1
Spectrum-efficient Resource Allocation Framework for Cooperative Opportunistic Wireless Networks Mohamed AbdelRaheem, Member, IEEE, Mohammad J. Abdel-Rahman, Member, IEEE, Mustafa El-Nainay, Member, IEEE, and Scott F. Midkiff, Senior Member, IEEE
Abstract—Dynamic spectrum access (DSA) is a promising approach to alleviate spectrum scarcity and improve spectrum utilization. Recently, several cooperative communication schemes have been proposed to further enhance spectrum utilization in DSA networks. Existing cooperation designs are either tailored for primary-secondary user (PU-SU) cooperation and not applicable to SU cooperation, or focus on the potential benefits of SUs cooperation without investigating how SUs agree on cooperating and the conditions that lead to improve their performance. In this paper, we introduce a spectrum-efficient resource allocation framework based on SUs cooperation, where the resources include the free spectrum access time, available channels, and relays. First, we formulate the interactions between the cooperating SUs and a PU using a discrete-time Markov chain (DTMC). Using this DTMC and Nash bargaining, we determine the new spectrum access times for SUs based on every nodes utility. We also derive the conditions under which all SUs improve their performance by cooperation. Second, considering a multi-channel multi-SU infrastructure network, we formulate two optimization problems for jointly allocating channels to SUs and selecting the cooperating SU pairs. We corroborate our analytical findings with detailed simulations that evaluate SUs cooperation gains and the optimality of the proposed joint allocation schemes. Index Terms—Dynamic spectrum access, cooperative communications, Markov chain, Nash bargaining.
I. I NTRODUCTION
T
HE massive growth in wireless devices and mobile traffic has motivated extensive research on improving spectrum utilization. Among the promising solutions is dynamic spectrum access (DSA). DSA tries to address the rising demand by allowing spectrum-agile devices with cognitive radio capabilities, a.k.a. secondary users (SUs), to access the available spectrum in a dynamic fashion, without interfering with colocated incumbent users, a.k.a. primary users (PUs). In this way, DSA can significantly improve the spectrum utilization. Cooperation among different nodes is shown to have the potential for enhancing the performance of DSA networks and it can be categorized into two categories: M. AbdelRaheem was with the Bradley Department of Electrical and Computer Engineering, Virginia Polytechnic Institute and State University, Blacksburg, VA 24061 USA. He is now with the Electrical Engineering Department, Assiut University, Assiut, Egypt (e-mail:
[email protected],
[email protected]). M. J. Abdel-Rahman, and S. F. Midkiff are with the Bradley Department of Electrical and Computer Engineering, Virginia Polytechnic Institute and State University, Blacksburg, VA 24061 USA (e-mail: { mo7ammad, midkiff}@vt.edu). M. El-Nainay is with the Computer and Systems Engineering Department, Alexandria University, Alexandria, Egypt (e-mail:
[email protected]).
Fig. 1: Examples of SU direct and cooperative transmissions. Cooperation between PUs and SUs – In this model, the PU provides part of its spectrum to SUs while SUs help the PU to improve its transmission performance. The authors in [1]–[7] modeled the cooperation between PUs and SUs as market-driven spectrum trading to reallocate the resources. • Cooperation between SUs – In this model, SUs cooperate with each other either (i) to enhance the sensing accuracy (see, for example, [8]) or (ii) to enhance the transmission characteristics, such as throughput (see, for example, [9]–[13]). In the PU-SU cooperation schemes proposed in [1]–[7], the PU is given a superior role over the SU. For example, the PU acts in [1]–[3] as a monopolist, in [4], [5] as a leader of the Stackelberg game, and in [6], [7] as a seller. These models cannot be used to study SUs cooperation, where no SU has a superior role over the others. Existing work on SUs cooperation focuses only on studying the potential performance gains brought by cooperation, without studying how SUs agree on cooperating with each other or the conditions under which cooperation is beneficial for all cooperating SUs. In this paper, we aim to answer these questions. Furthermore, considering a multi-channel multi-SU infrastructure network, we propose joint optimization schemes for allocating channels to SUs and for selecting the cooperating SU pairs. In our previous work [12], [13], we showed that utilizing cooperative transmission via intermediate relays reduces significantly the negative effect of PU interruption on the SUs transmission compared to the case when the SUs transmit directly to the destination. Figure 1 illustrates this idea. Assume a secondary network with multiple slow and fast SUs transmitting data packet to a secondary access point (SAP) by utilizing the available white spaces in the licensed spectrum. If the slow SU utilizes DT as •
2
in Figure 1(a), it has to abort its first two transmission attempts due to the interruption of the PU before it achieves a successful transmission in the third attempt. On the other hand, the SU may utilize cooperative transmission via an intermediate relay as shown in Figure 1(b). In the cooperative transmission, the two hops are done at higher data rates (shorter transmission times) than the direct transmission and the relay is able to buffer the transmitted packet till the PU is absent and so it will utilize the available white spaces more efficiently than the DT. Our Contribution – Based on the previous idea, we establish a spectrum-efficient resource allocation framework for cooperative SUs that allocates the free spectrum access time, channels and relays among SUs.The main contributions of this paper are as follows: 1. Considering a single-channel system that consists of a PU and a pair of cooperating SUs: • We formulate a discrete-time Markov chain (DTMC) model to capture the interactions between the PU and the cooperating SUs, assuming an interweave spectrum sharing paradigm [14], in which the PU and the SU cannot access the same spectrum portion simultaneously. The cooperating SU pair consists of a slow SU which has a low transmission rate and a fast SU which has a high transmission rate and relays the packets of the slow SU. Our model considers three different SUs’ channel access mechanisms.In contrast to existing Markov models (e.g., [15], [16]), our DTMC model explicitly captures the ability of SUs to transmit cooperatively and models the relay’s own transmission as well. We use our DTMC model to derive different transmission characteristics, such as the SUs spectrum efficiency and throughput. • Using our DTMC model, and adopting a utility function that considers both the throughput as well as the energy consumption, we use the Nash bargaining to determine the new free spectrum access time shares for the cooperating nodes based on their utility functions. We derive the conditions under which both SU and its relay improve their performance in terms of the throughput and the power efficiency by cooperation. 2. Considering a multi-channel multi-SU infrastructure network, we formulate two optimization problems for jointly (i) allocating channels to SUs and (ii) selecting the cooperating SU pairs based on the bargaining based free spectrum shares. The first optimization problem aims to maximize the overall network throughput subject to individual SU rate demands. The goal of the second optimization problem is to minimize the maximum (among SUs) difference between the throughput and the rate demand. These two points, sequentially, form a two-step fair and friendly resource allocation framework that optimizes the global network objective without harming any cooperating nodes. In this framework, every node gets a free spectrum time share that is proportional to its contribution in the cooperation process. Paper Organization – The rest of the paper is organized
Fig. 2: Cooperative multi-channel secondary network. as follows. We present our system model in Section II. The DTMC model of the PU-SUs is presented and the Nashbargaining-based SU spectrum access times are determined in Section III. In Section IV, we investigate the optimal channel allocation and SU pairing problem. Detailed performance evaluation is provided in Section V. Finally, in Section VI we conclude the paper and provide directions for future research. II. S YSTEM MODEL In this section, the system and network models are presented. Moreover, the motivation of the proposed work in later sections is established. A. Network Model As shown in Figure 2, the system model consists of a secondary infrastructure network with one SAP, number of secondary users (SUs) and secondary relays (SRs)1 . The secondary network operates under the coverage of more than one PU (three in Figure 2) where the SUs can access the licensed channels using an interweave spectrum sharing mechanism. The PU, SU and SR use synchronized slotted Media Access Control (MAC) protocol to access the spectrum where the data transmission time spans an integer numbers MP U , MSU and MSR of time slots for the PU, SU and SR, respectively. SUs are assumed to have the ability to perform accurate spectrum sensing at the beginning of each time slot. Once detecting a PU on a given channel, SUs immediately vacate this channel. We assume the network nodes are arranged in three different transmission ranges from the SAP. It is assumed that all SUs’ packets have the same length and the data rate of every SU depends on its distance to the SAP. We define three data rates named R1, R2, and R3 with transmission time spans 4m, 2m, and m time slots, respectively where m is a parameter that reflects the time resolution of the transmission. A node can transmit its packets directly to the destination, henceforth referred to as direct transmission, or through another node which acts as a relay, henceforth referred to as cooperative transmission. In the cooperation mode, the SU uses Decode 1 Generally, we will refer to secondary node with slow rate which asks for the help by (SU) and for the fast rate node that, besides transmitting its own data, can relay the slow nodes ones, by (SR) .
3
(a) DT
(b) L(1a)
(c) L(1b)
(d) L2
(a) EAP
Fig. 3: Example of secondary direct and cooperative transmissions at different cooperation levels between the SU and the SR.
and Forward (DF) cooperative communication. In DF, the SU transmits its data to an intermediate relay using rate R(SU →SR) in transmission time T(SU →SR) in the first hop. The relay decodes the data then forwards it to the destination (SAP) using rate R(SR→SAP ) in transmission time T(SR→SAP ) in the second hop. By neglecting the decoding time, the overall transmission time and data rate are given by (1) and (2), respectively [17]: TCC 1 RCC
= T(SU →SR) + T(SR→SAP ) , 1 1 + . = R(SU →SR) R(SR→SAP )
(1) (2)
We define two cooperation levels between the SU and the SR according to the two hops rates and the net achieved rate. The cooperation level is determined by the number of time slots (transmission time) required to transmit the SU packet MSU over the two-hops from the SU to the SR M(SU →SR) and from the SR to the SAP M(SR→SAP ) 2 . Considering that the SU non-cooperative direct transmission (DT) consumes 4m time slots; the two levels of cooperation between the SU and SR are defined as follows: 1) L(1) : MSU = 3m a) L(1a) : M(SU →SR) = m, M(SR→SAP ) = 2m b) L(1b) : M(SU →SR) = 2m, M(SR→SAP ) = m 2) L(2) : MSU = 2m, M(SU →SR) = m, M(SR→SAP ) = m Levels L(1a) and L(1b) have the same throughput performance, but they differ in the rate of each hop which is a concern in calculating the utility as will be shown in Section III-C. As a numerical example, if the SU DT rate to the SAP is 6 Mbps that consumes 4m time slots, it can use an intermediate relay in cooperation level L(1a) such that, the first hop rate is 24 Mbps (consumes m time slots) and the second hop rate is 12 Mbps (consumes 2m time slots). That yields to a net cooperative transmission that consumes 3m time slots and cooperative throughput of 8 Mbps. Figure 3 shows the DT and different cooperation levels of this example. B. Secondary User Access Mechanisms In this paper, we consider three spectrum access mechanism used by the SAP to control the secondary nodes’ (SUs and SRs) access to the free spectrum in the non-cooperative mode. These access mechanisms determine the secondary nodes 2 Here
we refer to the transmission in uplink direction but the same procedure applies for the downlink direction.
(b) ETT
(c) ESTT
Fig. 4: Illustration of SU and SR free spectrum shares at different access mechanisms.
disagreement utility if they are not cooperating. The three access mechanisms are defined as follows. •
•
•
Equal Access Probability (EAP): In this mechanism, the SAP gives equal access for all nodes regardless of their data rates, cooperation level, or the primary user activity. Equal Transmission Time (ETT): In this method, the SAP controls the access probability such that, on average, different nodes have equal access to the free spectrum. In this case, the SAP does not account for the node data rate or the transmission efficiency. Equal Successful Transmission Time (ESTT): In this mechanism, every node gets an equal successful transmission time. In other words, the SAP compensates each node for its loss due to interruption by the PU.
Figure 4 shows SU and SR shares of the free spectrum for the three different access mechanisms where tSU and tSR are the total transmission times (total shares) of the SU and SR, respectively, and τSU and τSR are the total successful transmission time of the SU and SR, respectively. The dashed portions represent the wasted times due to PU interruptions. As can be noticed from Figure 4, EAP is the most beneficial access mechanism for the SU and the worst for the SR as it does not give any access priority for any node over the other and allows every node to transmit the same number of packets regardless of its rate or transmission efficiency. That causes the SU (which transmits with low data rate) to occupy most of the available free spectrum time share. On the other hand, ETT is the best for the SR and the worst for the SU as it does not compensate a slow node for its lower rate nor its lost packets. ESTT can be considered a compromise access mechanism between EAP and ETT as it compensates the nodes for their lost packets. Detailed analysis of the different access mechanism performance is provided in Section III-B. Based on the adopted secondary access mechanisms, each node gets a certain free spectrum access time share in the noncooperative mode. If a pair of nodes agreed to cooperate, they
4
will re-divide their shares according to the Nash bargaining solution based on a utility function that combines throughput, energy consumption and the disagreement utility of each node. Based on these bargaining based free spectrum access shares, nodes are paired and channels are allocated in an optimum way to achieve global objective.
state (A2 A∗ a) means that the PU is actively transmitting its packet in its second time slot while the SU is waiting for the PU to be idle to start its own transmission and the SR is idle. State (An A∗ a) has the same meaning of (An A∗ a) but used to indicate that the PU started its transmission after the SU finished its first hop transmission to preserve the memoryless property of the Markov chain in the cooperative mode.
III. PU-SU-SR C OOPERATION M ODEL In this section, we investigate the cooperation process between an SU and an SR. The cooperation is modeled as a resource exchange process where the SR sacrifices part of its energy in forwarding the SU packets and in return, the SU vacates part of its dedicated free spectrum time share to the SR. The goal is to find the amount of free spectrum time the SU should give to the SR based on the utility both achieve after cooperating and the disagreement utility if they did not cooperate. We define the utility function to consider both throughput and energy. After defining the SU and SR utilities in cooperative and non-cooperative modes (disagreement points), we use the Nash Bargaining Solution (NBS) to find the new free spectrum shares after the cooperation. The cooperation between any SU and SR must not affect other secondary nodes’ spectrum shares as they only re-allocate their non-cooperative share using the bargaining process. To calculate the SU and SR utilities, we model the interaction between the PU, SU and SR using a DTMC and from this model we obtain the necessary transmission characteristics such as efficiency and throughput. A. PU-SU-SR Transmissions Interaction DTMC Model In this subsection, we present the PU, SU, SR interaction DTMC model in interweave spectrum sharing mechanism for the three secondary user access mechanisms presented in Section II. This model quantifies the effect of the PU activity on the performance of the secondary users in the noncooperative and cooperative modes. The PU activity affects the transmission performance of the secondary nodes as it forces them to re-transmit their packets due to the interruption caused by the PU transmission. From the analysis of the DTMC models we extract different transmission characteristics like transmission efficiency and throughput that will be used to calculate the SU and SR utilities in Section III-C. The transition diagrams shown in Figures 5(a) and 5(b) represent examples of the PU-SU-SR noncooperative and cooperative DTMC models, respectively, for MP U = 2, MSU = 3 (in non-cooperative mode), MSU = 2 (in cooperative mode), and MSR = 1. Each state 3 is labeled by three letters (P SR), where, P represents the PU status, S represents the SU status, and R represents the SR status. The letter (A) is used to indicate that the node (PU, SU or SR) is actively transmitting its own packet. The letter (A∗ ) indicates that the SU or the SR is waiting for the PU to finish its transmission to start its own. The letter (a) indicates that this secondary node (SU or SR) is waiting for its turn to access the free spectrum and start its transmission. For example, 3 In
this paper, we use the words ‘state’ and ‘time slot’ interchangeably.
The probability values PP UI and PP UA are the probability of the PU being idle or active, respectively and they describe the PU activity pattern. If values of PP UI and PP UA are exactly known and they are stable over the time we can use them directly in the proposed model. However, these values are usually unknown for the SAP and change according to the type of the transmitted data. The common characteristic known by the SAP about the PU activity is its activity level ρ or, by other words, the channel utilization level. To overcome this point, for a given value of ρ we calculate the corresponding range of values of PP UI and PP UA that result in this PU activity level. The SAP based its calculation for the SU and SR performance, for a given PU activity level, on the average performance over range of transition probabilities which give the same PU activity level. A separate DTMC model named stand-alone DTMC is designed to model the PU transmission for a given level of PU activity. From this DTMC model, the targeted transition probabilities are calculated. The DTMC model, the transition probabilities calculations, and their effect on the performance are provided in the appendix. The value of P(X→Y ) is the probability that secondary node Y starts a transmission after secondary node X has finished its transmission. The value of this probability is determined according to the secondary access mechanism used (EAP, ETT, or ESTT). The final values of the transition probabilities are calculated based on the PU activity and according to the adopted secondary user free spectrum access mechanism. For example, in the non-cooperative DTMC model shown in Figure 5(a), after state (IA3 a), which means the SU is active transmitting in the last time slot and the PU and SR are idle, the DTMC can move to state (A1 A∗ a) if the PU becomes active with probability (1 − PP UI ) and the SU stays active (SR is idle) with probability (P(SU →SU ) ) that gives a total transition probability of ((1 − PP UI ) P(SU →SU ) ). In the same way the DTMC can move from state (IA3 a) to state (IA1 a) with a transition probability equal to (PP UI P(SU →SU ) ), or to state (A1 aA∗ ) with a transition probability equal to ((1 − PP UI ) P(SU →SR) ), or to state (IaA) with a transition probability equal to (PP UI P(SU →SR) ). The main difference between the non-cooperative and the cooperative model is that, in the cooperative model, if the first hop is finished successfully, the SR can buffer the SU’s packet if the PU becomes active until the PU becomes idle again, then transmits the packet without the need to repeat the first hop transmission. For the PU, the PU activity level ρ equals the summation of all active state occupancy distributions for the different
5
(a)
(b)
Fig. 5: (a) PU-SU-SR non-cooperative DTMC (b) PU-SU-SR cooperative DTMC. transmission scenarios and calculated as: ρ=
M PU X
π(Ai A∗ a) + π(Ai A∗ a) + π(Ai aA∗ ) .
(3)
i=1
The calculated value of ρ using equation (3) must be equal to the given value to ensure that the SU and SR interaction with the PU is modeled correctly such that it does not affect the PU activity. The successful active occupancy distributions for the SU and SR can be calculated by multiplying the occupancy distribution of the last active state by the number of timeslots per transmission (by this way we count only the time slots resulted in the successful transmission) as shown in equations (4) and (5) for the SU and the SR, respectively. π(SUA ) = MSU π(IA(M ) a) SU π(SRA ) = MSR π(IaA(M ) ) .
(4) (5)
SR
The transmission efficiency of the SU and the SR can be calculated by dividing the spectrum occupancy state distributions resulting in a successful transmission over all active state occupancy distributions including those that were wasted due to the PU interruption. The SU and SR efficiencies are given by: π(SU ) ηSU = PMSU A (6) i=1 π(IAi a) π(SR ) ηSR = PMSR A . (7) i=1 π(IaAi ) The SU and SR throughputs are given by: TSU = RSU π(SUA )
(8)
TSR = RSR π(SRA ) ,
(9)
where RSU and RSR are the data rate of the SU and the SR, respectively. B. Analysis of Different Access Mechanisms In this subsection, we analyze the three non-cooperative access mechanisms proposed in Section II using the DTMC models shown in Fig. 5 (a) and (b). The goal is to calculate
the SU and SR transmission efficiency and the throughput, for each of the proposed secondary access mechanisms using the set of relations described by equations (6)-(9). 1) Non-cooperative mode: EAP – To achieve equal spectrum access probabilities for both the SU and the SR, the values of the transition probabilities are set as follows: P(SU →SU ) = P(SU →SR) = P(SR→SR) = P(SR→SU ) = 0.5.
(10)
The value of PP UI and PP UA are calculated from the standalone DTMC models shown in the appendix. The probability matrix P then can be constructed and the occupancy distributions of different states are calculated by solving equations (43) and (44) as done for the PU stand-alone DTMC model in the appendix. After finding the different state occupancy distributions, the transmission efficiency and throughput can be calculated using equations (6)-(9). ETT – In ETT, both the SU and the SR have equal free spectrum access time (tsu = tsr in Figure 4) which leads to equal summation of all the state occupancy distributions for the SU and the SR, M SR X i=1
π(IaAi ) =
M SU X
π(IAi a) =
i=1
1−ρ . 2
(11)
From the DTMC model, the relation between two consecutive SU or SR state occupancy distribution πn and πn−1 in the non-cooperative mode can be written as: πn = PP UI π(n−1) ,
(12)
which can be generalized as, πn = PPi UI π(n−i) .
(13)
By expressing the different state occupancy distributions of the SU using the last state π(IA(MSU ) a) according to equation (13) and by substituting its value in (11), then the value of π(IA(MSU ) a) can be calculated from it. The rest of SU state occupancy distributions can be calculated according to (13). The same procedure can be used for the SR.
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ESTT – In ESTT, the SU and SR have the same successful transmission time (τSU = τSR in Figure 4), which may be translated to the relation between the state occupancy distributions for the SU and SR using the following two equations: MSU π(IA(M ) a) = MSR π(IaA(M ) ) SU SR M SR X i=1
π(IaAi ) +
M SU X
π(IAi a) = 1 − ρ.
(14) (15)
i=1
As in ETT, the different state occupancy distributions can be expressed using the last state occupancy distribution and, by using equations (14) and (15), the different state occupancy distributions can be calculated. As in EAP, after finding the different state occupancy distributions, the transmission efficiency and throughput can be calculated using (6)-(9). The values of the access probability P(SU →SU ) , P(SU →SR) , P(SR→SU ) , and P(SR→SR) , can be calculated by substituting the PU, SU and SR occupancy states distributions in (43) and solving it with the following two equations: P(SU →SU ) + P(SU →SR) = 1
(16)
P(SR→SR) + P(SR→SU ) = 1.
(17)
2) Cooperative mode: If the SU and SR are cooperating and they adopt the same non-cooperative access method, the SU calculations are different from the non-cooperative mode for ETT and ESTT. For EAP, the transition probabilities have the same values as the non-cooperative case and the different state occupancy distribution, efficiency and throughput are calculated using the same techniques used in the non-cooperative mode. For ETT and ESTT, as the SU transmission is done over two hops, the calculations are different from the non-cooperative case. For the SU, if the first hop transmission spans l time slots and the second hop spans k time slots such that l + k = MSU , the relation between the last state occupancy distribution of the first hop transmission π(IAl a) and the last state occupancy distribution of the second hop transmission from the SR to the SAP π(IA(MSU ) a) = π(IA(l+k) a) is given by as: π(IAl a) = π(IA(l+k) a) .
(18)
That is because for a single SU cooperative transmission, the DTMC goes through the last state of the fist hop only one time as there is no-retransmission for the first hop if the DTMC reached this state. Also, in the same way, the DTMC goes through the last state of the second hop only one time at every cooperative transmission. By using equation (13), we can express any state occupancy distribution in the first hop using π(IAl a) as follows: π(IAl a) . (19) π(IA(l−i) a) = PPi UI The same can be applied for the second hop by using
π(IA(l+k) a) as follows: π(IA(l+k−i) a) =
π(IA(l+k) a) PPi UI
.
(20)
Using the last two equations, the relation between π(IA(l+k) a) and π(IA(l+i) a) can be found and so, as in the non cooperative case, we can express the different SU state occupancy distributions using π(IA(l+k) a) . Using the same procedure used in the non-cooperative mode for ETT and ESTT, the different state occupancy distribution, transmission efficiency and throughput can be calculated.
C. Utility Model The utility function for the SU and SR is defined as the difference between the achieved normalized throughput and the normalized energy [2]. The utility for node s is defined as follows: ¯s , Us = T¯s − Cs E (21) ¯s is where T¯s is the normalized throughput of node s and E its normalized energy. The factor Cs is the energy evaluation factor. The normalized throughput and energy for node s can be defined using the following two equations: Rs ηs Rmin ¯s = ts , E
T¯s = ts
(22) (23)
where ts is the free spectrum time share the node s gets, Rs is the data rate, Rmin is the lowest rate used in the model and the transmission power is set to be equal to one. The value of Cs indicates the preference of the node between the energy and throughput. For example, when Cs < 1, it means that the node prefers to achieve higher throughput over to save its energy. Equation (23) is valid only in the non-cooperative case where the SR does not contribute in the SU’s transmission. For the cooperative case, we account for the energy consumed by the SR to relay the SU packets, including the power consumed in the transmission and reception of the packet. In the cooperative mode, the definition of the normalized energy will be different for the SU and SR. For the SR, the normalized energy will be defined as: ¯(SR ) = t(SR ) + t(SU ) εSR + γ(1 − εSR ) tSU , (24) E coo coo coo where γ is the ratio of the power consumed in the SU packet reception by the SR to the power used in the transmission, εSR is the ratio of the time of the second hop cooperative transmission to the total time of the two hops cooperative transmission. The value of εSR depends on the cooperation level used, for example, εSR = (2/3) in L1a , (1/3) in L1b , and (1/2) in L2 . The values of t(SUcoo ) and t(SRcoo ) are the SU and SR free spectrum time shares in the cooperative mode. For the SU, the normalized energy in the cooperative mode is defined as: ¯SU = (1 − εSR ) t(SU ) . E (25) coo coo tsu and tsr are selected such that they satisfy, in both the cooperative and non-cooperative modes, the following
7
equation: 1 − ρ = tSU + tSR .
(26)
USU vs. USR using f = (USU − dSU )(USR − dSR )
1.5 1.25
D. Bargaining Model
1) Individual Rationality, IR: This axiom implies that every node get a bargaining utility higher than its disagreement one. To realize this axiom, the bargaining solution needs to satisfy the following equation, f1 (F, d) ≥ d1
and
f2 (F, d) ≥ d2
(27)
where (d1 , d2 ) are the disagreement utilities. 2) Pareto Optimality, PO: The bargaining solution is Paretooptimal. For a feasible set F , the allocation x = (x1 , x2 ) is Pareto efficient if there exists no other point y = (y1 , y2 ) such that Uy1 ≥ Ux1 and Uy2 ≥ Ux2 where the strict inequality is satisfied for at least one player and Uzn represents the utility resulted from the allocation z for player n. 3) Symmetry, SYM: The solution does not discriminate between players if they are indistinguishable. 4) Scale Invariant, SINV: Transforming the bargaining problem by any linear scale transformation ψ changes the solution by the same transformation. ψ(f (F, d)) = f (ψ(F ), ψ(d)).
(28)
5) Independence of Irrelevant Alternatives, IIA: The axiom states that for any closed and convex set Z, G ⊂ F andf (F, d) ∈ G ⇒ f (G, d) = f (F, d).
(29)
The axiom implies that eliminating the not chosen feasible alternatives should not affect the solution. The unique NBS for two players is obtained by solving the following equation: f (F, d) =
arg
max (x1 − d1 )(x2 − d2 )
(x1 ,x2 )∈F
subject to x1 ≥ d1
(30) and
x2 ≥ d2
where d1 and d2 are the disagreement points for players one and two, respectively. Figure 6 shows the graphical representation of NBS as the intersection of the Pareto optimal boundary of the utility and the hyperbola of equation (30) for different cooperation levels between the SU and SR. After finding the NBS solution (the
SR utility (U SR)
NBS solution point
To decide the shares of the cooperating SU and SR pair, we use the bargaining theory where both nodes bargain over their entire share. Nash bargaining solution (NBS) [18] is used to find the share of every node, where the original total access time shares assigned to both the SU and SR is subjected to the bargaining process. The two player bargaining problem consists of a pair (F, d), where F is called the feasible set of allocations and it is closed and convex and d is the disagreement point. The utility of each player in the noncooperative mode is used as a disagreement point if the nodes refused to cooperate. The NBS is unique and satisfies the following axioms.
1 USU vs. USR using tSU + tSR = (1 − ρ)
0.75 0.5 0.25
L1a L1b
0
L2
0
0.1
0.2
0.3
0.4
0.5
0.6
0.7
0.8
SU utility (USU)
Fig. 6: NBS graphical representation at different cooperation levels for ρ = 50%, CSU = CSR = 0.25, and γ = 0.7. values of USU and USR ), the cooperative free spectrum shares can be re-calculated using (21). IV. N ODE PAIRING AND C HANNEL A LLOCATION P ROBLEM In this section, we investigate the optimal way to pair the secondary nodes (slow and fast ones) and allocate channels to them in a secondary infrastructure network based on the NBS free spectrum time shares. A. Network Setup def
We consider an infrastructure network with a set N = {1, 2, . . . , N } of SUs uniformly distributed within a circular area that is divided into a number of regions characterized def by the direct transmission rate R ∈ RD = {R1, R2, . . . , Rl} between each region’s SUs and the SAP. Every SU n can transmit/receive packets from the SAP with a rate Rn ∈ R. In addition, each SU is able to transmit to other SU r using direct transmission rate Rnr ∈ {0, R1, R2, . . . , Rl} where Rnr = 0, means that these two SUs are out of the transmission range of each other. There is a set of transmission channels def C = {1, 2, . . . , C}, each one is characterized by its primary user activity ρc . The initial share for node n, In , defines the amount of free spectrum access time share the node will get compared to those of all nodes operating at the same channel in noncooperative mode. The initials shares are determined by the SAP by controlling the access probability of every node. The value of the initial share depends on the non-cooperative access mechanism used. For example, for N nodes operating at the same channel, the initial shares for at different secondary access mechanism are: R max • EAP: IEAP = [ η max , Rmax , . . . , ηR ] 1 ·R1 η2 ·R2 N ·RN • ETT: IET T = [1, 1, . . . , 1] 1 1 1 • ESTT: IEST T = [ , ,..., ] η1 η2 ηN where Rmax is the maximum rate in the network.
8
For every pair of SUs, if they agreed to cooperate, they redivide their initial shares among themselves according to their utilities using NBS. The share division ratio between node n and relay r over channel c is defined as Scnr and decides the shares for every combination of SU pairs at different channels where Scnr = (1 − Scrn ) and Scnn = 0.5 ∀n ∈ N , ∀c ∈ C, where Scnn represents the direct transmission share of SU n. The transmission rate Rcnr is the net achieved rate for SU n if it cooperates with SU r over channel c, and Rcnn represents the direct transmission rate of SU n over channel c. The values of S and η are pre-calculated as mentioned in Section III. B. Resource Allocation Problem Formulations Let xcn , c ∈ C, n ∈ N , be a binary variable that represent the channels allocation such that: ( 1, if SU n will operate over channel c xcn = 0, otherwise and ynr , n, r ∈ N , be a binary variable that indicates the cooperation relation between secondary nodes such that: ( 1, if nodes n and r will cooperate ynr = 0, otherwise.
minimum rate in RD . The SAP tries to satisfy β × 100% of each node’s demand where 0 ≤ β ≤ 1. We define two optimization problems with different objectives that use bargaining based shares and aims to maximize the total network throughput (BBS-1) or minimize the maximum difference between any node demand and the achieved throughput (BBS-2). BBS-1 aims to maximize the total network throughput and satisfies all nodes demands with a certain percentage β×100%. Problem 1 (BBS-1): (N ) X maximize Tn {xcn ,ynr }
(33)
n=1
subject to: X
xcn = 1, ∀n ∈ N
(34)
c∈C
ynr = yrn , ∀n, r ∈ N X yzr = 1, ∀z ∈ Ns
(35) (36)
r∈N
xcr ≥ xcn ynr , ∀c ∈ C, ∀n, r ∈ N (37) X ynn ynr ≤ 1, ∀n ∈ N (38) r∈N
Two notes are to be taken into consideration. First, if ynn = 1, that means that SU n uses direct transmission. Second, the cooperation rule between two SUs is not reversible, that means if node r helps node n, node n cannot help node r. The achieved throughput Tˆ of node n is defined as follows: ) ( C X N X 1 − ρ c , Tˆn = xcn ynr Bcnr Rnr ηcnr PNSU c=1 r=1 l=1 xcl Il (31) where Bcnr is the bargaining based spectrum time share for node n that cooperates with node r over channel c and equals to, ! PN y − 1 ni i=1 Bcnr = (In + Ir ) Scnr − In , (32) PN i=1 yni where the second term in (32) is subtracted to ensure that, in the case of an SR that helps more than one SU, the share of the SR is not counted more than one time in the summation over all nodes in (31). That can be illustrated by the following example. Suppose that SR (R) helps two SUs (S1 andS2 ) with initial shares are as follows IR = 20%, I(S1 ) = 40% and I(S2 ) = 40% and the bargaining based shares over channel (c) are S(cRS1 ) = S(cRS2 ) = 50% . If equation (32) includes only the first term, the nodes’ shares will be B(cRS1 ) = B(cRS2 ) = 30% and B(cS1 R) = B(cS2 R) = 30% , the sum of all shares in this case will be 120% which is incorrect as the share of the relay is counted twice. To avoid this calculation error, the second term is added to correct the share of the SR. According to (31) the value of B(cRS1 ) = B(cRS2 ) = 20%, so the SR will get only 40% of the free spectrum share of the three nodes and S1 and S2 , each will get 30%. Node n’s demand dn is set to be proportional to its data rate capability and equals to (Rn /Rmin ) where Rmin is the
Tn ≥ β dn , ∀n ∈ N
(39)
xcn ∈ {0, 1} , ∀c ∈ C, ∀n ∈ N
(40)
ynr ∈ {0, 1} , ∀n, r ∈ N .
(41)
Constraint (34) ensures that every SU operates only over one channel. Constraint (35) ensures that the cooperation matrix is symmetric. Constraint (36) ensures that every slow node s ∈ NS (nodes with low direct transmission data rate that asks for a relay help) receives help by at maximum one relay. To ensure that every cooperating pair’s nodes belong to the same channel, constraint (37) is used. If the SR n is helping at least one SU, the value of ynn must be set to 0 by constraint (38). For example, if SR n is helping SU m, that means ynm = 1. However, equation (33) will try to set also ynn to 1 to maximize the global throughput which will result in an incorrect value as the time share of the SR will be added twice. Constraint (38) will prevent both ynn and ynm from being equal to one at the same time. As the cooperation is always beneficial for both nodes and for the global objective, only ynm will be set to 1. Constraint (39) ensures that every node gets β × 100% of its demand for a given value of β. The previous formulation gives the slow nodes the minimum demand while allocating the rest of resources to the other nodes with high rate. The problem will fail to achieve a solution if any node does not receive β × 100% of its demand. The second problem (BBS-2) aims to minimize the maximum difference between any node demand and the achieved throughput such that it maximizes the excess capacity if what the node gets is higher than its demand or minimize the demand shortage if the demand is not satisfied. All the constraints of problem BBS-1 apply here also except of constraint (39) which is relaxed such that the problem has
9
TABLE I: Numerical values of various parameters. Parameter SU # of time slots per packet (MSU ) PU # of time slots per packet (MP U ) PP UA range Energy evaluation factor CSU = CSR γ Modulation Data rate Demand (d) Path loss exponent Transmission power Channel type Successful reception BER threshold Number of nodes N Number of channels C PU activity ρ
Value 32 16 0.2 to 0.8 0.1 0.7 (see [19]) BPSK, QPSK, 16QAM 6, 12, 24 Mbps 1, 2, 4 Mbps 3.5 0.5 mW Rayleigh flat fading 10−3 10 3 0.4, 0.6, 0.8
a solution in the case of demand shortage. Problem 2 (BBS-2): n minimize omaximum xcn ,ynr , c∈C,n,r,∈N
n∈N
β dn − Tn β dn
(42)
subject to: (34) − (38), (40), and (41).
V. P ERFORMANCE E VALUATION In this section, we evaluate the performance of cooperative communications in secondary infrastructure networks as compared to non-cooperative secondary networks. In these experiments, for the cooperation scheme, normalized metrics are obtained by dividing each metric by its non-cooperative counterpart. The values of the PU transition probabilities are calculated as in the appendix and the SU and SR performance are averaged over range of PP UA and its corresponding PP UI values. The numerical values of the simulation parameters are listed in Table I unless otherwise specified. A. Secondary Cooperative Transmission Performance In this experiment, we evaluate the effect of SU cooperation on the spectrum successful utilization using the DTMC model. We modify the DTMC model such that the relay is a passive relay that only helps the SU without transmitting its own packets. Figure 7 shows the SU transmission efficiency as a function of PU activity ρ at different cooperation levels and for the direct transmission case. As shown in the figure, utilizing cooperation enhances the efficiency of the SU transmission. As a consequence, the normalized transmission of the SU is enhanced significantly, especially at high values of PU activity as the cooperation is efficient in reducing the effect of PU interruption and so, enhance the throughput performance compared to the direct transmission as shown in Figure 8. B. Performance of Bargaining-based Cooperation In these experiments, we study the SU and SR performance under cooperation.
1) Effect of the PU activity: Figure 9 shows the SR NBS based free spectrum share percentage from the total shares dedicated for the SU and SR after cooperation. Also, the SR shares in the non-cooperative and cooperative modes with the same non-cooperative access mechanisms (EAP) as a function of the PU activity ρ are shown. When using bargaining based cooperation, the SR gets a higher share than that of the noncooperative mode or the cooperative mode with the same EAP access mechanism. Also, the NBS based SR free spectrum share increases as the PU activity increases to compensate for its increased energy dissipation in relaying the SU packets due to the increase in PU interruptions. Such compensation does not occur in the other two methods resulting in decreasing the SR shares with the increasing of PU activity. Figures 10 and 11 show the SR and SU normalized utility and throughput, respectively. As shown in the figures, both the SR and the SU achieve higher utility and throughput than the non-cooperative case and the rational enhancement (compared to the noncooperative case) increases as the PU activity increases where the cooperative transmission performance is much better than the non-cooperative case. 2) The effect of the non-cooperative access mechanism: As mentioned in Section III-D, the disagreement point determines the bargaining power of each player and affects the bargaining result. The effect of the non-cooperative access mechanism utility (disagreement point) is shown in Figure 12. When the nodes adopt ETT as a non-cooperative access mechanism, the SR has the highest NBS cooperative share compared to ESTT and EAP (and vice versa for EAP). When EAP is used in the non-cooperative share, the SR has the lowest cooperative share but it has the highest increasing rate with PU activity. 3) The effect of the power evaluation factor CK : Figure 13 shows the SR free spectrum share percentage (from the SU and SR original shares) as a function of energy evaluation factor CK . As shown in the figure, as the value of CK increases the amount of share the SR gets increases as its power value increases. That results in decreasing the SU shares and, subsequently, its throughput to the point where the SU cooperation throughput may be lower than the non cooperative one. At this point, the SU still achieves a higher utility as it transmits at lower throughput but with a higher efficiency that leads to an enhancement in the total utility compared to the non-cooperative case. Whether the SU achieves throughput enhancement or not depends on the value of the energy evaluation factor, the PU activity and the cooperation level. Figure 14 shows the PU activity threshold ρth for SU throughput to benefit form cooperation. The region to the left of every curve indicates the values of CSU = CSR and ρ where the SU achieves a beneficial cooperation in terms of the throughput. Also, it is clear that, as the cooperation level between the SU and SR increases the threshold value of CSU = CSR increases. This mean that, the SU and SR throughput enhancement at higher cooperation levels is able to compensate any increase in the energy consumption occurs compared to at lower levels, even if the nodes have a higher evaluation for their energy. For example, in L1a , the SU achieves a higher throughput for CSU = CSR lower than approximately 0.225 for any value of ρ. From CSU = CSR ≈ 0.225 to 0.3 the cooperation is bene-
10
0.6 0.4
Non-cooperative L1a and L1b
0.2
0
4 3 2 1 0
10 20 30 40 50 60 70 80
Coop. L2
0
10
PU Activity Level (ρ) (%)
Fig. 7: SU efficiency (ηSU ) vs. PU activity (ρ)(%).
40
50
60
70
80
40 30 20 10
2.5 2 1.5 0
10 20 30 40 50 60 70 80
PU Activity (ρ)(%)
Fig. 10: SU and SR normalized utility in the cooperative mode for cooperation level L1b .
10
20
30
40
50
60
70
80
Fig. 8: SU normalized throughput vs. PU
Fig. 9: SR free spectrum shares for differ-
activity (ρ)(%) .
ent cases at L1b .
Normalized Throughput
3
0
PU Activity Level (ρ)(%)
3.5 SU SR
3.5
Normalized Utility
30
50
PU Activity (ρ)(%)
4
1
20
EAP non-cooperative EAP cooperative NBS based cooperative
60
75
SU SR
3
SR free spectrum share (%)
0
L2
Non Cooperative Coop. L1a or L1b
SR free spectrum share (%)
0.8
SU Normalized throughput
Transmission efficiency (η)
5 1
2.5 2 1.5 1
0
10 20 30 40 50 60 70 80
PU Activity (ρ)(%)
Fig. 11: SU and SR normalized throughput in cooperative mode for cooperation level L1b .
fits for the SU after certain values of ρ. For CSU = CSR ≥ 0.3 the SU cannot get an enhancement in the throughput at any value of ρ. 4) Energy efficiency evaluation: Figure 15 shows the energy performance (normalized throughput to the normalized energy ratio) for NBS based cooperation for different cooperation levels compared to the non-cooperative counterparts. As indicated in the figure, cooperation enhances the energy performance more than in the non-cooperative case. Also, as the level of cooperation increases, the energy performance improves as the nodes transmit more packets at lower power. In all cases, the energy efficiency reduces as the PU activity increases with a more severe negative effect on the noncooperative cases. C. Node Pairing and Channel Allocation In these experiments, we evaluate the node pairing and channel allocation problem. We consider the EAP access mechanism in all experiments. All problems are formulated in CPLEX [20] with a confidence interval of 90%. 1) Effect of demand satisfaction percentage (β): Figure 16 compares the performance of BBS-1 and BBS-2 in terms of the average throughput for all nodes and for slow nodes
EAP ETT ESTT
70 65 60 55 50 45 40
0
10
20
30
40
50
60
70
80
PU activity (ρ)(%)
Fig. 12: SR NBS shares for different non-cooperative access mechanisms at L1b .
(nodes need SRs help) only. At a low value of β, BBS1 barely satisfies the demand of the slow nodes and gives the rest of resources to the nodes with high data rate. That results in low average throughput for the slow nodes but a high value of throughput averaged over all nodes. As β increases, the resource allocation is changed to satisfy the slow nodes’ demand (for example, assigning channels with lower PU activity to slow SUs), that may result in lowering the fast nodes’ rate and the total network rate. As a result, the slow nodes average rate increases and the average rate of all nodes decreases. The same trend continues until a certain value of β (0.4 in this experiment), where after that, there is no solution for the problem. For BBS-2, the achieved throughput is mainly constant for different values of β as expected and the value of β is constant for all nodes. 2) Effect of PU activity ρ: In this experiment, we study the effect of the PU activity on the achieved throughput for BBS2. To show the effect of node cooperation on the throughput for different values of ρ, we compare the throughput when cooperation is enabled between SUs with that when SUs use only direct transmission (direct transmission can be enforced by setting the value of ynn = 1, ∀n ∈ N in the optimization problem formulation). Figure 17 shows the normalized throughput as a function of ρ. As can be inferred from the
11
80
L1b L2
70 60 50 40 30
60
L1a
50
L1b
Total throughput/ Total energy
L1a
PU Activity threshold (%)
SR free spectrum share (%)
90
L2
40 30 20 10 0
0
0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8
0
0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8
CSU =CSR
3 2 1
Non-Coop. L1a Coop. L1a Non-Coop. L1b
0
Coop. L1b Non-Coop L2
-1
Coop. L2
0
CSU =CSR
10
20
30
40
50
60
70
80
PU Activity (ρ)(%)
Fig. 13: SR share vs. CK = CSU = CSR
Fig. 14: The PU activity threshold for SU
Fig. 15: Energy efficiency for non-
and ρ = 50%
throughput enhancement.
cooperative EAP.
2
1.5 1.25 1 0.75 0.5 0.25
0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1
β
2.25
2.75
BBS-2, all nodes
Normalized throughput
Throughput (Mbps)
1.75
Normalized throughput
3 BBS-1, all nodes BBS-2, all nodes BBS-1, slow nodes BBS-2, slow nodes
2.5 2.25 2 1.75 1.5 1.25 1
20
30
40
50
60
70
80
Average PU activity (ρ)(%)
BBS-2, slow nodes BBS-2, all nodes
2 1.75 1.5 1.25 10
20
30
Number of secondary nodes
Fig. 16: Average throughput vs. β for the
Fig. 17: Average normalized throughput
Fig. 18: Average normalized throughput
two proposed optimization problems.
vs. average PU activity ρ.
VS. number of nodes for C = 2.
figure, the cooperation-enabled throughput is always higher than that of the direct transmission and the enhancement increases as the PU activity increases because the cooperation can reduce the negative effect of PUs interruption compared to direct transmission. 3) Effect of the number of secondary nodes: As shown in Figure 18, for the slow nodes, the average normalized throughput increases as the node density increases because the availability of potential relays increases. The average normalized throughput for the entire network increases with an even higher rate than that of the slow nodes. That can be understood by referring to Figure 11 where as a result of cooperation, the relay (fast node) gets a much higher increase in the throughput compared to the nodes that it helps. VI. C ONCLUSIONS AND F UTURE R ESEARCH In this paper, we introduced a spectrum-efficient bargainingbased resource allocation framework for cooperative secondary users in cognitive radio networks. This framework takes into consideration the effect of the PU activity on the performance of the SUs. Our analytical and numerical results demonstrated the significant improvements in the successful free spectrum utilization and throughput achieved by the two-hop cooperative transmission as compared to the direct transmission. Based on this efficient way of utilizing the available free spectrum,
we proposed our cooperation framework between a secondary user and its relay. The cooperation is modeled as a resource exchange process where the secondary user vacates part of its dedicated free access time to the secondary relay in return for its relaying power. The interaction between a primary user, a secondary user and a secondary relay is modeled using a discrete time Markov chain to obtain different transmission characteristics like efficiency and throughput. The obtained characteristics are used to calculate a node utility function that combines both the achieved throughput and consumed energy. Based on this utility, Nash Bargaining Solution (NBS) is used to determine the secondary user and the relay free spectrum access shares in case of cooperation. We derived the conditions under which cooperation improves the performance of both cooperating nodes. Finally, considering a multi-channel multiSU secondary infrastructure network, by using the bargainingbased free spectrum time shares, we proposed two optimal joint channel allocation and node pairing schemes. The first scheme aims at maximizing the total network throughput, whereas the second scheme minimizes the maximum (among SUs) difference between the throughput and the rate demand. Our results showed that the cooperation gains are more noticeable when (i) the PU is highly active or (ii) the node density is high. In the future, we aim to optimize each secondary nodes’ free spectrum share jointly with node pairing and channel
12
allocation.We will also consider designing distributed resource allocation schemes and compare them with the centralized schemes proposed in this paper. A PPENDIX PU Stand-alone Model In this appendix, we develop the PU stand-alone DTMC model that used to calculate the PU transition probabilities for a given value for PU activity level ρ. The state space of the stand-alone DTMC consists of one idle state (denoted by I) and M active states (denoted by A1 , A2 , . . . , AM ), where M is the number of time slots required to transmit a certain packet. In Figure 19, we depict the stand alone DTMC for M states. For simplicity, we assume a fixed packet size and there is no new arrival during the ongoing transmission.
As the transition probabilities between different active states equal to 1, we have equal state occupancy for all active states πA . Given that πA = 1 − πI , PP UI can be such that πAM = M written as: πA (1 − PP UA ) PP UI = 1 − . (47) M (1 − πA ) To ensure that both PP UI and PP UA values are in the range from 0 to 1, we set PP UA in the following range: 1 ≥ PP UA ≥ 1 −
M (1 − πA ) . πA
(48)
For the PU, we define the PU activity level ρ as the percentage of time the PU is active. The desire value of ρ is obtained by changing the PU stand-alone probabilities such that: M X ρ = πA = πA i . (49) i=1
Fig. 19: Stand-alone Markov chains for PU transmission consumes M time slots.
The steady-state occupancy distribution, denoted by π, can be derived from the transition diagram of the DTMC shown in Figure 19. The steady-state probability of being in state j ∈ {A1 , A2 , . . . , AM , I}, denoted by πj , represents the percentage of time the PU stays in state j. Because the DTMC is irreducible, π is obtained by solving the following two equations [21]: π
= π×P
(43)
1
= π × 1,
(44)
where π = [πA1 , . . . , πAM , πI ], P is the (M + 1) × (M + 1) transition probability matrix, and 1 = [1, 1, . . . , 1](M +1)×1 . def PM Let πA = i=1 πAi , then πI = 1 − πA , and M = (N − 1), the values of PP UA and PP UI are calculated by solving equations (43) and (44) giving that (πI = 1 − πA ). The values of PP UA and PP UI are calculated as follows:
By referring to Figure 19, for a stand-alone DTMC of M +1 states, (43) can be written as: [πA1 , . . . , πAM , πI ] = [π1 , . . . , πM , πI ]× 0 1 0 ... 0 0 0 1 ... 0 .. . . . . . . . . . . . . . . PP UA · · · · · · · · · (1 − PP UA ) (1 − PP UI ) · · · · · · · · · PP UI (45) By solving the first or the last equation, we obtain the following equation: πAM (1 − PP UA ) = πI (1 − PP UI ).
(46)
The value of the chosen transition probabilities affects the SU performance as it changes the interruption rate caused by the PU. Figure 20 shows an example of three different PU activity patterns (different values of PP UA ) at, approximately, the same value of ρ. The figure shows the effect of the PU activity pattern on the availability and the width of the white spaces at the same channel utilization level. At low value of PP UA , the probability that the PU, immediately, starts a new transmission after the current one is low compared to higher values of PP UA where the PU is more likely to transmit a series of continuous packets without time gaps. That means, for the same channel utilization level, at low value of PP UA the PU interruptions to the SU’s transmissions will be higher than at higher values of PP UA . Figure 21 shows the performance of the SU’s transmission efficiency for different values of PP UA and for the averaged efficiency when PP UA changes over the range from 0.2 to 0.8. As shown in the figure, and as described before, for the same value of PU activity level ρ, at low values of PP UA , the SU has a lower transmission efficiency as it is more prone to the PU interruption than at the higher values.
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PPU =0.2 A
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0
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PU Activity Level (ρ) (%) Fig. 21: SU transmission efficiency at different values of PP UA . at cooperation level L2 Mohamed AbdelRaheem (S13-M16) is an assistant professor of Electrical Engineering at Assiut University, Egypt. He received his B.Sc. and M.Sc. in Electrical Engineering from Assiut University in 2004 and 2010 respectively and his Ph.D. in Electrical Engineering from Virginia Tech in 2015. His research interests include wireless networking, especially spectrum sharing, cognitive radio network, cooperative communication and LTE-U.
Mohammad J. Abdel-Rahman (S12-M15) received the PhD degree in electrical and computer engineering from The University of Arizona, Tucson, AZ, in 2014. He is currently a research associate with the Department of Electrical and Computer Engineering, Virginia Polytechnic Institute and State University, Blacksburg, VA. His research interests include the areas of wireless communications and networking, with emphasis on resource management, adaptive protocols, and security issues. He serves as a reviewer for several international conferences and journals. He is a member of the IEEE. Mustafa El-Nainay (M13) is an Associate Professor of the Computer and Systems Engineering department at Alexandria University, Egypt. He is also the associate director of the Virginia TechMiddle East and North Africa (VT-MENA) program for administration and research and adjunct faculty at Virginia Tech. He received his B.Sc. and M.Sc. in Computer Science from Alexandria University in 2001 and 2005 respectively and his Ph.D. in Computer Engineering from Virginia Tech in 2009. His research interests include wireless and mobile networks, cognitive radio and cognitive networks, and software testing automation and optimization. Scott F. Midkiff (S82-M85-SM92) is a Professor and the Vice President for Information Technology and the Chief Information Officer with Virginia Tech, Blacksburg, VA, USA. From 2009 to 2012, he was the Department Head of the Bradley Department of Electrical and Computer Engineering, Virginia Tech. From 2006 to 2009, he served as the Program Director with the National Science Foundation. His research interests include wireless and ad hoc networks, network services for pervasive computing, and cyber-physical systems.
