FMAC: A Fair MAC Protocol for Coexisting Cognitive Radio Networks

Transcription

1 FMAC: A Fair MAC Protocol for Coexisting Cognitive Radio Networks Yanxiao Zhao ECE Department South Dakota School of Mines and Technology Rapid City, SD 5771 yanxiao.zhao@sdsmt.edu Min Song EECS Department The University of Toledo Toledo, OH 4366 Min.Song@utoledo.edu ChunSheng Xin CS Department Norfolk State University Norfolk, VA 2354 cxin@nsu.edu Abstract Cognitive radio is viewed as a disruptive technology innovation to improve spectrum efficiency. The deployment of coexisting cognitive radio networks, however, raises a great challenge to the medium access control (MAC) protocol design. While there have been many MAC protocols developed for cognitive radio networks, most of them have not considered the coexistence of cognitive radio networks, and thus do not provide a mechanism to ensure fair and efficient coexistence of cognitive radio networks. In this paper, we introduce a novel MAC protocol, termed fairness-oriented media access control (FMAC), to address the dynamic availability of channels and achieve fair and efficient coexistence of cognitive radio networks. Different from the existing MACs, FMAC utilizes a three-state spectrum sensing model to distinguish whether a busy channel is being used by a primary user or a secondary user from an adjacent cognitive radio network. As a result, secondary users from coexisting cognitive radio networks are able to share the channel together, and hence to achieve fair and efficient coexistence. We develop an analytical model using two-level Markov chain to analyze the performance of FMAC including throughput and fairness. Numerical results verify that FMAC is able to significantly improve the fairness of coexisting cognitive radio networks while maintaining a high throughput. I. INTRODUCTION Cognitive radio is viewed as a disruptive technology innovation to improve spectrum efficiency. It is expected that the cognitive radio technology will soon emerge from laboratory trials to become a general-purpose programmable radio that serves as a universal platform for wireless networks development. Thus cognitive radio networks (CRNs) have attracted a great attention in the literature. In addition, the government, particularly the spectrum authority, has been making efforts to promote CRNs to enhance access to radio spectrum. For instance, the Federal Communications Commission (FCC) has proposed the 5 MHz national broadband plan. CRNs are expected to be ubiquitous and multiple CRNs often co-exist with each other. Therefore, the fair and efficient coexistence of CRNs is critical to the success of CRNs. Due to the dynamic availability of channels in CRNs, it is very challenging to design a fair and efficient MAC protocol for coexisting CRNs. There have been many MAC protocols proposed for CRNs [1] [5]. However, those studies have not considered coexistence of CRNs, and thus they do not have a mechanism incorporated in the MAC to ensure fair and efficient coexistence of CRNs. In the existing CRN MAC protocols, the two-state sensing model is employed, which classifies a channel into only two states: idle or busy. When a secondary user (SU) of a CRN, say CRN A, detects that the channel is busy, it perceives that he channel is being used by the primary user (PU). It will simply give up the current channel and switch to a new one, together with its communication peer (another SU of the same CRN). However, the channel is not necessarily being used by the PU when the channel is busy. It is possible that another SU in a different CRN, say CRN B, which uses a different waveform, is accessing the channel. The SU in CRN A could not know this because it does not recognize the waveform of CRN B, and thus it has to take a conservative approach, giving up the current channel and switching to a new one. However, simply switching to a new channel may result in significant overhead, as channel switching may take a significant time. Note that different from channel switching in WiFi, which is within a small band and takes a small time, channel switching in CRNs may be involved in a switching across a large spectrum band, which may require a long time of radio hardware tuning, and hence can result in one or more magnitudes of order larger switching time.

2 2 Furthermore, with the rapid proliferation of wireless services, the number of SUs from multiple CRNs typically exceeds the number of channels. This results in a situation where it is difficult to find a free channel to be switched to. Due to these reasons, channel switching is often not the best option. Therefore, several CRNs often have to co-exist on the same channel. In this scenario, if a MAC based on the two-state sensing model is used, then when the SUs of one CRN are accessing the channel, the SUs of other CRNs often starve. Hence such a MAC protocol is not coexistence friendly and results in poor fairness. For a MAC to be coexistence friendly, the SUs of one CRN must be able to share a channel with the SUs of another CRN. In this paper, we propose a novel MAC protocol, termed fairness-oriented media access control (FMAC), for CRNs, to achieve fair and efficient coexistence while significantly reduce the channel switching overhead. Different from the existing CRN MACs, FMAC is designed based on a three-state sensing model which classifies a channel into three states: H (idle), H 1 (occupied by a PU), and H 2 (occupied by an SU). The three-state sensing model is first proposed in [6], which focuses primarily on how to accurately detect each of the three states. In this paper, we design a novel MAC protocol based on the three-state sensing model. Specifically, when the channel is detected as busy, FMAC does not simply let the node switch to a new channel. Instead, it utilizes a spectrum sensing algorithm to distinguish that the busy channel is due to a PU signal or an SU signal of another CRN. In the latter case, the SUs of a CRN can have the option to share the channel with the SUs of other CRNs that are currently using the channel. Specifically, with FMAC, when an SU detects that a channel state is H 2, the SU may choose to compete for channel access with the SU (of another CRN) that are accessing the channel. In other words, as long as a channel is not used by the PU, the SUs of all CRNs can fairly compete for the channel. Therefore, FMAC achieves excellent fairness for coexisting CRNs. Furthermore, we develop an analytical model to evaluate the performance of FMAC using a two-level Markov chain. The first level represents the conditional probability transiting from one state to another state without considering the PU activity. The second level illustrates a renewal process for a specific state when the PU reappears. From the two-level Markov chain model, the access probability of SUs is mathematically derived, which is a significant parameter to evaluate the network performance. We derive a closed-form solution for the throughput of SUs. We will also employ a new fairness performance metric, All-level Fairness for All (ALFA), to evaluate the comprehensive fairness, from a short time period (microlevel) to a long time period (macro-level). Numerical results verify that FMAC can significantly improve ALFA among multiple coexisting CRNs, while not degrading throughput compared with existing MAC protocols. The rest of the paper is organized as follows. In Section II, we briefly introduce the related work. Section III introduces the system model and spectrum sensing technology. In Section IV, we describe the FMAC protocol. Section V presents the performance analysis of FMAC. The numerical results are presented in Section VI. Concluding remarks are drawn in Section VII. II. RELATED WORK For SUs to access a channel, a cognitive MAC protocol is critical. Although the concept of cognitive radio was introduced over a decade ago, the MAC design in CRNs is still in its infancy. The IEEE working group has been making efforts on proposing a standard MAC protocol for Wireless Regional Area Network (WRAN) [7]. A general MAC design in CRNs is still an open problem and has received increasing attention recently. In [8], the authors developed a decentralized cognitive MAC protocol for CRNs. The sensing errors and collisions between SUs and PUs are taken into account in this MAC protocol. In [9], a cognitive MAC protocol was designed for multi-channel wireless networks, where each available channel is divided into recurring superframes and a rendezvous channel is assigned delicately for coordination among SUs. Several researchers have dedicated themselves to design a cognitive MAC based on the well-known IEEE The authors in [1] considered a CRN with a single channel and assumed that the PU operates on a slot-by-slot basis. Each slot is further divided into mini-slots for SU transmission. In [11], authors designed a periodic MAC protocol, in which SUs cooperate to periodically sense channels, report channel states, and exchange control signals. In the MAC design, spectrum sensing is a fundamental issue and plays two critical roles in CRNs. In the existing studies on MAC design, the two-state model is predominantly employed; that is, the state of a channel is classified into H (idle) or H 1 (busy). This two-state model is predominantly used for CRNs in the literature. However, as discussed in the preceding section, it is not suitable for a scenario with multiple co-existing CRNs.

3 3 In this paper, we design a MAC protocol utilizing the three-state sensing model. The performance analysis for CRNs is a challenging problem, but has received considerable attention. The throughput limit in the presence of dynamic and distributed spectral activity was studied in [12] [13]. Quality of service (QoS) was involved in the throughput analysis recently [14]. In contrast, there is little research on fairness performance of SUs among multiple co-existing CRNs. In this paper, we design a MAC protocol with a goal to achieve fairness among SUs from co-existing CRNs. An analytical model is developed to study the performance of the designed MAC, including throughput and fairness. III. SYSTEM MODEL AND SPECTRUM SENSING We consider a system with one PU, and M co-existing CRNs, denoted as CRN 1,..., CRN M. The CRN i has N i SUs. Each SU is equipped with two radios; one is dedicated for spectrum sensing and the other is for data transmission. Within each CRN, we assume that a centralized device, e.g., a base station (BS), exists. The SUs of the same CRN conduct cooperative sensing so that the BS makes a final decision on the channel state. Spectrum sensing requires a certain amount of time. Let DT denote the spectrum sensing time. That is, SUs need to spend a duration of DT to determine the channel state. The channel state is updated periodically every DT period of time. As discussed previously, the MAC protocols based on the two-state sensing model do not work properly when multiple CRNs co-exist, because those MACs result in an unfair channel access among SUs from different CRNs. To attack this problem, we propose to use a three-state smart sensing model in FMAC. The distinction between the two-state and the three-state models is that the state H busy is split into H 1 (occupied by a PU) and H 2 (occupied by an SU). The three-state sensing model is described as: r i = n i, H x p + n i, H 1 x s + n i, H 2, (1) where x s is the signal that an SU transmits, x p is the signal that the PU transmits, r i is the signal that an SU received, n i is the zero-mean additive white Gaussian noise (AWGN). When the channel is detected as busy, FMAC utilizes a spectrum sensing algorithm to distinguish whether a busy channel is due to a PU signal or an SU signal of another CRN. A two-stage detection technology is utilized for this purpose, as described in [6]. Specifically, in the first stage, energy detection is employed to identify whether a channel is idle or not. If the channel is busy, the received signal is further analyzed at the second stage based on a distance estimation technique, with the objective to determine either H 1 or H 2. Using this sensing technology, SUs can determine a channel state to be H, H 1 or H 2. With FMAC, SUs take distinct actions based on each channel state, which will be described in detail in the subsequent section. IV. FMAC: FAIRNESS-ORIENTED MAC FMAC is designed based on the three-state smart sensing model, to achieve fairness among multiple coexisting CRNs. In a MAC protocol, fairness refers to the ability of an SU from one CRN to share a common channel with multiple users of other CRNs (hereafter multiple users mean that they are from different networks unless otherwise indicated). In this paper, the fairness performance is measured in terms of channel access time. For instance, if there are N users competing for a channel, the ideal fairness is achieved if each user accesses the channel for 1/N of the total period that the channel is available for SU access. In FMAC, PUs have a strictly higher priority over SUs, and thus two distinct channel access methods for PUs and SUs are employed. To guarantee the privilege of PUs, when PUs have traffic for transmission, they immediately begin to transmit when the channel is idle. Since it takes a while for SUs to withdraw from the channel, the PU waits for a period up to the tolerable maximum, denoted as T max (T max 2DT ), when an SU is accessing the channel. Moreover, when the PU transmit a message consisting of a burst of frames, we assume that the idle interval between two consecutive PU frames transmission is smaller than DT. Hence, the PU will continue to capture the channel until all frames of a burst have been transmitted. Prior to going into the details of FMAC, we discuss how an SU should respond to each channel state, when the SU has traffic to transmit. There are three possible states for a channel at any time, i.e., H, H 1 and H 2. An SU that has traffic for transmission takes distinct actions based on the detected state of the channel. Specifically, if the channel state is H 1, the SU does not simply switch to another channel. Instead, it keeps silent and continues to monitor the channel. If the channel state is H, the SU accesses the channel immediately. In contrast, if the channel state is H 2, the SU knows that the channel is

4 Fig. 1. Operation of MAC: (a) operation of a MAC with the twostate sensing model, (b) operation of FMAC. occupied by another SU, which may be from a different CRN, and can participate in competition for channel access. During SU transmission, the SUs keep sensing the channel. If the sensing result is H or H 2, SUs continue accessing the channel. However, they have to vacate the channel whenever the PU comes back. The operation of the FMAC protocol is illustrated in Fig. 1 (b), which is compared with a MAC with the two-state model in Fig. 1 (a). Note that once an SU accesses an idle channel, the channel state is changed from H to H 2 from the perspective of other SUs. Next we describe the details on how multiple SUs compete for the same channel under the state of H 2. In FMAC, the channel access scheme by SUs under state H 2 is based on the IEEE MAC protocol. Specifically, an SU monitors the channel activity when it has a packet to transmit. The SU starts transmitting only after an idle period equal to a Distributed Inter-Frame Space (DIFS). In the case that the channel is busy, i.e., another SU is currently occupying the channel, the SU randomly selects a backoff interval from [, W 1], where W represents the size of a contention window. The backoff time counter is decremented whenever the channel is sensed idle, stopped when a transmission is detected, and reactivated when the channel is sensed as idle again for a DIFS. The SU transmits when the backoff time counter reaches. In case that a collision occurs, i.e., two or more SUs transmit simultaneously, the same backoff mechanism is repeated. SUs continue sensing the channel during transmission or a backoff period. The packets transmission of an SU may be interrupted by the resurgence of the PU traffic. If the PU reappears to transmit packets, then after the PU s transmission, all SUs are treated to have the same opportunity as the interrupted SU to access the channel. In other words, all SUs enter a renewal process after the PU reappears. In the renewal process, an SU randomly selects a new backoff time from [, W 1]. Note that although FMAC is designed based on IEEE 82.11, we have made significant contributions to add the cognition or spectrum sensing capability that is required for operation in a scenario of co-existing CRNs, as well as design mechanisms to achieve fairness. As a legacy protocol, IEEE does not have the cognition or spectrum sensing capability. Spectrum sensing is the unique feature of CRNs and it is fully considered in the design of FMAC. A novel renewal process is proposed for the situation whenever the PU comes back. Furthermore, FMAC is based on the three-state sensing model and responds distinctly when the channel is used by the PU or another SU. This is critical to improve the fairness for coexistence of CRNs. At last, we utilize the same contention windows size to further improve the fairness. Recent studies pointed out that the fairness performance of IEEE is not satisfactory because of the binary exponential backoff technology [15]. As studied in [16], users with different contention window sizes have different channel access probabilities, which then results in poor fairness among users. Therefore to achieve optimal fairness among SUs, the binary exponential backoff technology is not adopted by FMAC. Instead, the same contention window size is used for all SUs, and hence the channel access probability is the same for all SUs, which results in optimal fairness. V. PERFORMANCE ANALYSIS In this section, we develop a novel mathematical model to analyze the performance of FMAC. We focus on two crucial performance metrics: throughput and fairness. First, we analyze the PU activity and provide a statistical model. Second, we model the operation of FMAC as a two-level Markov chain, from which the channel access probability of SUs is derived. At last, throughput and fairness are examined. A. PU Activity Analysis In this subsection, the PU behavior is studied with a focus on the probability that the channel is accessible or inaccessible by SUs, denoted as P and P 1, respectively. Let X be a random variable representing a time period that the PU is continuously transmitting on the channel. Let f X (x) denote the probability density function (pdf) for X. 4

5 5 Fig. 2 illustrates the PU traffic arrival and the channel occupation by the PU and SUs. Let a random variable Y represent the period that the channel is not accessible by SUs, caused by a PU transmission and the following spectrum sensing duration. With a little abuse of language, we say Y is the period of PU occupation of the channel. By examining Fig. 2, the following equation holds Y = ( X DT + 1 ) DT = X + DT. Given the distribution of X, let us derive the cumulative distribution function of Y, denoted by F Y (y). F Y (y) = Pr(x + DT y) = y DT Consequently, the pdf of Y can be written as: f Y (y) = F Y (y) f X (x)dx Let us consider a very long period of time t, and calculate the average value of Y in this period, denoted by E(Y ). We have E(Y ) = DT+t DT y f Y (y)dy. For example, if X follows the exponential distribution with parameter µ, i.e., then, we have and E(Y ) = f X (x; µ) = µexp{ µx}, f Y (y) = F Y (y) = µexp{ µ(y DT)} DT+t DT y µexp{ µ(y DT)}dy = 1 µ + DT. We assume that the PU traffic follows Poisson arrival with an arrival rate λ. Hence, the average number of PU traffic arrival time SU transmit DT PU tolerable delay PU transmit X Y SU transmit PU traffic arrival time PU tolerable delay PU transmit Time Fig. 2. Channel occupation by the PU and SUs. X denotes a period of PU transmission. Y denotes the period that the channel is not accessible by SUs, caused by a PU transmission and the following spectrum sensing duration. The PU tolerable delay is the period between the arrival time of the PU traffic and the time when the PU begins to transmit the PU traffic. arrivals of PU traffic is λ t in a period of t. Therefore, P 1 can be obtained as P 1 = λ t E(Y ) t = ( 1 + DT) λ. (2) µ Correspondingly, P can be obtained immediately as: B. SU Channel Access Probability P = 1 P 1. (3) We model the operation of an SU in FMAC as a Markov chain, with state w ( w W 1) indicating the backoff stage of the SU, as shown in Fig. 3 (a), in which the PU activity is fully taken into account. In this paper, we focus to analyze the saturation throughput (to be discussed), and hence we assume that each SU always has a packet to transmit at any time. There are total N SUs from all CRNs. For the sake of analysis, we virtually divide the time into slots based on the channel activity. Specifically, each slot is a period of either PU occupation, successful SU transmission, idle, or collision among multiple SUs. For a give time slot, the probability that it is a PU occupation slot is P 1. The probability that it is a successful SU transmission slot, denoted by P s (k), can be derived as: P s = P N P a (1 P a ) (N 1), (4) where P a is the channel access probability of each SU. The derivation of P a is postponed to the end of this subsection. The probability that a given slot is an idle slot is: P i = P (1 P a ) N. (5) The probability that a given slot is a slot of collision caused among multiple SUs, denoted by P cs, can be obtained as: [ P cs = P 1 (1 P a ) N N P a (1 P a ) N 1]. (6) An SU transmission starts when the backoff time counter reaches, i.e., when the Markov chain is in state. This transmission is either a successful transmission with a probability (1 P 1 P cs ); or a collision with other SUs, with a probability P cs ; or a collision with the PU, with a probability P 1. In the first two cases, the SU needs to randomly select another backoff time from [, W 1] for next transmission (either a new packet transmission, or a retransmission in case of collision). Therefore the transition probability from state to state k is 1 P 1 P cs W + P cs W = 1 P 1 W.

6 + " + +,+ 82!7"9559 #8$ 86 #%59 +, ,+, & '( *'( ,+ +,+ '( *'(,,,, Fig. 3. State transition diagram of the Markov chain; (a) the transition probability among the W states of the Markov chain, where each state may conduct a renewal process; (b) an example of the renewal process at state k. Note that the renewal process applies to each state. Next let us study the case with a non-zero time counter. At the backoff stage k,(k > ), there are three possibilities. Specifically, the time counter k can decrease to (k 1) with a probability of P i, or goes to a renewal process with a probability of P 1 if the PU reappears, or stay at the same time counter with a probability of (1 P 1 P i ). Note that the PU may reappear at any time and disturb a back off process. We assume that every SU enters a renewal process whenever the PU comes back for a transmission, no matter that the SU switches to a different channel or chooses to stay on this channel. In the renewal process, an SU randomly selects a backoff time j from [, W 1] and the Markov chain then transits to state j from state k with a probability of P1 W, which is illustrated as the lower level chain in Fig. 3 (a) and further described in Fig. 3 (b). Based on the above Markov chain model, the conditional probabilities of the two-level Markov chain can be written as follows, where P k,j represent the transition probability from state k to state j. P,k = 1 P 1 W + P 1 W = 1, for k [, W 1] W P k,k 1 = P i + P 1, for k [1, W 1] W P k,j = P 1 W, for k [1, W 1], j k 1, k P k,k = 1 P 1 P i + P 1 W, for k Next we will get W equilibrium equations of the Markov chain. The stationary probabilities of the states of a Markov chain is typically denoted by a vector π, with π = [ π, π 1,..., π W 1 ] where π is the stationary probability that the Markov chain is at the state. Since we have π j = π k P k,j, k, j [, W 1], the equilibrium equations can be written down as follows, (1 1 W )π = (P i + P 1 W )π 1 + P 1 W ( and for k [1, W 1], j,1 6 π j ), (7) ( P 1 W P 1 P i )π k = 1 W π + (P i + P 1 W )π k+1+ P 1 W ( π j ). (8) j k,k+1 From (7) and (8), we get π = W P i + (W 1) P 1 W P i + (W 1) P 1 + (W 1) 2. (9) In a general case that W >> 1, it is reasonable to assume that W = (W 1). Then π in Eq. (9) can be simplified as π = P i + P 1 P i + P 1 + W (1) Recalling that SU transmissions only occur at state, π is actually the transmission probability of SUs, which is denoted as P a. Substituting P i in Eq. (5) into Eq. (1), we get the following equation: P a = 1 W P (1 P a ) N + P 1 + W. (11) Note that Eq. (11) is a non-linear function. This can be solved through a numerical method and get the value of P a, given other parameters. P a is an important parameter and will be used in the throughput and fairness analysis in the next two subsections.

7 7 C. SU Throughput Analysis We concentrate on throughput analysis of SUs, and hence ignore the time periods of PU transmissions. As a result, the SU throughput is calculated as: θ = P s T s P i σ + P s T s + P cs T cs + P 1 T cp, (12) where σ is the duration of an idle time slot, T s is the average time of a successful SU transmission slot, T cs is the average time of a collision slot caused by other SUs, and T cp is the average time of a collision slot caused by the PU. By [16], T s and T cs can be represented as follows in case of the RTS/CTS access mechanism: T s = RTS + SIFS + δ + CTS + SIFS + δ + H + T DATA + SIFS + δ + ACK + DIFS + δ T cs = DIFS + RTS + δ The T cp is referred to as the tolerable delay of the PU in Fig. 2 and can be expressed as T cp = E[(1 + τ) DT], where τ follows a uniform distribution in [, 1]. Hence T cp is given as T cp = 3 DT. (13) 2 The saturation throughput is the optimization of Eq. (12) and represented as: θ = max{θ}. (14) It can be seen that several parameters such as W, P a, P 1, and N play significant roles in the calculation of throughput. We will evaluate their impacts in Section VI. D. Fairness Analysis As discussed in Section I, we will focus on the proposed fairness metric ALFA in our analysis. Suppose that N CRNs use FMAC to contend for channel access. Since no SU is permitted to occupy the channel during the transmission of the PU, the period of PU transmission is ignored with regard to the fairness analysis. Let denote a short period of time, termed a cycle. We record the transmission time of each CRN continuously in K cycles. Let the vector T(k) = [T 1 (k),..., T N (k)] denote the recorded transmission time of the N CRNs in the first k cycles (with a period of k ). Next we calculate the Jain Index on vector T(k) for 1 k K as J( T(k)) = ( 1 T T (k)) 2 N T(k) 2, (15) where 1 = [1, 1,...,1] is a 1 N row vector whose elements are all 1. The larger the Jain Index, the better the fairness is. In the ideal case, the Jain Index is 1. The ALFA is characterized by a Mean-Deviation Fairness Model (MDFM). Specifically, the mean denoted by E[ T] and the standard deviation denoted by D[ T] are calculated from J( T(1)) to J( T(K)) as follows E[ T] = 1 K D[ T] = 1 K K k=1 K J( T(k)), (16) k=1 ( J( T(k)) E[ T]) 2. (17) A large E[ T] together with a small D[ T] indicates a good ALFA. A small E[ T] together with a large or small D[ T] indicates a poor ALFA. VI. NUMERICAL RESULTS In this section, the throughput and fairness of FMAC will be evaluated and compared with another scheme, in which the IEEE is used together with the two-state sensing model. The latter scheme is called as Two-state MAC (TMAC). We will show that the fairness of FMAC is significantly improved, while maintaining similar throughput as TMAC. The major parameters for channel access are listed in Table I. A. Throughput Evaluation In the first experiment, we study three scenarios with 2, 3, and 4 co-existing CRNs, respectively. Each CRN is assumed to have 1 users. We assume that the PU traffic arrival rate λ is.2, and the mean PU transmission time 1 µ is 1, which result in a PU activity probability P.8 by Eq. (3). In Fig. 4, each curve represents the throughput of FMAC or TMAC as a function of the contention window size. Note that the throughput TABLE I PARAMETERS FOR CHANNEL ACCESS Parameter Value MAC header 272 bits PHY header 128 bits ACK 112 bits + PHY header RTS 16 bits + PHY header CTS 112 bits + PHY header Channel Bit Rate 1 Mbits/s Propagation Delay 1 µs Slot Time 5 µs SIFS 28 µs DIFS 128 µs DT 6 µs

8 8 has been normalized with regard to the nominal channel data rate. With TMAC, only SUs within the same CRN is able to access the channel at any time. Thus, the number of SUs that compete for channel access is always 1, no matter how many CRNs co-exist. In contrast, with FMAC, the SUs of all co-existing CRNs have the opportunity to share the channel. The number of competing SUs is larger with FMAC. For instance, with 2 co-existing CRNs, there are total 2 SUs (N = 2) that share the channel. With 3 co-existing CRNs, 3 SUs (N = 3) compete for the channel. We can see that the optimal contention window size, i.e., the contention window size that maximizes the throughput, increases when the number of SUs grows. From Fig. 4, one can see that all scenarios have similar optimal throughput, which is the throughput at the optimal contention window size, i.e., the peak point of a curve in the figure. To further verify this, Fig. 5 plots the optimal throughput of TMAC and FMAC with 2 co-existing CRNs. This figure indicates that the optimal throughput of FMAC only slightly decreases compared with the one of TMAC. In the second experiment, we examine the impact of the PU activity on the SU throughput. We vary the PU traffic arrival rate λ to produce varying PU activity probabilities P, and plot the optimal throughput in Fig. 6. We can see that the optimal throughput of SUs gradually decreases when P or the PU activity decreases. This is because SUs have a smaller opportunity to transmit when the PU occupies the channel for more time. From Figs. 4 and 6, we can see that FMAC is able to maintain a similar optimal throughput as the one of TMAC. B. Fairness Evaluation In order to evaluate the fairness performance, two scenarios with 5 and 1 co-existing CRNs are studied. Throughput TMAC FMAC (N=2) FMAC (N=3) FMAC (N=4) Window Size Fig. 4. Throughput of FMAC and TMAC, P =.8 Optimal Throughput TMAC FMAC The total number of SUs from multiple CRNs Fig. 5. Optimal throughput of FMAC and TMAC, P =.8 Optimal Throughput TMAC FMAC P Fig. 6. Optimal throughput of FMAC and TMAC as a function of the PU activity (P ) We assume each CRN contains the same number of SUs. The observation period is 2 cycles. The is assumed to be equal to the time to transmit 5 frames. In the case of FMAC, all CRNs contend for channel access with an equal access probability P a. With TMAC, we assume that each CRN has 5 successive frames to transmit once it grasps the channel. Fig. 7 shows the Jain Index for 2 cycles, with 5 and 1 CRNs, respectively. It can be seen that the fairness of FMAC is dramatically improved compared with TMAC. In particular, the fairness of FMAC is very good even in a short period of time. Next we examine the influence of the number of CRNs on fairness. When the number of co-existing CRNs increases from 5 to 1, the fairness of TMAC degrades drastically. This suggests that the number of CRNs has a significant impact on fairness and a smaller number of CRNs achieves better fairness. However, in FMAC, the fairness is hardly affected by the number of CRNs. This further verifies the advantages of FMAC, from the perspective of fairness, especially with a large number of co-existing networks.

9 9 Fig. 7. Jain Index CRNs with FMAC 1 CRNs with TMAC 5 CRNs with FMAC 5 CRNs with TMAC Time Period ( ) Jain Index calculated from 1 to 2 for FMAC and TMAC TABLE II MEAN-DEVIATION FAIRNESS MODEL (MDFM) 5 SUs 5 SUs 1 SUs 1 SUs (FMAC) (TMAC) (FMAC) (TMAC) E[ T] D[ T] At last, we evaluate ALFA and record the results of E[ T] and D[ T] in Table II. It can be seen that the ALFA of FMAC is very good, with E[ T] as.913 for 5 CRNs and.8768 for 1 CRNs, and D[ T] as.15 for 5 CRNs and.132 for 1 CRNs. In contrast, the ALFA of TMAC is poor, with a considerably lower mean and higher deviation than FMAC. VII. CONCLUSIONS In this paper, we have considered multiple CRNs coexisting in an area and proposed a fairness-oriented MAC (FMAC) to improve the fairness among SUs from different CRNs. FMAC is based on the three-state sensing model. SUs take distinct actions for each state of the channel. In addition, FMAC fully takes the PU activity and fairness among CRNs into account. A twolevel Markov chain model and an analytical model have been developed for the proposed FMAC. Furthermore, the throughput and fairness of FMAC have been thoroughly examined. Numerical results have verified that the fairness of FMAC is significantly improved, while maintaining a high throughput. ACKNOWLEDGEMENT The research of Min Song is supported in part by NSF CAREER Award CNS and NSF IPA Independent Research and Development (IR/D) Program. Any opinion, finding, and conclusions or recommendations expressed in this material, are those of the authors and do not necessarily reflect the views of the National Science Foundation. The research of ChunSheng Xin is supported in part by NSF under grants CNS , CNS , and ECCS REFERENCES [1] Y. Kondareddy and P. Agrawal, Synchronized mac protocol for multi-hop cognitive radio networks, in IEEE ICC, 28, pp [2] M. Timmers, S. Pollin, A. Dejonghe, L. Van der Perre, and F. Catthoor, A distributed multichannel mac protocol for multihop cognitive radio networks, IEEE Transactions on Vehicular Technology, vol. 59, no. 1, pp , 21. [3] X. Zhang and H. Su, Cream-mac: Cognitive radio-enabled multi-channel mac protocol over dynamic spectrum access networks, Selected Topics in Signal Processing, IEEE Journal of, vol. 5, no. 1, pp , 211. [4] S. Yoo, H. Nan, and T. Hyon, Dcr-mac: distributed cognitive radio mac protocol for wireless ad hoc networks, Wireless Communications and Mobile Computing, vol. 9, no. 5, pp , 29. [5] Y. Wang, P. Ren, and G. Wu, A throughput-aimed mac protocol with qos provision for cognitive ad hoc networks, IEICE Transactions on Communications, vol. 93, pp , 21. [6] Y. Zhao, M. Song, C. Xin, and M. Wadhwa, Spectrum sensing based on three-state model to accomplish all-level fairness for co-existing multiple cognitive radio networks. in IEEE INFOCOM, 212, pp [7] C. Stevenson, G. Chouinard, Z. Lei, W. Hu, S. Shellhammer, and W. Caldwell, Ieee 82.22: The first cognitive radio wireless regional area network standard, IEEE Communications Magazine, vol. 47, no. 1, pp , 29. [8] Q. Zhao, L. Tong, A. Swami, and Y. Chen, Decentralized cognitive mac for opportunistic spectrum access in ad hoc networks: A pomdp framework, IEEE Journal on Selected Areas in Communications, vol. 25, no. 3, pp , 27. [9] C. Cordeiro and K. Challapali, C-mac: A cognitive mac protocol for multi-channel wireless networks, in IEEE DySPAN, 27, pp [1] Y. Bae, A. Alfa, and B. Choi, Performance analysis of modified ieee based cognitive radio networks, IEEE Communications Letters, vol. 14, no. 1, pp , 21. [11] D. Xue, E. Ekici, and X. Wang, Opportunistic periodic mac protocol for cognitive radio networks, in Proceedings of the IEEE Global Telecommunications Conference, 21, pp [12] S. Jafar and S. Srinivasa, Capacity limits of cognitive radio with distributed and dynamic spectral activity, IEEE Journal on Selected Areas in Communications, vol. 25, no. 3, pp , 27. [13] S. Akin and M. Cenk Gursoy, Performance analysis of cognitive radio systems under qos constraints and channel uncertainty, IEEE transactions on wireless communications, vol. 1, no. 9, pp , 211. [14] P. Wang, D. Niyato, and H. Jiang, Voice-service capacity analysis for cognitive radio networks, IEEE Transactions on Vehicular Technology, vol. 59, no. 4, pp , 21. [15] G. Berger-Sabbatel, A. Duda, M. Heusse, and F. Rousseau, Short-term fairness of networks with several hosts, Mobile and Wireless Communication Networks, pp , 25. [16] G. Bianchi, Performance analysis of the ieee distributed coordination function, IEEE Journal on Selected Areas in Communications, vol. 18, no. 3, pp , 2.