Delay performance of cognitive radio networks for point-to-point and point-to-multipoint communications

Transcription

1 Tran et al. EURASIP Journal on Wireless Counications and Networking 2012, 2012:9 R E S E A R C H Open Access Delay perforance of cognitive radio networks for point-to-point and point-to-ultipoint counications Hung Tran *, Trung Q Duong and Hans-Jürgen Zepernick Abstract In this paper, we analyze the packet transission tie in spectru sharing systes where a secondary user (SU siultaneously accesses the spectru licensed to priary users (PUs. In particular, under the assuption of an independent identical distributed Rayleigh block fading channel, we investigate the effect of the peak interference power constraint iposed by ultiple PUs on the packet transission tie of the SU. Utilizing the concept of tieout, exact closed-for expressions of outage probability and average packet transission tie of the SU are derived. In addition, eploying the characteristics of the M/G/1 queuing odel, the ipact of the nuber of PUs and their peak interference power constraint on the stable transission condition and the average waiting tie of packets at the SU are exained. Moreover, we then extend the analysis for point-to-point to point-to-ultipoint counications allowing for ultiple SUs and derive the related closed-for expressions for outage probability and successful transission probability for the best channel condition. Nuerical results are provided to corroborate our theoretical results and to illustrate applications of the derived closed-for expressions for perforance evaluation of cognitive radio networks. Keywords: cognitive radio networks; spectru sharing; outage probability; packet transission tie; queueing analysis. 1 Introduction Radio spectru is one of the ost precious and liited resources in wireless counications. It has becoe scarce due to the rapid growth of a variety of obile devices and the eerging of any new obile services. However, recent easureent capaigns conducted by the Federal Counications Coission in the United States have revealed that vast portions of the allocated spectru are heavily under-utilized [1]. Clearly, the scarcity of the spectru is due to its inefficient usage rather than a shortage of spectru resources. As a consequence, the spectru utilization proble has becoe ore crucial and has stiulated new research such as extensive work on cognitive radio networks (CRN [2]. In CRNs, there are two types of users who are referred to as priary user (PU and secondaryuser(su.thepulicensesthespectruwhilea * Correspondence: hung.tran@bth.se Radio Counications Group, Blekinge Institute of Technology, SE Karlskrona, Sweden SU ay access the spectru owned by the PU provided that it does not coproise the quality of service (QoS delivered to the PU. Therefore, a ajor challenge with the design of CRNs is to aintain the desirable QoS at the PU while offering a sufficiently high transission rate to the SUs. Recently, the spectru sharing approach is considered as a proising solution to utilize the licensed radio frequency. Particularly, the SU and the PU can transit siultaneously as long as the interference caused by the SU to the PU is lower than a predefined threshold. In [3], considering different fading channels, the ergodic capacity of the spectru sharing syste is investigated for either peak interference power constraint or average received interference power at the PU-Rx. This work has revealed that if the link fro the secondary transitter (SU-Tx to the priary receiver (PU-Rx resides in a deep fade, the power of the SU-Tx can be increased to iprove the link to the SU-Rx without coproising the peak interference 2012 Tran et al.; licensee Springer. This is an Open Access article distributed under the ters of the Creative Coons Attribution License ( which perits unrestricted use, distribution, and reproduction in any ediu, provided the original work is properly cited.

2 Tran et al. EURASIP Journal on Wireless Counications and Networking 2012, 2012:9 Page 2 of 14 power constraint. Later, the fundaental capacity liits with iperfect channel knowledge have been studied in [4, 5]. In [6], the authors have considered a new sophisticated approach for spectru sharing systes where the ipact of channel knowledge on the perforance of a secondary user has been studied. The results show that the channel knowledge of the PU-Tx PU-Rx link is iportant to itigate the interference fro the SU-Tx PU-Rx link while the channel knowledge of the SU-Tx PU-Rx link has little ipact on the SU capacity. In [7], different notions of capacity are investigated for the Rayleigh fading channel subject to both the peak and average interference power constraints. Especially, the ergodic capacity and outage capacity which are considered suitable for delay-insensitive and delay-sensitive applications are studied. In [8 10], the novel concept of effective capacity has been introduced to investigate the QoS requireents such as delay constraint in wireless counication systes. In particular, the effective capacity is defined as the axiu constant arrival rate that can be provided by the channel while the delay constraint of the spectru sharing syste is satisfied [9]. The results in [9] have also shown that for a given peak and average interference power constraint at the PU-Rx, the axial effective capacity is achieved under the optial power control policy. In relation to the delay constraint in the spectru sharing syste, in [11, 12], we have used another approach, which is based on the packet transission tie to investigate the perforance of CRN. These results have revealed the ipact of the peak interference power constraint on the delay of packets for different types of fading channels. However, we analyzed the spectru sharing syste with peak interference power constraint only for a single PU. In this paper, we therefore extend our previous work [11] toconsidertheorerealisticcaseofacrnunder thepeakinterferencepowerconstraintinthepresence of ultiple PUs. Specifically, we exaine the delay perforance for two scenarios, point-to-point and point-toultipoint counications. In the latter scenario, we extend the investigation fro ultiple PUs to also allow for ultiple SUs at the receiving end. We assue that each packet of the SU-Tx has a delay constraint. In order to not cause harful interference to any surrounding PU-Rx, the SU-Tx needs to adapt its transit power and coence transission before the packet delay threshold is reached. Given this setting, in the point-to-point scenario, we derive the probability density function (PDF and cuulative density function (CDF for the packet transission tie, outage probability and average transission tie of packets at the SU-Tx. Furtherore, assuing that packet arrivals at the SU-Tx follow a Poisson process, the queueing odel for point-to-point scenario can be described as an M/G/1 syste in which packet inter-arrival ties are exponentially distributed, service tie is a general distribution and traffic is processed by a single server. In the point-to-ultipoint scenario, also known as ulticast, a secondary base station (SBS transits a coon packet toallsu-rxwhilekeepingthepeakinterferencepowerto the surrounding PU-Rx below a given threshold. By applying the obtained PDF and CDF for the point-to-point scenario, a closed-for expression for the outage probabilitythatthesbscannottransitthecoonpacketsuccessfully to a nuber of SU-Rx are obtained. Moreover, a closed-for expression for the probability that the SBS can transit the coon packet successfully to all SU-Rx, i.e. the best channel condition, is also achieved. Therestofthepaperisorganizedasfollows.InSection2, the syste odel and assuptions for the point-to-point and point-to-ultipoint scenarios are introduced. In Section 3, analytical forulations for the point-to-point scenario such as the PDF and CDF of the packet transission tie, the outage probability, and the oent of packet transission tie is derived. On this basis, queueing theoretical conclusions are drawn. In Section 4,we present the delay perforance for the point-to-ultipoint scenario. Section 5 provides nuerical results and discussions. Finally, conclusions are presented in Section 6. 2 Systeodel In the sequel, we introduce the point-to-point and pointto-ultipoint scenarios in the context of a spectru sharing syste where the SU operates in the area of ultiple PUs. As for the radio links between the different entities, we assue identical and independent distributed (i.i.d. Rayleigh block fading channels with unit-ean in the presence of additive white Gaussian noise (AWGN. The additive noises at both SU-Rx and PU-Rx constitute independent circular syetric coplex Gaussian rando variables with zero-ean and variance N 0,denoted as CN(0, N 0. As the SU and the PUs ay transit siultaneously, the interference caused by the SU to the PUs should not exceed a certain threshold. 2.1 Point-to-point scenario Let us consider point-to-point counications in which an SU-Tx is transitting packets to an SU-Rx while a nuber M of PU-Rx are operating on the priary network as showninfigure1.thepowergainofthesu-tx SU-Rx link is denoted by h 1. Siilarly, the interference channel power gain of the SU-Tx PU-Rx link is denoted by g, = 1, 2,..., M. Note that channel state inforation (CSI of the secondary syste can be provided to the SU-Tx through feedback fro the SU-Rx while CSI of the SU-Tx to the PU-Rx can be exchanged using a dedicated coon control channel [13]. In our study, we follow the assuption given in [3, 5, 14, 15] that the SU-Tx is close to the PU- Rx but the SU-Rx is far away fro the priary transitters (PU-Tx. Therefore, only the SU-Tx causes interference to thepu-rxwhileinterferencecausedbythepu-txtothe SU-Rx is luped with the AWGN.

3 Tran et al. EURASIP Journal on Wireless Counications and Networking 2012, 2012:9 Page 3 of 14 Figure 1 Point-to-point counication of the considered spectru sharing syste with ultiple PUs (solid line: counication fro SU-Tx to SU-Rx; dashed line: interference fro SU-Tx to surrounding PU-Rx Peak interference power constraint In order to process the offered traffic, the SU-Tx is equipped with a buffer which stores incoing packets of the sae size. The SU-Tx transfors the stored packets into bit streas and adopts its transission power based on the joined CSI which shall be denoted as (M +1-tuple (g 1, g 2,...,g M ; h 1. The ain objective for the considered spectru sharing syste ay be posed as to iniize the transission tie of packets at the SU while not causing harful interference to the PU-Rx. Following [16], the tie taken by an SU-Rx to decode L bits inforation of a packet can be expressed as T = L B log 2 (1 + γ B log e (1 + γ where B is the syste bandwidth, B=L log e (2/B,andγ is the signal-to-noise ratio (SNR at the SU-Rx given by γ = h 1P ( g 1, g 2,...,g M ; h 1 (1 N 0 (2 In (2, N 0 represents the noise power spectral density and P(g 1, g 2,...,g M ; h 1 is the power allocation policy for the SU-Tx corresponding to the joined CSI given as (g 1, g 2,..., g M ; h 1. According to [3], the transission power of the SU-Tx with respect to PU-Rx should be adjusted to be lower than an allowable level: g P ( g 1, g 2,...,g M ; h 1 Q pk, =1,2,...,M (3 where Q pk is the peak interference power that the PU-Rx can tolerate without scarifying QoS. Furtherore, let us assue that the tolerable peak interference power is the sae for all PU-Rx, i.e. Q pk = Q pk for = 1,2,...,M. In order to not cause harful interference to any PU-Rx in the priary syste, the transission power of the SU-Tx ust then satisfy the peak interference power constraint given as P ( g 1, g 2,...,g M ; h 1 Q pk ax { g } ( Delay constraint As far as the transission tie of packets is concerned, this is clearly non-deterinistic due to the fading channel. In the sequel, the transission of a packet is considered as successful if the packet transission tie is less than a predefined threshold, t out, referred to as tieout. Figure 2 shows an exaple of a tiing diagra of packet transission for point-to-point counication between SU-Tx and SU-Rx. Recall that the SU-Tx receives packets fro higher layers which it will convert into bit streas at the lower layer prior to transission over the fading channel. Once the SU-Rx has received a sufficient nuber of bits and decoded the related packets successfully, it will respond with an acknowledgeent (ACK packet that is assued to be error-free and incurs negligible delay to the SU-Tx. This ACK indicates the SU-Tx that it can eliinate the corresponding packet at the head of the buffer and ay continue with transitting the subsequent packets. In the exaple shown in Figure 2, the first packet is transitted unsuccessfully as the SU-Tx does not receive an ACK

4 Tran et al. EURASIP Journal on Wireless Counications and Networking 2012, 2012:9 Page 4 of 14 packet transission tie, respectively. Furtherore, the following result fro queueing theory can be applied for the stability of transission of the SU. Stability condition [20] Transission of the SU-Tx is stable if and only if the average arrival rate λ is less than the average transission rate μ,thatis λ < μ (7 where average transission rate is defined by the inverse of the average transission tie as μ = 1 E[T] (8 Figure 2 Exaple of a tiing diagra for point-to-point counication between SU-Tx and SU-Rx. within t out,i.e.t 1 t out. In this case, the SU-Tx considers the packet as dropped. In contrast, the second and third packet are transitted successfully as their transission ties are less than the tieout t out,i.e.t 2, T 3 < t out Queuing odel for point-to-point counications The packets arriving at the SU are stored in a buffer and served in first-in first-out (FIFO order. Assuing that the packet arrival follows a Poisson process with arrival rate λ, the considered point-to-point scenario ay be odeled as an M/G/1 queueing syste [17], [19] withservice tie given as general distribution and the syste being equipped with a single server [20]. Fro (1 and(2 and the peak interference power constraint (4, we can conclude that the packet transission tie depends on both the channel gain and the peak interference power constraint. Clearly, once the distribution of transission tie is deterined, the average waiting tie of packets at the SU-Tx can be calculated by applying the Pollaczek-Khinchin s equation [20, Eq. (8.34] as follows E[W]=E[T]+E [ ] T q (5 where E[W] is the total average waiting tie of packets at the SU-Tx and E[T q ] is the average waiting tie of packets in the buffer. It is noted that E[T q ]canbeforulatedas E [ T q ] = λe [ T 2] 2(1 ρ where ρ = λe[t] is referred to as channel utilization and E[T i ], i = 1, 2 denotes the first and second oent of (6 2.2 Point-to-ultipoint scenario In this scenario, we consider a spectru sharing syste as shown in Figure 3 in which a secondary base station (SBS transits a coon packet to a nuber N of SU-Rx in its coverage range. This scenario is also known as obile ulticast network in which the base station transits coon inforation to ultiple receivers over broadcast channels [21, 22] Peak interference power constraint In this spectru sharing scenario, the power allocation proble becoes ore coplicated as the SBS ust not only adjust its power to guarantee successful packet transission to all SU-Rx in the secondary syste but ust also liit the interference power caused to the active PU-Rx in the priary syste. Clearly, the transission tie of a coon packet will vary aong the different SU-Rx n due to the involved i.i.d. Rayleigh fading channels. Siilar to (1, the transission tie of a packet to an SU-Rx n can be expressed as T n B, log e (1 + γ n n =1,2,...,N (9 and γ n is the SNR at the nth SU-Rx n which can be forulated as γ n = h np ( g 1, g 2,...,g M ; h 1, h 2,...,h N n =1,2,...,N N 0, (10 where h n is the channel gain fro the SBS to the SU-Rx n while the optial transission power P(g 1, g 2,...,g M ; h 1, h 2,...,h N ofthesbsisgivenwithrespecttothejoined CSI denoted as (M + N-tuple (g 1, g 2,...,g M ; h 1, h 2,...,h N.

5 Tran et al. EURASIP Journal on Wireless Counications and Networking 2012, 2012:9 Page 5 of 14 Figure 3 Point-to-ultipoint counication of the considered spectru sharing syste with ultiple PUs and ultiple SUs (solid line: counication fro SU-Tx to surrounding SU-Rx; dashed line: interference fro SU-Tx to surrounding PU-Rx. The transission power policy of the SBS with respect to the PU-Rx should then satisfy the following condition: g P ( g 1, g 2,...,g M ; h 1, h 2,...,h N Q pk, =1,2,...,M (11 Siilar to the point-to-point scenario, we assue Q pk = Q pk which leads to the condition for the instantaneous transission power of SBS as P ( g 1, g 2,...,g M ; h 1, h 2,...,h N Q pk ax { g } ( Delay constraint In the point-to-ultipoint scenario, the SBS tries to broadcast coon packets to all SU-Rx in its coverage range. Each coon packet has a tie-to-live which should be less than t out. If an SU-Rx receives a coon packet, it feeds back an ACK to the SBS before t out.thiseansthat the SU-Rx has received the coon packet successfully. Otherwise, the SBS iplies that the SU-Rx has not received the transitted packet. Figure 4 shows an exaple of a tiing diagra where the SBS transits coon packets to two SU-Rx. In particular, the SBS transits the first packet successfully as both transission ties T 1,1 and T 2,1 corresponding to SU-Rx 1 and SU-Rx 2,respectively, are less than the tieout t out.itisnotedthatt 1,1 ay be different fro T 2,1 due to the different fading channel and spatial separation of SU-Rx 1 and SU-Rx 2.Incontrast, the second coon packet is transitted unsuccessfully to SU-Rx 2 asthesbsdoesnotreceiveanackfrosu- Rx 2 before tieout t out. Figure 4 Exaple of a tiing diagra for counication between the SBS and two SU-Rx. Clearly, if the SBS receives ACKs fro all SU-Rx before t out, it can be considered as the best channel condition. On the other hand, the SBS ay not transit the coon packet successfully to all SU-Rx due to the fading environent. 3 Perforance analysis for point-to-point counications In this section, we derive closed-for expressions for the PDF and CDF of packet transission tie as well as outage probability. Based on these results, we not only quantify the first and second oent of packet transission tie but also investigate the queueing theoretical characteristics of the considered spectru sharing syste.

6 Tran et al. EURASIP Journal on Wireless Counications and Networking 2012, 2012:9 Page 6 of PDF of packet transission tie In this scenario, the SU-Tx wants to transit with axiu transission rate in order to reduce dropped packets due to tieout. On the other hand, the SU-Tx not only needs to adjust its transission power in response to changes of the transission environent but also guaranteetheqosofanypu-rxaround.givenperfectcsi,the axiu instantaneous transission power of the SU-Tx in (4 can be expressed with equality as P ( g 1, g 2...,g M ; h 1 = Q pk ax { g } (13 By substituting (13into(2, we can rewrite (1as T = B log e ( 1+(h1 / ax { g } (Qpk /N 0 (14 It is easy to see that the packet transission tie, T, now turns out to be a function of ultiple rando variables, i.e. h 1, g, =1,2,...,M. Therefore, in order to investigate the delay perforance, we need to derive the PDF of T in the sequel. Let us start with the CDF of g 0 = ax {g } where g is the channel gain. Because the channel coefficients undergo Rayleigh fading, the channel gain, g,isarando variable distributed following an exponential distribution with unit-ean, given by F g (y=1 e y (15 Using order statistics, we can easily obtain the CDF and PDF of g 0, respectively, as follows: F g0 (y= ( 1 e y M f g0 (y=me y ( 1 e y M 1 (16 (17 For convenient derivation, let us denote Z = h 1 /g 0.The PDF of Z can be obtained by applying the ethod presented in [23]as ( M 1 ( 1 M f Z (z= (18 (1 + + z 2 On the other hand, the CDF of T can be forulated as { F T (x=pr{t < x} =1 Pr Z <(e B/x 1 N } 0 Q pk ( M 1 =1 ( 1 (e B/x 1M (1 + (e B/x + Q pk /N 0 + G (19 and the PDF of T can be derived by differentiating (19with respect to x as ( M 1 ( 1 BMQ pk f T (x= N 0 exp ( B/x (20 ( exp ( B/x + Q pk /N 0 + G 2, x 0 where G = Q pk N 0 1 is introduced for brevity. It is noted that (20 exactly leads to the PDF of [11, Eq.(10]forthepeak interference power constraint of a single PU-Rx by setting K =1. In the subsequent sections, the iportant result in (20 will be used to investigate the outage probability, the average transission tie and the average waiting tie of packets. 3.2 Outage probability Given the channel conditions and the peak interference power constraint, the outage probability P out is defined as the probability that the packet transission tie T exceeds the interval t out : P out = Pr(T t out (21 Fro (19,we can easily obtain the closed-for expression for the outage probability as P out =1 Pr(T < t out =1 F T (t out ( M 1 = ( 1 M 1+ exp ( B/t out 1 exp ( B/t out + Qpk /N 0 + G (22 On the other hand, let T suc denote the transission tie of a packet given that it is not dropped, i.e., T suc = {T T < t out } (23

7 Tran et al. EURASIP Journal on Wireless Counications and Networking 2012, 2012:9 Page 7 of 14 Accordingly, applying Bayes rule, the probability that the event T suc takes place can be expressed as P {T T < t out } = P {T, T < t out} P {T < t out } = P {T, T < t out} 1 P out (24 Based on (24, we can express the CDF of T suc as follows: F Tsuc (x= 1 1 P out x 0 f T (tdt, 0 x < t out (25 and F Tsuc (x =0forx t out. Differentiating both sides of (25withrespecttox, the PDF of the packet transission tie without being tied out can be presented as f Tsuc (x= d dx F T suc (x= f T(x 1 P out, 0 x < t out (26 and f Tsuc (x=0forx t out. Substituting (20into(26, the PDF of packet transission tie without being tied out can be obtained as ( M 1 ( 1 BMQ pk f Tsuc (x= (1 P out N 0 exp ( B/x [ exp ( B/x + Q pk /N 0 + G ] 2, (27 0 x < t out while f Tsuc (x =0forx t out. In the following, the PDF f Tsuc (x given in (27 will be used to derive the oent of packet transission tie. 3.3 Moent of packet transission tie Let us recall that a transitted packet can be received successfully or not due to the fading channel. Therefore, exaining average transission tie shall consider both packet transission tie without and with tieout. Let us start with the average transission tie of packet without tieout as follows tout E [T suc ] = xf Tsuc (xdx 0 MQ pk ( M 1 = (1 P out N 0 tout 0 B exp ( B/x ( 1 (28 x [ exp ( B/x + Q pk /N 0 + G ] 2 dx By setting t = exp( B/x and applying an exchange of variables in the integral of (28, we finally obtain the first oent of packet transission tie without tieout as where E [T suc ] = ψ 1 (a, b= MQ pk ( ψ 1 exp ( B/t out, G (1 P out N 0 ( M 1 ( 1 a B (log e t ( t + Q pk /N 0 + b 2 dt (29 (30 Siilarly, we can calculate the second oent of packet transission tie without tieout as follows E [ Tsuc 2 ] tout = x 2 f Tsuc (tdt 0 MQ pk ( M 1 = (1 P out N 0 tout B exp ( B/x [ 0 exp ( B/x + Q pk /N 0 + G ] 2 dx ( 1 (31 Using siilar exchange of variables as above for (31, we obtain the second oent of T suc as where E [ Tsuc 2 ] MQ pk ( = ψ 2 exp ( B/t out, G (1 P out N 0 ψ 2 (a, b= ( M 1 ( 1 a B 2 (log 2 e t [ t + Q pk /N 0 + b ] 2 dt (32 (33 Finally, by applying the law of total expectation, the first and the second oent of packet transission tie (including dropped packets can be given by E[T i ]=(1 P out E [ T i suc] + t i out P out, i =1,2 (34 where P out is given by (22 ande[tsuc i ], i =1,2canbecalculated by (29and(32, respectively. 3.4 Queuing theoretical characteristics Firstly, the expression for the average waiting tie of packets in the buffer of SU-Tx can be obtained by substituting

8 Tran et al. EURASIP Journal on Wireless Counications and Networking 2012, 2012:9 Page 8 of 14 (34withrespecttoi =1,2into(5and(6as E[W]= N 0t out P out + MQ pk ψ 1 ( exp ( B/t out, G N 0 + [ ( λmq pk ψ 2 exp ( B/t out, G + λn 0 tout 2 P ] out / [ 2 [ ( N 0 λmq pk ψ 1 exp ( B/t out, G ]] λt out P out (35 Secondly, the transission of an SU is stable if and only if theaveragearrivalrateislessthantheaveragetransission rate. Thus, we can ake a stateent about the stable transission condition as follows: Reark Given the channel state inforation and the peak interference power constraint of M PUs, the transission of the SU is stable if and only if the average arrival rate of packet, λ, satisfies the condition λ < 1 (1 P out E [T suc ] + t out P out (36 The inequality (36 is derived by substituting (34fori =1 into (7. Finally, by using the Little theore [20, Eq. (8.2], the average nuber of packets waiting in the buffer of the SU-Tx can be forulated as N = λe[w] (37 where E[W]isgivenby(35. 4 Perforance analysis for point-to-ultipoint counications In this section, we consider point-to-ultipoint counications, in which both SU and PU links undergo Rayleigh fading. We first derive the exact closed-for expression for the outage probability of the secondary syste, and then we consider the probability for the special case that the SBS can transit the coon packet successfully to all SU-Rx in its coverage range. 4.1 Outage probability In the point-to-ultipoint scenario, the SBS transits coon packets to SU-Rx in its coverage. Soe SU-Rx ay not receive the coon packets successfully due to fading environent. In order to analyze the perforance of this scenario, we will calculate the probability that k out of the total of N SU-Rx cannot receive the coon packets successfully, known as outage probability. Siilar to point-to-point counications, the event that the SU-Rx n cannotreceiveapacketsuccessfullyisforulated as T n t out where T n is an i.i.d. rando variable distributed following the CDF given by (19. Therefore, the outage probability in this case can be forulated as P k out = ( N k N k = j=0 Pr k {T n t out } (1 Pr{T n t out } N k ( N k ( N k j [ ( 1 j ( M 1 ( 1 M(exp( B/t out 1 (1 + (exp( B/t out +Q pk /N 0 + G ] k+j (38 where (38 is obtainedby using the binoialtheoreand the help of ( Best channel condition For point-to-ultipoint counications, the SBS ay transit coon packets successfully to all SU-Rx if the channel condition is ideal. This is known as the best channel condition which can be expressed as the longest transission tie for one coon packet to be less than t out, i.e., {ax n {T n } < t out }. Therefore, the probability that the SBS transits the coon packet to N SU-Rx with the best channel condition can be given as { } Pr ax {T n} < t out n N = Pr{T n < t out } = n=1 [ M 1 ( M 1 ( 1 M(exp( B/t out 1 (1 + (exp( B/t out +Q pk /N 0 + G ] N where (39 can be calculated with the help of (19. (39 5 Nuerical results We first provide nuerical results for point-to-point counications. In particular, we study the ipact of the peakinterferencepowerconstraintandthenuberofpus on the outage probability, average transission tie and queuing theoretical characteristics of the secondary syste. We then discuss results about the outage probability and the probability that the SBS can transit the coon packet successfully under the best channel condition for point-to-ultipoint counications. The syste paraeters are selected following [16] as follows:

9 Tran et al. EURASIP Journal on Wireless Counications and Networking 2012, 2012:9 Page 9 of 14 Figure 5 Ipact of the nuber of PUs, M, on the outage probability P out of transission at the SU-Tx for different values of the peak interference power Q pk. Syste bandwidth: B =1MHz Packet size: L =4096bits (512 bytes Tieout:t out =10s Noise power spectral density: N 0 =1W/Hz 5.1 Point-to-point counications In the sequel, we focus on the ipact of the peak interference power constraint and the nuber of PUs on the perforance of an SU Outage probability Figure 5 shows the outage probability as a function of the nuber of PUs, M, for given peak interference power of Q pk = 5, 10, 15 db. As can clearly be observed fro the figure, the analysis atches very well with the siulation results in all cases of Q pk. The outage probability increases fast with M if the peak interference power is set to a low value such as Q pk = 5 db. On the other hand, the outage probability increases slowly when the peak interference power is high, Q pk = 10, 15 db and specifically saturates fast for Q pk = 15 db. These results are thought to be due to the fact that an SU-Tx can transit with relative high transission power and hence increased transission rate when the peak interference power Q pk is large. Asaresult,thetransissiontieforthepacketscanbe kept low which in turn reduces the outage probability. On the other hand, for a fixed value of the peak interference power, Q pk, the ore PUs operate actively in the priary network, the ore constraints are put on the transission powerofansu-txresultinginanincreasedoutageprobability (see also (3and( Average transission tie Figure 6 depicts the average transission tie of packets at the SU-Tx as a function of the peak interference power, Q pk,forthenuberofpusgivenasm =1,4,7,10. Again, analytical and siulation results are in excellent agreeent. It can be seen fro the figure that the average transission tie for the packets fro the SU-Tx decreasesasthepeakinterferencepowerincreases.typically, the average transission tie reduces very fast in the high regie of the peak interference power of about Q pk 16.5 db. This is due to the sae reason as discussed above for the outage probability, i.e., an increase of the allowed peak interference power induces a higher transission rate and hence a decrease of transission tie of packets fro the SU-Tx. It should also be noted that theresultsfortheaveragetransissiontieatchesexactly with our previous results reported in [11,Fig.3]where we considered the special case of only a single PU being present, i.e., M = 1. The results shown in Figure 7 enable us to study the ipact of the nuber of PUs on the average transission tie of packets at the SU-Tx. Apparently, the nuber of PUs has a significant influence on the average transission tie at low values of the peak interference power, say Q pk = 5 db, causing it to rapidly increase with

10 Tran et al. EURASIP Journal on Wireless Counications and Networking 2012, 2012:9 Page 10 of 14 Figure 6 Average transission tie of packets at the SU-Tx versus peak interference power Q pk for different nuber of PUs, M. Figure 7 Average transission tie of packets at the SU-Tx versus nuber of PUs, M. M. In contrast, for higher peak interference power such as Q pk = 10 db, an increase of the nuber of PUs increases the average transission tie only slowly and has alost now ipact for Q pk =15dBonceM > 4. These results are consistent with the behavior observed for the outage probability Queuing theoretical results In the following, we exaine the queuing characteristics of the SU-Tx under the peak interference power constraint (4 with related results shown in Figures 8 and 9. Specifically,wehavesetthenuberofPUstoM =1,3,5 and observe the average waiting tie and channel utiliza-

11 Tran et al. EURASIP Journal on Wireless Counications and Networking 2012, 2012:9 Page 11 of 14 Figure 8 Average waiting tie of packets in the queue of the SU-Tx versus peak interference power Q pk for different nuber of PUs, M (analysis. Figure 9 Ipact of peak interference power Q pk on the channel utilization ρ with different nuber of PUs, M (analysis. tion for two values of average arrival rate given as λ = 10, 50 packets/s. Figure 8 illustrates that the average waiting tie increasesasthenuberofpusandarrivalrateincrease. Apparently, these results are in line with the behavior observed for the outage probability and average transission tie above and ay be explained as follows. At a fixed value of Q pk,anincreasingnuberofpusleadstoanin-

12 Tran et al. EURASIP Journal on Wireless Counications and Networking 2012, 2012:9 Page 12 of 14 Figure 10 Ipact of peak interference power Q pk on the outage probability P out of point-to-ultipoint counications in which the nuber of priary users and secondary users are set to N = M =5(k denotes the nuber of secondary users that cannot receive the coon packets successfully. crease of average transission tie due to the reasons explained above and hence an increase of average waiting tie. Siilarly, when the arrival rate increases, the nuber of packets to be stored in the buffer increases as well and await transission. On the other hand, as the transission rate is restricted due to the peak interference power constraint, the packets have to stay longer in the buffer before they are transitted. Figure 9 provides insights into the stable transission condition as a function of the peak interference power, Q pk, with the nuber of PUs given as M = 1,3,5 and arrival rates being λ = 10, 50 packets/s. The results show that for a given value of the nuber of PUs, M, andfixedvalueof the peak interference power Q pk, the channel utilization ρ = λe[t] for arrival rate λ = 10 packets/s outperfors the result for λ = 50 packets/s. In other words, the significant lower channel utilization for λ =10 packets/s coparedto λ = 50 packets/s provides a ore stable transission with respect to the service rate μ in ters of the stable condition forulated in (36. Clearly, the service rate μ of an SU-Tx is restricted for a fixed value of the peak interference power Q pk whileahigherarrivalratecausesorepacketstobe processed by the buffer expecting tiely transission. Accordingly, the ratio of arrival rate to service rate, relating to the stable transission condition λ/μ < 1,has to be carefully considered in order to not exceed the capacity of the secondary syste. It can also be observed fro the figure that the stable transission condition can be easily satisfied in the high regie of the peak interference power, say Q pk 16.5 db, as the channel utilization is sufficiently low. 5.2 Point-to-ultipoint counications We now focus on the ipact of the peak interference power on the outage probability of the point-to-ultipoint counications as shown in Figure 10. In particular,we set the nuber of SUs and PUs as N = M =5andplotthe outage probability as a function of the peak interference power, Q pk, under the condition that k =1,2,3,4,5 out of the total of N = 5 SU-Rx cannot receive the coon packets successfully. Clearly, we can deduce fro the results that the probability of exactly k out of the N =5SU-Rxnot beingabletoreceivethecoonpacketsuccessfullydecreasesas k increases. In addition, the outage perforance iprovesasthepeakinterferencepowerincreasesasexpected. Figure 11 presents the probability that all SU-Rx can receive the coon packets successfully as a function of the peak interference power for the nuber of PUs fixed to M = 8 and the nuber of SUs given as N =3,5,8.Thisscenario relates to the best channel condition as outlined in Section 4.2. It can be seen fro the figure that the probability of the SBS transitting the coon packets successfully to all SUs is quite high (above 0.8 in the high regie of the peak interference power, Q pk 19 db. The

13 Tran et al. EURASIP Journal on Wireless Counications and Networking 2012, 2012:9 Page 13 of 14 Figure 11 Ipact of the peak interference power Q pk on the probability of successful packet transission for the best channel condition (nuber of PU-Rx, M = 8; nuber of SU-Rx, N =3,5,8. figurealsoindicatesthatfornuberofpusfixedatm =8, the probability of successful transission decreases with an increase of the nuber of SU-Rx, N = 3,5,8. Siilar to point-to-point counications, an increasing nuber of SUs leads to an increase of the peak interference power constraint at the SBS. Thus, the tie it takes to transit the coon packet ay be longer while the probability of successful transission decrease for the best channel condition. 6Conclusions In this paper, we have analyzed the delay perforance of spectru sharing systes for point-to-point and pointto-ultipoint counications. In particular, we have assued that each packet has a delay threshold, transission channels undergo Rayleigh fading, SUs posses perfect CSIs and ACKs are transitted without error and delay. Closed-for expressions for the outage probability and average transission tie for point-to-point counications are obtained. In addition, we have utilized the M/G/1 queuing odel to analyze the queueing characteristics of such systes including the average transission tie, the packet waiting tie and the stable transission condition of an SU. Based on the analytical fraework established for point-to-point counications, we have also derived closed-for expressions for the outage probability and the successful transission probability for point-to-ultipoint counications under best channel conditions. Nuerical results for representative scenarios have been provided to quantify the ipact of an increase of the nuber of SUs and PUs on syste perforance. In particular, it has been shown that an increasing nuber of SUs or PUs significantly increases packet delay if the peak interference power is constraint by the PUs to be low while sall perforance degradation is observed if the PUs tolerate sufficiently large peak interference power. Accordingly, the developed analytical fraework for point-to-point and point-to-ultipoint counications in spectral sharing systes ay serve to efficiently exaine syste perforance. For exaple, it ay be used to deduce a trade-off between QoS requireents of the secondary syste and interference constraints posed by the priary syste. Copeting interests The authors declare that they have no copeting interests. Acknowledgeent Part of this work was presented at the IEEE International Syposiu on Wireless and Pervasive Coputing, Hong Kong, China, February Received: 26 August 2011 Accepted: 10 Noveber 2011 References 1. Facilitating opportunities for flexible, efficient, and reliable spectru use eploying cognitive radio technologies, Technical Report , Federal Counications Coission (FCC, J Mitola, GQ Maguire, Cognitive radio: Making software radios ore personal. IEEE Pers Coun 6(4,13 18 (1999

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