Performance Analysis of Cognitive Radio Spectrum Access with Prioritized Traffic

Transcription

1 Performance Analysis of Cognitive Radio Spectrum Access with Prioritized Traffic Vamsi Krishna Tumuluru, Ping Wang, and Dusit Niyato Center for Multimedia and Networ Technology (CeMNeT) School of Computer Engineering, Nanyang Technological University, Singapore. Abstract Dynamic spectrum access (DSA) is an important design aspect for the cognitive radio networs. Most of the existing DSA schemes are to govern the unlicensed user (i.e., secondary user) traffic in a licensed spectrum without compromising the transmissions of the licensed users, in which all the unlicensed users are typically treated equally. In this paper, prioritized unlicensed user traffic is considered. Specifically, we prioritize the unlicensed user traffic into two priority classes (i.e., high and low priority). Two different DSA policies are proposed to manage the handoff for prioritized unlicensed user traffic (i.e., reassigning new channels to the secondary users which paved way for licensed user). These two policies are different in which one allows to drop the ongoing low priority secondary users to accommodate more high priority secondary users being replaced by the presence of licensed user while the other does not allow that. We also study the impact of sub-channel reservation for the high priority secondary users in both DSA policies. Both DSA policies are analyzed using Marov chain. For performance measures, we derive the blocing probability, the probability of forced termination and the throughput for both high and low priority unlicensed users. The numerical results are verified using simulations. Keywords Cognitive radio, dynamic spectrum access, Marov chain analysis, priority. I. INTRODUCTION In recent years, several spectrum surveys have been conducted to understand the spectrum utilization in the licensed and unlicensed portions of the radio spectrum [], [2]. These surveys revealed that under the present spectrum regulatory policies, major portions of the licensed spectrum are underutilized for most of the time, while the unlicensed spectrum is heavily used and is often insufficient. Among the efforts to improve the overall spectrum utilization, the concept of cognitive radio is gaining much importance [3]. The cognitive radio networ (CRN) is composed of licensed users and unlicensed users sharing the licensed spectrum. In most cases, the licensed users (also called primary users) are oblivious of the existence of the unlicensed users (also called secondary users). In the CRN, the secondary users are allowed to dynamically access unused channels (i.e., frequency bands) in the primary user spectrum, thereby improving the overall spectrum utilization. Secondary user transmissions in the CRN can be effectively managed by a dynamic spectrum access (DSA) policy. Using the DSA policy, the secondary users are assigned unused channels in the primary user spectrum. In the event of a primary user s arrival, the secondary users transmissions on the corresponding channel are either reassigned to another unused licensed channel or terminated. Recently, some wors dealt with the performance evaluation of the CRN under different DSA policies, using continuous time Marov chain (CTMC) analysis [4]-[7]. According to the DSA policy in [4], the secondary users which experience unsuccessful handoff are queued till they find the transmission opportunities. In [5], DSA policy considered channel reservation for secondary user handoff. In [6], the secondary user arrivals wait in a queue when a channel 2 is not available. In [7], the DSA policy assigns variable bandwidth to the secondary users. In all these wors, the CRN was modeled as a call admission control system which receives calls from both primary users (PUs) and secondary users (SUs). During the spectrum access, the PU calls have a higher priority over the SU calls. Unlie the above wors, in this paper, we consider prioritization among the SUs while accessing the licensed spectrum. For example, the SUs with real-time traffic have higher priority than those with non real-time traffic. To date, only a few wors ([8] and [9]) have taen prioritized SU traffic into consideration. However, these wors have not addressed the issue of spectrum handoff under prioritized SU traffic. For the simplicity of presentation, we consider that the SU traffic is composed of two priority classes 3 (i.e., high and low priority). We propose two DSA policies to handle the spectrum access for the SUs in the licensed spectrum. The two DSA policies have different SU handoff mechanisms. Further, we also introduce sub-channel reservation for the high priority SU call arrivals in both the DSA policies. We develop analytical models for the CRN under both the DSA policies using CTMC models. The performance of the DSA policies is evaluated in terms of the blocing probability, the probability of forced termination, and the throughput for both high and low priority SUs. II. SYSTEM MODEL The licensed spectrum is divided into M channels, each of which is further divided into N sub-channels, as shown in Fig.. A PU call is assigned one channel whereas a SU call is assigned one sub-channel for data transmission. The licensed The process of reassigning a displaced secondary user transmission is referred to as handoff. 2 In this paper, the terms licensed channel and channel are used interchangeably. 3 Please note that the proposed analytical model is not restricted to the two priority class case and can be extended to the case of more than two priority classes.

2 spectrum is shared by the PUs and SUs. The PUs have the highest priority in accessing the channels. The secondary users are classified into two priority classes. The high priority SUs are denoted as SU while the low priority SUs are denoted as SU 2. Similar to [4], we assume that a central controller exists to implement the DSA policy. The objective of the DSA policy is to assign idle sub-channels to the incoming SU calls, and moderate their handoff. We consider two DSA policies for our system model. They are denoted as DSA-C and DSA-C2. sub-channel N channel Licensed spectrum Fig.. System model. N(M-)+ A. Sub-channel Reservation under DSA-C and DSA-C2 Under both the DSA policies, a number of sub-channels are reserved for high priority secondary user SU, i.e., when the total number of idle sub-channels is less than ζ which is the number of sub-channels reserved for SU, the new SU 2 call will be rejected. In this way, we provide higher priority for the SU calls over the SU 2 calls 4. Call arrivals occur independently as Poisson processes with mean arrival rates λ p, λ and λ 2 for PU, SU and SU 2, respectively. The service times independently follow exponential distributions with mean service rates of µ p, µ and µ 2 for PU, SU and SU 2 calls, respectively. The number of ongoing PU calls is denoted as and the number of occupied sub-channels is denoted as Y. The new calls are dropped when the system becomes full (i.e., Y = MN for SU call, Y = MN ζ for SU 2 calls and N = M for PU calls). B. Handoff Mechanism under DSA-C When a new PU call claims a channel occupied by the SUs, the handoff mechanism is initiated. During handoff, the idle sub-channels (if any) are first assigned to the displaced SU calls. Thereafter, the remaining idle sub-channels are assigned to the displaced SU 2 calls. If the required idle sub-channels are not available for SU handoff, then some ongoing SU 2 calls are terminated and the resulting idle sub-channels are assigned to the displaced SU calls. When the idle sub-channels are not enough to accommodate all the displaced SU or SU 2 calls, some of the displaced calls will be terminated. C. Handoff Mechanism under DSA-C2 DSA-C2 policy is similar to DSA-C policy except that no ongoing SU 2 calls are terminated for the sae of SU handoff. In other words, if a displaced SU call does not find an idle sub-channel, it is terminated. 4 Note that the PUs are not affected by such sub-channel reservation. M MN III. PERFORMANCE ANALYSIS In this section, we develop analytical models for the CRN corresponding to each DSA policy using continuous time Marov Chain (CTMC). The state of the CTMC (for both DSA policies) is defined as z = [i, j, ]. Here, i {,,..., MN}, j {,,..., MN ζ} and {,,..., M} represent the number of ongoing SU, SU 2, and PU calls in the system, respectively. The total number of occupied sub-channels in the state z is calculated as Y = i + j + N. For a valid state, Y should not exceed MN. Let l (where l {,,..., N}) and m (where m {,,..., N}) denote respectively the number of SU and SU 2 calls displaced by an incoming PU call when the state is [i, j, ]. l and m should satisfy the following conditions: l i, m j and l + m {,,..., N} r = MN Y (N (l + m)) and r s = (l + m) min(r, l + m). () In Eq. (), the first condition gives the maximum number of SUs that can be displaced upon a PU arrival whereas the second condition gives the number of sub-channels available for handoff (denoted as r) for the displaced SU calls. Accordingly, the total number of unsuccessful handoff calls (denoted as s) is calculated. The evolution of the state [i, j, ] of the CTMC is presented under three cases of Y : ) Y N(M ): The system has at least N idle subchannels. 2) N(M ) < Y < MN: The system has idle subchannel in the range {,..., N }. 3) Y = MN: The system has no idle sub-channel. For the case Y N(M ), all displaced SU and SU 2 calls perform successful handoff (i.e., s = ) when displaced by a PU arrival. In other words, no calls are terminated (under both DSA-C and DSA-C2) due to an incoming PU call. For the case N(M ) Y MN, s = {,..., N } number of SU calls experience unsuccessful handoff, whereas when Y = MN, s = N SU calls experience unsuccessful handoff. The exact number of terminated SU and SU 2 calls under each centralized DSA policy are explained later. Let l and m denote the number of terminated SU and SU 2 calls, respectively. Thus, l + m = s. A. State Transitions under DSA-C Policy Under the DSA-C policy, the transitions for the state [i, j, ] for different cases of Y are explained in Fig. 2. State transitions from/to the state [i, j, ] occur due to any of the six possible events, namely PU arrival, SU arrival, SU 2 arrival, PU departure, SU departure and SU 2 departure. Each state transition is represented by its corresponding rate. Taing as an example, a SU 2 arrival in state [i, j, ] causes transition to state [i, j, ] with a rate δ λ 2, where δ = (i+(j )+N<MN ζ) specifies the condition for subchannel reservation (i.e., a new SU 2 call is accepted by the system only when the condition i + (j ) + N < MN ζ 2

3 holds), where ( ) is the indicator function which returns the value when the condition given inside the parenthesis is true and returns otherwise. In Fig. 2, δ 2 = (i+j+n<mn ζ) (condition for sub-channel reservation in state [i, j, ]) and δ 3 = (i+j+( )N N(M )). The transition rate γ i,j, from state [i, j, ] to state [i l, j m, + ] is calculated as follows: ) Let N denote the set containing the valid combinations of (l, m ). 2) For every valid pair of (l, m ) in the set N, find R which represents the number of valid combinations of l, m, r and s = l + m. Valid l, m, r and s for given [i, j, ] found using Eq. (). 3) Then, the transition rate γ i,j, is given by γ i,j, = R ( ) N R λ p. (2) Taing into consideration the handoff mechanism explained in Section II-B, the variables l and m in Eq. (2) are given by l = s min(j, s) and m = min(j, s). The value of s is determined by Eq. (). i, j, δ λ 2 i, j, Fig. 2. i µ λ j µ 2 i l, j m, + γ i, j, l, m µ p δ λ p 3 λ ( j + ) µ 2 ( + ) µ p δ 2 λ 2 + i +, j, ( i + ) µ i, j +, State transitions for the DSA policies, DSA-C and DSA-C2. For the cases Y N(M ) and N(M ) < Y < MN, all the transitions shown in Fig. 2 are valid. For the case Y = MN, the transitions between the states [i, j, ] and [i+, j, ], and between [i, j, ] and [i, j +, ] are not considered as the system is full (i.e., idle sub-channels not available). Apart from the state transitions shown in Fig. 2, when Y = MN few transitions occur from the states in which the number of ongoing calls is greater than N(M ) to the state [i, j, ] due to a PU arrival. These transitions are described below. Transition from state [i, j+j, ] to state [i, j, ] occurs with rate γ i,j+j,,j, where j > and < j < N. The rate γ i,j+j, is calculated using Eq. (2) corresponding,j to the state [i, j + j, ]. During this state transition, j SU 2 calls are terminated. Transition from state [i + (s j ), j + j, ] to state [i, j, ] occurs with rate γ i+(s j ),j+j, s j,j, where j =, < s < N and j < s. The rate γ i+(s j ),j+j, s j,j is calculated using Eq. (2) corresponding to the state [i + 3 (s j ), j + j, ]. During this state transition, s j SU calls and j SU 2 calls are terminated. B. State Transitions under DSA-C2 Policy Fig. 2 also represents the state transitions under the DSA-C2 policy for the various cases of Y. According to the handoff mechanism under DSA-C2 policy, the number of terminated SU and SU 2 calls are given as l = l min(r, l) and m = max(, m max(, r l)), respectively. All state transitions shown in Fig. 2 occur similar to the DSA-C policy. Apart from the state transitions given in Fig. 2, transitions occur from states [i+i, j +j, ] (in which i+j +( )N = N(M )) to the state [i, j, ] when Y = MN, where i, j < N and < i + j < N. C. Performance Measures The performance measures for each DSA policy are expressed using the steady state probability distribution of its corresponding CTMC. We derive performance measures (for both SU and SU 2 calls) such as blocing probability, probability of forced termination, and throughput. Let Π z denote the steady state distribution of a CTMC whose state is denoted as z = [i, j, ]. To simplify the presentation, we use the same notations under all DSA policies. For any DSA policy, the corresponding steady state probability distribution Π z is obtained by finding the corresponding transition rate matrix Q and applying the Gauss-Seidel algorithm []. Each row of Q represents the transitions with respect to a specific state z, as a balance equation. For example, referring to Fig. 2, one balance equation with respect to the state [i, j, ] under the DSA-C policy is expressed as follows: [µ p + δ 2 λ 2 + λ + λ p + iµ + jµ 2 ] Π [i,j,] = λ p Π [i,j, ] + (j + )µ 2 Π [i,j+,] + (i + )µ Π [i+,j,] + ( + )µ p Π [i,j,+] + λ Π [i,j,] + δ λ 2 Π [i,j,] (3) where Π [i,j,] represents the steady state probability for state [i, j, ] under DSA-C policy. ) Blocing Probability: The blocing probability represents the probability that an incoming SU call (SU or SU 2 ) is not permitted to enter into the system. The blocing probability of SU calls denoted as P B is expressed as P B = z Π z. The blocing probability of SU 2 calls Y =MN denoted as P B2 is expressed as P B2 = Π z. z Y MN ζ 2) Probability of Forced Termination: The probability of forced termination represents the probability that an ongoing SU call (SU or SU 2 ) is terminated by an incoming PU call. The probability of forced termination for the SU calls, denoted as P F, is expressed as follows: P F = z i l, j m l γ i,j, Π z λ ( P B ). (4) In Eq. (4), the numerator denotes the rate that l SU calls are terminated in state z whereas the denominator denotes the

4 effective rate with which a new SU call is assigned a subchannel. Similarly, the probability of forced termination for the SU 2 calls, denoted as P F 2, is expressed as follows: P F 2 = z i l, j m m γ i,j, Π z. (5) λ 2 ( P B2 ) In Eqs. (4) and (5), l and m depend on the DSA policy. 3) Throughput: The throughput under a given SU priority class is expressed as the mean number of ongoing calls in the system. Let η and η 2 denote the throughput for SU and SU 2 calls, respectively. The throughput η is given by η = λ ( P B )( P F ) whereas The throughput η 2 is given by η 2 = λ 2 ( P B2 )( P F 2 ). IV. RESULTS AND DISCUSSION In this section, we compare the two DSA policies based on the performance measures described in Section III-C. The accuracy of the analytical models is verified through simulations. In the experiments, we set M = 3 and N = 5. The symbols (a) and (s) in the figures indicate analytical and simulation results, respectively. A. Blocing Probabilities The blocing probabilities corresponding to the DSA-C2 policy are same as that corresponding to the DSA-C policy (because the DSA policies only differ in the handoff mechanism), and hence they are not shown for brevity of paper. Fig. 3 shows the blocing probabilities of the SU and SU 2 calls under the DSA-C policy with various PU arrival rate (λ p ). The following parameters are chosen for this experiment: λ =.4, λ 2 =.4, λ p [.3,.2], µ =.8, µ 2 =.8, µ p =.9, and η = 2. It can be seen that all the blocing probabilities (i.e., for both SU classes) increase as the PU arrival rate increases. This is because the number of busy sub-channels increases with an increase in the PU arrival rate, resulting in higher blocing probabilities for the SUs. Fig. 3 also shows that the analysis results match well with the simulation results. Blocing probabilities of SU and SU2 calls.4.2. PB, PB, PB2, PB2, Fig. 3. Blocing probabilities of SU and SU 2 calls under both DSA policies. 4 B. Forced Termination Probabilities Fig. 4 and Fig. 5 respectively show the forced termination probabilities of the SU and SU 2 calls under both DSA policies with various PU arrival rate λ p. The following parameters are set for this experiment: λ =.8, λ 2 =.8, λ p [.3,.2], µ =.35, µ 2 =.35, µ p =.9 and η = 2. It can be observed that as λ p increases, the forced termination probabilities of SU and SU 2 calls also increase with both DSA policies. Fig. 4 shows that DSA- C policy has lower force termination probability for the SU calls compared to DSA-C2 policy. Fig. 5 shows higher force termination probability of the SU 2 calls using DSA- C policy compared to DSA-C2 policy. Such observations accord with our expectation. Compared to the DSA-C2 policy, DSA-C policy reduces handoff failures for the SU calls by terminating some ongoing SU 2 calls during handoff. Again, the analysis and simulation results match well. Fig. 4. Fig. 5. Forced termination probability of SU calls, PF Forced termination probability of SU2 calls, PF2 Forced termination probability of SU2 calls, PF Forced termination probability of SU calls under both DSA policies Forced termination probability of SU 2 calls under both DSA policies SU arrival rate, λ Fig. 6. Effect of SU arrival rate on forced termination probability of SU 2 calls under both DSA policies.

5 Fig. 6 shows the effect of SU arrival rate (λ ) on the forced termination probability of the low priority SU 2 calls. In this experiment, we set λ p = and vary λ. It can be seen that as λ increases, the forced termination probability of SU 2 calls also increases with both DSA policies. This is because when λ increases, the number of SU 2 calls entering the system decreases. This leads to an increase in P F 2 along with λ. With DSA-C policy, apart from terminations caused by the PU arrivals, the SU 2 calls are also terminated by SU calls during handoff. Thus, P F 2 of DSA-C policy is higher than that of DSA-C2 policy. C. Optimal Sub-channel Reservation As mentioned in Section II-A, some sub-channels (ζ) are reserved for the SU call arrivals. Using the sub-channel reservation, we bloc some low priority SU calls to improve the performance of the high priority SU calls. Based on the given parameter settings and blocing probability requirement of the SU calls, an optimal number of sub-channels (ζ) to be reserved under the DSA policies can be determined from our analysis. Here, optimal number means the minimum number of sub-channels to be reserved in order to guarantee that the blocing probability requirement of the SU calls is satisfied. For instance, consider the following parameter setting: λ =.8, λ 2 =.8, λ p =, µ =.8, µ 2 =.3, µ p =.9 and a desired blocing probability of 5% for the SU calls. From the analysis, we found that the optimal value of ζ is 4 for both DSA policies. The analysis results can be verified from simulation. Fig. 7 shows the simulation results for the above parameter settings under different values of ζ. Fig. 7 shows that the desired blocing probability of 5% for the SU calls is satisfied when ζ = 4 sub-channels. Blocing probability of SU calls, PB Number of sub-channels reserved for SU calls (ζ) Fig. 7. Effect of ζ on blocing probability of SU calls under both DSA policies. D. Throughput Evaluation We verify the throughput calculated in the analysis with the simulation results. For the simulation, the throughput for a given SU priority class is calculated by taing the ratio of the total number of SU calls corresponding to that priority class completing service, to the total duration of the simulation. In our simulations, call arrivals are generated for a duration of 8 time units. For the parameter setting λ =.8, λ 2 =.8, λ p =.3, µ =.3, µ 2 =, µ p =.4 and ζ =, we obtained the following values for the throughput 5 from the analysis: η =.9975 and η 2 =.3462 for DSA-C policy whereas η =.789 and η 2 =.3997 for DSA-C2 policy. In the simulation, under DSA-C policy, SU calls and SU 2 calls completed service whereas under DSA- C2 policy, SU calls and SU 2 calls completed service. Therefore, from simulations, η =.9974 and η 2 =.3464 for DSA-C policy whereas η =.7986 and η 2 =.396 for DSA-C2 policy. The analysis results and simulation results for the throughput of the SUs correspond closely. As expected, DSA-C policy gives higher throughput for SU compared to DSA-C2 policy, at the expense of sacrificing the throughput of SU 2. This phenomenon holds under various parameter settings. V. CONCLUSION We have investigated the dynamic spectrum access in the cognitive radio networs under a special case in which the SU traffic is prioritized. Two different DSA policies have been developed to handle the spectrum assignment and handoff for the SU traffic with two priority classes. We have developed the analytical models for two proposed DSA policies. For performance evaluation, we have derived the blocing probability, the forced termination probability, and the throughput for the two priority classes of SU traffic. 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