Spectrum Sharing with Adjacent Channel Constraints

Spectrum Sharing with Adjacent Channel Constraints icholas Misiunas, Miroslava Raspopovic, Charles Thompson and Kavitha Chandra Center for Advanced Computation and Telecommunications Department of Electrical and Computer Engineering University of Massachusetts Lowell Lowell, MA 01854 Faculty of Information Technology Belgrade Metropolitan University Belgrade, Serbia Abstract The problem of sharing radio spectrum is analyzed using a multiple server queueing model which represents channels owned by primary users and allowed opportunistic access by a secondary user group. The primary users are constrained to occupy a group of adjacent channels for wideband transmission, whereas the secondary users utilize a single channel for narrowband transmission. The blocking performance of wideband and narrowband users are compared under two policies of channel allocation among the primary and secondary users. These policies differentiate the performance based on allocation of nonoverlapping and overlapping blocks of contiguous channels to the wideband and narrowband users. The influence of the number of excess channels that can only be utilized by secondary users is also presented. A computational model developed to estimate the blocking probabilities of B and B users is shown to be expressed as a function of the offered loads (ρ, ρ ) and the ratio of the service rates µ µ. The performance impact of providing B users a block of adjacent channels instead of distributing the requirement across the group of available channels is analyzed. The adjacency constraint will in general decrease the channel availability of B users, but can improve the probability of channel allocation to B users. The proposed scheme allows estimation of feasible operating regions of ρ, given a B group size and ρ. I. ITRODUCTIO The problem of more efficient usage of the radio spectrum in certain licensed radio frequency bands by allowing opportunistic access by users in the congested unlicensed bands has been a topic of great interest. The licensed users are referred as the primary group, whereas the opportunistic users are the secondary group. The critical issues are in minimizing the interference to the primary users and maintaining a prescribed quality of service for the secondary group. Cognitive radios with software defined functionality for adaptive physical layer access are expected to perform spectrum sensing and dynamic channel allocation to more optimally balance the utilization across the radio frequencies designated for sharing. Queueing models have been proposed for obtaining the baseline blocking and delay performance metrics of primary and secondary users in a shared radio spectrum [1] [5]. These models assume that the channels are perfectly sensed and they are in a binary state, either busy due to occupancy by a primary or secondary user or in an unoccupied or idle state. Most previous studies have approached this problem assuming that the channel requirements of primary and secondary users on arrival to the channel pool are the same, each typically requiring access to one narrowband channel in the group. In [4] three secondary access schemes are addressed considering a prioritized access to the primary users. The schemes include the random assignment of an available channel to the primary that can result in the service termination of a secondary user utilizing the assigned channel, the search and assignment of unoccupied channels to the primary so as to avoid collision to an existing secondary user and thirdly a scheme that limits the secondary users to a subset of the available channels, this number being optimized to the secondary user arrival rate. They show that the third method can support the highest level of secondary user traffic at the prescribed grade of service metrics. In [5] a Markov chain model of the shared spectrum model incorporates an addition to the shared channels, a set of unlicensed channels that can only be occupied by secondary users. Primary users are given priority and the secondary users call blocking and call dropping probabilities are evaluated to yield the number of secondary users per second that can be supported on the shared system. In this paper the problem of a shared radio system in which the primary users require wideband (B) transmission using a group of adjacent channels and secondary users occupy a single narrowband (B)channel is analyzed. This model extends previous work where an uncontrolled channel access scheme was applied to allow B and B users access a common spectrum band [1]. In that work B users were not constrained to use adjacent channels for transmission. It was shown that the B blocking probability was lower bounded by the B blocking probability for all values of the B utilization factor. Improved performance was achieved by providing additional channels that could only be occupied by narrowband channels, or controlling the offered loads of both user types and also by controlling the population size of B users [3]. There are many reasons why it is desirable to design a system for which contiguous or adjacent channel allocation is necessary. Assigment of non-contiguous channels can pose difficulty for building an infrastructure for dynamic spectrum

allocation in wireless systems. Furthermore, when transmitting over non-adjacent channels, complex filtering is necessary in order to avoid co-channel interference with neighboring channels that are not used for transmission. hen using nonadjacent channels, a synchronization is needed in order to achieve simultaneous allocation and transmission. Due to the randomness in traffic and co-channel interference this channel synchronization can be difficult to achieve in practice. The use of a contiguous band of frequencies is referred to as channel bonding in the literature for IEEE 802.22, a proposed protocol for cognitive radio that can be handled by a single RF circuitry. A non-contiguous band of frequencies, also referred to as channel aggregation, cannot be implemented with a single RF circuitry [6]. In addition to architectural costs, other benefits of channel bonding over channel aggregation are higher capacity and range, as well better interference mitigation [7]. hen using contiguous channels these issues may not be as problematic. Therefore this paper designs and evaluates a controlled channel access scheme designed to allocate an adjacent block of channels, the size of which is determined by the B source. The paper is organized as follows. Section II presents the channel sharing schemes for B and B users, that allow B users to transmit on adjacent channels. The Markovchain model and system state probabilities are obtained for an example case of four total channels with the primary users occupying two. The primary blocking probabilities are analyzed in Section III. Three allocation methods are examined in Section IV, the conclusion in Section V. II. ADJACET CHAEL MODEL A system consisting of K channels that are shared by B and B users is modeled as a queueing system with K servers. Both B and B arrivals are assumed to be drawn from independent Poisson processes with arrival rates λ and λ respectively. B users require one channel for transmission and they complete channel occupancy at the rate. The primary B users require K adjacent channels for transmission, that after service are released simultaneously at the rate µ. There is no waiting room and B and B arrivals that cannot find the requisite number of channels are blocked on arrival. The offered loads for B and B users are ρ = λ / and ρ = λ /µ respectively. The channels are pre-assigned into non-overlapping groups, and = K K. It is assumed that upon request for spectrum allotment from B users, the B user is assigned a group of width K, if available. The B users are allocated a single channel so as to pack any partially occupied group of contiguous K channels. A channel group that is occupied by B users is termed a split channel group. During channel allocation, channels from partially filled, split groups are allocated first, so that channels in a group are completely filled. This is done to ensure higher availability of channel groups for B users. A channel from a new group is allocated to a B user only if all other groups are filled. The split group can be occupied only by B users until the last B user in λ λ [0,0,0] µ [1,0,0] [2,0,0] Ν [0,1,1] [0,2,1] [1,1,1] [0,2,2] Ν λ λ λ λ Ν Ν Ν Ν λ µ λ µ λν λν λ Ν [0,3,2] [0,4,2] µ µ 4µ µ Ν Ν Ν Ν Ν Ν [1,2,1] Fig. 1. State transition diagram; K = 4 and K = 2. this group completes its transmission. In such a case the group becomes empty and available for allotment, either to B or B users. An analytical model is derived for B and B users respectively. The system state is given by three variables [i,j,k]where irepresentsnumberofbusersinthesystem, j is the number of B users and k is the number of split groups. The two-dimensional state transition diagram for K = 4 and K = 2 is shown in Fig. 1. States will change from i to i+1 upon arrival of a B user, and the probability of making this transition in the time interval t is λ t + O( t). Similarly, with the arrival and spectrum allotment to a B user, the system transitions from j to j+1 state. This transition occurs with probability of λ t+o( t). Once the B users fully occupy one group, the next B user requesting spectrum allocation will be allowed to occupy a channel in a new group if available. Hence, the number of groups used by B users is increased from k to k+1. The state variable k will increase to k + 1, such that k = j/k. The transition probabilities between the states that occur due to service completions are for some states constrained and others not. hen only one group is occupied, i.e. k = 1, upon departure of a B user the transition from j + 1 to j occurs with probability ((j + 1) ) t + O( t). The probability of transition from i + 1 to i indicating the release of a channel group by a B user has a value [(i + 1)µ + O( t)]. But when k = 2, and j is not an integer multiple of k, as in state [0,3,2] the departure of a B user can be from either of the two groups occupied. Therefore the transition to j = 2 takes place to either of the two states [0,2,1] or [0,2,2]. The transition probability from [0,3,2] to [0,2,2] is t, indicating departure of one B user from either the first or second group. The transition from [0,3,2] to [0,2,1] occurs with probability t.

By defining the steady state probability of finding the system in state [i,j,k] as p(i,j,k), the two-dimensional state transition diagram in Fig. 1 is described by the set of 10 balance equations applied for i = 0,..., j = 0,...K and k = 0,.... Due to the independent departures of B users from split channels, the local balance method cannot be applied in this model to enable a product form solution for the system. In particular, the local balance across a boundary between states [0,1,1] and [0,2,1],[0,2,2] is not satisified in the global balance equations. The transition between [0, 2, 2] and [0,1,1] bypasses the [0,2,1] state and removes its dependency from neighboring states. Therefore, the solution for the steady state probabilities is obtained directly from the flow equations. The steady state probability vector p can be obtained from the solution of P p = 0 where P represents the transition matrix comprised of the state transition probabilities given in Fig. 1. A symbolic representation of the steady-state probabilities as a function of the idle state is obtained as, p(0,2,1) = ρ2 2 (6 + ρ ) Ŷ p(0,2,2) = ρ 3 Ŷ p(0,3,2) = ρ3 2 (2 + ρ ) Ŷ p(0,4,2) = ρ4 8 (2 + ρ ) Ŷ p(1,0,0) = ρ p(2,0,0) = ρ2 2 ( p(0,1,1) = ρ 1 + 2ρ2 ρ ) µ ( p(1,1,1) = ρ ρ 1 2ρ2 µ ) µ + 2ρ 3 p(1,2,1) = ρ2 2 ρ where 1 2ρ (1 + ρ ) µ2 µ 2 + 2ρ ) (1 + 2ρ ) µ + 2ρ 3 = µ2 µ 2 (ρ + 1)[(ρ + 6)(ρ + 1) + 2ρ ] + µ [(ρ + 3)(ρ + 2)(2ρ + 3)] (1) + 12ρ (ρ + 1) + 3(ρ + 2) [ (ρ + 1) 2 + 1 ] Ŷ = µ2 µ 2 (1+ρ ) 2 + µ (1+ρ )(2ρ +3)+(1+ρ ) 2 +1 (2) It can be seen that the probabilities are functions of ρ,ρ and µ. This is due to the choice of substitution of ρ µ for λ in order to simplify the set of equations. The system is still dependent on ρ and not λ or µ individually. The blocking probabilities for B and B users are determined for the system shown in Fig.1. Blocking of B users will occur when all K channels are occupied. All channels are occupied in states [2,0,0], [0,4,2] and [1,2,1]. The blocking of B users is given by, P[B] = p(2,0,0) + p(0,4,2) + p(1,2,1) Each one of the above terms has a distinct pattern of variation with the offered load ρ. The probability p(2,0,0) = ρ2 2 will tend to decrease with ρ since the probability of the idle state decreases with increasing load. On the other hand, the other two terms increase with ρ and ρ with the probability p(0,4,2) governing the behavior of P[B] for large ρ. The combination of these terms exhibit a rich set of non-monotonic dynamics with ρ for a given ρ, the channels available K and the group size K. TheBuserwillexperienceblockingiftherearenogroups that have all K channels available for allotment. Blocking of B users is represented as the sum of probabilities that describe the system being in a state in which at least one user of either type is in every group in the spectrum. P[B] = p(0,2,2) + p(2,0,0) + p(1,1,1) + p(1,2,1) + p(0,3,2) + p(0,4,2) It is seen that P[ B] includes P[ B] and therefore it is lower bounded by the B blocking probability. The blocking probabilities can be generalized in terms of steady state probabilities. Blocking for B users can be obtained as P[B] = i=0 p(i,k ik, i) and blocking for B users is obtained as P[B] = K ik i=0 j= p(i,j, i i). III. RESULTS A. Comparison of analytical and simulation results The blocking probability of B and B users obtained under the constraint of contiguous channel allocation for B users is discussed in this section. The blocking probabilities derived in the previous section will be compared to simulation results and the performance sensitivity to parameters will be discussed. The simulation was carried out for 10 6 realizations of B and B users. In Fig. 2 the points represent the analytical blocking probabilities of the B and B users obtained from the queueing model as a function of ρ for the case K = 4 and K = 2 and ρ = 0.5. The simulation results are shown by the solid lines. The agreement validates the model results. ith increase in ρ, the terms contributing to P[B], i.e. p(2,0,0) and p(1,2,1) dominate relative to the third term p(0,4,2) which increases as ρ 4 for ρ < 1. These two probabilities represent the blocking of B users due (3)

P[B]:ρ =0.5 K=6,K =2 Fixed K P[B]:ρ =0.5 Probability of Blocking 0.01 P[B]:ρ = P[B]:ρ = Probability of B Blocking K=4,K =2 Fixed K=6,K =3 K=8,K =4 K=6,K =6 Analytical P[B] Analytical P[B] 0.001 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1 ρ 0.01 1 2 3 4 5 ρ Fig. 2. Simulated and Analytical Blocking Probability and Effect of Change in B load for K = 4, K = 2, ρ = {, 0.5}. Fig. 3. Blocking of B users for changes in and K for ρ = 0.5. to occupancy of the system by B users and they decrease with increase in ρ. However, depending on the B load ρ, as ρ is increaesd, the downward trend resulting from these terms become subdominant relative to the blocking of B by B users, given by p(0,4,2) and the blocking probability changes direction, increasing with ρ. P[B] on the other hand always increases monotonically with ρ. B. Blocking dependence on load factors Changing the operating point of the B offered load ρ has a significant effect on the blocking probabilities of B and B users. This is shown in Fig. 2 considering two cases, ρ = 0.5 and ρ =. The limiting values of P[B] and P[B] as ρ approaches zero change in proportion to ρ. The behavior of P[B] is particularly sensitive to ρ for values of ρ < 1, but as ρ increases both blocking probabilities approach their common asymptote independent of B dynamics, being proportional to B load factor alone. C. Influence of the channel group size and B bandwidth requirement In this section the effect of the parameters and K are analyzed. First, the parameters K and K are varied, holding the number of channel groupings fixed at = 2. Fig. 3 shows three curves for cases: (1) K = 4, K = 2, (2) K = 6, K = 3, and (3) K = 8, K = 4. B blocking is plotted versus ρ for ρ = 0.5. By increasing K the channel resources for B users increase and the allocated subgroups of larger K width provide more channels. The B blocking is however invariant to changes in K and K and depends only on the fixed group size. The bandwidth allocated to B users is analyzed next by fixing the number of channels K while increasing K. Fig.3 shiows cases K = 2,3,6 for K = 6. As expected, P[B] increases with increasing K. B users will experience higher blocking when they require more bandwidth for their transmission as the number of provided groups will be decreased for a fixed K. P[B] however experiences a different behavior, as shown in Fig. 3. As ρ goes to zero the startingvalueof P[B]increaseswith K butthendecreases towards an inflection point as ρ is increased. Beyond this point, results for all three cases appear relatively independent of the group width. IV. COMPARISO OF PRIMARY ALLOCATIO METHODS A. Adjacent, sequential, and hybrid models In this section three different channel allocation methods for primary users are discussed. The grouped adjacent channel requirement described in the previous section will also be compared with a sequential adjacent and a hybrid allocation scheme. All three methods will also be evaluated with respect to the non-adjacent channel allocation results. In the sequential adjacent allocation method, the B user will occupy the first contiguous set of K channels. The blocking probabilities were derived using the same methods as described in section II. The sequential method provides an increased number of groups that can be accessed by the primary relative to the method previously described. The hybrid scheme is one which draws on the features of both the grouped and sequential adjacent methods. This method looks to place the B user in one of the grouped sets as a priority, and if a group is not available, a sequential

Probability of B Blocking Grouped Primary Sequential Primary Hybrid Primary on-adjacent 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1 ρ Fig. 4. Comparison of P[B] for All Primary Allocation Methods for K = 6, 7, 8, K = 3, ρ = 0.5 search is performed to place the B user in the first set of K contiguous channels. K=6 K=7 K=8 B. Performance of Allocation Methods In this section the results of aforementioned allocation types are analyzed. The influence of adding additional channels that will be available for secondary access is also examined. Fig. 4 shows the B blocking probability as a function of the narrowband load for the three primary allocation methods and the results for non-adjacent allocation of K channels. The parameters considered are K = 6,7,8,K = 3,ρ = 0.5. For all these cases the number of primary groups available is = 2. For all three values of K the non-adjacent allocation scheme performs the best, although for K = 6 the difference in blocking among the three allocation methods and the nonadjacent scheme is small. The difference between the schemes becomes more distinguishable with increase in K as can be seen for the cases K = 7 and K = 8. It is also seen that the grouped adjacent scheme has the highest probability of blocking whereas the sequential adjacent scheme performs the best for allocating adjacent groups of channels. The hybrid scheme shows very slight improvement compared to the sequential approach thus suggesting that the search for a sequential group of channels is the best strategy for constraining primary users to occupy an adjacent group of channels. where the width of each channel group corresponded to the bandwidth required for B transmission. This channel access method required B users to use only one group at a time. By keeping track of the number of users in the system, and the number of groups occupied by B users, the parameters dictating the quality of performance for both user types were identified and analyzed. This channel access method has shown to be high in complexity due to the increasing number of states and inter-state dependencies. Therefore, whereas for the system that may not require high sensitivity analysis this method may not be necessary for performance evaluation. However, this method provides better insight to tendencies of blocking probabilities and the dominating parameters that cause those tendencies. It was shown that for a fixed K/K a larger K,K resulted in a lower minimum value of P[B]. Holding K fixed while changing K was shown to have greatly different starting values for ρ approaching zero, with all converging as ρ increased. The channel adjacency requirement results in a higher P[B] for all cases of K with the sequential adjacent allocation method providing the lowest adjacent blocking rate. It was seen that for ρ < 1 allocation methods provide minimal benefit in terms of blocking of primary users, with the primary impact coming from introduction of excess channels. icholas Misiunas acknowledges support from GK-12 Vibes and aves in Action Fellowship through SF grant o. 0841392. REFERECES [1] M. Raspopovic, C. Thompson, and K. Chandra, Performance models for wireless spectrum shared by wideband and narrowband sources, in Proc. MILCOM 05, pp. 1642 1647, October 2005. [2] S. M. Y. Xing, R. Chandramouli and S. Shankar, Dynamic spectrum access in open spectrum wireless networks, IEEE J. Selec. Commun. 34(3), pp. 626 637, 2006. [3] M. Raspopovic and C. Thompson, Finite population model for performance evaluation between narrowband and wideband users in the shared radio spectrum, in Proc. DYSPA 07, pp. 340 346, April 2007. [4] P.K.Tang and Y.H.Chew, On the modeling and performance of three opportunistic spectrum access schemes, IEEE Trans. Veh. Tech. (8), pp. 4070 4078, 2010. [5] G. Liu, X. Zhu, and H. Lajos, Dynamic spectrum sharing models for cognitive radio aided ad hoc networks and their performance analysis, in Proc. IEEE GLOBECOM, 2011. [6] S. F. A. Shah and A. H. Tewfik, Efficient design of ofdma-based programmable wireless radios, in EURASIP Journal on ireless Communications and etworking, p. 10, 2008. [7] K. Challapali, C. Cordeiro, and D. Birru, Evolution of spectrum-agile cognitive radios: First wireless internet standard and beyond, in ICO 06: Proceedings of the 2nd annual international workshop on ireless internet, p. 27, ACM, (ew York, Y, USA), 2006. V. SUMMARY In this paper, a channel access scheme was developed in order to allow B users to transmit over adjacent channels. The algorithm sectioned the available spectrum in groups,