QoS-Aware Spectrum Sharing in Cognitive Wireless Networks

Transcription

1 QoS-Aware Spectrum Sharng n Cogntve reless Networks Long Le and Ekram Hossan Abstract e consder QoS-aware spectrum sharng n cogntve wreless networks where secondary users are allowed to access the spectrum owned by a prmary network provder. The nterference from secondary users to prmary users s constraned to be below the tolerable lmt. Also, sgnal to nterference plus nose rato (SINR) of each secondary user s mantaned hgher than a desred level for QoS nsurance. hen network load s hgh, admsson control needs to be performed to satsfy both QoS and nterference constrants. e propose an admsson control algorthm whch s performed jontly wth power control such that QoS requrements of all admtted secondary users are satsfed whle keepng the nterference to prmary users below the tolerable lmt. hen all secondary users can be supported at mnmum rates, we allow them to ncrease ther transmsson rates and share the spectrum n a far manner. e formulate the jont power/rate allocaton wth max-mn farness crteron as an optmzaton problem. e show how to transform t nto a convex optmzaton problem so that ts globally optmal soluton can be obtaned. Numercal results show that the proposed admsson control algorthm acheves performance very close to the optmal soluton. Also, mpacts of dfferent system and QoS parameters on the network performance are nvestgated for both admsson control and rate/power allocaton problems. I. INTRODUCTION Implementaton of emergng hgh-speed wreless applcatons requres exponental growth n spectrum demand. However, t has been reported that current utlzaton of allocated spectrum can be as low as 15 % [1]. Thus, there s an ncreasng nterest n developng effcent method for spectrum management and sharng whch s encouraged by both ndustry and FCC authorty [2]. Ths motvates to explot the spectrum opportuntes n space, tme, frequency whle protectng users of the prmary network owner from excessve nterference due to opportunstc spectrum access [3]. In fact, t s requred that an nterference lmt correspondng to an nterference temperature level be mantaned at the recevng ponts of the prmary network. The key challenge n cogntve rado networks s how to construct spectrum access/sharng schemes such that users of the prmary network (wll be called prmary users n the sequel) are protected from excessve nterference due to secondary spectrum access and QoS performance of secondary users are guaranteed. A graph-theoretc model for spectrum sharng/access among secondary users was proposed n [4] where dfferent objectve functons were nvestgated. The formulaton of channel allocaton problem usng game theory was proposed n [5]. In ths work, the proposed utlty functons capture the nterference perceved by one user on each channel and/or the nter- Long Le and Ekram Hossan are wth the Department of Electrcal and Computer Engneerng, Unversty of Mantoba, nnpeg, MB, Canada. E-mal: {long, ekram}@ee.umantoba.ca. ference ths user creates for neghborng ones. However, prmary users were not explctly protected from nterference due to spectrum access of secondary users. In [6], heurstc-based channel and power allocaton algorthm was proposed where nterference constrant for prmary users was consdered. In ths paper, we present a spectrum sharng framework for cogntve CDMA wreless networks wth explct nterference protecton for prmary users and QoS constrants for secondary users. Secondary users have mnmum transmsson rates wth requred QoS performance n terms of SINR (or equvalent bt error rate (BER)) and maxmum power constrants. hen the network load s hgh, an admsson control algorthm s proposed to guarantee QoS constrants for secondary users and nterference constrants for prmary users. hen all secondary users can be supported, we present a jont rate and power allocaton soluton wth QoS and nterference constrants. The rest of ths paper s organzed as follows. System models and problem defnton are presented n Secton II. Admsson control algorthm for spectrum access of secondary users s proposed n Secton III. The power/rate allocaton formulaton s presented n Secton IV. Numercal results are presented n Secton V. Secton VI concludes the paper. II. SYSTEM MODELS AND PROBLEM DEFINITION e consder the spectrum sharng problem among unlcensed users (secondary users) and lcensed users (prmary users). The problem consdered n ths paper apples to both centralzed networks (e.g., cellular networks) and dstrbuted networks (e.g., ad hoc and sensor networks). For ease of presentaton, we wll dscuss dfferent problem aspects n the context of centralzed settng most of the tme. e assume that there are a number of prmary and secondary users communcatng wth ther partners smultaneously. Here, the term user wll be used broadly where t can be a moble node or base staton/access pont n centralzed networks or smply a moble node n ad hoc networks. The CDMA technology wll be assumed although the model can be extended for other technologes as well. Smultaneous communcatons among users (.e., both prmary and secondary users) wll nterfere wth each other. The enttes we wll work wth are communcaton lnks each of whch s a par of users communcatng wth each other. e wll refer to communcaton lnks belongng to secondary networks as secondary lnks. e wll also consder the nterference constrants at the recevng nodes of prmary networks whch wll be referred to as prmary recevng ponts n the sequel. e assume that each prmary recevng pont can tolerate a maxmum nterference level. Also, secondary lnks have desred QoS performance n terms of BER. Fg. 1 llustrates the transmsson settng consdered n ths paper. One possble example for the 3563

2 where total nterference at the prmary recevng pont j should be smaller the tolerable lmt. e wll assume that transmsson rate of secondary lnk can be adjusted n an allowable range wth mnmum and maxmum values are R mn and R max, respectvely. Also, power of secondary lnk s constraned to be smaller than the maxmum lmt P max. Fg. 1. Secondary users Prmary users Communcaton lnk Interference to prmary user Spectrum sharng among prmary and secondary users. nvestgated network settng s where prmary users communcate wth ther BS n the uplnk drecton n a cellular network and secondary users communcate wth each other n an ad hoc mode. Here, the total nterference that secondary lnks create at each BS of the prmary network should be smaller that the tolerable level. A. QoS and Interference Constrant Modelng Assume that there are M prmary recevng ponts and N secondary communcaton lnks n the consdered geographcal area. Let us denote the channel gan from the transmttng node of secondary lnk to recevng node of secondary lnk j by j, whle the channel gan from the transmttng node of secondary lnk to prmary recevng pont j as j,. If N denotes the total nose and nterference at the recevng sde of secondary lnk, for wreless access based on CDMA, the correspondng effectve bt-energy-to-nose spectral densty rato can be wrtten as [9] µ = R P N j=1,j = g(s) P j + N (1) where s the spectrum bandwdth, R s the transmsson rate of secondary lnk. Here, /R s the processng gan whch s usually requred to be larger than a partcular value. The processng gan s smply equal to one for other multple access technologes such as FDMA and µ denotes the SINR. In the sequel, we wll abuse a bt by referrng µ as SINR n all cases. Now, f a partcular modulaton scheme s employed, there wll be an explct relaton between BER and SINR. Thus, for a specfc requred BER level of secondary lnk, µ s requred to be larger than a correspondng value γ. Hence, the QoS requrement for secondary lnk can be expressed as µ γ, =1, 2,,N. (2) Now, let T j be the maxmum nterference level tolerable by prmary recevng pont j. The nterference constrant for prmary recevng pont j can be wrtten as =1 j, P T j, j =1, 2,,M (3) B. Admsson Control Problem Here, we are nterested n the scenaro where a number of secondary lnks wsh to access the spectrum wth mnmum transmsson rate (.e., R = R mn ) and both the QoS requrements (n (2)) as well as the nterference constrants (n (3)) need to be satsfed. The problem s how to choose the subset of requestng lnks wth maxmum sze such that the constrants n (2) and (3) are both satsfed. C. Jont Rate and Power Allocaton Problem hen the network load s low, all requestng secondary lnks wth mnmum transmsson rates can be supported whle satsfyng both QoS and nterference constrants n (2), (3). If t s the case, secondary lnks would ncrease ther transmsson rates above the mnmum values and share the spectrum n a far manner. For farness ssue, we adopt the max-mn crteron whch ams to maxmze the transmsson rate of the secondary lnk wth a mnmum transmsson rate. e wll arrange power, rate and other quanttes of all secondary lnks nto the correspondng vectors for notatonal convenence. For example, P wll denote a column vector whose element P s the transmsson power of secondary lnk. The jont rate and power allocaton problem can be stated as maxmze {mn R } R mn R R max (4) P P max, and the constrants n (2), (3). e wll show how to solve both admsson control problem as well as jont rate and power allocaton problem n the followng sectons. III. ADMISSION CONTROL ALGORITHM As has been mentoned n Secton II, we wll consder the admsson control problem when the network load s hgh and all secondary lnks transmt wth ther mnmum rate (f admtted). Now, usng equaton (1), we can rewrte the QoS constrant n (2) as follows: P j=1,j = γ R mn P j + γr mn N, =1, 2,,N. (5) The constrants for all secondary lnks can be wrtten n the matrx form as follows: (I F )P u (6) where I s an dentty matrx of order N N, u s a column vector whch can be wrtten as ( ) γ 1 R1 mn N 1 u = g, γ2r 2 mn N 2 (s) 1,1 g,, γnr N mn N N (s) 2,2 N,N 3564

3 where (.) denotes the matrx/vector transpose. And F s an N N matrx whose (, j)-th element s γ R mn F =, f j. 0, f = j A. Constraned Power Control Recall that we are nterested n the scenaro where not all N secondary lnks can be admtted nto the network whle satsfyng both QoS and nterference constrants stated n (2), (3). e wll frst focus on the power allocaton problem under maxmum power constrant (.e., P P max ) and QoS constrants and gnore the nterference constrants for a whle. In [8], the authors proposed an effcent teratve power control algorthm whch can be mplemented dstrbutvely. Specfcally, let P (t) and P (t+ t) be the power levels of secondary lnk after two consecutve power updates at tme nstants t and t+ t, respectvely. The power of secondary lnk s updated as follows: { P (t + t) =mn P max,p (t) γ } (7) µ (t) where µ (t) s the nstantaneous SINR at the recevng sde of secondary lnk at tme nstant t whch can be wrtten as µ (t) = P (t) R N j=1,j = g(s) P j(t)+n It was shown n [8] that ths power control algorthm converges to the fxed pont soluton of P = mn {P max,fp + u} (8) whch wll be referred to as statonary power vector. Let Ω be the set of secondary lnks and P Ω be the statonary power vector when the power algorthm wth the rule as n (7) s run wth secondary lnk set Ω. From the results of [7], we have the followng facts: Fact 1: If all secondary lnks n Ω can be supported (.e., the power control algorthm n (7) results n a statonary power vector P Ω satsfyng QoS constrants n (2)), the QoS constrants wll be satsfed wth equalty. Fact 2: If a subset Ω 0 Ω s the set of secondary lnks whch are not supported wth statonary power vector P Ω, then P Ω = P max for Ω 0. Now, let us defne the followng nterference measures : α (P Ω ) = P Ω j, + N g(s) P Ω (9) γ R j=1,j = β (P Ω ) = j=1,j = P Ω j + N g(s) γ R P Ω (10) D Ω (P Ω ) = Ω β (P Ω ). (11) e can easly see that D Ω (P Ω )= β (P Ω )= α (P Ω ). (12) Ω Ω e can also see that f the QoS constrant for secondary lnk s satsfed wth equalty, then β (P Ω )=0. Also, D Ω (P Ω )=0 f and only f all secondary lnks n Ω are supported. In general, we have β (P Ω ) 0 and the value of β (P Ω ) reflects the degree n whch the QoS constrant for secondary lnk s volated. Also, t s ntutve that α (P Ω ) quantfes the aggregate relatve nterference that secondary lnk creates for other lnks n Ω. In [7], the authors proposed several removal algorthms whch am at maxmzng the number of lnks whch can be admtted nto the network whle satsfyng the QoS requrements. Among these proposed algorthms, SMIRA and SMART(R) are the two most effcent ones. e have observed through smulaton that these two algorthms acheve very close performance; therefore, we wll only descrbe the SMIRA algorthm here. Note that the nterference measures defned n (9)-(11) are not the same wth those n [7]. However, the sprt of the SMIRA algorthm remans the same n ths paper. In fact, SMIRA algorthm runs the power control algorthm n (7) and removes lnks from the network one by one and untl the remanng set of lnks can be supported. The removal crteron of SMIRA s as follows: = argmax Ω { max ( α (P Ω ),β (P Ω ) )}. (13) Intutvely, SMIRA algorthm removes the lnk whch volates QoS constrants the most and/or creates the largest amount of nterference to other lnks n each step. Thus, t can potentally remove the least number of lnks from the network. B. Admsson Control wth QoS and Interference Constrants In our spectrum sharng problem, besdes QoS constrant, admsson and power control should be done such that nterference constrants for prmary lnks stated n (3) are also satsfed. e have the followng result on the complexty of ths admsson control problem. Proposton 1: The admsson control problem wth QoS and nterference constrants s NP-hard. Proof: It was shown n [7] that the admsson control wth only QoS constrants s NP-hard. Because the admsson control wth QoS constrants s a specal case of that wth both QoS and nterference constrants (they become the same when I j for j =1,,M). Therefore, our nvestgated admsson control problem s also NP-hard. Because of the complexty of the problem, we propose a lowcomplexty admsson control algorthm s ths sub-secton. The proposed algorthm also removes the worst lnk one-by-one. In each step, we perform the power control algorthm as n (7) and remove one lnk untl the remanng set satsfes both QoS and nterference constrants. Here, the key ssue s to construct a removal crteron whch acheves good overall performance. Because there are two dfferent knds of constrants, we consder the followng cases n each removal step. Case 1: Interference constrants for all prmary recevng ponts stated n (3) are satsfed but QoS constrants n (2) are volated In ths case, we employ the SMIRA algorthm as presented n Secton III.A. 3565

4 Case 2: Interference constrants for prmary recevng ponts stated n (3) are volated Note that ths case covers both scenaros where QoS constrants n (2) are volated or not. In ths case, we would remove the lnk whch volates both QoS and nterference constrants the most n each step. Now, we defne the measure whch quantfes degree of volaton at prmary recevng pont j as follows: η j (Ω) = T j =1 j, P Ω. (14) e propose a removal algorthm wth the followng removal metrc M η j (Ω) = argmax Ω D Ω (P Ω )+ M k=1 η k(ω) g(p) j, P Ω j=1 D Ω (P Ω ) + D Ω (P Ω )+ M k=1 η k(ω) max j, P Ω, j Ω,j = g(s) j Ω,j = j Ω,j = P Ω j In fact, j, P Ω denotes the total nterference that secondary lnk creates to other secondary lnks whle j Ω,j = g(s) P j Ω s the total nterference receved at the recevng end of lnk. In addton, j, P Ω denotes the nterference that secondary lnk creates for prmary recevng pont j. Recall that D Ω (P Ω ) quantfes the degree of volaton for QoS constrants and η j (Ω) quantfes the degree of volaton for the nterference constrant of prmary recevng pont j. Therefore, the proposed crteron removes n each step the secondary lnk whch creates the largest amount of nterference for prmary recevng ponts and other secondary lnks n the weghted average sense. As a result, t would potentally remove the least number of secondary lnks from the network. e wll refer to ths algorthm as nterference-aware SMIRA (I-SMIRA) n the sequel. The computaton complexty of I-SMIRA s just O(N 2 ) whch s qute acceptable. IV. JOINT RATE AND POER ALLOCATION OPTIMIZATION hen the network load s low, all secondary lnks can be admtted nto the network and they would ncrease ther transmsson rates above the mnmum values. In essence, we wsh to solve the optmzaton problem stated n (4). The decson varables are transmsson rates R and powers P. e wll show how to transform ths problem nto a convex optmzaton problem where globally optmal soluton can be obtaned. e would lke to note that the jont rate and power allocaton for cellular CDMA networks has been an actve research topcs over the last several years. e refer the readers to [9] and references theren for exstng lterature on the problem. However, the work n [9] s one of the frst papers whch adapt the problem to the ad hoc network settng. Here, the objectve s to mnmze the maxmum servce tme on dfferent transmsson lnks. In ths paper, we proceed one step further by solvng the jont rate and power allocaton problem n the spectrum sharng context where nterference constrants for prmary recevng ponts are taken nto account. Now, the objectve functon n (4) s equvalent to mnmze {max 1/R }. By ntroducng a new varable t and wrtng down all the constrants explctly, the optmzaton problem (4) s equvalent to mnmze t 1/R t, =1, 2,,N R P P N γ, =1, 2,,N. j=1,j = g(s) Pj+N N =1 g(p) j, P T j, j =1, 2,,M R mn R R max, =1, 2,,N P P max, =1, 2,,N (15) The optmzaton problem n (15) s not convex. However, we can transform t nto a geometrc program whch can be solved effcently (chapter 4, [10]). Now, we show how to transform the optmzaton problem (15) nto a geometrc program whch can be transformed nto a convex optmzaton problem. Specfcally, optmzaton problem n (15) s equvalent to mnmze t t 1 R 1 1, =1, 2,,N R P 1 N j=1,j = g(s) γ N j, =1 R mn R 1 (R max (P max P j + γn R P 1 1, =1, 2,,N T j P 1, j =1, 2,,M 1, =1, 2,,N ) 1 R 1, =1, 2,,N ) 1 P 1, =1, 2,,N (16) Now, defnng P = e x, R = e y and t = e s, substtutng these new varables nto (16), and takng ln n both the objectve and the constrant functons, we acheve a convex optmzaton problem whch can be solved by the standard nteror pont algorthm [10]. e have the followng property on the soluton of jont rate and power allocaton problem. Proposton 2: The optmal soluton of the jont rate and power allocaton problem satsfes R = R j,, j. Proof: Ths can be proved by contradcton followng a procedure smlar to the one for proposton 3 n [9]. Hence, the rate and power allocaton problem acheves perfectly far rate for all secondary lnks n the sense that optmal transmsson rates for all lnks are the same. V. NUMERICAL RESULTS e present the numercal results for a smple network settng as shown n Fg. 1. Assume that prmary users communcate wth ts BS n the uplnk drecton (.e., a sngle cell s consdered). Transmttng nodes of secondary lnks are randomly located n a rectangular area and the BS of the prmary network s located at the center of the rectangular area. The sze of the rectangular area s 2000m 2000m. Also, recevng node of each secondary lnk s generated randomly n a 1000m 1000m rectangle wth ts transmttng node beng at the center

5 Number of addmtted lnks N = 5 N = 7 Optmal Removal 3.5 I SMIRA SMIRA Desred SINR (db) Fg. 2. Average number of accepted lnks versus desred SINR (for I = 5N 0 ). The channel gans are modeled as = K 0.µ (p).(d(p) ) 4, where d (s) = K 0.µ (s).(d(s) ) 4, are the corre- and d(p) spondng dstances, µ (s) and µ(p) are random Gaussan varables wth zero mean and standard devaton equal 6 db, K 0 = 10 3 whch captures system and transmsson effects such as antenna gan, carrer frequency, etc. The total nose and nterference at the recevng node of all secondary lnks s chosen to be N = N 0 = The maxmum transmsson power on secondary lnks s P max = 0.1. The spectrum bandwdth s = 5.12 MHz. e wll denote the tolerable nterference lmt at the prmary recevng pont (.e., BS) as I. The mnmum transmsson rate on secondary lnks s R mn = 64 Kbps and maxmum transmsson rate s R max = /PG where PG s the mnmum processng gan. For each smulaton run, the locatons of secondary lnks (.e., transmttng and recevng nodes) are generated randomly. The measure of nterest s obtaned by averagng over 10 3 smulaton runs. The average number of accepted lnk versus the desred SINR for each secondary lnk (.e., γ ) s shown n Fg. 2 for SMIRA, I-SMIRA algorthms and optmal removal. The result for optmal removal s obtaned by an exhaustve search wth the least number of removed lnks. As s evdent from ths fgure, the performance of I-SMIRA algorthm s very close to that of optmal removal. Also, I-SMIRA algorthm acheves much hgher performance than SMIRA algorthm. Ths s due to the fact that I-SMIRA captures both QoS and nterference constrants whle SMIRA only takes care of the QoS constrants. Note that I-SMIRA algorthm has much lower computatonal complexty than the optmal removal. In addton, the number of accepted lnks decreases wth the desred SINR. Ths s because a smaller number of lnks should be accepted to keep the congeston level low enough so that hgher desred SINR can be acheved. In Fg. 3, we show the total throughput versus the mnmum processng gan for dfferent sets of constrants. As expected, the more strngent the QoS and nterference constrants are, the lower the total throughput that can be acheved. Also, when the mnmum processng gan ncreases, the throughput gap between these two curves n Fg. 3 becomes smaller. In fact, when the mnmum processng gan ncreases, the maxmum transmsson rate decreases (because R max Total throughput (Kbps) Fg. 3. N=5) = /PG). Thus, when SINR = 10dB, I = 20N 0 SINR = 15dB, I = 5N Mnmum processng gan Throughput per secondary lnk versus mnmum processng gan (for the mnmum processng gan s hgh enough (e.g., close to 40), the throughput s more lmted by the maxmum transmsson rate so the mpacts of QoS and nterference constrants dmnsh. VI. CONCLUSIONS e have presented a soluton approach to the spectrum sharng problem n cogntve wreless networks. In partcular, an admsson control algorthm has been proposed whch ams to remove the least number of secondary lnks so that both QoS constrants n terms of desred SINR for accepted lnks and nterference constrants for prmary lnks are satsfed. e have also formulated the jont rate and power allocaton problem for the secondary lnks as an optmzaton problem wth both QoS and nterference constrants. Numercal results shown the superor performance of the proposed admsson control algorthm. Also, several nterestng mpacts of system, QoS and nterference constrant parameters on network performance were nvestgated and dscussed. REFERENCES [1] FCC. Spectrum polcy task force report, FCC Nov [2] FCC. Facltatng opportuntes for flexble, effcent, and relable spectrum use employng cogntve rado technologes, notce of proposed rule makng and order, FCC Dec [3] Q. Zhao and B. M. Sadler, A survey of dynamc spectrum access: Sgnal processng, networkng, and regulatory polcy, IEEE Sgnal Processng Mag., to appear. [4] H. Zheng and C. Peng, Collaboratve and farness n opportunstc spectrum access, n Proc. IEEE ICC 05. [5] N. Ne and C. Comancu, Adaptve channel allocaton spectrum etquette for cogntve rado networks, n Proc. IEEE DySPAN 05. [6] A. T. Hoang and Y. -C. Lang, A two-phase channel and power allocaton scheme for cogntve rado networks, n Proc. IEEE PIMRC 06. [7] M. Andersn, Z. Rosberg, and J. Zander, Gradual removals n cellular PCS wth constraned power control and nose, ACM/Baltzer reless Networks J., vol. 2, no. 1, pp , [8] S. A. Grandh and J. Zander, Constraned power control, reless Personal Commun., vol. 1, no. 4, [9] A. Muqattash, M. Krunz, and T. Shu, Performance enhancement of adaptve orthogonal modulaton n wreless CDMA systems, IEEE J. Sel. Areas Commun., vol. 24, no. 3, pp , Mar [10] S. Boyd and L. Vandenberge, Convex Optmzaton, Cambrdge Unversty Press,