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  IEEE COMMUNICATIONS LETTERS, VOL. 13, NO. 6, JUNE 2009 393 VoIP Capacity Analysis in Cognitive Radio System Howon Lee and Dong-Ho Cho  Abstract —In this letter, we analyze a voice over IP (VoIP)capacity in a cognitive radio system. We formulate the systemas a two-dimensional discrete time Markov chain (DTMC).The VoIP traf  fi c and wireless channel in the cognitive radiosystem are described as a Markov modulated Poisson process(MMPP) model and a Markov channel model, respectively. Wedemonstrate various numerical and simulation results, such aspacket dropping probability and VoIP capacity.  Index Terms —Cognitive radio, VoIP service, Markov modu-lated Poisson process, discrete-time Markov chain. I. I NTRODUCTION C OGNITIVE radio is a promising and challengeable tech-nology for maximizing radio resource utilization in afuture wireless communication system because conventionalsystems exploit most available frequency bands for wirelesscommunications and these frequency bands are not alwaysfully utilized in general [1]. In addition, Voice over IP (VoIP)will be an essential service in the future because, throughVoIP technology,wireless users can utilize voice services morecheaply. Therefore, supporting as many voice users as possiblewhile using limited radio resources is a very important issuethat could be a key to the success of the future systems [2][3].In [4], the authors proposed a discrete-time Markov chain(DTMC) framework based on a Markov modulated Poissonprocess (MMPP) traf  fi c model to analyze VoIP performance.However, they did not consider the cognitive radio system.Also, in [5], Q. Bi et al. analyzed the VoIP capacity of 1xEV-DO system. In this letter, we analyze VoIP capacity in acognitive radio system through a queuing model based on theMMPP traf  fi c model and a Markov channel model. Here, VoIPpackets can be transmitted when the wireless channel is notutilized by a primary user. To the best of our knowledge, theVoIP capacity analysis has not been studied yet in the cognitiveradio system.The remainder of this letter is organized as follows. InSection II, we present the VoIP traf  fi c model based on theMMPP and the Markov channel model for cognitive radiosystem. In Section III, we propose a two-dimensional DTMCframework considering multi-user VoIP queuing and wirelesschannel occupancy variations. In Section IV, we demonstratenumerical and simulation results and conclude this letter.II. V O IP T RAFFIC AND  C HANNEL  M ODELING 1) VoIP Traf   fi c Modeling:  In general, we can formulatethe VoIP traf  fi c of a single user as a simple on-off model.The probability that the status of the users is inactive (= Manuscript received December 23, 2008. The associate editor coordinatingthe review of this letter and approving it for publication was H.-H. Chen.The authors are with KAIST, Republic of Korea (e-mail:hwlee@comis.kaist.ac.kr).Digital Object Identi fi er 10.1109/LCOMM.2009.082189 (Unoccupied) (Occupied) p 01 p 10 p 00 p 11 Fig. 1. Markov channel model for cognitive radio system. off) in the simple on-off model can be obtained by  p off   = β  − 1 / ( α − 1 + β  − 1 )  , and  p on  = 1 −  p off  . Here,  1 /α  and  1 /β   arethe mean values of the on and off periods which are distributedexponentially. Furthermore, all the traf  fi c generated by theVoIP users in the cell can be modeled as a two-state MMPPmodel [6]. This MMPP model is highly suitable for formulat-ing the multi-user VoIP traf  fi cs because the MMPP capturesthe interframe dependency between consecutive frames. Here,the transition rate matrix ( R ) and the Poisson arrival ratematrix ( Λ ) of the MMPP can be expressed as follows: R =   − r 1  r 1 r 2  − r 2  ,  Λ =   λ 1  00  λ 2  .  (1)In order to utilize the MMPP model, we should match theMMPP parameters ( r 1 ,r 2 ,λ 1  and  λ 2 ) in Eqn. (1) with the pa-rameters of the simple on-off model ( α  and  β  ). We here adoptthe IDC (index of dispersion for counts) matching techniquebecause it yields adequate results for the matching of param-eters and has appropriate computation complexity comparedwith other matching techniques [4]. Then, r 1 ,  r 2 ,  λ 1 , and  λ 2  inEqn. (1) can be calculated by  r 1  =  2( λ 2 − λ avg )( λ avg − λ 1 ) 2 ( λ 2 − λ 1 ) λ avg ( IDC  ( ∞ ) − 1) , r 2  =  2( λ 2 − λ avg ) 2 ( λ avg − λ 1 )( λ 2 − λ 1 ) λ avg ( IDC  ( ∞ ) − 1) ,  λ 1  =  A  ·  N act avgi =0  i · π i  N act avgj =0  π j , and λ 2  =  A  ·  N i = N act avg +1  i · π i  N j = N act avg +1  π j . Here,  N   is the total number of VoIP users in the system, and  A  is the emission rate in the on-state ( A  =  1 T  basic ) .  T  basic  is a frame duration of voice codec,and the average arrival rate is  λ avg  =  N   ×  A  ×  p on . Also,the average number of active users is  N  act avg  =   N   ×  p on  ,and the steady-state probability of an one-dimensional Markovchain when considering  N   independent simple on-off voiceusers can be calculated by  π i  = N   C  i  ·  p ion  ·  (1  −  p on ) N  − i .Moreover,  IDC  ( ∞ )  is given in [6]. 2) Channel Modeling in Cognitive Radio System:  In acognitive radio system, a wireless channel can be modeledas a two-state Markov process, as shown in Fig. 1 [7]. Anoccupied state means that the wireless channel is utilized by aprimary user. Given that the channel status is ‘Occupied’, thecognitive user cannot use the channel. In this letter, we assumethat there are ‘ M  ’ wireless channels. Then, the transition 1089-7798/09$25.00 c   2009 IEEE Authorized licensed use limited to: Korea Advanced Institute of Science and Technology. Downloaded on May 31,2010 at 14:02:45 UTC from IEEE Xplore. Restrictions apply.  394 IEEE COMMUNICATIONS LETTERS, VOL. 13, NO. 6, JUNE 2009 B ( i,m ) , ( j,n )  = M   k =0  U · D (  j − max ( i − k, 0))  ·  P  s ( k  |  x c  =  m )  · min ( m,M  − n )  x  = max (0 ,m − n )  mx    p x  01  p m − x  00  M   −  my    p y  10  p M  − m − y  11  .  (5) probability ( P  m,n ) that there are  m  unoccupied channels ( x c )in the current frame, and there will be  n  unoccupied channelsin the next frame can be represented by P  m,n  = min ( m,M  − n )  x  = max (0 ,m − n )  mx    p x  01  p m − x  00  M   − my    p y  10  p M  − m − y  11  . (2)Here,  y  =  n − m + x  , where  x  and  y  denote the numbers of channels whose status are altered from ‘Unoccupied’ to ‘Oc-cupied’ and from ‘Occupied’ to ‘Unoccupied’, respectively.III. S YSTEM  M ODELING 1) Assumptions:  Perfect informationfor channel occupancyof primary users is available in the base station (BS), andone VoIP packet can be transmitted through one unoccupiedwireless channel. If all the channels are used by the primaryusers, the VoIP packets cannot be sent. Also, we assume thatthere are no packet retransmissions. That is, unreceived anddestroyed packets are not sent again. 2) System Modeling:  We can formulate a multi-user queu-ing model for VoIP services in a cognitive radio system asa two-dimensional DTMC. In other words, we can analyzethe behavior of queuing packets in the BS with this DTMCmodel. Then, the transition matrix ( P ) can be de fi ned as P =  A 0 , 0  A 0 , 1  · · ·  A 0 ,L max ............ A L max , 0  A L max , 1  · · ·  A L max ,L max   (3)where  L max  is maximum queue length and submatrix ( A i,j )is expressed as A i,j  =  B ( i, 0) , ( j, 0)  B ( i, 0) , ( j, 1)  · · ·  B ( i, 0) , ( j,M  ) ............ B ( i,M  ) , ( j, 0)  B ( i,M  ) , ( j, 1)  · · ·  B ( i,M  ) , ( j,M  )  . (4)In Eqn. (4),  A i,j  represents the variation of the number of queuing packets. That is, there are  i  packets in the currentframe, and there will be  j  packets in the next frame. In  A i,j ,each element ( B ( i,m ) , ( j,n ) ) indicates the transitions betweenthe numbers of unoccupied channels when the number of queuing packets is changed from  i  to  j . Also,  B ( i,m ) , ( j,n ) is a 2-by-2 matrix because our MMPP model has two phases,such as underloading and overloading. When the number of queuing packets is  i , given that  k  packets are scheduled, (  j  − max ( i − k, 0))  packets should arrive so that the numberof packets becomes  j . Hence,  B ( i,m ) , ( j,n )  can be calculatedby Eqn. (5). Here,  P  s ( k  |  x c  =  m )  is the probability that theBS serves  k  packets when the number of unoccupied channelsis  m . In this letter, since we assumed that one VoIP packetcan be transmitted through one unoccupied wireless channel, P  s ( m  |  x c  =  m ) = 1 . In addition, in Eqn. (5),  U  and D ( m )  are the transition probability matrix and the diagonalprobability matrix of the two-state MMPP model [4]. Eachelement of   D ( m )  means the probability that  m  VoIP packetsarrive at the BS during the MAC frame duration ( T  f  ) in eachphase of the two-state MMPP.Through the transition matrix ( P ) in Eqn. (3), we canobtain the steady-state probability matrix ( π  p ) for our two-dimensional DTMC model, which can be calculated by solvingequations  π  p  · P  =  π  p  and  π  p  · 1  = 1 . Here,  π  p  is ‘ 1 ’ by‘ 2 × ( M  +1) × ( L max +1) ’ matrix. Therefore, the probabilitythat  k  VoIP packets are queued in the BS can be expressed as π ( k ) =  2( M  +1) − 1 l =0  π  p (2  ·  ( M   + 1)  · k  + l ) .  (6)Through Eqn. (6), the ‘ 1 ’ by ‘ ( L max +1) ’ steady-state proba-bility matrix of the DTMC model can be obtained as follows: π  = [ π (0)  π (1)  π (2)  ···  π ( L max )] . Therefore, by usingthis steady-state probability, we can present various analyticalresults, such as the average number of arrived packets, theaverage queue-length, the average number of serviced VoIPpackets, the average VoIP throughput, and the packet droppingprobability. First, the average queue-length ( L avg ) and theaverage arrival rate ( ρ ) can be calculated by L avg  =  L max i =0  i · π ( k ) .  (7) ρ  = s ·  N  × A max m =0  m · D ( m )  · 1 .  (8)In Eqn. (8),  s  is calculated by solving  s · U  =  s , and  1  is acolumn matrix of ones. Also,  A max  is the maximum numberof packets that can arrive from each VoIP user during  T  f  .Similar to the average arrival rate, the average number of serviced VoIP packets ( κ avg ) can be expressed as κ avg  = M   i =0 M   j =0 L max  k =0 min(  j,k )  · π ( k )  · P  s (  j  |  x c  =  i )  · π ch ( i ) .  (9)Here,  π ch ( i )  is the steady-state probability that the number of unoccupied channels are  i , and can be expressed as π ch ( i ) =  M i  (  p 10  p 01  +  p 10 ) i ·  (  p 01  p 01  +  p 10 ) M  − i .  (10)Moreover, the average throughput is represented by  S  avg  = κ avg  ×  l PDU  . Here,  l PDU   is the size of VoIP PDU. Also,we can calculate the dropping probability of VoIP packets asfollows:  P  drop  = 1 − κ avg /ρ . Hence, by using  P  drop , we cande fi ne the VoIP capacity as following C  V oIP   = arg max  N   ∈ { N   |  1  − κ avg /ρ  ≤  P  limit } .  (11)Here,  P  limit  is the upper threshold of the packet droppingprobability for VoIP services.IV. N UMERICAL AND  S IMULATION  R ESULTS We evaluated the VoIP performance of the cognitive radiosystem by using MATLAB. We included all the essential fac-tors required for performance evaluation, such as round-robin Authorized licensed use limited to: Korea Advanced Institute of Science and Technology. Downloaded on May 31,2010 at 14:02:45 UTC from IEEE Xplore. Restrictions apply.  LEE and CHO: VOIP CAPACITY ANALYSIS IN COGNITIVE RADIO SYSTEM 395 010203040506070801E-30.010.11 P  limit     P  a  c   k  e   t   d  r  o  p  p   i  n  g  p  r  o   b  a   b   i   l   i   t  y Number of users  sim, p o =0.8 sim, p o =0.5 sim, p o =0.2 anal, p 01 =0.8, p 10 =0.2 anal, p 01 =0.5, p 10 =0.5 anal, p 01 =0.2, p 10 =0.80.02 Fig. 2. Packet dropping probability versus numberof users according to variation of channel occu-pancy probability when M=10. 01020304050607080050100150200250300350400    A  v  e  r  a  g  e   t   h  r  o  u  g   h  p  u   t   (   k   b  p  s   ) Number of users  sim, p o =0.8 sim, p o =0.5 sim, p o =0.2 anal, p 01 =0.8, p 10 =0.2 anal, p 01 =0.5, p 10 =0.5 anal, p 01 =0.2, p 10 =0.8 Fig. 3. Average throughput (Kbps) versus numberof users according to variation of channel occu-pancy probability when M=10. 15202530354045500.010.10.02 P  limit     P  a  c   k  e   t   d  r  o  p  p   i  n  g  p  r  o   b  a   b   i   l   i   t  y Number of users  anal, p 00 =0.2, p 01 =0.8, p 10 =0.8, p 11 =0.2 anal, p 00 =0.5, p 01 =0.5, p 10 =0.5, p 11 =0.5 anal, p 00 =0.8, p 01 =0.2, p 10 =0.2, p 11 =0.8 Fig. 4. Packet dropping probability versus numberof users according to variation of channel-statetransition probability when M=10.TABLE IV O IP  CAPACITY ACCORDING TO VARIATION OF  DL/UL  FRAME RATIO                          CapacityDL/UL frame ratioDL:UL = 1:1 DL:UL = 2:1Downlink capacity 13 24Uplink capacity 33 21 scheduler, packet-size and packet-generation period variationsof VoIP codecs, and so on.To obtain results, we assumed that  M   = 10 ,  T  f   = 5 ms,  L max  = 50 , and  A max  = 200 . We utilized the G.729Bcodec where  T  basic  is  10  ms. This codec has two data rates( 8  kbps and  0  kbps), and voice activity factor is 0.4, in thisletter. We assumed that the size of the RTP/UDP/IPv4 headercompressed by payload header suppression (PHS) is  16  bytes.Also, the size of the MAC header is  6  bytes. In the simulation,we used an on-off source model for each VoIP user.As shown in Fig. 2, we can show  P  drop  versus the numberof users according to variation of channel occupancy probabil-ity (  p o ). In this letter, we assume that  P  limit  = 0 . 02 . Here,  p o means the probability that the primary users utilize wirelesschannels, and also denotes the steady-state probability whenchannel status is ‘Occupied’. For a low loading condition, theMMPP based numerical results have lower packet droppingprobabilities than the on-off based simulation results mainlydue to the characteristic of the IDC matching technique [4].In addition, the average throughputgrows linearly accordingto the increment of the number of VoIP users up to thesaturation point, as shown in Fig. 3. Since resource saturationoccurs at this point, the BS cannot assign channels to surplususers beyond the saturation point. Thus, even though thenumber of users increases, the average throughput cannot beenlarged without limit. Given that  p o  is small, there exist moreunoccupied channels that can be utilized by cognitive users.Thus, the throughput when  p o  is small could be higher thanthe throughput when  p o  is large. Also, from Fig. 2 and Fig. 3,it can be seen that the performance of analysis and simulationare almost the same.The VoIP capacity can be varied according to the variationof channel-state transition probability, as shown in Fig.4. Here,the steady-state transition probabilities of the Markov channelmodels for all the cases are the same. However, if the  p 01 and  p 01  are larger, the state transitions occur more frequently.Thus, the VoIP capacity could be smaller. On the other hand,we can apply our formulation to VoIP admission control in thecognitive radio system. If the channel occupancy variations aredynamic, we can adjust the maximum supportable number of users based on the results demonstrated in this letter.Furthermore, given that the total number of channels is  30 ,the overhead caused by control signaling is  30 % [8], and  p o  =0 . 5 , we can obtain both downlink and uplink capacitythrough our analysis method. As shown in Table I, whenDL/UL frame ratio is 1:1, we can show that the VoIP capacityis restricted by the downlink owing to the overhead caused bycontrol signaling. However, when the DL/UL ratio is 2:1, thecapacity is limited by the uplink due to the fact that the sizeof uplink frame is much smaller than that of downlink frame.Therefore, we can conclude that the VoIP capacity is deter-mined by bottleneck-link, which can be different according tosystem parameters such as the DL/UL ratio.R EFERENCES[1] I. F. Akyildiz, W.-Y. Lee, M. C. Vuran, and S. Mohanty, “NeXtgeneration/dynamic spectrum access/cognitive radio wireless networks:a survey,”  Computer Networks: The International J. of Computer and Telecommun. Networking , vol. 50, no. 13, pp. 2127–2159, Sept. 2006.[2] S. McBeath, J. Smith, L. Chen, and A. C. K. Soong, “VoIP support usinggroup resource allocation based on the UMB system,”  IEEE Commun. Mag. , vol 46, no. 1, pp. 114–120, Jan. 2008.[3] F. Wang, A. Ghosh, C. Sankaran, P. Fleming, F. Hsieh, and S. J. Benes,“Mobile WiMAX systems: performance and evolution,”  IEEE Commun. Mag. , vol. 46, no. 10, pp. 41–49, Oct. 2008.[4] J.-W. So, “Performance analysis of VoIP services in the IEEE 802.16eOFDMA system with inband signaling,”  IEEE Trans. Veh. Technol. , vol.57, no. 3, pp. 1876–1886, May 2008.[5] Q. Bi, P.-C. Chen, Y. Yang, and Q. Zhang, “An analysis of VoIP serviceusing 1xEV-DO Revision A system,”  IEEE J. Select. Areas Commun. ,vol 24, no. 1, pp. 36–44, Jan. 2006.[6] H. Heffes and D. M. Lucantoni, “A Markov modulated characterizationof packetized voice and data traf  fi c and related statistical multiplexerperformance,”  IEEE J. Select. Areas Commun. , vol 4, no. 6, pp. 856–868, Sept. 1986.[7] Q. Zhao, L. Tong, A. Swami, and Y. Chen, “Decentralized cognitiveMAC for opportunistic spectrum access in ad hoc networks: a POMDPframework,”  IEEE J. Select. Areas Commun. , vol. 25, no. 3, pp. 589–600,Apr. 2007.[8] F. Wang, A. Ghosh, C. Sankaran, P. Fleming, F. Hsieh, and S. J. Benes,“Mobile WiMAX systems: performance and evolution,”  IEEE Commun. Mag. , vol. 46, no. 10, pp. 41–49, Oct. 2008. Authorized licensed use limited to: Korea Advanced Institute of Science and Technology. Downloaded on May 31,2010 at 14:02:45 UTC from IEEE Xplore. Restrictions apply.
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