A Versatile Coexistence Decision-Making System for Efficient TV Whitespace Sharing among Whitespace Objects

Transcription

1 A Versatile Coexistene Deision-Maing System for Effiient V Whitespae Sharing among Whitespae Obets M Asif Raza Zafar Iqbal Sang-Seon Byun Hyundu Kang Heung-No Lee * Abstrat In this paper a oexistene deision maing (CDM) system for effiient V whitespae (VWS) sharing among whitespae obets (WSOs) registered in oexistene managers in IEEE system is introdued he proposed system is onsidered versatile in funtionality as it ointly taes are of three distint hannel alloation features; a) optimizing system quality of servie (QoS) performane metris b) improving VWS utility and ) satisfying WSO hannel demands Regarding system QoS performane metris the VWS sharing problem is defined as an optimization problem with an aim to maximize the system throughput and minimizing unfairness in alloation Supporting the WSOs hannel demands in a VWS sharing problem is a multifold tas whih requires elaborate onsideration in different aspets of the system performane o this end the variations of the SNR of wireless frequeny hannels whih result in variable throughput gain of the WSOs are also taen are of the proposed CDM system A fast hannel alloation algorithm is then designed that implements the VWS sharing mehanism in a reasonable amount of time Additionally the proposed algorithm improves the VWS utility by promoting a novel frequeny reuse method by exploiting the inter-wso interferene information Simulation results show the superiority of the proposed algorithm over existing VWS sharing algorithms Index erms Frequeny Reuse Lagrangian Relaxation Linear Approximation Proportional Fairness V Whitespae A I INRODUCION N unpreedented inrease in the deployment of ontent delivery networs (CDNs) has resulted in the rapid growth of IP traffi It is reported that by the end of 216 global IP 21 traffi exeeded 1 zettabytes ( 1 bytes) per year of whih 62% is attributed to CDNs [1] It is also antiipated that by 219 M Asif Raza is with the Shool of Eletrial Engineering and Computer Siene Gwangu Institute of Siene and ehnology Gwangu South Korea raza@gistar Zafar Iqbal is with the Shool of Eletrial Engineering and Computer Siene Gwangu Institute of Siene and ehnology Gwangu South Korea zafar@gistar Sang-Seon Byun is with the Computer Engineering Department Catholi University of Pusan Busan South Korea ssbyun@gmailom Hyundu Kang is with Eletronis and eleommuniations Researh Institute 218 Gaeong-ro Yuseong-gu Daeeon 35-7 South Korea henry@etrirer Heung-No Lee * is with the Shool of Eletrial Engineering and Computer Siene Gwangu Institute of Siene and ehnology Gwangu South Korea heungno@gistar( * the orresponding author) nearly two-thirds of global IP traffi will originate from non-pc devies mainly portable and mobile devies [1] On the other hand urrently available wireless spetrum is onsidered insuffiient for aommodating suh large volumes of data Fortunately the digitization of V transmission has partially relinquished VHF and UHF spetrum [2] Owing to its low loss and exellent propagation harateristis the V spetrum is onsidered a promising andidate for supporting the growing traffi over wireless hannels Considering the growing demand of the wireless spetrum the regulatory bodies worldwide [3] [4] [5] have permitted unliensed use of the V spetrum under ertain limits to protet the inumbents However the problem of oexistene of seondary devies operating in the same V band was not dealt by the regulatory bodies he oexistene among seondary devies operating in V spetrum is onsidered a hallenging tas due to signal propagation harateristis of V hannels spatiotemporal variation of V spetrum and disparity in networ tehnologies of devies operating in the V spetrum [6] hese diversities may ause oexistene issues suh as an unresolvable interferene spetrum ongestion diversity in networ size et as explained in [6] [7] [8] [9] o address oexistene issues and regulate aess to V spetrum IEEE has proposed an standard [1] he standard provides a set of proedures to enable oexistene among seondary networs operating in heterogeneous networ tehnologies in VWS namely WSOs A set of proedures that ensures peaeful oexistene among a set of WSOs operating in the same spetrum is referred to as CDM [11] In this paper we define an ompliant CDM system that performs VWS sharing among a set of WSOs operating in dissimilar MAC/PHY layer tehnologies and registered in the oexistene manager (CM); an entity in oexistene system as shall be defined in setion III-A Note that the VWS refers to the V spetrum not in use by liensed operators in a spatio-temporal region [1] he VWS sharing problem is modeled as an optimization problem with an aim to maximize the system performane metris lie system throughput and fairness in VWS alloation he optimization problem is onstrained that the hannel demands of the WSOs registered in the neighboring CMs are satisfied In this perspetive variations of the SNR of wireless frequeny hannels whih result in variable throughput gain of the WSOs are taen are of Note that the neighboring CMs refer to the set of CMs whose WSOs reate interferene to eah other and suh WSOs are neighboring WSOs hus the proposed CDM

2 system differs from the notion of traditional node-based lin-based or base-station based hannel alloation as reported in the VWS sharing literature Moreover the proposed system also improves the VWS utility by implementing a frequeny reuse (FR) method to spatially reuse the available V spetrum in a oint time-frequeny domain in an ad ho oexisting environment In this paper the ad ho oexisting environment refers to the oexistene of both infrastruture based WSOs lie WLAN and ad ho WSOs lie personal area networ An ad ho WSO aounts for a loal area networ that is built spontaneously as devies onnet with eah other he CDM system proposed in this paper is unique to the of our nowledge in the sense that it ointly fouses three distint VWS sharing obetives; a) optimizing system performane metris during VWS sharing among WSOs registered in neighboring CMs in system b) improving the VWS utility by implementing the FR in a oint time-frequeny domain ) taing are of the hannel demands of the heterogeneous-wsos Suh a oint fous to implement multiple distint hannel alloation features maes the proposed system a versatile CDM system he remainder of the paper is organized as follows Setion II reviews some related studies Setion III summarizes tehnial baground required to establish the baseline for the tehniques used in the paper he system desription and problem formulation are defined in Setion IV Setion V disusses the solution method and the proposed algorithm Setion VI presents the simulation results and ompares the proposed algorithm with existing algorithms Finally Setion VII onludes the paper II PREVIOUS WORK In this setion we summarize some standards and algorithms developed for ahieving oexistene among seondary users IEEE [12] and [13] have partially addressed the oexistene issue among devies operating on wireless loal area networs and low power wireless personal area networs respetively However these networs operate on industrial sientifi and medial bands On the other hand IEEE 8222 has reently defined PHY and MAC layer extensions for VWS Similarly IEEE 8211af [14] has adopted new ognitive radio features to protet inumbents and ahieve effiient spetrum utilization among unliensed devies IEEE has also defined methods for peaeful oexistene when a low-power liensed devie suh as a mirophone broadaster and an unliensed devie both oexist and share the same hannel [15] he European Computer Manufaturers Assoiation (ECMA) has also defined a speifiation (ECMA 392) for personal/portable ognitive wireless networs operating in VWS [16] However all these standards define self-oexistene in VWS operations Non-availability of ross-platform oexistene mehanisms shall ause issues suh as an inability to diagnose interferene among networs with dissimilar networ tehnologies and may lead to ineffiient utilization of the sare wireless spetrum [11] Pereiving the need for ross-platform oexistene mehanisms IEEE has defined an standard his standard provides oexistene protools and poliies for effiient utilization of VWS aross platforms [1] On algorithmi perspetive a CDM algorithm that results in fair VWS sharing among neighboring CMs is presented in [1] he algorithm applies max-min fairness tehnique to establish fair share distribution during the VWS sharing proess he issue with the algorithm in [1] is that it fouses fairness in alloation while no onsideration to effetive utilization of the available VWS is taen are Considering the sarity of the V spetrum espeially in highly ongested spetrum environments the effetive utilization of the available V spetrum is also an important fator to be onsidered Hessar and Roy [17] have disussed the VWS sharing formulations in seondary ellular networs he authors adopt heuristi based approahes to defining greedy algorithms to tale the identified VWS sharing problems However the proposed greedy algorithm for throughput maximization sub-problem searhes the entire networ to find an optimal solution For suh an algorithm searh over the spae of a possibly very large number of networ and hannel olloation ombinations leads to a high runtime omplexity to find an optimal solution An algorithm for opportunisti whitespae sharing among seondary networs has been presented as a graph oloring problem in [18] he hannel sharing algorithm in [18] solves the sharing problem by lassifying the sharing proess as networ wide hannel sharing and its loalized version his sheme however has performane issue when interferene among neighboring aess points is relatively high his situation is quite ommon in highly ongested areas where many olloated WSOs are deployed Bahra and Par [1] proposed an algorithm for CDM among heterogeneous networs he sharing problem in [1] is modeled as a weighted-sum multi-obetive optimization problem (MOOP) that is solved using a modified Boltzmann mahine However an issue in the weighted-sum approah is that it does not find Pareto optimal points in non-onvex regions of the solution spae boundary [19] hus some of the potential Pareto optimal points are possibly missed by the weighted-sum method Khalil et al have also performed VWS sharing among heterogeneous networs by defining an interferene graph of the networs [2] A two-stage algorithm is then designed to ahieve spetrum sharing among graph nodes he algorithm maximizes fairness by maximizing the frequeny reuse However the hannel sharing algorithm in [2] has polynomial runtime omplexity 3 ( N ) for the number of networs (N) his omplexity shows that in areas with a high number of deployed networs the algorithm shall require substantial hannel alloation time Zhang et al [21] adapt eology based speies ompetition model to develop a oexistene mehanism alled eologial Speies Competition based HEterogeneous networs oexistene MEhanism (SCHEME) he SCHEME enables eah oexisting networ to adust ahieved bandwidth per its QoS requirements dynamially However the SCHEME requires the number of hannels to be larger than the number of oexisting networs Suh ondition annot be fulfilled in highly ongested urban areas where a limited number of V hannels is available for unliensed use We have addressed this issue in the

3 hannel alloation mehanism defined in this paper On the other hand some of the existing VWS sharing algorithms have implemented the onept of FR For example in [22] Bian et al have implemented the onept of FR in sharing a single V hannel among Cognitive Radios (CR) he CR networs operating in orthogonal frequeny division multiple aess apply the uplin soft FR onept [23] Again the proposed method is defined for CR systems deployed in ellular infrastruture Similarly Hessar and Roy [17] have presented an FR method in ellular networs operating in VWS Moreover the algorithm proposed in [17] orthogonalizes WSOs in frequeny domain only None of the existing VWS sharing algorithms reuses VWS in a oint time-frequeny domain for WSOs operating in an ad ho oexisting environment Spetrum reuse in both time and frequeny domains shall result in even a better utilization of the available VWS as disussed in Setion VI-C Some geneti algorithms (GA) defined for implementing the hannel sharing problem also exist in the literature For example the authors in [24] use a GA-based reliability model to assign hannels to mobile hosts based on the reliability of the base station and the hannels to enhane the overall reliability of the mobile networ system he results show that this method requires higher number of iterations and generally higher number of available hannels than the number of mobile hosts in order to ahieve higher reliability Similarly Shrestha et al proposes a GA-based oint out-of-band spetrum sensing and hannel alloation sheme for ognitive radio networs [25] he oint sensing and resoure alloation optimization problem has been formulated using fitness funtions of sensing utility and the data transmission utility Jao and Joe onsider a new ognitive radio networ model with heterogeneous primary users operating simultaneously via multi-radio aess tehnology [26] It fouses on energy effiient resoure alloation and use a GA-based sheme to obtain an optimal solution in terms of power and bandwidth he authors in [27] proposed solutions for the problem of effiient resoure alloation (radio spetrum and power) in the OFDMA-based multiast wireless system that balanes the tradeoff between maximizing the total throughput and ensuring a flexible and ontrollable spetrum sharing among multiast groups It proposes two separate optimization methods for subarriers and power and a GA-based oint optimization sheme is used Results show that the proposed shemes an attain a high total sum-rate and more flexible and fair distribution of the available bandwidth among multiast groups he GA in these and suh literature wor [28] [29] are well suited for multi-obetive optimization problems that require searhing over a large spae under several onstraints However GA-based methods are omputationally expensive and therefore not suitable for the optimization problem with single obetive funtion and a small searh spae lie the one defined in this paper herefore GA suffers from the drawbas of slow onvergene speed and low stability he hannel alloation in highly dynami spetrum environments requires an algorithm that an do alloation proess in a qui runtime herefore rather than applying the GA method the Fig 1 IEEE VWS system arhiteture he VWS database and WSOs interat with the arhiteture externally nonlinear binary onstrained optimization problem defined in this paper is transformed into linear optimization problem Suh formulation helps us to apply linear programming solvers to solve the optimization problem and omplete the alloation proess in a qui linear runtime III ECHNICAL ERMS AND RESEARCH FOCUS A ehnial erms In this setion we define tehnial terms that form baseline of the proposed VWS sharing system defined in the next setion he proposed system is based on the oexistene system arhiteture as desribed in [1] and shown in Fig 1 he oexistene system in [1] has three logial omponents: oexistene manager (CM) oexistene enabler (CE) and a oexistene disovery and information server (CDIS) he CE registers a WSO to the CM and ats as a ommuniation bridge by translating messages between the WSO and the CM serving the WSO he CM maes oexistene deisions for WSOs registered in it Moreover it is required to interat with other CMs alled as neighboring CMs in [1] to resolve oexistene issues among WSOs served by neighboring CMs In general it sends onfiguration ommands and ontrol information to the CE he CDIS provides oexistene disovery servies lie oexistene set information to CMs for registered WSOs he VWS database (VDB) as shown in Fig 1 is not part of the oexistene system arhiteture It ontains information about hannels available in the geographi region of eah WSO registered with the system he VWS database provides information about the set of V hannels free for whitespae ativity to the CMs A WSO may register with the IEEE system before operating in the V spetrum In the registration proess a general priniple for a WSO to aquire a V hannel is defined in IEEE summarized as follows A WSO may perform spetrum sensing to identify and selet an available free V hannel or alternatively it may send a hannel

4 alloation request to its serving CM If no free hannel is available in the geographi region of the WSO the CM may perform hannel sharing among the requesting WSO and the WSOs pre-alloated a V hannel If suh WSOs are registered with other CMs the CM serving the hannel requesting WSO interats with the other CMs to perform hannel sharing hese CMs are alled as neighboring CMs to the requesting CM In this hannel sharing proedure two types of topologies are defined in the [1] A distributed CDM topology where neighboring CMs mutually interat to perform hannel sharing among WSOs registered within them A entralized CDM topology where multiple CMs agree to selet one of them a master CM (MCM) and rest of the CMs beome slave CM (SCM) [1] as shown in Fig 1 Eah SCM provides essential information about operating parameters inluding the hannel harateristis of eah WSO registered within it and its hannel demands to the MCM he MCM performs oexistene servies lie radio resoure alloation to WSOs registered in the SCMs Some other terms used in the paper are defined as follows A WSO is an entity in system that represents a VWS devie or networ of devies he hannel oupany is the duty yle in a perentage that a networ (WSO) oupies a hannel [1] he window time is a slot duration of a sheduling repetition period that satisfies the essential system QoS performane [1] he Coexistene Set (CS) of a w th WSO is a set of WSOs that are registered in the neighboring CMs that may affet the performane of the w th WSO In other words it is a set of WSOs whih reate interferene to the w th WSO B Researh Fous he VWS sharing problem is defined as Given a set of available V hannels a set of CMs with eah CM having at least one WSO registered in it and WSOs hannel demands share the V hannels among WSOs suh that the following obetives are ahieved 1) Maximize the system throughput 2) Minimize unfairness in alloation among WSOs registered in neighboring CMs and 3) Fulfill desired hannel demands of the alloated WSOs hese obetives ontradit eah other For example maximizing the system throughput shall derease fairness in alloation Note that from a spetrum alloation perspetive fairness is regarded as equity in aess to the resoure the V spetrum In other words being free to use eah networ should have an equal opportunity to an aess to the given V spetrum Similarly fulfilling the seond and third obetives in onuntion under the sarity of the available VWS restrits the system aommodating as many as WSOs in the VWS hus maximizing the fairness while satisfying the hannel demands of eah alloated WSO is quite ompliated in highly ongested spetrum environments [3] herefore the fairness in alloation is measured at CM level he fairness among CMs is deemed at minimum if at least a single WSO in eah CM gets the hannel Considering the above onditions we design a CDM system as will be defined in Setion IV-A he system is designed to implement at the MCM in the entralized topology in as shown in Fig 1 he system maes use of the information from information messages defined in the [1] to apply various proedures for defining the proposed VWS sharing problem as an optimization problem For example the WSO registration lause in [1] defines different information aquiring messages that permit a CM to ollet desired hannel demands hannel statistis oexistene set elements available V hannels and related information from WSOs registered within it or with neighboring CMs Moreover the inter-cm information sharing messages are also defined in [1] We assume that using suh message templates the neighboring CMs exhange respetive WSOs information with MCM In order to solve the VWS sharing problem the CDM system in MCM then implements a hannel alloation proess as will be defined in setion V-C he algorithm maes use of suh information available at MCM to implement the subgradient method to solve the VWS sharing dual problem Setion V-B to identify a set of WSOs to alloate the V hannels he hannel alloation proess also implements a novel spetrum reuse in able 3 to have an effiient use of the available VWS he spetrum reuse step is also made in ompliant with the by repeated hannel alloation using an interferene matrix he CDM defines the interferene matrix using the WSOs CS information available at MCM as shall be disussed in Setion V-D Note that the CS information is provided by the oexistene disovery algorithm as defined in [1] he hannel alloation proess is then exeuted repeatedly to spatially reuse the V spetrum to the unalloated WSOs that should not ause interferene to pre-alloated WSOs he proposed hannel alloation solution is thus made smoothly integrable to the system IV SYSEM DESCRIPION AND PROBLEM FORMULAION In the following setion a entralized CDM system is designed that implements a hannel alloation proess as shall be disussed in Setion V to implement the VWS sharing problem defined in Setion III-B A System Model he CDM system is defined as follows X VWS( ) (1) he system parameters are defined as follows Let be an index to a set of C neighboring CMs in the system denoted as in able 1 Let be a set of networ IDs of WSOs registered in the th CM as shown in able 1 Let the networ ID NIDw represents an identifier of the networ the w th WSO registered in th CM represents For example in the ase of IEEE 8211 type WSO the NID ontains the basi servie set identifier used by the WSO Let be an index to the set of all permissible V whitespae 12 J where eah set element hannels orresponds to a V hannel number defined on the basis of

5 Oupany ime WSO1 the regulatory authority rulings For example in USA where FCC defines eah V hannel to be 6 MHz bandwidth in in the V/UHF band therefore USA Sine the availability of a V hannel to a w th WSO is a funtion of geographi loation of the WSO and the primary user ativity in the region herefore the availability of a V hannel for the seondary use varies spatiotemporally and needs to be determined We assume that a hannel sensing mehanism as defined in [1] is implemented suh that the VDB ontains the set of V whitespae hannels available in the geographi region of eah WSO registered in the CMs in the system Let be an index to the set then th hannel availability status to the w th WSO registered in th CM is represented by an indiator funtion defined as z w Window ime Oupany ime WSO2 th th 1 if hannel in is available to w WSO : (2) otherwise he availability of J hannels to the w th WSO registered in th CM are thus represented by a vetor of indiator funtions defined as z z z w w1 w J he set of hannels available to W WSOs registered in th CM is defined as he system parameter Oupany ime WSO3 1 2 W Z z z z is then defined as follows 1 2 C Z Z Z (3) he parameter in the system in (1) represents the set of window times for the hannels in the set In an algorithm is provided that enables CMs to define the slot duration of the window time We assume the CMs implement suh an algorithm to define the window time whih is then used to define system parameter as Oupany ime WSO1 Window ime Oupany ime WSO2 Oupany ime WSO3 Fig 2 Sheduling transmission periods for three WSOs on a V hannel ime 1 J (4) he system parameter in (1) enodes hannel demands of CMs defined as follows In [1] a Disovery Information abstration is provided that allows WSOs to send hannel statistis and hannel demands lie SINR desired hannel oupany desired bandwidth et to their serving CM [1] Suh information of heterogeneous-wsos is used to define a set of hannel demands of w th WSO as follows Let SINR w represents the quality of th hannels to w th WSOs registered in th CM he hannel quality is measured in terms of signal to interferene and noise ratio (SINR) whih depends on interferene from primary-to-seondary users and noise floor due to environmental fators We assume that an interferene disovery mehanism is in plae that enables eah WSO to measure SINR value on eah of the hannels in as will be further disuss in Setion V-D he quality of all J hannels to w th WSO is then defined as Let s p w w SINRw1 SINRw2 SINRw J w be the allowed transmission power to w th WSO in the th hannel he allowed transmission power to w th WSO on J hannels is then defined as p p p w w w1 w J Let B w be the bandwidth demand of w th WSO he number of hannels required by w th WSO is then alulated as b w B b ABLE 1 DEFINED PARAMEERS Input Variables Symbol Desription Value I O w wm w y w z w x w A set of C CMs in the system A set of NID of W WSOs registered in the th CM A set of permissible V hannels in the system Channel demands of WSOs as defined in the system in (1) CO that translates desired oupany demand of w th WSO on a th hannel Indiator variable enoding m th WSO interferene to w th WSO on a th hannel m Set of WSOs suh that m th WSO transmission interferes w th WSO transmission on th hannel A variable indiating whether m th WSO interferes w th WSO on the th hannel? Z defining aessibility of th w n w where represents the hannel bandwidth Let O w translates to a timeslot here alled as hannel oupany time (CO) in a window time suh that the w th WSO registered in th CM an ahieve its desired hannel oupany in the alloated th hannel he relation of CO to a hannel window time is shown in Fig 2 where three WSOs are sheduled in the window time in a single V hannel he COs of w th WSO in J V hannels are then represented as O I 1 2 C NID1 NID2 NID W {12 J} - w Ow Ow 1 J wm y w w 1 if m interfers w : otherwise m 1 w : m : else w th An element of the matrix 1 if aessible to w WSO else hannel to w th WSO Output Variables Element of matrix X defining alloation status of w th WSO on th 1 if hannelalloated x w : otherwise hannel

6 o O O w w1 w J he hannel demand set of w th WSO is then defined as follows s p n o w (5) w w w w he hannel demand set of th CM is then defined using hannel demands of its registered WSOs as follows N where 1 s s s W 1 p p p W 1 N n n W C o o o W Let Ss s s 1 2 C 1 2 C 1 2 C N N N N s p o (6) and P p p p O o o o the system parameter is then defined using the hannel demands of all neighboring CMs as follows S P N O (7) he system in (1) then exeutes the hannel alloation algorithm as will be disussed in Setion V to alloate V hannels to the WSOs registered in the neighboring CMs suh that the alloation satisfies the required system QoS performane he system QoS performane is preserved if the following alloation ondition is satisfied Ow (8) w where refers to the window time in a th hannel he algorithm proposed in Setion V solves the VWS sharing optimization problem as will be defined in (14) and outputs a hannel alloation matrix defined as follows Let xw 1 be a binary deision variable suh that if xw 1 the th hannel is alloated to the w th WSO registered in th CM; otherwise x he alloation status of WSOs registered in w the neighboring CMs is then represented by a matrix X as X x11 x12 x 1 J x 1 x 1 x 1 W 1 W 2 W J X : x11 x12 x (9) 1 J C C C x C x C x C W 1 W 2 W J where W ie the number of WSOs registered in the th CM he w th row in the X represents the hannels alloation status in the set to the w th WSO registered in th CM he th olumn in the X represents the hannels alloation status of all the WSOs from all the CMs in the set he alloation matrix X thus orthogonalizes WSOs registered in the neighboring CMs in a oint frequeny-time domain he WSOs sheduled on different hannels an transmit at the same time using their respetive allotted hannel (frequeny slot) while WSOs sheduled on the same hannel an transmit in their respetive time slot (here CO) he system in (1) thus implements the VWS sharing problem defined in Setion III-B as an optimization problem as disussed in the following setion B Problem Formulation In this setion the proposed VWS sharing problem is formulated as an optimization problem using well-established proportional fairness method It is beause the proportional fairness is onsidered one of the most suitable methods to ahieve a trade-off between two ompeting interests [31] [32] [33] Originally Kelly defined the proportional fairness as an adustment proess whih adusts the rates of users aording to the harges they pay he proportional fairness method thus was defined for elasti traffi in omputer networ servies [34] Similarly in the hannel sharing literature a proportionally fair alloation mostly has been ahieved by adusting the rates of the users based upon some performane riteria lie maximizing the resoure utilization et [35] [36] However applying the proportional fairness in its original to model the VWS sharing problem proposed in this paper is not suitable It is beause the third obetive in the problem defined in Setion III-B maes the resoure alloation as binary deision alloation ie a hannel is either alloated to a WSO x 1 or not x herefore w WSO alloation (here CO) adustment is not possible Consequently we rewrite the proportional fairness in a binary deision alloation perspetive as follows Let the maximum data rate the w th WSO an ahieve on th hannel be defined by using Shannon hannel apaity formula r b log 1 SINR (1) w w he maximum rate r w is then used to defined a utility w funtion as a normalized rate ahieved by th CM in th hannel as follows w w w Ow O w w x r (11) where defines Kroneer delta funtion as: O w Ow 1 if Ow : otherwise his funtion prevents denominator term in (11) from beoming zero he utility funtion in (11) measures the worth of the resoure (hannel) to th CM ie given a hannel is alloated to the WSOs in the th CM for the duration of O how does it translate for the CM in terms of the w w ahieved throughput In other words maximizing the funtion in

7 (11) shall prefer a CM with WSOs ahieving high data rate and lower hannel oupany demand over a CM with WSOs ahieving low data rate and high hannel oupany demand Suh preferene based alloation shall lead to an effiient use of the resoures (VWS) he distribution U is then said CJ to be proportionally fair if it is feasible and for all other feasible solutions V v CJ the following holds [34] v (12) It has been shown in [34] [37] that the rates ahieved by users beome proportionally fair if the sum of logarithmi rates obtained is optimized Moreover it is shown in [38] that if all rates are proportionally fair they maximize the throughput over all other feasible throughputs herefore if the logarithmi sum of the utility funtion in (11) is maximized the normalized rate ahieved by neighboring CMs shall beome proportionally fair Let a th hannel is said to be alloated to the th CM if at least one of its registered WSO is sheduled on the hannel he alloation status of the hannels in the to the th CM is then defined as follows x11 x12 x 1 J x : (13) x x x W 1 W 2 W J Let J Let O O be the th olumn vetor in CO demand matrix in the system parameter defined as C O1 O2 O 1 O 1 O C W W O where W Let X X represents the th olumn vetor of the alloation matrix X he VWS sharing problem is then defined as follows O max log 1 (14 a) subet to x Z (14 b) X x1 (14 ) N (14 d) x 1 (14 e) he onstraint in (14b) ensures that a hannel an be alloated to the WSOs registered in th CM only if the hannel is available in their respetive region ie xw x 1 iff zw z w 1 he onstraint in (14) ensures that the WSOs sheduled in a th hannel preserve the system QoS performane as defined in (8) ie the total alloated hannel oupany time of oexisting WSOs must preserve the hannel window time he onstraint in (14d) ensures that the number of hannels alloated to the th CM is restrited by the number of hannels desired by its WSOs Finally (14e) fores the deision variable to be binary valued he onstraints in (14e) and (14) helps the system in (1) to satisfy the third obetive of VWS sharing problem in Setion III-B he optimization problem in (14) sees to optimize a onave obetive funtion over a onvex set he problem in (14) has a unique solution as from the optimization theory [39] maximizing a onave funtion over a onvex set has a unique solution A solution approah to the problem in (14) is presented in the following setion V SOLUION MEHOD he nonlinear obetive funtion (14a) and binary-valued onstraint (14b) maes the problem in (14) a nonlinear ombinatorial optimization problem Determining the optimal solution of suh a problem is a hallenging tas as the problem beomes intratable as the number of disrete variables inreases [4] herefore to ease the solution approah the problem in (14) is transformed into a linear programming problem with relaxed binary onstraint A Linearization he obetive funtion (14a) is linearized using a pieewise linear approximation In this proess tangent line approximation is used to approximate the obetive funtion in (14a) denoted as F he detailed desription of linear approximation is provided in Appendix A Using this funtion the problem in (14) is linearized as max F (15 a) subet to x Z (15 b) X (15 ) O x1 N (15 d) x 1 (15 e) o tale the binary-valued onstraint (15b) we apply Lagrangian relaxation as explained followings B Lagrangian Relaxation Lagrangian relaxation [41] relaxes a subset of onstraints by adding them to the obetive funtion with a penalty term alled the Lagrangian multiplier Let λ : w be the Lagrangian WJ multipliers matrix hen the relaxed problem an be defined as X λ λ Z x max P F (16 a) X O subet to : X (16 b) x1 N (16 ) x 1 (16 d) For a given λ the Lagrangian relaxation an be defined as h λ max P X λ : onstraints(16 b) (16 ) (16 d) (17) X hen the generalized dual problem of the relaxed problem is defined as followings

8 ABLE 2 ALGORIHM: DUAL PROBLEM BASED ON LAGRANGIAN RELAXAION Step : * h L min λ : λ (18) λ he solution to (17) is the upper bound of the solution to the original problem (16) Note that (17) is a onave funtion For a onave funtion a gradient-based approah is generally used to ompute a value as lose as desired to the optimal value hus if h would have been differentiable we an use a gradient desent method to have a onvergene toward the optimal value he proposed problem however annot be solved using a gradient desent method It is beause the obetive funtion is pieewise linear whih is non-differentiable at the intersetion point of adaent linear piees but sub-differentiable at this point he subdifferential of h λ at suh a point is the set of all subgradients at that point hus we need to ompute a sequene of λ suh that either hλ onverges to the optimal a) Choose initial values of b) Set parameters for example min 2 1 max 1 solution using the subgradient method whih is given in the following dual algorithm he onvergene property of the subgradient algorithm is presented in Appendix B C Subgradient Algorithm for Lagrangian Relaxation based VWS Sharing Problem he algorithm defined in able 2 an be desribed as follows In Step the input parameters to the algorithm are defined as follows he initial values of λ are defined randomly he parameter is used in defining step size t λ iter max iter 5 upper F h Step 1: a) Inrement as 1 1 Step 2: Step 3: Step 4: Step 5: iter iter = h b) Given λ solve the relaxed problem using any linear programming tehnique and obtain Validate X w X as: set xw : if z Perform frequeny reuse as in able 3 and get Use X X X WJ to ompute the value of the funtion in (16a) alled as F and fairness index value H in (2) If F F a) Use X : F F to ompute: h upper F and X X h - Subgradient vetor as hλ w w - Dual obetive in (18) upper h hλ - Step size as t hλ 2 1 b) Update the dual variable as λ λ t hλ Step 6: If h hλ then h hλ max iter min else if iter then max 2 iter Step 7: max and If t 1 or > stop; otherwise go to Step 1 max defined in the range limit of maxiter min parameter is updated he 2 [41] he iter with upper ounts the number of iterations after whih the max is defined as stopping riteria for the algorithm he algorithm uses variables initialized in Step to apply a linear programming (LP) solver to solve the dual problem and obtain the th iteration alloation matrix X LP solvers are available on both the ommerial and freeware basis he entries in X are then adusted based upon the orresponding entries in Z w suh that x x x X are set equal to w w w zero if the orresponding element z z z Z is zero his validation ensures the onstraint in (14b) he algorithm then applies the FR proess in Step 3 in able 2 In this proess the algorithm maes use of the urrent alloation vetor and interferene matrix as shall be disussed in Setion IV-D to identify a set of WSOs whih do not get the hannel he algorithm then repeatedly applies LP solver to performs hannel alloation to the unalloated WSOs suh that they do not ause interferene to the alloated WSOs of neighboring CMs he FR proess is detailed in Setion V-E he outome of FR proess is an updated alloation matrix whih is then used to ompute the funtion values in (16a) and the fairness in alloation among neighboring CMs Several fairness measures or metris are used in the literature to determine whether networs are reeiving a fair share of spetrum or not For example max-min fairness Jain s fairness index fairly shared spetrum effiieny worst-ase fairness In this paper we adopt Jain s fairness index [42] to measure fairness in alloation among neighboring CMs he reason is that it satisfies the desired properties of fairness measure lie population size independene ontinuity et as listed in [43] hese properties are important to be onsidered in measuring the fairness in alloation For example the ontinuity property shows any slight hange in the alloation of individual WSO hus an ineffiient use of the VWS is identified by the fairness index as a WSO with bad hannel harateristis gets a high proportion of the spetrum It is ensured through the use of the ontinuous alloation metri lie fration of throughput demand as defined in (19) Suh an alloation metri is suitable to measure the fairness in alloation for the ase where WSOs demand unequal hannel bandwidth [43] herefore based on the fration of throughput demand of CMs an alloation metri is defined as follows d (19) d X where d and d represents the maximum data the th CM desire to transmit and it an transmit using its alloated hannels respetively hese terms are defined as follows Let the maximum data the th CM an transmit using its alloated hannels is defined in terms of the data the WSOs registered in it an transmit defined as follows w w w w X d x O r (2)

9 Note that hannels are onsidered as additive white Gaussian noise (AWGN) he data the CM desires to transmit is defined as d O r w w w he normalized throughput vetor is then adopted to measure fairness in alloation using Jain s fairness index [42] as 1 2 H C C 1 C 2 2 (21) Funtion H in (21) outputs a value in the range of [ 1]; when the value is loser to 1 the alloation is deemed fairer If the urrent iteration value of the obetive funtion F is optimal then F is updated with F and X with iteration progresses the feasible primal h λ F X As the and lower bound approah gradually to the integer optimal by adusting using the subgradient method as defined in Step 5 In Step 5 the sub-gradient vetor of the obetive funtion and the Lagrangian multiplier vetor for the th iteration are alulated he step size t is used to alulate the multiplier vetor for the next iteration he Lagrange multipliers are thus adusted iteratively he onvergene property of the subgradient algorithm is disussed under Appendix B he algorithm terminates as one of the termination onditions satisfied: Dual step size beomes less than a set threshold or the number of iterations exeeds the maximum number of iterations After the overall iteration ends we regard the final value of F as the approximated optimal solution and the orresponding alloation matrix X is the algorithm output he interferene matrix Y that is used to implement the FR step in able 3 is defined in the following setion D Interferene Matrix he WSOs registered in the neighboring CMs and interfering on the available V hannels is represented using an interfering matrix alled as Y-matrix in this paper Note that the Y-matrix does not model the interferene among oexisting WSOs Rather it represents the set of WSOs whih annot transmit simultaneously on the available VWS due to interfering transmission regions In fat in IEEE [1] a oexistene disovery algorithm is presented that the CDIS and CM run to perform the statistial analysis of the expeted interferene among oexisting WSOs Briefly the algorithm in [1] taes the WSOs geographi loation transmitter and reeiver harateristis antenna height and diretivity height above average terrain and other related parameters to exeute interferene disovery proess In this proess a umulative distribution funtion of the potential interferene from m th WSO to w th WSO is estimated Both of these m th and w th WSOs ould register to the same CM or different CMs in the system he minimum interferene level experiened by 9% λ devies of the w th WSO is then taen as the potential interferene value from an m th WSO to w th WSO he measured interferene value is then ompared to a threshold If the value is greater than the threshold the m th WSO is onsidered potential interferer to the w th WSO and is inluded in its CS A similar rule is applied for interferene disovery of the w th WSO into the m th WSO hus the outome of the interferene analysis proess is a CS of eah WSO registered in the CMs in the system he system in (1) then maes use of the CS of eah WSO to generate a Y-matrix as follows Let a set I m be an enoded CS of w th w w m WSO on a th hannel suh that an indiator variable I wm 1 if m th WSO interferes w th WSO transmission on the th hannel as defined in able 1; otherwise he enoded CS of all I wm the WSOs oexisting on th hannel are then used to define a th hannel interferene matrix as follows where y I12 I1 W y : (22) IW1 IW2 in diagonal vetor in y represents don t are ondition his ondition translate a self-interferene indiator variable I having no meaning he w th row in ww matrix represents enoded CS of w th WSO he interferene matries for all hannels in the system are then used to define an interferene matrix Y as follows 1 2 J Y y y y (23) he VWS sharing algorithm in able 2 maes use of the interferene matrix Y to implement FR in sharing VWS among heterogeneous WSOs as disussed in the following subsetion E Frequeny Reuse he frequeny reuse (FR) subroutine in able 3 performs spatial reuse of the V spetrum to enhane its effetive utilization he FR proess is implemented to the WSOs do not getting hannel in the initial alloation phase in Step 1 able 2 his requires to identify a set of unalloated WSOs eligible for the FR In this proess an enoded CS w m and an interferene matrix Y are used to define the set of unalloated WSOs o generate enoded CS and Y-matrix we mae use of the CS of eah WSO available at MCM Note that the defines different message lauses that enable CMs to exhange their WSO related information [1] Let us assume the CS of WSOs are available to CDM at MCM Given suh information available an enoded CS of WSOs w m and an interferene matrix Y are generated as defined in Setion V-D Initially the Y-matrix is filled with all ones Let X be an initial alloation matrix available from Step 2 able 2 he Y-matrix is then updated based on the X and m in w y

10 Input: Output: ABLE 3 SUBROUINE: FREQUENCY REUSE λ X X CS X Step : Given CS generate enoded CS ie w w and Step 1: interferene matrix Y as defined in Setion V-D Given update y Y as: For eah w th WSO do: if X xw 1 : xm 1 and w m Iwm m : Step 1 able 3 as follows For eah th hannel in the system update interferene matrix y Y as 1) If th hannel is alloated to w th WSO set all w th row elements in y y Y equal to zero or 2) If th hannel is alloated to m th WSO and w th WSO is in the CS of m th WSO set all w th row elements in the matrix y equal to zero he above two steps identify the eligibility of the WSOs for implementing the FR proess For example if the w th WSO is already alloated a hannel we aim to restrit it in taing part the FR proess herefore the w th row entries in the entire Y-matrix are flipped zero in the first step above Similarly if a th hannel is already alloated to m th WSO and if w th WSO transmission in the th hannel shall reate harmful interferene to the m th WSO transmission the th hannel annot be spatially reused at unalloated w th WSO herefore Y-matrix entries orresponding to w th row are also flipped zero he updated Y-matrix thus defines a set of unalloated WSOs hese are the WSOs for whih at least one nonzero entry exists in the orresponding row in the Y-matrix as defined in Step 2 able 3 he subroutine in Step 3 able 3 then repeatedly alloates the available V hannels to the WSOs in the set as follows he relaxed problem in (17) is solved using any LP solver for the WSOs in the set and an alloation matrix X is obtained he X is then used to update X and Y-matrix as defined in Step 3-b)2) 3-b)3) and 3-b)4) respetively his repetitive update and alloation proess ontinues until all WSOs in the set get the hannel or no more FR is possible Let us apply the FR implementation in the oexisting senario shown in Fig 3 In this figure four WSOs operating in three networ tehnologies an IEEE 8222 regional area or Iwm m Step 2: Define unalloated WSO set in the system as Step 3: w : Iwm m While I wm and w m λ {} a) Given and ; solve the relaxed problem using any linear programming solver and obtain X b) Perform following updates: 1) Update 2) Update 3) Update X X w as xw : if z as X X X 4) Update Y as in Step 1 do \ w : xw 1 as if Fig 3 IEEE 8222 wireless regional area networ (WRAN) IEEE 8211 hotspots (HS1 HS2) and IEEE personal area networ (PAN) oexisting in some geographi region networ IEEE 8211 loal area networs and IEEE personal area networ are deployed in some geographi region he shaded area around eah transmitter denotes its transmission radius he irular lins between a transmitter and reeivers show wireless onnetivity between them he reeiver nodes in some networs reeive interfering signals from other olloated transmitters as shown in the figure Let WRAN HS1 HS2 and PAN are labelled as WSO and 4 respetively Let us assume eah of the WSO is registered in a dediated CM ie four neighboring CMs are available in the CDM system Let us suppose that a single V hannel is available in the region for seondary use hen based on oexisting senario shown in the figure the enoded CS of eah WSO an be defined as follows he Y-matrix is then populated from the bitwise OR operation on the CS of the WSOs he generated Y-matrix is Y 1111 Let for some given input parameters as listed in able 1 the algorithm in able 2 finds an initial alloation vetor X 1 1 he alloation vetor shows WSO 1 and WSO 3 are alloated the hannel he FR proess is then invoed he Y-matrix is updated to identify WSOs eligible for spatially reusing the hannel as follows he XOR operation is performed as Y XY his operation turns the entries in Y-matrix equal to zero where the orresponding entries in X-matrix are ones he Y-matrix at this stage loos lie Y 1 1 It is then updated using the CS of allotted WSOs as previously defined in the seond rule of Y-matrix update he seond entry in Y-matrix is thus flipped zero as WSO 2 is in the CS of allotted WSO 1 he updated Y-matrix then loos lie Y 1 he algorithm then solves the dual problem again and alloates the hannel to WSO 4 he final alloation matrix then loos lie X he final alloation shows that the available V hannel is reused at WSO 4 without ausing harmful interferene to allotted WSO 1 and WSO 3 F Sheduling Map One the alloation proess in able 2 and frequeny reuse in able 3 terminates the CDM system generates a sheduling map to send it to the CMs in the system he sheduling map (SM) is a map showing the WSOs sheduling periods arranged in window time in the alloated hannels In this paper the

11 sheduling period of a w th WSO refers to its hannel timeslot ie CO For example SM of three WSOs sheduled in an alloated V hannel is shown in terms of their CO defined in the window time in Fig 2 hus given the CO of WSOs and the alloation matrix X from the algorithm in able 2 the SM is a simple proedure of defining two timing parameters; transmission start time and transmission end time he CDM system defines the timing parameters for WSOs registered in the CMs in the system as follows Let a pair of transmission variables preisely define the time instane the w th WSO registered in th CM may start and stop its transmission on an allotted th hannel respetively he a variable C w m ( w ) start t w between two WSOs and stop t w start stop w tw t are alulated as follows Let be defined as the ost of sharing a hannel wm where mw represents a WSO m sharing a hannel with WSO w Let represents the ontrol overhead assoiated with MAC tehnology of the w th WSO he ontrol overhead is defined as the amount of time required to perform ontrol signaling while operating in the VWS his value is fixed and predetermined based upon the underlying networ tehnology of the WSO For example if an 8222 WSO employs OFDMA one OFDM symbol is used for both the frame preamble and the frame header; exept for the first frame in the superframe whih onsumes two additional symbols (1/4 yli prefix mode) If we onsider two OFDM symbols per frame as a ontrol region then using a symbol duration Sym=3733 ms [44] the ontrol overhead per frame is omputed as 7466 ms Other settings may generate different overhead Similarly if a WSO m operates in a different networ tehnology than that of the WSO w its ontrol overhead will be different from that of WSO w he total overhead in a hannel varies as the hannel is shared among heterogeneous WSOs he value of the parameter C is then defined simply by adding the ontrol overhead w m( w) of all WSOs sharing a hannel as follows: w m if MACw MACm w m Cw m( w) : (24) otherwise where refers to the set of WSOs with NID listed before NID of w th WSO in he timing parameters are omputed as start tw Om xm Cm mw and tw stop tw start Ow (25) m start hus the t w refers to the time instane in the sheduling window that all the WSOs m have utilized the hannel for the duration of their respetive CO Note that in defining the sheduling map we mae a simplifying assumption that the timers of WSOs in the system are pre-synhronized and WSOs sharing a th hannel have agreed on the referene time (the time instane the window time starts) as defined in [1] imer synhronization may be done by having agreements between servie providers managing the WSOs whih is outside the sope of this paper he CDM defines SM and send it to the SCMs he SCMs send the SM to the registered WSOs Suh implementation w shall redue the ontrol signaling between the WSOs and the pertinent CM he ontrol signaling is otherwise inevitable while performing ontext swithing among WSOs sheduled in the V hannel One the spetrum has been alloated the SM remains unhanged unless i) an inumbent appears in one of the assigned hannels ii) a hange in a WSO's hannel oupany demand or some other oexisting WSO's demand requires readusting the WSO's alloation VI SIMULAIONS AND ANALYSIS he performane of the proposed hannel sharing algorithm is ompared with two other hannel alloation algorithms proposed in [18] and [17] A Comparative Channel Alloation Shemes In this setion we summarize the alloation mehanism of the omparative VWS alloation shemes In [17] two VWS sharing problems are defined; one for maximizing the number of hannels alloated to the networs and the seond for maximizing the total throughput under the minimum fairness onstraint of alloating at least a single hannel to eah networ In this simulation setup we implement the seond problem as it losely mathes with the hannel sharing sheme proposed in this paper he VWS sharing algorithm proposed in [17] then selets a node (WSO) having a minimum of the assigned hannels and the minimum number of the available hannels to it he algorithm assigns a V hannel to the seleted WSO and alulates the total throughput It eeps assigning the hannel to other WSOs as long as the total throughput is inreasing his proedure is repeated for every hannel he algorithm terminates as no more inrease in the throughput is observed he VWS sharing problem in [18] is modeled as a lexiographi ordering of throughputs of aess points of oexisting networs he proposed problem is then transformed into a graph oloring problem An algorithm alled as Share is then proposed to solve the graph oloring problem he Share algorithm operates in three phases In the first phase of alloation it orthogonalizes the WSOs in the available V hannels (frequeny slots) In the seond phase a mutual hannel sharing is performed among allotted WSOs of the first phase under the ondition that their first phase throughputs do not derease he fairness is improved in the third phase by sharing the hannel with unalloated WSOs suh that lexiographially ordered throughputs do not derease We selet the algorithms in [18] and [17] due to the lose resemblane of their VWS sharing problems to the proposed hannel sharing mehanism For example both onsiders optimizing throughput under minimum fairness in alloation However there exist some fundamental differenes as well For example both the alloation shemes orthogonalize the WSOs in frequeny domain by alloating a dediated hannel to eah alloated WSO while the proposed sheme orthogonalize WSOs in a oint time-frequeny domain by sliing the available VWS in the frequeny bands and further sliing eah hannel (frequeny band) into a number of COs in the hannel window time as disussed in setion IV Moreover the algorithm in [17] is intended for VWS hannel alloation to ellular networs