IEEE INFOCOM 2 Workshop On Cogntve & Cooperatve Networks Selectve Sensng and Transmsson for Mult-Channel Cogntve Rado Networks You Xu, Yunzhou L, Yfe Zhao, Hongxng Zou and Athanasos V. Vaslakos Insttute of Informaton Processng, Department of Automaton, Tsnghua Unversty, Bejng 84, Chna Emal: xuyou6@mals.tsnghua.edu.cn Research Insttute of Informaton Technology, Tsnghua Unversty, Bejng 84, Chna Emal: lyunzhou@mal.tsnghua.edu.cn Natonal Techncal Unversty of Athens, Heroon Polytechnou 9, 578 Zografou, Greece Emal: vaslako@ath.forthnet.gr Abstract To maxmze SU s temporal channel utlzaton whle lmtng ts nterference to PUs, a selectve sensng and selectve access (SS-SA) strategy for one slotted SU overlayng a nontme-slotted ON/OFF contnuous tme Markov chan (CTMC) modeled mult-channel prmary network s proposed. Under the proposed selectve sensng strategy, each channel wll be detected approxmate perodcally wth dfferent perods accordng to the parameter T c, whch reflects the maxmal perod that each channel should be probed. Once the spectrum hole s found, f the sensng perod s sutable, the SU could contnuously access the channel untl t sense ths channel next tme. Numercal smulatons llustrate that T c s a vald measurement to ndcate how often the channel should be sensed, and wth the SS-SA strategy, SU can effectvely utlze the channels and consume less energy and tme for sensng than two reference strateges. I. INTRODUCTION FCC s report ndcates that the current spectrum management polcy has resulted n an under-utlzed spectrum []. To mprove spectrum utlzaton, cogntve rado (CR) [2] s proposed. Its basc dea s to allow secondary user (SU) to search for and utlze nstantaneous spectrum opportuntes left by prmary user, whle lmtng ts nterference to PU. To utlze spectrum opportuntes, the SU should frst model PU s behavor. There are manly two models, namely, dscretetme and contnuous-tme models. In dscrete-tme model, both PU and SU are tme-slotted. In [3], a dynamc programmng approach to search the optmal sensng order s proposed. In [4], an opportunstc MAC protocol wth random and negotaton-based sensng for ad-hoc networks s proposed. In [5], the authors derve the optmal spectrum sensng and access strateges under the formulaton of POMDP. For ths model, snce the synchronzaton of all PUs and SUs s necessary, t causes more overhead and tme offset may be fatal for SU s MAC strategy. In contnuous-tme model, the PUs are nonslotted but the SUs are stll slotted mostly. Snce PU s state may change at any tme, ths model s more dffcult to analyze. The authors of [6] derve the optmal access strategy wth Ths work was supported by Natonal Basc Research Program of Chna (27CB368), Natonal Natural Scence Foundaton of Chna (68328), Chna s 863 Project (29AA5), Natonal S&T Major Project (28ZX3O3-4), NCET, PCSIRT and Tsnghua-Qualcomm Jont Research Program. perodc sensng for one SU overlappng a CTMC modeled mult-channel prmary network. In [7], [8], the optmal access strategy wth fully sensng strategy s obtaned. However, none of these works nvestgate the magntude of sensng perod. In [9] [], the optmal sensng perod s derved for the smplest sngle-channel model. In ths paper, we consder a CR network whch has multple channels avalable for transmssons by prmary and secondary users. We assume each channel s assgned to an ndependent PU and the tme behavor of each channel s modeled by a two-state (ON/OFF) frst-order CTMC model. Meanwhle, one slotted SU can access all of these channels smultaneously. Snce generally how often each channel should be sensed s dstnct and t wll take more energy and tme to sense all channels smultaneously, SU could only sense part of the channels. Thus, SU could save more energy and tme for transmsson. We assume that SU senses only one channel n each slot (the proposed sensng strategy can be easly be generalzed to the case when SU probes multple channels each tme). Therefore, n each slot, SU decdes whch channel should be sensed frst and n whch channels to transmt. Furthermore, the magntude of sensng perod s also consdered. The man contrbutons of ths paper are as follows. To maxmze SU s temporal channel utlzaton whle lmtng ts nterference to PUs, we propose a selectve sensng and selectve access (SS-SA) strategy for one slotted SU overlayng a non-tme-slotted ON/OFF CTMC modeled mult-channel prmary network. Wth SS strategy, each channel wll be detected approxmate perodcally wth dfferent perod accordng to T c. The parameter T c, whch s related to channel s characterstc parameters and nterference tolerances, s a vald measurement to ndcate how often each channel should be sensed. If sensng perod s sutable, the SA strategy can be regarded as greedy access strategy. Wth SS-SA strategy, SU can effectvely utlze these channels and adopt larger sensng perod than reference strateges, whch means SU could consume less energy and tme for sensng. Furthermore, SS-SA strategy s smple and easy to mplement. The rest of the paper s organzed as follows. After ntroducng the system model and problem formulaton n Secton II, 978--4244-992-5//$26. 2 IEEE 47
the PS-SA and SS-SA strateges are studed n Secton III and IV, respectvely. In Secton V, the smulaton results are present and dscussed. Fnally, conclusons are stated n Secton VI. II. SYSTEM MODEL AND PROBLEM FORMULATION A. System Model We consder a mult-channel CR network whch has multple channels avalable for prmary and secondary users. Partcularly, there are N channels and each channel s assgned to an ndependent PU respectvely. We assume there s only one SU who can access these channels smultaneously, and ts transmsson on one channel wll not nterfere wth other channels. To acheve ths, we can smply adopt D-OFDM as the PHY technque wth a sngle rado equpment [2]. We assume that all PUs exhbt a non-tme-slotted behavor and ther actvtes are ndependent, whle SU employs a tme slotted protocol wth perod T s >. Furthermore, SU adopts a Lsten-Before-Talk strategy. Snce generally how often each channel should be sensed s dstnct and t wll take more energy and tme to sense all channels smultaneously, SU could sense part of these channels each tme. For the convenence of analyss, we assume SU senses only one channel t each slot. Therefore, SU needs a sensng and access strategy to decde whch channel should be sensed frst and n whch channels to transmt, whch s the man objectve of ths paper. Besdes, for ease of analyss, we assume perfect sensng and sensng tme s short enough to be gnored. The tme behavors of prmary and secondary users are shown n Fg.. B. The Channel Model The channel s tme behavor s modeled as a two-state (ON/OFF) frst-order CTMC. Ths CTMC model has been consdered n many spectrum sharng studes ncludng theoretcal analyss and hardware tests [6] [8], [3] [5]. Based on stochastc theory [6], for any channel, holdng tmes n ON and OFF states are exponentally dstrbuted wth parameters μ and λ, respectvely, and the transton matrx s P(τ)= [ ] μ +λ e (λ +μ )τ λ λ e (λ +μ )τ λ +μ μ μ e (λ+μ)τ λ +μ e (λ+μ)τ. () If sensng result s OFF at tme t, then the probablty of channel state beng ON at tme t + τ s λ +μ (λ λ e (λ +μ )τ ). C. Problem Formulaton We focus on maxmzng SU s total channel utlzaton whle lmtng ts nterference to PUs. Partcularly, the nterference between PU and SU s modeled by average temporal overlap, namely, the nterference tme dvded by total tme. Mathematcally, the nterference I between SU and PU s I = lm T T {A (τ) B (τ)} dτ T where { } s the ndcator functon of the event enclosed n the brackets; A (τ) and B (τ) denote the event that PU and SU access channel at tme τ, respectvely. (2) Fg.. The tme behavor of prmary and secondary users (4 channels). The channel utlzaton s defned as SU s temporal utlzaton rato (.e., the transmsson tme dvded by total tme). Mathematcally, SU s channel utlzaton U on channel s T U = lm {B (τ)} dτ. (3) T T Therefore, we focus on the problem P: N max = U (4) s.t. I C, =,,N (5) where C [, ] s the maxmum nterference level tolerable by prmary user. Generally, C s very small. Snce SU s sensng and access strategy and sensng perod T s jontly affect SU s nterference to PUs and channel utlzaton, we wll study SU s sensng and access strategy and the effect of sensng perod T s. III. PERIODIC SENSING AND SELECTIVE ACCESS In ths secton, we study the optmal access strategy wth perodc sensng (PS). Snce SU detects these channels one by one, each channel s also probed perodcally wth perod T P = NT s. A. Sub-problems of the Orgnal Problem P We frst smplfy problem P to facltate analyss. From the perspectve of tme, n each slot, SU should decde how to access N channels. Snce the nterferences between SU and each PU don t nteract wth each other, problem P can be decoupled nto N ndependent sub-problems P : max U (6) s.t. I C. (7) That s to maxmze SU s channel utlzaton on channel whle lmtng ts nterference to PU. Therefore, from the perspectve of each channel, SU should decde how to access the N slots between two adjacent sensng events. If all N sub-problems P acheve optmal smultaneously, then the orgnal problem P wll be optmal. B. Selectve Access Strategy We frst analyze the property of nterference caused by SU s transmsson. Wthout loss of generalty, we assume that SU senses channel at tme t =. If the sensng result s OFF and SU decdes to access ths channel n the followng m-th slot, then the expect nterference to PU n the m-slot s φ (m) = T s mts (m )T s λ λ e (λ+μ)τ λ + μ dτ. (8) 48
Smlar to [7], we can obtan the followng lemma. Lemma : If the sensng result s OFF, the nterference caused by SU s transmsson n the former slot s less than the one n the latter slot. That s, f n<m( n, m N), then φ (n) <φ (m). Snce t can be easly obtaned from (8), we omt the proof of ths lemma. Based on lemma, we can obtan the followng ntutve lemma drectly. Lemma 2: Once SU dscovers spectrum hole, t should transmt consecutvely n the followng earler slots (.e., durng [,ρ NT s ], where ρ =, N, 2 N,, ). Based on lemma 2, the SU knows how to access the channel qualtatvely, but not quanttatvely. In other words, the rato ρ s unknown. Accordng to Lemma 2, SU s nterference to PU s ρ T P λ λ e (λ +μ )τ I = k dτ (9) T P λ + μ where k = μ μ +λ s the probablty of the sensng result beng OFF. Therefore, the sub-problem P s equvalent to max ρ,t P U = k ρ () s.t. λ λ e (λ +μ )τ λ +μ dτ C () k T P ρ T P where ρ = {, N, 2 N,, } and T P = NT s >. It s very smlar to our prevous work [], n whch ρ s contnuous varable. In [], we have proved that: ) If T P Tc (the threshold Tc wll be gven latter), then ρ =and SU s channel utlzaton s the maxmal. 2) If T P >Tc, then ρ < and SU s channel utlzaton wll decrease as T P ncreases. Remark: If T P s small, durng [,T P ], the probablty p that PU s dle state changes s very small. Thus, SU can access N slots (.e., durng [,T P ]) and wll not cause much nterference to PU.AsT P ncreases, p ncreases, especally at the end of duraton [,T P ]. Therefore, SU should reduce ts transmsson tme and transmt as early as possble. Furthermore, n [], we have obtaned that ( W ( m e m ) m ) Tc = (2) λ + μ where m = C k (when C ( k ) <k ( k )) and W (x) denotes the Lambert s W functon [7]. Therefore, f λ and μ are bg (.e., channel s state changes fast) or C s small (.e., nterference constrant s strct), then Tc s small. It s n accord wth ntuton. Accordng to the above dscusson, f T P Tc, SU s channel utlzaton on channel s the maxmal. Therefore, we have the followng optmal access theorem. Theorem : Wth PS strategy, f sensng perod T s T c N, the optmal access strategy for SU to access channel s that once SU dscovers spectrum hole, t can greedly access all subsequent slots untl channel s probed next tme. And then, SU s channel utlzaton on channel s the maxmal, whch equals to channel s dle probablty (.e., μ μ +λ ). The access strategy can { be regarded as greedy access strategy. If T s mn T c /N }, then the greedy access N strategy can be adopted for all channels. We call t perodc sensng and selectve access (PS-SA) strategy. Wth PS-SA strategy, all sub-problems acheve optmal smultaneously. Therefore, SU s total channel utlzaton s maxmal. However, snce all channels are treated equally, most sensng opportuntes are wasted on those channels that don t need to be sensed yet. Thus, the PS strategy s not effcent. Therefore, a selectve sensng strategy, whch makes SU frst sense the channel that needs to be probed the most, s requred. IV. SELECTIVE SENSING AND SELECTIVE ACCESS A. Selectve Sensng Strategy Based on the former dscusson, we fnd that Tc, whch s related to the channel s characterstc parameters (μ,λ ) and nterference constrant threshold (C ), reflects the frequency that channel should be probed. Thus naturally, we propose a selectve sensng strategy, whch makes each channel almost be probed perodcally wth perod Tc. Partcularly, SU senses the channel, whose age of last sensng result s closest to Tc. Mathematcally, ths selectve sensng strategy leads to { p T c a T s } CH =arg mn (3) N where a N s the age (n terms of number of slots) of last sensng result of channel and p (, ) s a constant coeffcent. Snce when the sensng tme nterval s greater than Tc, SU s channel utlzaton wll degrade. Thus, the parameter p s ntroduced n order to make SU sense each channel n advance. Accordng to smulaton result, we obtan that when p =.9, sensng perod s the maxmal for most stuatons. Thus, we choose p =.9. The SS strategy s not strct perodc generally. However, snce each channel wll be sensed when sensng tme nterval s close to ptc, the SS strategy for each channel can be regarded as perodc approxmately. B. Selectve Access Strategy Accordng to lemma 2, once the spectrum opportunty s found, SU should access the channel as early as possble. Wth the SS strategy, f the sensng tme nterval for any channel less than Tc, then the greedy access strategy s also sutable for the SS strategy. Snce the SS strategy can be regarded as perodc approxmately for each channel, wth the greedy access strategy, SU s channel utlzaton on channel s about k, whch equals to the one wth PS-SA strategy. Therefore, smlar to PS-SA strategy, we also adopt the smple greedy access strategy. On the other, snce the channel wth small Tc wll be probed frequently (namely, fewer slots), the sensng perod T s could be larger than PS strategy. Therefore, wth SS-SA strategy, SU could acheve the same channel utlzaton as the case wth PS-SA strategy and meanwhle consume less tme and energy to sense the channels. It s noteworthy that unlke the PS-SA strategy, we could not gve the expresson of T s. However, the approxmate T s can 49
be obtan by smulaton. Gven channels parameters (μ,λ ), we can generate all channels states and smulate the SS-SA strategy for dfferent T s. Then, we can obtan SU s channel utlzaton and ts nterference to each PU. The approxmate T s s the maxmal T s that makes the nterference to all PUs not exceed ther thresholds (C ). V. SIMULATION RESULTS A. Intutve Sensng and Selectve Access Strategy We frst ntroduce a reference strategy, that s, Intutve Sensng and Selectve Access (IS-SA) strategy. We consder an ntutve sensng strategy: SU frst senses the channel whose state (ON/OFF) s most lkely to change. Partcularly, we assume that channel was last sensed n slot t, then n slot t(> t ), the age of last sensng result s a = t t. Thus, channel s state varyng durng the perod of ((t )T s, (t )T s ) s equvalent to the holdng tme beng less than a T s. Snce the holdng tmes are exponentally dstrbuted, the probablty P that holdng tme beng less than a T s s at s P = θ e θt dt = e θ a T s (4) where { μ, the last sensng result s ON θ = λ, the last sensng result s OFF. (5) Thus, we can obtan the ntutve sensng strategy: max {P } max {a θ }. (6) N N If the age of sensng result (.e., a ) s large or the channel states vary fast (.e., θ s larger), the channel wll be probed frst. Ths s the same as ntuton. However, t s apparent that IS strategy s nvald for dfferent nterference thresholds. Smlar to PS and SS strateges, SU can also adopt greedy access strategy f sensng perod s sutable. B. Example : Performance for Dfferent Holdng Tmes We study the case that holdng tmes are dfferent. Partcularly, we assume N = 5, λ = μ = [2, 4, 6, 8, ] (second) and C = 5% ( ). Thus, we have T c = [.464,.928,.392,.857, 2.32] (second). The channel utlzaton for PS-SA, SS-SA and IS-SA strateges are shown n Fg. 2. Fg. 2 shows that SU s channel utlzaton on each channel s 5%, whch equals to the dle probablty, and SU s total channel utlzaton s the same for dfferent strateges. Fg. 3, Fg. 4 and Fg. 5 show the nterference wth PS- SA, SS-SA and IS-SA strategy, respectvely. Fg. 3 shows when T s 93 (ms), the nterference to each PU s less than the threshold (5%). Thus, the maxmal sensng perod s about 93 (ms), whch s n accord wth the theoretcal value mn { Tc/N } = 92.8 (ms). Smlarly, the maxmal sensng perod for SS-SA and IS-SA strateges are 84 and 83.5 (ms), whch are approxmately the same n ths case. Therefore, SU consumes less tme and energy to probe the channels by adoptng SS-SA or IS-SA strategy. Temporal Channel Utlzaton Fg. 2. Fg. 3. Fg. 4. 3 2.5 2.5.5 Total utlazaton rato Channel,2,3,4,5 2 4 6 8 2 4 6 8 2 The channel utlzaton under PS-SA, SS-SA and IS-SA strategy..8.7.6.5.4.3.2. μ =λ =8 μ =λ = 5 6 7 8 9 2 3 4 5 The nterference under PS-SA strategy for dfferent holdng tmes..8.7.6.5.4.3 μ =λ =8 μ =λ =.2 2 4 6 8 2 22 24 26 The nterference under SS-SA strategy for dfferent holdng tmes. C. Example 2: Performance for Dfferent Thresholds C We focus on the case that N = 5, λ = μ = 3 ( ) and C = [2%, 4%, 6%, 8%, %]. Therefore, T c = [254, 539, 865, 242, 689] (ms). Smlar to Example, snce the dle probablty of each channel s 5%, SU s total channel utlzaton for each strategy s 2.5. Snce the parameters λ and μ are the same, wth IS-SA strategy, all channels wll be regarded as the same. Thus, IS- 5
Fg. 5..7.65.6.55.5.45.4.35.3.25 μ =λ =8 μ =λ =.2 2 4 6 8 2 22 24 26 The nterference under IS-SA strategy for dfferent holdng tmes..7.6.5.4.3.2. λ =μ =3, C=2% λ =μ =3, C=4% λ =μ =3, C=6% λ =μ =3, C=8% λ =μ =3, C=% 2 4 6 8 2 4 6 8 2 Fg. 6. The nterference under IS-SA (PS-SA) strategy for dfferent C..4.2..8.6.4.2 μ =λ =3, C=2% μ =λ =3, C=4% μ =λ =3, C=6% μ =λ =3, C=8% μ =λ =3, C=% 2 4 6 8 2 4 6 8 2 Fg. 7. The nterference under SS-SA strategy for dfferent C. SA strategy s the same as PS-SA strategy and the fve curves n Fg. 6 overlap each other. Due to mn{c } = 2%, the maxmal sensng perod s about 5 (ms), whch s n accord wth the theoretcal value. Snce SS-SA strategy takes nto account both channel s parameters and nterference tolerances, these channels wll not be regarded as the same any more. The nterference wth SS-SA strategy s llustrated n Fg. 7, whch shows that the maxmal sensng perod s about 8 (ms), whch s twce as much as IS-SA strategy. Thus n ths case, SS-SA strategy s better than IS-SA and PS-SA strateges. VI. CONCLUSION In ths paper, we propose a selectve sensng and selectve access (SS-SA) strategy for one slotted SU overlayng a nontme-slotted ON/OFF CTMC modeled mult-channel prmary network. Wth SS strategy, each channel s probed approxmate perodcally wth dfferent perods accordng to the parameter T c, whch reflects the maxmal perod that each channel should be detected. If sensng perod s sutable, SA strategy can be regarded as greedy access strategy. We also gve two reference strateges (namely, PS-SA and IS-SA). Numercal smulatons llustrate that T c s a vald measurement to ndcate how often each channel should be sensed, and wth SS-SA strategy, SU can effectvely utlze each channel and consume less energy and tme for sensng than PS-SA and IS-SA strateges. REFERENCES [] Federal Communcatons Commsson, Spectrum Polcy Task Force, ET Docket No. 2-35, Tech. Rep., Nov. 22. [2] J. Mtola et al., Cogntve rado: Makng software rados more personal, IEEE Pers. Commun., vol. 6, no. 4, pp. 3-8, Aug. 999. [3] H. Jang, L. La, R. Fan, and H. V. Poor, Optmal selecton of channel sensng rrder n cogntve rado, IEEE Trans. Wreless Commun., vol. 8, no., Jan. 29. [4] H. Su and X. Zhang, Cross-layer based opportunstc MAC protocols for QoS provsonngs over cogntve rado moble wreless networks, IEEE J. Sel. Areas Commun., vol. 26, no., pp. 8-29, Jan. 28. [5] Q. Zhao, L. Tong, A. Swam, and Y.-X. Chen, Decentralzed cogntve MAC for opportunstc spectrum access n ad hoc networks: A POMDP framework, IEEE J. Sel. Areas Commun., vol. 25, no. 3, Aprl 27. [6] Q. Zhao, S. Gerhofer, L. Tong and B. M. Sadler, Opportunstc spectrum access va perodc channel sensng, IEEE Trans. Sgnal Process., vol. 56, no. 2, Feb. 28. [7] S. Gerhofer, L. Tong and B. M. Sadler, -aware OFDMA resource allocaton: A predctve approach, IEEE MILCOM 28, Nov. 28. [8] S. Gerhofer, L. Tong and B. M. Sadler, A sensng-based cogntve coexstence method for nterferng nfrastructure and ad-hoc systems, Wrel. Commun. Mob. Comput., vol., no., pp. 6-3, Jan. 2. [9] Y. Pe, A. T. Hoang, and Y. Lang, Sensng-throughput tradeoff n cogntve rado networks: How frequently should spectrum sensng be carred out? Proc. of 8th IEEE PIMRC, Athens, Greece, Sep. 27. [] Y. Xu, Y. L, H. Zou, X. Yang, Jont sensng perod optmzaton and transmsson tme allocaton for cogntve rado networks, WCSP 29, Nanjng, Chna, Nov. 29. [] Y. Xu, Y. Sun, Y. L, Y. Zhao, and H. Zou, Jont sensng perod and transmsson tme optmzaton for energy-constraned cogntve rados, EURASIP Journal on Wreless Communcatons and Networkng, 2. [2] J. Poston and W. Horne, Dscontguous OFDM consderatons for dynamc spectrum access n dle TV channels, IEEE DySPAN 25, pp. 67-6, 25. [3] S. Gerhofer, L. Tong and B. M. Sadler, Dynamc spectrum access n the tme doman: Modelng and explotng whtespace, IEEE Commun. Mag., vol. 45, no. 5, pp. 66-72, May 27. [4] S. Gerhofer, J. Z. Sun, L. Tong, and B. M. Sadler, Cogntve frequency hoppng based on nterference predcton: Theory and expermental results, ACM SIGMOBILE Mob. Comput. and Commun. Rev., vol. 3, no. 2, pp. 49-6, Apr. 29. [5] X. L, Q. Zhao, X. Guan, and L. Tong, Optmal cogntve access of Markovan channels under tght collson constrants, IEEE J. Sel. Areas Commun., 2, to appear. [6] S. I. Resnck, Adventures n Stochastc Processes. Brkhauser, 992. [7] R. M. Corless, G. H. Gonnet, D. E. G. Hare, D. J. Jeffrey and D. E. Knuth, On the Lambert W functon, Advances n Computatonal Mathematcs, vol. 5, no., pp. 329-359, 996. 5