [11] T. Theodoros and V. Kostantnos, Wmax network plannng and systems performance evaluaton, n Wreless Communcatons and Networkng Conference, 007.WCNC 007. IEEE, March 007, pp [1] M. Molna-Garca and J. I. Alonso, Plannng and szng tool for wmax networks, Rado and Wreless Symposum, 007 IEEE, pp , Jan [13] J. Garca-Fragoso and G. Galvan-Tejada, Cell plannng based on the wmax standard for home access: a practcal case, n Electrcal and Electroncs Engneerng, 00 nd Internatonal Conference on, Sept. 00, pp. 9 9.