Delay Analysis of Spatio-Temporal Channel Access for Cognitive Networks

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1 Dela Analsis o Spatio-Temporal Channel Access or Cognitive Networks Chia-han Lee chiahan@citi.sinica.edu.tw Research Center or IT Innovation Academia Sinica Taipei, Taiwan Martin Haenggi mhaenggi@nd.edu Department o Electrical Engineering Universit o Notre Dame Notre Dame, IN, USA Abstract Most channel access schemes or cognitive radio onl consider using the idle periods o the primar users. Such schemes are not using the spectrum eicientl, since opportunities also arise when a primar transmitter is active but its corresponding primar receiver is ar awa rom the cognitive user. B detecting the signal power o the acknowledgments, a cognitive user is able to estimate the distance and channel condition between the primar receiver and itsel. Then i the primar receiver is ar awa, the cognitive user can transmit simultaneousl with the primar transmitter without aecting the primar link. Based on this idea, the spatio-temporal channel access scheme, utilizing both idle periods and spatial reuse, can be applied. This paper provides undamental analsis o the channel access delas and shows the advantage o using the spatio-temporal access scheme in the carrier sense multiple access (CSMA)-based network with bi-directional links. I. INTRODUCTION Channel access or cognitive radio networks is an active research area due to the increasing demand or spectrum resources. Traditional cognitive radio channel access schemes use the idle periods o the primar users. In wireless networks, opportunities arise not onl in time and requenc but also in space [: As long as the transmitter is ar enough rom other receivers, spatial reuse is possible. This idea can be applied to the cognitive radio channel access in which the cognitive user transmits simultaneousl with the primar transmitter when the primar receiver is ar awa (this is a orm o the intererence temperature model schemes [). In practical applications, the distances can be estimated b detecting the acknowledgments (ACK) rom the primar receiver. In this paper, the spatio-temporal (ST) channel access scheme, which utilizes both the idle duration and the idea o spatial reuse, is analzed. The cognitive users are considered to be emploed in a carrier sense multiple access (CSMA)-based primar network with bi-directional links, and our analsis is ocused on the channel access dela (CAD). The cognitive user channel access dela (CAD) is deined as the duration between the time that the cognitive is requested and the time that the next opportunit appears. The primar user channel access dela (PUCAD) discussed here is the dela due to the intererence rom cognitive s. The channel access dela inherent in the CSMA-based primar network (without the cognitive users) is well studied and not considered here. The primar user channel access dela is thus deined as the duration between the time the primar user would transmit i the network onl has primar users and the time that the channel is ree o intererence rom the cognitive users. Man papers had considered the cognitive radio channel access problem, but most o them assumed time-slotted sstems (see [ and the surve [4) and ver ew o them had considered using the ACKs or improved spatial reuse. The paper b Lapiccirella et al. [5 uses the ACK inormation, but their model is dierent rom ours in man was: this paper considers bi-directional links (the assume one-directional) and the CSMA-based network (theirs is a time-slotted sstem). This CSMA model with bi-directional links is better suited to model toda s wireless networks, and the one-directional link model is included as a special case. To our best knowledge, this is the irst paper to consider the cognitive radio channel access in CSMA-based networks with bi-directional links. II. SYSTEM MODEL Let us consider a cognitive network consisting o two primar users (PU) (one primar user pair), one is close to the cognitive user (denoted with the subscript n) and the other is ar awa (denoted with the subscript ); see Fig.. The primar user link is assumed bi-directional and works as ollows. It starts with an idle duration and then either the near or the ar primar user transmits. Let (resp. p ) denote the probabilit that the near (resp. ar) primar user transmits given that one o the primar users transmits. The is ollowed immediatel b a phsical laer ACK with the short interrame spacing (SIFS) in between. Right ater the ACK is another idle duration, so the primar user s are alwas separated b ACKs and idle durations. Let the random variables τ n (with support [τ n,min, τ n,max and mean τ n ) and τ (with support [τ,min, τ,max and mean τ ) denote the length o the near and the ar primar users. Deine the distributions F n (x) = P(τ n x) and F (x) = P(τ x), and let n (x) and (x) be the corresponding densities (PDFs). In order to simpli the notation, let the total length o the SIFS and the ACK signal be τ a, which is a ixed value. The random variable τ i (with support [τ i,min, τ i,max and mean ) is used to denote

2 intererence C W Far PU Near data Near ACK Near data Strong Far ACK Small Far data Far ACK intererence intererence Near data SIFS Far data Idle duration τ i τ a length τ n length τ Figure. The relative locations o the primar users and the cognitive user under consideration. Near TRAN Far ACK Far TRAN Near tran. SIFS Far tran. Idle duration τ i τ a Near data Near ACK Near data Figure. length τ n length τ Near ACK Near TRAN Far ACK Far ACK Far data Far ACK An example showing the s o primar users. Near data SIFS Far data Idle duration τ I τ A the length idleτ N duration. Deine length the distribution τ F F i (x) = P(τ i x) and let i (x) be the corresponding densit. For an time t, the cognitive user observes the primar users to be in one o the states s {IDLE, NEAR_TRAN, FAR_TRAN, ACK}, which represents idle, the rom the near PU, the rom the ar PU, and the ACK, respectivel. The ACK state is a combination o the SIFS and the ACK signal since an SIFS alwas precedes the ACK. Also, the SIFS+ACK duration is assumed to be too short or cognitive user. The states NEAR_ACK and FAR_ACK (ACKs rom the near and the ar user) are combined into one single state ACK since or the purpose o analzing the channel access schemes, there is no need to distinguish which primar user the ACK signal is rom. The probabilities that the primar users are in each state are p i,,t, p,t, and p a, respectivel. Let = + τ n + p τ + τ a, then p i = τi pn τn,,t =, p,t = p τ, and p a = τa. Note that = pn,t p,t+p,t and p =,t,t+p,t. Suppose the above statistics are collected b the cognitive users during the sensing phase, and assume the statistics (PDFs) and the locations o the primar users do not change over time. Let us also assume the cognitive users perorm perect spectrum sensing beore taking actions, so the primar user state is known to the cognitive users. In addition, assume the cognitive request is equall likel to happen at an time instance t, and let the cognitive user length (including the length o ACK) be a random variable with support [,min,,max. Although onl the case τ n,min,min <,max τ n,max is considered in this paper, other scenarios ollow similar steps. Deine the distribution F c (x) = P( x) and let c (x) be the corresponding densit (PDF). III. ANALYSIS OF CHANNEL ACCESS SCHEMES Consider the example in Fig.. It is obvious that two dierent channel access opportunities are available to a cognitive user: utilizing the idle duration or transmitting along with the near primar user. The white space channel access opportunit, using the idle duration o the primar s, is the cognitive radio channel access scheme that previous work request τ N τ N D G D G C W request C G τ i τ n P G Figure. An example showing the channel access dela Near orpu the cognitive user and Near thepu primar users whenp using G the white re space and the gra space. Note that onl the case with non-zero cognitive user channel access dela is shown. τ n P W re PU ACK corrupted PU ACK corrupted request considered. The gra space opportunit, which is based on the undamental act that when studing the eect o intererence, it is the receiver C G that matters, not the transmitter. This exposed terminal problem tells us that transmitting simultaneousl with the primar users causes no harm as long as the receiver is ar awa. In order to use the gra space, the distance to the ar primar user needs to be estimated. B detecting the signal power o the phsical laer ACK signal rom the ar PU, the distance inormation is available. The spatio-temporal channel access scheme is to take advantage o both the idle duration and the spatial reuse, i.e., in this scheme, the cognitive user uses the next available opportunit, no matter whether it is white or gra space. In this section, we will derive the channel access delas or the spatio-temporal channel access scheme. The cognitive user channel access dela is the time the cognitive user must wait beore the channel is available. Since the idle duration and the length o the primar and cognitive s are random, it is unavoidable that the cognitive s cause intererence to the primar users, resulting in backo or even re. The primar user channel access dela thus relects the primar user s waiting or re time. A. White space channel access opportunit The white space scheme is to utilize the next available idle duration or cognitive s. The cognitive user channel access dela, the time to wait or the next white space opportunit to show up, can be calculated as the ollowing. I the current state is IDLE, the cognitive user can transmit immediatel (the channel access dela is zero); i the current state is NEAR_TRAN or FAR_TRAN, the cognitive user needs to wait until the end o the primar and the ACK signal; i the current state is ACK, the cognitive user needs to wait until the ACK signal is over. The expected

3 C G = p i = k= p k [E [ τ i + (k ) ( + τ + τ a ) +k ( + τ a ) + (k ) τ } + p a ( p ) + { k= } + p,t k= p k [k + (k ) τ + p k [E [ τ ( k ) } τ a () p i ( p ) E [ τ i + p,t ( p ) E [ τ + (p i p + p,t + p a ) + (p i p + p,t p + p a p ) τ [ p i p + p,t + p a ( + p ) τ a }. () channel access dela C W or the cognitive user using the white space alone is then given b C W =,t (E [ τ n + τ a ) + p,t (E [ τ + τ a ) + p a τ a, () where the random variables τ n and τ are the residual time o the near and the ar primar users given that the cognitive request happens during the state NEAR_TRAN and FAR_TRAN, respectivel. Consider the event E n ={The cognitive request happens during the state NEAR_TRAN}, and then deine the distribution F n (x) = P(τ n x E n ) and let n (x) be the corresponding densit (PDF). It is ound that ˆ τn,max x E [ τ n = dx n () d, (4) τ n,min where n () instead o n () is used since the longer the is, the more likel it is that the cognitive request happens during this primar. Thus n () = τ n,max τ n,min and we get E [ τ n = τ n,max τn,min ( ). (5) τn,max τn,min E [ τ can be obtained in a similar wa. When using the white space, i the cognitive user is longer than the current idle duration, it will cause dela to the next primar user since CSMA is applied (see Fig. ). PW, the expected channel access dela o the primar users (due to the presence o cognitive users), is given b P W =,min τ i,min ( x) i (x) dx c () d. (6) I is uniorml distributed and τ i is exponentiall distributed with mean /λ, then τ i,min =, i (x) = λe λx, and c () =,max,min. A simple calculation leads to [ τ P W =,max,min e λτc,max e λτc,min λ,max,min λ. (7) B. Gra space channel access opportunit For the gra space scheme, the cognitive user transmits along with the next o the near primar user. The ACK signals are too short or practical use so onl periods are utilized. Now let us calculate the expected channel access dela C G or the cognitive user. I the current state is NEAR_TRAN, the cognitive can start immediatel (the channel access dela is zero); i the current state is IDLE, the next state could be either NEAR_TRAN or FAR_TRAN; i the current state is FAR_TRAN, the next state must be IDLE, but ater that, the state could be NEAR_TRAN or FAR_TRAN. It is obvious that a cognitive user might observe several FAR_TRAN and IDLE states beore eventuall observing the NEAR_TRAN state. Thereore, C G is given b (), where the random variable τ i is the residual idle duration given the cognitive request happens during the idle state. The calculation o E [ τ i is similar to the derivation o E [ τ n. I > τ n, the ACK signal rom the ar primar user will be corrupted, causing re. Due to CSMA, the re can onl happen ater the cognitive is inished (see Fig. ), so the intererence not onl causes dela but also wastes energ or re. On the other hand, i < τ n, the intererence level is determined b the distance to the ar primar user and the channel condition, which is a unction o the detected ACK signal power o the ar primar user, assuming the channel condition is smmetric. First let us calculate the expected channel access dela or the primar users P G due to the intererence rom the cognitive user. PG consists o two parts: when the current state is NEAR_TRAN, the cognitive starts immediatel rom the middle o the near primar ; otherwise, the cognitive starts rom the beginning o the next near primar. Thereore, P G,begin is given b P G,begin = P G = (,t ) P G,begin +,t PG,mid. (),min τ n,min n (x) dx c () d. () The cognitive user signal is weakl detected b the ar primar user, so, based on the CSMA rule, the ar primar user assumes it is sae to send ACK.

4 P G,mid = {ˆ τn,max,min P G,mid = τn,max τn,min z z ˆ x + z z dx n () d + τ n,min {( ) τ n,max τn,min (τc,max +,min ) } x + z dx n () d c (z) dz. (8) + τ ( n,max τ c,max +,max,min + τc,min) ( ) τ c,max + τc,min (τc,max +,min ) 6 τ n,min } 4. (9) Let τ o be the oset o the starting time o the cognitive to the starting time o the near primar. I < τ n, the intererence can happen onl when τ n < τ o < τ n ; i > τ n, the intererence happens no matter what τ o is (but note that < τ o < τ n ). Thereore, P G,mid is given b (8). I both the length o the primar and the cognitive users are uniorml distributed, P G,begin = ( ( ) τc,max τc,min) τn,min τ, 6 (,max,min ) (τ n,max τ n,min ) and P G,mid is given b (9). Ī G, the expected intererence superimposed on the primar when no re is caused, is a unction o the cognitive user power η c and the actor h that describes the channel condition (including the large scale and the small scale path loss). h can be estimated b observing the signal power o the ACK rom the ar primar user. Thus, [ˆ τn,max Ī G = η c h n (x) dx c () d. (),min When both the length o the primar and the cognitive s are uniorml distributed, it is eas to obtain Ī G = η c h τ ( ) ( n,max τ τ ). 6 (τ n,max τ n,min ) (,max,min ) () Finall, the expected re length R G is simpl τ n. C. Spatio-temporal channel access scheme The spatio-temporal access scheme utilizes both the white space and the gra space opportunities, i.e., whenever an idle duration or a near primar appears, the cognitive user can transmit. I the current state is either IDLE or NEAR_TRAN, the cognitive user channel access dela is zero; i the current state is FAR_TRAN, the cognitive user will wait until the next available opportunit, which is the white space, so the dela is E [ τ + τ a ; i the current state is ACK, the average channel access dela is τa. The expected channel access dela or the cognitive user using the spatio-temporal scheme is thus given b C ST = p,t (E [ τ + τ a ) + p a τ a. (4) Since onl when the current state is NEAR_TRAN would the gra space be used, the expected re length R ST is simpl,t RG and the expected intererence ĪST is,t Ī G. The expected channel access dela or the primar users P ST is given b P ST =,t PG,mid + (,t ) P W, (5) where P G,mid instead o PG is used because i the gra space is utilized in the spatio-temporal scheme, it must start somewhere in the middle o the near primar. IV. NUMERICAL EXAMPLES Now let us evaluate the perormance o the spatio-temporal channel access scheme b showing some numerical examples. I η c h is small due to the distant ar primar user, the large path loss, or the small cognitive power, then Ī G is negligible. Fig. 4 compares the channel access delas or the cognitive user and or the primar user. Schemes utilizing white space alone, gra space alone, and spatiotemporal channel access are compared under dierent mean idle durations, using the equations derived in the previous section. The idle duration is assumed exponentiall distributed. Assume the length o the near primar s is uniorml distributed with τ n,min = and τ n,max =, the length o the cognitive s is uniorml distributed with,min = and,max =, and τ a =. The cognitive requests are assumed to occur equall likel at an time t. For the bi-directional links, assume 7% o the s are rom the near primar user, i.e., =.7 and p =.. Fig. 4 shows that when becomes larger, the cognitive user channel access dela using the gra space opportunit increases whereas the cognitive user channel access dela using the other two schemes decreases. This is intuitive since increasing will increase p i and decrease,t, making the interval between consecutive near primar s larger. Notice that the average cognitive user channel access dela using the spatio-temporal scheme is the smallest, and as expected the average cognitive user dela when using the gra space alone is the largest due to the uncertaint o the link direction o the next primar. However, when is smaller than, the average CAD using the gra space is smaller than using the white space. This is eas to understand since the primar users have higher probabilit to be in the NEAR_TRAN state when is smaller. The smaller average CAD o the spatio-temporal scheme is obtained at

5 5 Cognitive user channel access dela 5 5 White space onl Gra space onl Spatio Temporal CST / CW =.7 =.5 = Primar user channel access dela 5 5 White space onl Gra space onl Spatio Temporal Figure 4. Channel access dela or the cognitive user and the primar user using the white space, the gra space, and the spatio-temporal access when =.7. PST / PW =.7 =.5 = Figure 5. The ratio o the channel access dela using the spatio-temporal access scheme to the dela using onl the white space or the cognitive user and the primar user. the cost o causing larger average PUCAD compared to using the white space alone, as shown in Fig. 4. In order to understand the eect o, Fig. 5 shows the ratio o the average CAD using the spatio-temporal access scheme to the average CAD using onl the white space and Fig. 5 shows the ratio o the average PUCAD using the spatio-temporal access scheme to the average PUCAD using onl the white space under dierent. The average CAD using the spatio-temporal scheme is onl about 7%, 5%, and % o the average CAD using the white space when =., =.5, and =.7, respectivel. When becomes larger, the spatio-temporal scheme is more eicient compared to using the white space alone, and this improvement does not change with dierent settings. However, the PUCAD becomes larger with the increase in, and the dierence becomes more signiicant with larger mean idle duration. V. CONCLUSION The opportunities or the cognitive user arise not onl in time but also in space. This paper analzed the channel access delas o the spatio-temporal channel access scheme which utilizes both the white space and the gra space. Compared to using the white space alone, we have shown that the spatiotemporal scheme has much shorter cognitive user channel access dela with slightl larger primar user channel access dela. When more s are rom the near primar user, the spatio-temporal scheme is signiicantl more eicient than using the white space alone. Our uture work includes: () extension to the scenario with multiple cognitive users; () perormance analsis when the primar user signals cannot be perectl detected due to, or example, ading or shadowing; () sstem analsis with other metrics, such as throughput and scalabilit, and comparison with the results rom network simulators. ACKNOWLEDGMENTS The partial support o NSF (grants CNS , CCF 7876) and the DARPA/IPTO IT-MANET program (grant W9NF-7--8) is grateull acknowledged. REFERENCES [ B. Alawieh, Y. Zhang, C. Assi, and H. Moutah, Improving spatial reuse in multihop wireless networks- a surve, IEEE Communications Surves & Tutorials, vol., no., pp. 7-9, Third Quarter 9. [ S. Hakin, Cognitive radio: brain-empowered wireless communications, IEEE Journal on Selected Areas in Communications, vol., no., pp. -, Feb. 5. [ S. Geirhoer, L. Tong, and B. M. Sadler, Cognitive medium access: constraining intererence based on experimental models, IEEE Journal on Selected Areas in Comm., vol. 6, no., pp. 95-5, Jan. 8. [4 Q. Zhao and B. M. Sadler, A surve o dnamic spectrum access, IEEE Signal Processing Magazine, vol. 4, no., pp , Ma 7. [5 F. E. Lapiccirella, Z. Ding, and X. Liu, Cognitive spectrum access control based on intrinsic primar ARQ inormation, ICC.

Comments on Problems. 3.1 This problem offers some practice in deriving utility functions from indifference curve specifications.

Comments on Problems. 3.1 This problem offers some practice in deriving utility functions from indifference curve specifications. CHAPTER 3 PREFERENCES AND UTILITY These problems provide some practice in eamining utilit unctions b looking at indierence curve maps and at a ew unctional orms. The primar ocus is on illustrating the