International Conference on Automation, Mechanical Control and Comutational Engineering (AMCCE 205) Performance analyi in cognitive radio ytem under erfect ectrum ening Chen Song, Gu Shuainan, Zhang Yankui Zhengzhou Intitute of Information Science and Technology, Zhengzhou 45000, China Keyword: cognitive radio; ectrum ening ; continuou time markov chain, tranmit colliion; channel utilization Abtract: Sening eriod and otimization of uer acce in cognitive radio ytem are analyzed. By introducing birth and death roce into cognitive radio ytem, a model of the queuing of rimary uer i built, baed on which the robability of ectrum ening and how the re-enter of the rimary uer effect on the ectrum uage of cognitive radio uer are tudied theoretically. Simulation reult have jutified the fitne of the model of joint analyi in the ractical environment. Therefore we may conclude that it will achieve the highet overall ectrum efficiency by etting u configuration in a cognitive ytem according to the theory above. Introduction According to the fact that the ectrum i in hort and ued efficiently, cognitive radio technologie get the free ectrum reource and ue them by ening technology under the remie that Primary Uer (PU) with ectrum authorization ha no ene [] [2]. In order to imrove the efficiency of cognitive radio technology reource, according to the buine need, uer acce characteritic, ectrum ening method and ome other characteritic of the cognitive ytem, ytem modeling, arameter otimization, erformance analyi and ome other reearche were made in the exiting literature. In [3], the aearing characteritic of PU wa decribed by Continuou-Time Markov Chain (CTMC). Cumulative time and ditribution robability of PU' occuying channel were met by analyzing. In [4] and [5], cognitive radio ytem wa ytem modeled by tate5' and tate8' CTMC. Then, Secondary Uer (SU) acce otimization algorithm wa ut forward and the ectrum utilization efficiency and uer fairne were in good comromie. In [6], according to the SU coexitence of different tye, the ytem wa modeled by Markov model tack. Markov chain of different tate were etablihed and were connected by few core tate. The method imlified the modeling and analyi of SU of multile tye cognitive radio ytem. In [7], cognitive radio ytem model wa etablihed baed on retaurant game theory and Semi-Markov roce. The analyi comlexity of cognitive radio ytem wa reduced effectively under the ubjective effect and ytem analyi frame wa contructed baed on ocial dynamic influence. In [8], for VolP buine, general Markov chain model wa etablihed and adjacent tranition relation of tate are olved. Uer connection roertie and data acket lo erformance were analyzed. The imulation how the ytem model wa effective. Markov chain wa introduced to model for the cognitive radio ytem in the literal above. Sytem erformance ha been analyzed and otimized for arameter and condition of different ytem. It can be een that the continuou-time Markov chain can decribe the cognitive radio ytem very well. Baed on thi characteritic, under ideal teting condition, thi aer ha conducted the ytem model with CTMC-N. Sytem general equation i etablihed and the ytem of equation of general olution i given baed on "flow equilibrium" theory. Finally, relation between colliion robability, channel utilization, SU arrival identity the number of channel and the fale detection robability are analyzed and decribed through the numerical imulation of the ytem. Sytem modeling The running tate and running roce of the ytem have been decribed and art of ytem 205. The author - Publihed by Atlanti Pre 2343
erformance wa analyzed by continuou time Markov chain model in [9]. Make the aumtion that i i the amount of PU occuied channel, j i the amount of PU occuied channel, the amount of ytem i M and i+ j M, i 0, j 0. According to the definition of continuou Markov chain, et tate ( i, j ) a the general condition, then the tate tranition relation of the model i a hown in Figure. Figure Sytem tate tranition diagram Aume that the ectrum detection of SU on PU i ideal teting. There are M authorized channel in PU ytem and channel are ditributed and controlled by control center. PU and SU ytem are indeendent of each other. When SU detect that the authorized channel of PU i free, it elect a random channel for data tranmiion. We aume that arrival robability of PU and SU obey Poion ditribution with arameter λ and λ, and the ervice time alo obey the exonential ditribution with arameter µ and µ. The number of PU and SU i much larger than the number of authorized channel. Modeling and erformance analyi Solve tranition robability According to the ytem model of Figure, in order to obtain the ditribution robability of tate, the tranition robability need to be olved. Tranition robabilitie were olved a follow,. Get P P rereent that the amount of PU and SU i unchangeable and the ytem tate i tranmitting at the ame lace. There may be e oible reaon. () When the new PU arrive, the total M channel were occuied by PU, that i i = M The robability i: P = P( M,0) () (2) When the new PU arrive, a channel which SU i uing i occuied. The robability i: j P 2= (2) M i (3) When the new PU arrive, the total M channel were occuied by PU where i channel were occuied by PU and j channel were occuied by PU. And i+ j = M. The robability i: P 3 = P( i, j) i+ j = M (3) So, P can be exreed a: P = λ( P + P 2) + λp 3 (4) In the above 3 ituation, PU and SU have colliion in (2), which will reult in the lo of ytem erformance. 2. get P 2 P 2 rereent that the new arrival SU occuied a free channel uccefully. The robability i: P2 = λ (5) 3. get P 3 P rereent that the new arrival PU occuied a free channel uccefully and doen t caue 3 2344
interference to other uer in the ytem. The tranition robability i: M i j P3 = λ M i 4. get P 4 P rereent that PU wa erved and left. The tranition robability i: 4 5. get P 5 An SU wa erved and left. The tranition robability i: (6) P4 = iµ (7) P = 5 jµ (8) 6. Solve tate tationary ditribution Having obtained the tranition robability, linear equation of CTMC i PQ = 0, where P = P i j i+ j M which rereent the robability vector of tate tationary ditribution. { i, j 0, 0, } Q rereent the tranition robability vector. P can be exreed : The vector Q can be exreed: ( P0,0, P0, j, P0, M, P,0,, P, M, P2,0,, Pi, j,, PM,0 ) P = (9) The element of P um u, which can be exreed: P i, j= (0) i j Equation can be olved by relacing the element of lat line of Q with, then the new vector * Q can be obtained, that i: PQ * = b () Where b = ( 0,0,,), Q i a quare matrix of ( + )( + 2) 2, o P can be olved by matrix inverion. * P = bq (2) Sytem colliion robability and ectrum utilization In the cognitive radio ytem, the ytem ectrum utilization and uer colliion robability are the imortant evaluation indexe for ytem erformance. The increae of ectrum utilization i the original intention of cognitive radio ytem. The colliion robability of uer can not only influence ytem ectrum utilization, but alo influence the need of different uer buinee. Auming that SU i ideally erceived, the main SU colliion eize the channel SU i uing only when PU arrive. Then the colliion robability i: Pi, jp 2l Pcolliion = i, j P+ P2 + P3 + P4 + P5 (3) The definition of SU ytem ectrum utilization i: l Λ= ( Pcolliion ) µ (4) 2345
Where, λ µ i the traffic intenity of SU. Performance imulation and analyi The numerical imulation analyi wa baed on the ytem model above in thi art. The imulation condition are et a follow: PU ervice buine trength wa baed on VoIP (Voice over Internet Protocol) [0]. That i P H = 0.65, P 0 H = λ µ = 0.35, µ =, µ = 2 0.024 0.022 0.02 P-colliion M=5 M=0 M=5 M=20 M=25 0.08 0.06 P-colliion 0.04 0.02 0.0 0.008 0.006 0.004 0 0.2 0.4 0.6 0.8.2.4.6.8 2 l Figure 2 colliion robability under different number of channel 0.9 0.8 M=5 M=0 M=5 M=20 M=25 Lambda- 0.7 0.6 L 0.5 0.4 0.3 0.2 0. 0 0 0.2 0.4 0.6 0.8.2.4.6.8 2 λ Figure 3 colliion robability under different number of channel Figure 2 and Figure 3 how that under different number of channel, the arrival intenity variation ha influence on ytem colliion robability and ectrum utilization. Figure 2 and Figure 3 how that with the increae of channel, the colliion robability of uer decreae obviouly. Thi i becaue the arrival intenity of PU i certain. With the number of channel increae, the robability of free channel increae. Under the ideal ening condition, colliion robability between uer i not high and ha few influence on overall channel utilization. 0.07 0.06 P-colliion l =0.2 l =0.4 l =0.6 l =0.8 l = 0.05 P-colliion 0.04 0.03 0.02 0.0 0 0.2 0.4 0.6 0.8.2.4.6.8 2 l Figure 4 colliion robability under different PU acce rate 2346
0 0.2 0.4 0.6 0.8.2.4.6.8 2 0.9 0.8 0.7 λ =0.2 λ =0.4 λ =0.6 λ =0.8 λ = Lambda- 0.6 0.5 L 0.4 0.3 0.2 0. 0 Figure 5 colliion robability under different PU acce rate Figure 4 and Figure 5 how that under different arrival intenity of PU, the arrival intenity variation of SU ha influence on ytem colliion robability and ectrum utilization. Figure 4 and Figure 5 how that with arrival intenity of PU increae, channel utilization decreae and the colliion robability gradually increae. Thi i becaue the aearing robability of PU i higher; the robability of eizing SU channel i higher, which caued more lo on channel utilization. From the imulation reult above, under the ideal ectrum ening condition, channel utilization increae with the arrival intenity of SU increae while ytem colliion robability increae with the arrival identity of SU increae. However, colliion between uer caue little lo on ytem ectrum utilization. λ Concluion Thi aer model and analyze on cognitive radio ytem under ideal ening condition baed on continue time markov model, the relation between number of ytem channel, arrival intenity of PU and SU, the channel utilization and main SU colliion robability were obtained by numerical imulation. When deign cognitive radio ytem according with the ytem model above, the model and concluion can rovide ytem arameter etting and erformance otimization comromie with ome reference and direction. However, in the aer, only modeling under ideal ening condition wa taken into account. So the following main tak i ytem modeling and analyi under non-ideal ening condition. Reference [] Federal Communication Commiion. Notice of rooed rule making and order: Facilitating oortunitie for flexible, efficient, and reliable ectrum ue emloying cognitive radio technologie [J]. ET docket, 2005 (03-08): 73. [2] Haykin S. Cognitive radio: brain-emowered wirele communication [J]. Selected Area in Communication, IEEE Journal on, 2005, 23(2): 20-220. [3] Lu L, Zhou X, Li G Y. Otimal equential detection in cognitive radio network[c]//wirele Communication and Networking Conference (WCNC), 202 IEEE. IEEE, 202: 289-293. [4] Wang B, Ji Z, Liu K J R. Primary-rioritized Markov aroach for dynamic ectrum acce[c]//new Frontier in Dynamic Sectrum Acce Network, 2007. DySPAN 2007. 2nd IEEE International Symoium on. IEEE, 2007: 507-55. [5] Wu Y, Wang B, Liu K J R, et al. Reeated oen ectrum haring game with cheat-roof trategie[j]. Wirele Communication, IEEE Tranaction on, 2009, 8(4): 922-933. [6] Li X, Xiong C. Markov model bank for heterogenou cognitive radio network with multile diimilar uer and channel[c]//comuting, Networking and Communication (ICNC), 204 International Conference on. IEEE, 204: 93-97. [7] Jiang C, Chen Y, Yang Y, et al. Dynamic Chinee Retaurant Game: Theory and Alication to Cognitive Radio Network[J]. Wirele Communication, IEEE Tranaction on, 204, 3(4): 960-973. 2347
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