Topology Realization using Gain Control for Wireless Testbeds

Transcription

1 Topology Realzaton usng Gan Control for Wreless Testbeds Samer S. Hanna Dept. of Eng. Mathematcs and Physcs Alexandra Unversty Alexandra, Egypt Karm G. Seddk ECNG Dept. Amercan Unversty n Caro Caro, Egypt kseddk@aucegypt.edu Amr A. El-Sherf Wreless Intellgent Networks Center (WINC) Nle Unversty Gza, Egypt aelsherf@nu.edu.eg ABSTRACT Wreless testbeds present a convenent and cost effectve opton for researchers n communcatons to valdate ther work. The man drawback of these testbeds s ther relance on nodes wth fxed placement; ths lmts expermenters ablty to test protocols that depend on a complex connectvty between the nodes such as relayng. In ths work, we present a way to overcome ths lmtaton; ths method attempts to realze a gven topology between a set of nodes by adjustng each node s transmt power and receve gan n a manner to connect and dsconnect the lnks between the nodes as desred. We start by expressng the topology realzaton as an optmzaton problem usng two dfferent forms. The topology realzed s dependent on some characterstcs of rado-frequency (RF) hardware. Hence, we evaluate theses parameters for a specfc platform. A computer evaluaton for the two formulatons s carred out, followed by a real world experment to valdate the proposed method. Durng ths experment, the values of gans requred to realze a gven topology are calculated, then tested usng hardware. CCS Concepts Networks Physcal topologes; Physcal lnks; Hardware Wreless devces; A. El-Sherf s also afflated wth Dept. of Electrcal Engneerng, Alexandra Unversty, Alexandra, Egypt Permsson to make dgtal or hard copes of all or part of ths work for personal or classroom use s granted wthout fee provded that copes are not made or dstrbuted for proft or commercal advantage and that copes bear ths notce and the full ctaton on the frst page. Copyrghts for components of ths work owned by others than ACM must be honored. Abstractng wth credt s permtted. To copy otherwse, or republsh, to post on servers or to redstrbute to lsts, requres pror specfc permsson and/or a fee. Request permssons from permssons@acm.org. WNTECH 16, October 3-7, 216, New York Cty, NY, USA c 216 ACM. ISBN /16/1... $15. DOI: Keywords Wreless Topology; Software Defned Rados; Wreless Testbed 1. INTRODUCTION Wreless researchers tryng to valdate ther work have several optons. The frst and most popular opton s smulatons. The problem wth usng smulators s n the abstractons they use, whch mght hde some aspects of hardware and wreless envronment. The second opton s purchasng and deployng hardware. Ths choce s not accessble to all researchers due to the cost assocated wth hgh-end RF devces lke SDRs (Software Defned Rados). Besdes, the low utlzaton of hardware, f acqured, makes ths opton uneconomcal. Ths makes usng remotely accessble testbeds the most sutable method, as t enables researchers to work usng real hardware wthout the trouble and cost of purchasng and settng up equpment. Testbeds, despte beng more realstc, mpose restrctons on expermenters. As most wreless testbeds that are accessble remotely use fxed nstallatons for ther nodes, testbed users do not have the capablty to change the placement of the nodes the way they desre. They are also bound to the capabltes of the avalable hardware. These factors (placement and hardware) lmt the topologes achevable by an expermenter. In order for a wreless testbed to be able to accommodate varous experments wth ther topology requrements, despte havng a fxed node placement, a method to modfy connectvty to realze dfferent topologes s needed. Transmt power has been used to control the topology n ad-hoc networks. In [7], a dstrbuted algorthm where each node makes a local decson on ts transmsson power to guarantee global connectvty was suggested. In [5], to create a desred topology an optmzaton problem s proposed wth the purpose of reducng the maxmum power used n an ad-hoc network; greedy algorthms were developed to calculate the values of the transmtted power. Both these methods, although they

2 use transmt power to control topologes as our work, make assumptons that are not vald for testbeds. OR- BIT testbed [6] enables ts users to realze topologes. ORBIT conssts of a 2 2 nodes grd, each node havng a WF nterface. All these nodes get allocated to a sngle user. To realze a topology, ORBIT s method [3] uses organzed tral and error to map the topology to nodes n the grd. The problem wth ORBIT s topology realzaton s ts relance on the avalablty of excess nodes. To realze a 5 node topology, a user must have exclusve access over all 4 nodes. Gven a set of wreless nodes and a desred topology between them, our proposed method adjusts ther transmt powers and receve gans to realze the topology. Ths method gves users the flexblty of settng the connectvty between the nodes the way they desre, thus, overcomng the lmtaton mposed by fxed node placements. The suggested method reles on knowng, for each type of modulaton, the mnmum power at recever for a wreless lnk to be consdered connected and the maxmum power for a lnk to be dsconnected. These powers are constant for a gven hardware platform. After measurng the channel coeffcents between the nodes and knowng these constants, we formulate the topology realzaton as an optmzaton problem, whch s solved to obtan the gans. Compared to the method proposed by ORBIT, our soluton has the advantage of not needng more nodes than the number requred by the experment. The rest of the paper s organzed as follows; a motvatng scenaro hghlghtng the need for a topology realzaton method s presented n Secton 2. In Secton 3 the needed background nformaton s presented. Secton 4 dscusses two formulatons of the problem. The hardware dependent factors are calculated for the SDR platform of choce n Secton 5. Whle n Secton 6, the two suggested methods are compared and a real world experment s performed to valdate ths work. Secton 7 dscusses the lmtatons of ths method. 2. MOTIVATING SCENARIO To motvate our work, we consder the followng scenaro. A user wants to experment wth dfferent relayng schemes to extend the possble range of communcaton. To test such a scenaro the user wants a specfc topology to be realzed; he wants the transmtter and the recever nodes to be out of range of each other and the relay node should be capable of communcatng wth both nodes. Let us dscuss how ths topology can be realzed. If the user physcally possesses three nodes, placed n an arbtrary placement as shown n Fgure 1 n black. Each node has a transmsson range r t shown as dashed crcles. The user wll move them to postons smlar to the ones drawn n blue n Fgure 1. A remotely accessble testbed user wll not be able to move the nodes. Assumng he has access to a bg num- r t N1 N2 N3 N1 N2 N3 Fgure 1: To test a relay scenaro, startng from nodes dsplayed wth black, the user can change gans as shown n red, or change the placement of nodes shown n blue. Dashed crcles present the transmsson range. ber of nodes. Instead of physcally movng the nodes, he wll use tral and error untl he fnds nodes that realze hs topology. The method used n ORBIT testbed performs ths mappng for the user. Assumng the user only has only three nodes, he wll change the gans to realze the topology. For example, he wll attempt to tune the transmt power of node 1 untl node 2 can receve but 3 wll not be able to receve. Ths can be vsualzed as the user changng the radus of transmsson r t. Ths scenaro s hghlghted n red n Fgure 1. Our proposed method determnes these gans for the user. 3. BACKGROUND 3.1 Wreless Channel The connectvty of nodes n a testbed does not only depend on the dstance between the nodes, t also depends on the envronment surroundng them. Some of these factors nclude whether the nodes are placed n lne of sght (LOS) of each other or not, the materal and thckness of the walls, etc. These are just the statc factors; other factors of random nature are also present. If the testbed s placed n a non dedcated room (for example n hallways), the movement of the people n the buldng, the locaton of the furnture, etc, wll result n non determnstc changes n the channel coeffcents between the testbed nodes. Any system that attempts to realze a topology must try to keep t stable despte these channel varatons. 3.2 Qualty Metrc In communcatons, several metrcs can be used to assess the qualty of the receved sgnal, such as Bt Error Rate (BER) or Packet Error Rate (PER). Based on the value of the qualty metrc, we wll consder two nodes to

3 be connected or dsconnected. In ths work, we selected the packet error rate as the performance metrc. The reason for selectng PER over BER s ts ease of calculaton. To calculate BER the recever needs to be aware of the transmtted data and has to be synchronzed wth the transmtter. Ths s wll add unjustfed complexty to the mplementaton. PER on the other hand can be calculated by checkng the cyclc redundancy check (CRC) of the receved packet. We wll consder a lnk between two nodes connected f the PER of ths lnk s below 1% and a lnk dsconnected f the PER s of ths lnk s above 9%. In between, the lnk state wll be assumed undecded and we wll try to keep lnks away from ths state. 3.3 SDR characterstcs Several characterstcs of an SDR platform contrbute to the realzaton of a topology. Some of them are relevant to the transmt chan and others to the receve chan Transmt chan The power levels that the transmt chan can provde help n determnng the connectvty t can acheve. The hgher the maxmum power level s, the bgger the dstance that t can cover. Assumng the transmtted power s dgtally controlled (can only take a dscrete set values) by settng the transmt gan (tx-gan), the dfference between two possble values n the varable power levels determnes to whch extent the user has control on the transmtted power. The purpose of ths work s to have control over the topology, allowng some nodes to communcate wth each other whle other nodes cannot. Ths s the reason why havng fne graned control over the power level s desrable Receve chan As dscussed n [4], the recever senstvty s defned as the sgnal level requred for a partcular qualty of receved nformaton. Recever senstvty plays an mportant role n determnng whether two nodes are connected or not. It depends on how the recever crcut s mplemented and the nose fgure of each of ts components; ths makes t depend on the SDR kt used. Recever senstvty value depends on the type of modulaton used. Also, the receve chan could contan a receve gan (rx-gan) whch can be used to properly condton the receved sgnal. Note that both chans suffer from nonlneartes, so ncreasng tx-gan above a certan level could lead to dstorton. Also, SDRs are bult to operate over a wde range of frequences and ther RF characterstcs vary wth frequency. 4. PROBLEM FORMULATION Let us suppose that a testbed user has reserved N nodes. Node has two varables: transmtted power p T n dbm and amplfcaton at recever a R n db. The user wants to realze a topology on hs N nodes defned by an N N connectvty matrx C; each element c j where j takes a value of 1 f the user wants the drectonal lnk between nodes and j, L j, connected and zero otherwse (the dagonal elements are meanngless). Then let us defne the set of connected drectonal lnks CL whch corresponds to all L j where c j equals one, and the set of dsconnected lnks DL whch corresponds to all L j where c j equals zero. h j s the channel coeffcent between nodes and j n db. We assume that the channel coeffcents between the testbed nodes are already known (they can be measured ether perodcally or before attemptng to realze the topology). Channel coeffcents depend on multple factors lke the dstance between the nodes, the obstacles between them, etc. They are subject to random varatons due to changes n the envronment. PC mod s the mnmum receved power n dbm from one node to the other for the lnk between them to be connected accordng the defnton made n Secton 3.2 when usng a modulaton of type mod. PD mod s the maxmum power receved to consder the lnk to be dsconnected when usng mod. Both PC mod and PD mod are dependent on the characterstcs of hardware used and can be evaluated as wll be explaned later. For the user desred topology defned by the matrx C to be realzed on the N nodes usng modulaton of type mod the followng condtons must be satsfed p T + h j + a R j P mod C, {, j L j CL} (1) p T + h j + a R j PD mod, {, j L j DL} (2) The LHS of equatons (1) and (2) presents the power receved by node j from node n dbm. Equaton (1) s for connected lnks and Equaton (2) s for dsconnected lnks. Addtonally, there are hardware constrants lke the mnmal and maxmal possble values of gans, whch wll be mentoned later. There are several ways to defne an optmal soluton among all feasble ponts. One of these could be mnmzng the transmtted power (mn p T ). Consderng that the testbed uses fxed nodes whch draw ther electrcty from the power grd and are not battery powered, power s not a crucal factor. What s more mportant than power s the robustness of a soluton. As mentoned earler, channel coeffcents are subject to random varaton. If the selected soluton s on the boundary of the feasble regon formed by the constrants, any varaton n channel coeffcents could move the soluton outsde of the feasble regon. A better soluton would be more robust aganst the expected varaton n channel coeffcents. 4.1 Maxmzng Mnmum Slack Formulaton In a testbed wth N nodes, we have N (N 1) channel coeffcents, each of them s subject to random

4 varaton. Each lnk L j has a slack s j. If the channel coeffcent of ths lnk, h j, changes wthn the slack n the drecton opposte to what we desre (ncreased for lnks we want dsconnected or decreased for lnks we want connected), the soluton obtaned wll reman feasble. The objectve of ths formulaton s to maxmze the mnmum of all slacks, as follows max s, (3) where s = mn s j j. The problem constrants are p T + h j s + a R j P mod C, {, j L j CL}, (4) p T + h j + s + a R j P mod D, {, j L j DL}. (5) Ths problem can be solved usng a Lnear Programmng solver. 4.2 Transmtter Based Formulaton The problem wth the prevous formulaton s the symmetry between p T and a R. As we wll dscuss later, the ncrease of recever amplfcaton a R s not always guaranteed to mprove the sgnal qualty. Realzng the soluton usng values of p T bgger than a R, f possble, s preferred. Ths can be done by gvng a hgher prorty to p T usng the objectve functon. Such objectve s hard to descrbe usng a lnear formulaton. Hence, we modfy the formulaton as follows. We start by transformng all varables n dbm to mw and db to rato usng p r.t = 1 p T 1, a r.r = 1 a R 1, and h r j = 1 h j 1. (6) The r n superscrpt denotes the varable transformed to rato. The same transform s appled to the constants PD r.mod and PC r.mod. The objectve we chose s mn (p r.t ) 2 h r j a r.r j,j L j DL + 1 α,j L j CL (p r.t 1 ) 2 h r j ar.r j. (7) The frst term represents the receved power from the undesred lnks whch we are tryng to mnmze, whle the second s the nverse of the receved power from the desred lnks whch we are tryng to maxmze. The parameter α controls whether dsconnectng the unwanted lnks or connectng the wanted ones has a hgher prorty. The squarng of p r.t forces the solver to be based towards the transmtted power, p r.t, and gves t a hgher prorty. Ths formulaton can be solved usng a geometrc programmng solver. The problem constrants after applyng the transformatons become p r.t p r.t h r j a r.r j h r j a r.r j P r.mod C, {, j L j CL}, (8) P r.mod D, {, j L j DL}. (9) 5. PARTICULARIZATION TO A HARD- WARE PLATFORM In order to use ths method, frst, the characterstcs of the used hardware platform need to be evaluated. The constants PC mod (mnmum power for a lnk to be connected when usng modulaton type mod) and PD mod (maxmum power below whch a lnk s consdered to be dsconnected when usng modulaton type mod) are hardware-dependent. For nstance, recever wth a lower nose fgure wll have a lower value of PC mod, and hence, wll be capable to decode sgnals wth lower power. Other than the values of the constants, the prevously mentoned constrants are not suffcent to descrbe actual RF hardware. As, there are constrants dctated by the hardware, for example, the mnmal and maxmal powers that can be transmtted. We wll llustrate how the problem can be adapted usng a USRP N21 [1] usng WBX daughterboard. A USRP has two varables tx-gan g T and rx-gan g R. g T and g R are related to the power transmtted n dbm (p T ) and the amplfcaton at the recever (a R ) usng the followng relatons p T = g T + P T mn and a R = g R + A R mn, (1) where Pmn T s the mnmal power n dbm whch the USRP transmts and A R mn s the mnmal amplfcaton, n db, whch the USRP receve chan provdes. Power measurements reported by the USRP are not calbrated; the values reported by a USRP should be adjusted to the true power by a factor as follows p rep = p R + C R, (11) where p R s the true power receved by the USRP n dbm, C R s the calbraton factor n db and p rep s the reported power whch s referenced to an unknown power level and we wll refer to ts unt as dbx. When one USRP s transmttng to another the receved power can be expressed as p R = p T + h j + a R j, (12) whch can be rewrtten n terms of the known values as p rep = g T + h j + g R j + X, (13) where X s a constant whch equals P T mn + AR mn CR. As long as all the nodes are USRPs of the same type and do not exhbt large varablty, the value of X wll be constant for all calculatons. We wll carry on wth all power measurement measured n dbx and the value of X wll be part of the RHS constants n all nequaltes. In ths secton, we frst start by descrbng the hardware constrants concernng the possble set of gans. Then, we study the relaton between tx-gan and the packet delvery rato 1. Afterwards, we study the effect of changng the rx-gan on delvery rato. From these 1 Packet Delvery Rato = 1 - Packet Error Rate

5 relatons, we wll determne the thresholds 2 PC mod and PD mod. Unless otherwse stated, measurements n ths secton were obtaned by takng the average of multple readngs. 5.1 USRP constrants The USRP hardware has a dscrete set of values for the gans. Besdes the mnmal and maxmal values for gans (G T mn and GT max), the gans can only take values that are multples of half. Hence, the followng constrants are added, G T mn g T G T max, g T = k/2, k Z, (14) G R mn g R G R max, and g R = k/2, k Z. (15) 5.2 Relaton between receved power and packet delvery rato To quantfy the relaton between the receved power and the packet delvery rato, a transmtter and recever were confgured to operate for a perod of 1 seconds; after that perod the recever reports the average power receved and the packets delvery rato. As the packet delvery rato depends on the packet sze, we have to menton that for all experments performed n ths work packets wth a payload of 15 bytes were used. To ensure the valdty of the results, multple runs were conducted n a random order coverng dfferent modulaton types and dfferent values of tx-gan and Values obtaned were averaged. Results are shown n Fgure 2. From ths fgure, the receved power needed to obtan the threshold for a lnk to be connected or dsconnected (more than 9% and less than 1% delvery ratos, respectvely) for a gven modulaton type could be obtaned. Whle makng the measurements for ths fgure only tx-gan was changed; the effect of rx-gan wll be dscussed n the next secton. As the power receved ncreases the delvery rato would reman near 1% untl the USRP s amplfers start to saturate. If the power receved by a USRP exceeded a threshold, the amplfers n the RF front-ends wll start saturatng. Ths wll cause a dstorton n the sgnal and worsen the delvery rato. To measure ths level, two USRPs were placed n proxmty of each other. Gans were vared and power and delvery rato at recever were measured. The results are shown n Fgure 3. The followng constrant wll be added to account for saturaton g T + h j + gj R PSAT, {, j L j CL}, (16) where PSAT s the maxmal power receved n dbx to avod saturaton. X n the superscrpt denotes a value n dbx. 2 The results obtaned are not guaranteed to be vald for all smlar hardware because electronc components are subject to batch varablty, though for the USRPs used no major varablty was found. % Packets Delvered bpsk qpsk gfsk gmsk psk4 qam4 psk16 qam Receved Power (dbx) Fgure 2: Relaton between the receved power and the packet delvery rato for dfferent types of modulaton. % Packets Delvered Receved power Fgure 3: Saturaton occurs when the power receved s too hgh. BPSK modulaton was used. % Packets Delvered Rx-gan (db) Fgure 4: The effect of changng the rx-gan on packet delvery when tx-gan s constant. 5.3 Effect of changng rx-gan on packet delvery rato Theoretcally, ncreasng the rx-gan at the recever should have no effect on the throughput, as the rx-gan ncreases both the sgnal and nose powers. Nevertheless, when takng nto consderaton the complexty of the recevng crcut, the rx-gan helps condton the receved sgnal to meet the dynamc range of the Analog to Dgtal Converter (ADC). It can ether amplfy t to exceed the nose floor of a component or attenuate t to avod saturaton. Ths argument s supported by observng the delvery rato whle only the rx-gan s changng as shown n Fgure 4. Although the rx-gan has caused an mprovement n delvery rato as shown n Fgure 4, ncreasng the rxgan does not always mprove recepton. If the power arrvng at the recever of the antenna s too low (ether due to weak transmsson power or any other reason), ncreasng the rx-gan would ncrease the receved power level (probably due to the amplfcaton of nose), but

6 t would have no effect over packet delvery. To nvestgate ths, measurements were made where the sum of both tx-gan and rx-gan was held constant at 3 db; the contrbuton of tx-gan to ths sum of gans of 3 db was vared, whle observng the receved power and the packet delvery rato. In Fgure 5a, ncreasng the tx-gan and reducng the rx-gan keeps the receved power almost constant whle the packet delvery rato changes as shown n Fgure 5b. To account for ths phenomenon, a new varable s ntroduced Power at Recever Antenna; ths value s not measured drectly, and s obtaned by subtractng the value of rx-gan from the power receved. Its value for the same measurements s shown n Fgure 5c. From ths Fgure, and other conducted measurements, the power at the recever antenna AC for correct recepton should be bgger than P whch s the mnmum power at the antenna for a lnk to be connected. Ths wll be ncorporated nto the problem by addng the followng constrant g T + h j PAC, {, j L j CL}. (17) 6. CASE STUDY 6.1 Problem Formulaton In ths secton, we wll dscuss an mplementaton of the proposed problem for a specfed connectvty. The topology we are tryng to realze s shown n Fgure 6. In ths topology, lnks on the sdes of the rectangle formed by the nodes should be connected (belong to CL) whle the ones on the dagonals are supposed to be dsconnected (belong to DL). We wll confne ourselves here to BPSK modulaton, although our method should be vald for any other type of modulaton. Ths topology can be used, for example, to test cogntve rado networks routng protocols, where node 1 s sendng and recevng data from node 4. Due to the actvty by a prmary user the drect lnk from node 1 to node 4 can no longer be used. The cogntve routng protocol wll reroute packets to node 4 through nodes 2 and Evaluaton Both the Maxmzng the Mnmum Slack Formulaton (MMSF) and the Transmtter Based Formulaton (TBF) were evaluated usng channel coeffcents values that were measured usng real hardware, though values n ths secton were only evaluated mathematcally. The MMSF was solved usng a Mxed Integer Lnear Programmng (MILP) solver; GLPK (GNU Lnear Programmng Kt) was used. The TBF was solved usng a geometrc programmng solver; CVX [2] was used and the gan values obtaned n ratos from CVX were transformed to db and then rounded to the nearest half. We now compare the two formulatons, by solvng them for the same channel coeffcents; the values of Receved power (dbx) % Packets Delvered Power at Anten. (dbx) Tx-gan (db) (a) Power Receved Tx-gan (db) (b) Packets Delvery Rato Tx-gan (db) (c) Power at the antenna Fgure 5: From top to bottom power receved, packet delvery rato and estmated power at the antenna when the sum of tx-gan and rx-gan s held constant at 3 db. node 1 node 2 node 4 node 3 Fgure 6: The topology of the case study, sde lnks are connected, dagonal lnks are dsconnected. slack varables, s j, calculated from both solutons are shown n Fgure (7). From ths Fgure, we can see that the slack of the lnk L 21, L 23, L 24, and L 42 usng MMSF s.5 db whle t s zero for the TBF. Ths s one of the advantages of the MMSF as t guarantees a mnmal slack for all lnks. The TBF, on the other hand, gves a soluton wth hgher values for transmt gans on the average. Other than that, the MMSF uses an MILP solver whch s orders of magntude faster than the GP

7 Slack of lnk (db) L 12 L 13 L 14 L 21 L 23 L 24 L 31 L 32 L 34 L 41 L 42 L 43 Lnk MMSF TBF Fgure 7: Comparson of the slack obtaned the GP and LP solutons m 1 Fgure 8: Poston of the nodes durng the experment. solver used by the TBF. 6.3 Hardware Valdaton The suggested work was valdated usng real world measurements. To test ths the four nodes were placed n the lab floor as shown n Fgure 8. BPSK modulaton was used throughout ths experment. The procedure went as follows: 1. Estmate Channel Coeffcents (a) Node 1 transmts at maxmum tx-gan of 3 db (G T max) whle rx-gan equals zero. (b) The rest of the nodes 2, 3, and 4 measure receved power for 1 seconds. (c) Subtract 3 from all measurements; ths gves h 12, h 13, and h 14. (d) The transmtter s changed and the same steps are repeated for the rest of the nodes untl all channel coeffcents were measured. 2. Solve the optmzaton problem to obtan values of tx-gan and rx-gan. 3. Test the valdty of these gans. (a) Node 1 sends packets usng the tx-gan obtaned from the optmzaton problem. 4 (b) The rest of the nodes 2, 3, 4 lsten for packets usng the values of rx-gan from the soluton for 2 seconds. (c) Nodes 2, 3, 4 report the packet delvery rato and the power receved at each node. (d) The transmtter s changed and the same steps are repeated for the rest of the nodes. These procedures were contnuously repeated over a twenty four hour perod from 12 PM to 12 PM the followng day n the lab faclty. Durng these tests, the TBF was used. Although, n Fgure 2, the threshold for receved power for a lnk to exst PC s around -9 dbx, P was set to -85 dbx to avod a zero C C slack soluton. Increasng P method wll only work n a good placement (wth channel coeffcents of lnks desred to be dsconnected much lower than that of the connected ones). In a problem wth bad placement, ths change could make a soluton whch s feasble at -9 dbx nfeasble. The MMSF s superor n ths aspect as t avods zero slack solutons f possble wthout C. havng to ncrease P Fgures 9 11 show a subset of the results where node 2 s the transmtter. Each pont n these fgures represents a sngle result. In Fgure 9, the measured channel coeffcents between node 2 and the rest of the nodes are shown. Fgures 1 and 11 show the receved power n dbx and the packet delvery rato durng the evaluaton of the calculated gans, respectvely. Fgure 11 shows that nodes 1 and 3 were capable of recevng packets wth delvery rato of up to 99% whle packet delvery rato of node 4 was almost equal to zero percent the entre tme except at the perod from 1 PM to 11 PM. The experment was run n a lab durng a normal work day, so n the perod from 9 AM to 5 PM people where present ths reflected n varaton of the channel coeffcents. From 1 PM to 11 PM a meetng was held n the room where node 1 was placed, and ths led to bg varatons n the channel durng the experment. Ths caused the undesred recepton of node 4 from node 2. Smlar curves were obtaned when nodes 1, 3 and 4 were transmttng. From these curves, the dagonal lnks that we wanted to be dsconnected showed low packet delvery rato wth mnor dsturbance at the mornng perod, and sde lnks were always connected. Ths proves that our method was capable of settng the gans to values that realze our desred topology. Ths was demonstrated wth over 29 runs usng the prevously descrbed procedures over a perod of 24 hours. 7. LIMITATIONS The suggested method has ts lmtatons. The ablty of ths scheme to mplement a topology s lmted by the channel coeffcents and hardware characterstcs. For example, f all nodes were placed far from each other and the maxmal transmtted power level and recever

8 Channel Coeff (db) Power Receved (dbx) L 21 L 23 L Tme of readng (hours of day) Fgure 9: Measured channel coeffcents. L 21 L 23 L Tme of readng (hours of day) Fgure 1: Power receved whle testng the soluton. % Packets Delvered L 21 L 23 L Tme of readng (hours of day) Fgure 11: Packet delvery rato whle testng the soluton. gan of the hardware are not hgh enough, ths method wll fal to connect any of the nodes. Other than the obvous cases, some combnatons of channel coeffcents alongsde wth hardware constrants mght fal to mplement a set of topologes. These mpossble to realze topologes make the optmzaton problem nfeasble to be solved under the gven constrants. Also, ncreased actvty n the place where the experment s conducted mght affect the valdty of the gans obtaned. The gan optmzaton problem dscussed assumes that the physcal nodes have been mapped adequately to the nodes of the topology. If the mappng has been performed llogcally, ths method could return an nfeasble soluton. For example, assgnng nodes dsconnected n the topology to physcal nodes placed closely, whle nodes connected n the topology to hardware separated by a long dstance s very lkely to be nfeasble. A more logcal mappng mght, on the other hand, make ths problem solvable. 8. CONCLUSION In ths work, we presented a method to realze a desred topology n a wreless testbed wth fxed nodes by varyng the transmtted power and the recever gan. Two formulatons were frst developed one focuses on maxmzng slack (MMSF) and the other on havng a soluton favorng transmt gan (TBF). The characterstcs of a hardware platform were studed to obtan the values of the parameters of the problem. A case study was then developed usng a square topology. An evaluaton of the two methods was performed whch showed that TBF s superor as t gves bgger transmtter gans, whle MMSF gves a more robust soluton wth a bgger value of mnmal slack. Real world testng was carred over an entre day and t proved the effectveness of our proposed formulatons n achevng a desred topology n a real envronment. 9. ACKNOWLEDGEMENT Ths work s supported n part by a grant from the Egyptan Natonal Telecommuncaton Regulatory Authorty (NTRA). 1. REFERENCES [1] Ettus Research, KIT. USRPâĎć n2/n21 networked seres. [2] M. Grant and S. Boyd. CVX: Matlab software for dscplned convex programmng, verson Mar [3] S. K. Kaul, M. Gruteser, and I. Seskar. Creatng wreless mult-hop topologes on space-constraned ndoor testbeds through nose njecton. In Testbeds and Research Infrastructures for the Development of Networks and Communtes, 26. TRIDENTCOM 26. 2nd Internatonal Conference on, pages 1 pp. IEEE, 26. [4] Matt Loy. Understandng and Enhancng Senstvty n Recevers for Wreless Applcatons. Techncal Report SWRA3, Texas Instrument. [5] R. Ramanathan and R. Rosales-Han. Topology control of multhop wreless networks usng transmt power adjustment. In INFOCOM 2. Proceedngs. IEEE, volume 2, pages IEEE, 2. [6] D. Raychaudhur, I. Seskar, M. Ott, S. Ganu, K. Ramachandran, H. Kremo, R. Sracusa, H. Lu, and M. Sngh. Overvew of the ORBIT rado grd testbed for evaluaton of next-generaton wreless network protocols. In Wreless Communcatons and Networkng Conference, 25 IEEE, volume 3, pages IEEE, 25. [7] R. Wattenhofer, L. L, P. Bahl, and Y.-M. Wang. Dstrbuted topology control for power effcent operaton n multhop wreless ad hoc networks. In INFOCOM 21. Proceedngs. IEEE, volume 3, pages IEEE, 21.