Probabilistic Spectrum Assignment for QoS-constrained Cognitive Radios with Parallel Transmission Capability

Transcription

1 Pobabilistic Spectum Assignment fo QoS-constained Cognitive Radios with Paallel Tansmission Capability Haythem Ahmad any Salameh epatment of Telecommunication Engineeing Yamouk Univesity Abstact n this pape, we popose a multi-channel paallel tansmission mechanism fo channel assignment in cognitive adio CR netwoks The poposed mechanism enables seconday uses SUs to effectively utilize the spectum while limiting the disuption ate at both SUs and pimay uses PUs The main novelty in ou mechanism lies in consideing the andomness of link-quality conditions and lifetime duations of idle channels to povide a statistical pefomance guaantee fo SUs This consideation esults in impoved spectum utilization Specifically, ou mechanism attempts at minimizing the equied spectum esouces fo SU tansmissions subject to minimum ate demand and minimum success pobability equiements Simulation esults indicate that ou poposed assignment satisfies the pefomance equiements at SUs Results also show that utilizing the paallel tansmission capability of CRs while consideing the andomly time-vaying natue of thei opeating envionment allows fo highe spectum utilization and moe enegy saving TROUCTO Recently, CRs ae ecognized as the key enabling technology to enhance spectum utilization though oppotunistic access to the licensed spectum ue to the andomness of PU channel availabilities and link-quality conditions, the opeating envionment of CR netwoks CRs is chaacteized by thei andom time-vaying natue This dynamic and andom natue poses many challenges elated to development of distibuted channel assignment/access mechanisms that capable of poviding efficient SU communications [] [6] Specifically, a CR is epected to opeate ove a set of highly-sepaated fequency channels with diffeent popagation chaacteistics and timevaying link-quality conditions Wose yet, the availability of these channels and thei lifetimes ae also dynamically changing due to the andomness of PU activities [] Even afte identifying an idle channel o channels and using it fo a SU tansmission, the SU may be equied to immediately inteupt its tansmission, vacate the opeating channel channels, and enegotiate the opeating channels if new PUs become active Theefoe, the tansmission time needed fo a successful SU tansmission can be quite citical Thus, to impove spectum utilization, SUs should select thei opeating channels while jointly consideing the equied tansmission times ove the selected channels and the andomness in thei lifetime duations Such consideation can significantly impove the packet success pobability, which consequently educes the aveage numbe of etansmission attempts fo a successful packet delivey This peseves moe channels fo potential futue SUs, which educes the SU blocking pobability and allows fo highe spectum utilization and moe enegy saving n this pape, we develop a statistical appoach by which SUs can oppotunistically communicate ove multiple channels while pobabilistically guaanteeing thei pefomance Ou appoach leveages the unique capabilities of CRs while consideing the peculia chaacteistics of thei opeating envionment Specifically, the contibutions of this pape ae as follows ased on geneic stochastic models of PUs activity, we fist deive a geneal epession fo the pobability of success fo a SU packet tansmission ove multiple channels We show that the deived epession is a function of the instantaneous link-quality conditions and the statistical distibution of the availability duations of PU channels ased on the deived epession, we fomulate the spectum assignment poblem as an optimization poblem with the objective of minimizing the equied spectum esouces fo a given SU tansmission while satisfying pe-specified pobability of success and ate demand equiements We show that this optimization poblem constitutes a binay linea pogamming LP poblem, which is, in geneal, P-had Since computing the optimal solution fo such poblem gows eponentially with the numbe of idle channels, we develop a polynomial-time appoimate algoithm fo the LP based on a sequential fiing pocedue that povides a nea-optimal solution Though simulations, we show that the appoimate solution is within % of the optimal one The esults indicate that ou algoithm statistically satisfies the pefomance equiements unde diffeent taffic loads Ou simulation esults also show that ou assignment sults to a significant pefomance impovement in tems of thoughput and enegy consumption ove efeence channel assignment algoithms The est of the pape is oganized as follows n section -A, the netwok model is pesented An analytical epession fo the packet success pobability is deived in section - n section, the ou poblem is fomulated Section V descibes the poposed solution n section V, we pesent numeical and simulation esults Conclusions ae pesented in section V PRELMARES A System Model We conside a licensed spectum containing K nonovelapping channels of the same bandwidth The status of channel i is modeled as an independent -state model altenating between USY and LE states The USY peiod epesents the time that some PUs ae tansmitting ove channel i n this case, channel i cannot be used fo SU tansmissions The LE peiod epesents the time that //$ EEE

2 no PUs ae tansmitting ove channel i, and thus this channel can oppotunistically be used by SUs We assume that and ae geneally distibuted independent andom vaiables with finite means denoted by and, espectively Let F i T and F i T espectively denote the cumulative density functions CFs of and At any given time, the ith channel is available with pobabilityp i = / + We also conside a distibuted netwok of SUs, whee each SU is equipped with n tansceives that can be used simultaneously The n tansceives can be dynamically tuned to any idle channel in K Fo channel i, i K, the tansmission powe that a SU can use is if the channel is busy, o P ma i if channel i is idle, whee P ma i is the FCC egulatoy maimum tansmission powe ove channel i n addition, the total tansmission powe ove all selected channels fo a given SU tansmission is limited to P ma, whee P ma is the maimum powe suppoted by the CR s battey We assume that each SU can sense the spectum and estimate the instantaneous intefeence ove each channel Each SU equies a minimum tansmission ate, ie, the aggegate data ate ove all assigned channels should be geate than a pespecified tansmission ate equiement The pobability of successfully tansmitting a SU packet, denoted by P suc, is ou main quality of sevice QoS metic of inteest ecause of the andom natue of the opeating envionment of SUs, hee we conside a soft success pobability equiement in the fom P suc γ, whee γ is a given paamete Pobability of Success Analysis We now deive an epession fo P suc as a function of netwok paametes fo a SU data packet of size L with a given channel assignment Ω = {m,m,,m Ω }, whee m j epesents the jth channel in Ω efoe poceeding futhe, we need to detemine the distibution of the esidual time duation of the vaious PU channels Let the andom vaiable denote the esidual time duation of channel i The CF can be computed in tems of the CF of LE duation as [7]: T i of F i T t = t F T i t dt Let M K and R = {R i, i M} espectively denote the set of all idle channels sensed by communicating SUs and the set of achieved tansmission ates ove all channels in M Given the channel assignment Ω M and the tansmission ates ove the channels in Ω, the equied tansmission time ove the assigned channels t Ω can be computed as: t Ω = L Ri To poceed in ou analysis, we note that a packet tansmission is consideed to be successful ove the channels in Ω if the esidual idle duations of all channels in Ω ae geate than the equied tansmission time t Ω Given the above and noting that LE duations of PU channels ae statistically independent, the packet success pobability ove the selected channels in Ω P suc Ω can be computed as: P Ω suc = P min = PT m {, i Ω } t Ω,T m = P T i t Ω t Ω t Ω,,T m Ω t Ω = F i T t Ω Substituting into, P suc Ω can be ewitten in tems of as follows: P Ω suc = t Ω F T i τ dτ To make ou analysis tactable, we model the status of a PU channel i, i K as a Makov enewal pocess MRP that altenates between LE and USY states This model was peviously used in eg, [8] [] This model can captue the tempoal chaacteistics of PU channel availabilities Accoding to this model, LE USY duations fo the vaious channels ae statistically independent eponentially distibuted andom vaiables n addition, fo a given channel i, the duations of successive LE and USY duations ae independent of each othe ased on this model and using, we can show that F T i substituting F T i P Ω suc = ep t t = F i T t = e y t into, P suc Ω can be epessed as: t Ω = ep t Ω Fo i K, let i be a binay vaiable that is defined as: {, if channel i Ω i =, othewise y intoducing the binay vaiable i, P suc Ω can be ewitten in tems of i as: P Ω suc = P t Ω i = ep t Ω L M = ep M i= Ri i i i= i whee t Ω = L Ri i We note that the epession in 7 will be used in fomulating ou channel assignment poblem in Section PROLEM FORMULATO A ESG COSTRATS Ou objective is to optimize spectum-utilization efficiency by minimizing the total spectum esouce needed fo successful SU tansmissions Specifically, ou teatment is tageted at a distibuted CR that uses CSMA/CA-like policy fo contol communications to esolve channel contention between diffeent SU pais CSMA/CA-based potocols ensue that only one tansmission a SU tansmitte-eceive pai can 6 7

3 access the contol channel at any given time Fo this SU tansmission, the tansmitte and the eceive need to select the minimum numbe of channels to use while meeting the following constaints: C Hadwae constaint: Each SU is equipped with n tansceives that can be used simultaneously, ie, i n 8 C Received SR and aggegate data ate constaints: The eceived signal-to-intefeence-noise atio SR ove a selected channel i must be geate than a pe-specified theshold µ This constaint can be ensued by setting i = fo any channel i with SR < µ n addition, the aggegate ate ove all selected channels must be geate than o equal to a given ate demand R, ie, R i i R 9 C Total tansmit powe constaint: Fo a SU tansmission, the total tansmission powe P tot ove all selected channels is esticted to P ma, ie, P ma i i P ma whee P ma is the maimum powe suppoted by the CR s battey C Pobability of success constaint: The pobability of success P suc Ω fo a given SU tansmission must be geate than a pe-specified value γ This constaint can be epessed as: suc = ep L Ri i P Ω i γ y taking the natual log of both sides of and algebaically manipulating the esult, this constaint can be lineaized as: lnγ L Ri + c i i whee c i = Recall that ou objective is to compute the optimal assignment Ω that uses the least spectum esouce ie, minimum possible numbe of channels fo a given SU tansmission such that the pefomance equiements ae guaanteed Fomally, ou poblem can be fomulated as: minimize i i subject to C-C f multiple solutions eist fo this optimization poblem, we seek the one with the maimum aggegate ate This can be ensued by adding the tem Ri Ri i = i i to the objective R function, whee i = i ote that the intoduced tem is always < Hence, fo Ri any two feasible assignment Ω with Ω channels and Ω with Ω > Ω channels, ou fomulation will selects Ω ove Ω, iespective of thei Ω = aggegate tansmission ates t is clea that the optimization poblem in with the new objective function ie, i i constitutes a LP poblem V A EAR-OPTMAL APPROXMATO ecause ou poblem is a LP poblem, which is, in geneal, P-had, we develop a polynomial-time appoimate algoithm to solve ou LP based on a sequential fiing pocedue that povides a nea-optimal solution We note hee that the use of sequential fiing-based suboptimal algoithms in solving intege pogamming poblems wee peviously poposed and evaluated in seveal studies eg, [], [] The key idea of ou algoithm is to iteatively detemine the binay vaiables i s by solving a sequence of elaed LP RLP poblems with one i is finalized to a binay value in each iteation The details of ou sequential fiing algoithm is descibed as follows: The algoithm fist sets i s fo all idle channels with SR < µ to and elaes all unfied i s into eal numbes in [,] The algoithm then solves the esulting RLP f the RLP is infeasible, then ou LP has no feasible solution ie, no feasible assignment Othewise, among the eal-valued i s solution to the RLP, the algoithm sets the lagest to The algoithm then checks the constaints C-C assuming that all unfied i s ae set to zeo f these constaints ae met, the selected channel is ou feasible assignment Othewise, at iteation j, j =,, M, the algoithm elaes all unfied i s to eal values in [,] Then, it checks the feasibility egion of the new RLP at iteation j f this egion is empty, this means the last fied vaiable in the j iteation should be changed to and the jth RLP should be updated The algoithm then solves the esulting RLP, whose vaiables ae all unfied i s, and sets the lagest i to Given all fied i s at iteation j, the algoithm checks the constaints C-C assuming that all unfied i s ae set to zeo f these constaints ae met, the set of selected channels up to the jth iteation is the feasible channel assignment This pocess is epeated until a feasible assignment is computed, o a total of n i s ae fied to o all i s ae fied, ie, j = M and no feasible assignment can be found We note that ou algoithm can detemine a feasible solution o no feasible solution in no moe than M iteations Hence, its time compleity is bounded by the compleity of the LP solve times M, which is polynomial V PERFORMACE EVALUATO We fist conside a single SU tansmission, and investigate the accuacy of ou algoithm though MATLA simulations We conside a licensed spectum containing nonovelapping channels, each with bandwidth MHz The status of a PU channel is detemined accoding to the -state MRP model descibed in Section -A The T aveage idle duations fo the channels ae,,,,,,,,,,,,,,,,,,, ms, espectively We set the idle pobability P i = P fo all channels The tansmission powe fo each PU is Watt

4 omalized Cost Function 6 8 Optimization instance a omalized cost wt the optimal γ = omalized Cost Function 6 8 Optimization instance b omalized cost wt the optimal γ = 9 o of Channels pe Received Packet P a γ = eaopt, R = Mbps MaRate, R = Mbps Madle, R = Mbps eaopt, R = Mbps MaRate, R = Mbps Madle, R = Mbps Pobability of Success 9 7 R R R = Mbps P c P suc vs P fo γ = Pobability of Success 9 7 R R R = Mbps P d P suc vs P fo γ = 9 Fig Algoithm veification fo diffeent values of γ The simulation esults ae pesented fo optimization instances that can poduce feasible solutions Fo each instant, the souce-destination distance is andomly geneated fom the ange [,] mete Each SU geneates -K data packets, and equies a minimum data ate R and a minimum P suc of γ We set the SR theshold to µ = d, P ma = Watt, P ma i = Watt, i K, and the themal noise to Watt/Hz To descibe the fading channel between any two SUs, a Rayleigh fading channel model with path loss eponent n = is consideed Fig a and b plot the nomalized cost obtained using ou algoithm elative to the optimal cost obtained though ehaustive seach fo instances fo n =, P = and fo diffeent values of γ n most cases, ou solution is identical to the optimal solution Hence, ou algoithm achieves a neaoptimal solution within % of the optimal Fig c and d plot P suc as a function of P fo diffeent values of R and γ These figues show that the bound onp suc is always satisfied Fig investigates the pefomance of ou nea-optimal algoithm eaopt as a function of the idle pobability P fo diffeent values of R and γ = and 9 Ou algoithm is compaed with two multi-channel assignment algoithms: The link-quality-awae efeed to as MaRate [] and lifetimeawae efeed to as Madle MaRate Madle sots idle channels in a descending ode of thei data ates lifetime duations, then it picks the minimum numbe of channels fom the top of the soted list such that the ate demand The pefomance of ou algoithm is compaable to the one fo the optimal solution Hence, fo claity, the optimal solution is not shown in ou figues o of Channels pe Received Packet eaopt, R MaRate, R = Mbps Madle, R eaopt, R MaRate, R = Mbps Madle, R P b fo γ = 9 Fig Pefomance of a single SU link: Aveage numbe of channels pe eceived packet R is satisfied f the numbe of selected channels eceeds n o all idle channels cannot suppot R, o P suc ove the selected channels computed using does not satisfy the equiement γ, then no feasible channel assignment can be found Fig eveals that eaopt equies less numbe of channels fo a successful packet tansmission, which esults in impoved spectum utilization Fig plots the aveage enegy consumption fo a successful packet tansmission fo γ = and 9 t is clea that the pefomance of ou eaopt significantly outpefoms the pefomance of the othe algoithms in tems of enegy consumption We now evaluate the pefomance of ou algoithm in a multi-use envionment via simulations Specifically, we simulate a CR with SUs distibuted ove a mete aea We set n = To esolve channel contention between SUs, we adopt the multi-channel CSMA/CA MAC potocol pesented in [] As shown in Figs and, eaopt achieves highe netwok thoughput and and lowe enegy consumption than the othe two algoithms unde diffeent SU and PU taffic loads Othe esults indicate that the bound on P suc is always satisfied fo all algoithms n summay, ou algoithm allows fo bette spectum utilization and moe enegy saving V COCLUSO We poposed a multi-channel paallel tansmission mechanism fo channel assignment in CRs Ou mechanism consid-

5 Enegy Consumption pe eliveed Packet mj eaopt, R Madle, R MaRate, R = Mbp eaopt, R Madle, R MaRate, R = Mbp 9 7 P a γ = Thoughput Mbps eaopt, P = MaRate, P = Madle, P = eaopt, P = MaRate, P = Madle, P = a γ = Enegy Consumption mj/packet 6 eaopt, R MaRate,R Madle, R eaopt, R MaRate, R Madle, R P b γ = 9 Thoughput Mbps eaopt, P = MaRate, P = Madle, P = eaopt, P = MaRate, P = Madle, P = b γ = 9 Fig Pefomance of a single SU link: Aveage enegy consumption es the andomness of link qualities and lifetime duations of PU channels to povide a statistical pefomance guaantee fo SUs Simulation esults showed that this consideation esults in impoved spectum utilization and moe enegy saving REFERECES [] H any Salameh and M Kunz, Channel access potocols fo multihop oppotunistic netwoks: Challenges and ecent developments, EEE etwok, 9 [] H Khalife, Malouch, and S Fdida, Multihop cognitive adio netwoks: to oute o not to oute, EEE etwok, vol, no, pp, 9 [] H Kim and KG Shin, Efficient discovey of spectum oppotunities with mac-laye sensing in cognitive adio netwoks, EEE Tansactions on Mobile Computing, vol 7, no, pp, 8 [] V Pla, S e Vuyst, K e Tuck, E enal-mo, J Matinez-auset, and S Wittevongel, Satuation thoughput in a heteogeneous multichannel cognitive adio netwok, in Poceedings of the EEE ntenational Confeence on Communications CC, June, pp [] F ogonovo, M Cesana, and L Fatta, Thoughput and elay ounds fo Cognitive Tansmissions, ntenational Fedeation fo nfomation Pocessing, vol 6, no, pp 79 9, 8 [6] H any Salameh, M Kunz, and O Younis, Coopeative adaptive spectum shaing in cognitive adio netwoks, EEE/ACM Tansactions on etwoking, vol 8, no, pp 8 9, [7] K Tivedi, Pobability and Statistics with Reliability, Queuing and Compute Science Applications, John Wiley and Sons,, nd edition [8] A Min and K Shin, Eploiting multi-channel divesity in spectumagile netwoks, in Poceedings of the EEE FOCOM Confeence, 8, pp 9 99 [9] A Motamedi and A ahai, MAC potocol design fo spectum-agile wieless netwoks: Stochastic contol appoach, in Poceedings of the EEE yspa Confeence, 7 Fig Thoughput pefomance vs numbe of SUs fo diffeent values of γ and R = Mbps simila behavios wee obseved fo diffeent values of R Enegy Consumption mj/packet eaopt, P = MaRate, P = Madle, P = eaopt, P = MaRate, P = Madle, P = Fig Enegy Consumption vs numbe of SUs fo γ = 9 and R = Mbps simila behavios wee obseved fo diffeent values of γ and R [] Y Xing, R Chandamouli, S Mangold, and S Shanka, ynamic spectum access in open spectum wieless netwoks, EEE Jounal on Selected Aeas in Communications, vol, no, pp 66 67, 6 [] H any Salameh, M Kunz, and O Younis, MAC potocol fo oppotunistic cognitive adio netwoks with soft guaantees, EEE Tansactions on Mobile Computing, vol 8, no 6, 9 [] H any Salameh, Rate-maimization channel assignment scheme fo cognitive adio netwoks, in Poceedings of the EEE GLOECOM Confeence, ec, pp [] Y Hou, Y Shi, and H Sheali, Optimal spectum shaing fo multihop softwae defined adio netwoks, in Poceedings of the EEE FOCOM Confeence, 7, pp 9 [] T Shu and M Kunz, Coodinated channel access in cognitive adio netwoks: A multi-level spectum oppotunity pespective, in Poceedings of the EEE FOCOM Confeence, 9, pp