IN conventional spectrum management, most of the spectrum

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1 2164 IEEE TRANSACTIONS ON VEHICULAR TECHNOLOGY, VOL. 60, NO. 5, JUNE 2011 A Two-Level AC Protocol Strategy for Opportunistic Spectrum Access in Cognitive Radio Networks Qian Chen, Student ember, IEEE, Ying-Chang Liang, Fellow, IEEE, ehul otani, ember, IEEE, and Wai-Choong (Lawrence) Wong, Senior ember, IEEE Abstract In this paper, we consider medium access control (AC) protocol design for random-access cognitive radio (CR) networks. A two-level opportunistic spectrum access strategy is proposed to optimize the system performance of the secondary network and to adequately protect the operation of the primary network. At the first level, secondary users (SUs) maintain a sufficient detection probability to avoid interference with primary users (PUs), and the spectrum sensing time is optimized to control the total traffic rate of the secondary network allowed for random access when the channel is detected to be available. At the second level, two AC protocols called the slotted cognitive radio ALOHA (CR-ALOHA) and cognitive-radio-based carrier-sensing multiple access (CR-CSA) are developed to deal with the packet scheduling of the secondary network. We employ normalized throughput and average packet delay as the network metrics and derive closed-form expressions to evaluate the performance of the secondary network for our proposed protocols. oreover, we use the interference and agility factors as the performance parameters to measure the protection effects on the primary network. For various frame lengths and numbers of SUs, the optimal performance of throughput and delay can be achieved at the same spectrum sensing time, and there also exists a tradeoff between the achievable performance of the secondary network and the effects of protection on the primary network. Simulation results show that the CR-CSA protocol outperforms the slotted CR-ALOHA protocol and that the PUs activities have an influence on the performance of SUs for both the slotted CR-ALOHA and CR-CSA. Index Terms Cognitive radio networks, CR-ALOHA, CR-CSA, opportunistic spectrum access. anuscript received July 27, 2010; revised December 23, 2010 and arch 16, 2011; accepted arch 20, Date of publication April 11, 2011; date of current version June 20, This work was supported in part by the Interactive and Digital edia Project Office, edia Development Authority of Singapore, through the National Research Funding Grant NRF2007ID- ID on Life Spaces. The review of this paper was coordinated by Prof. J. Chun. Q. Chen is with the Department of Electrical and Computer Engineering, National University of Singapore, Singapore , and also with the Institute for Infocomm Research, A*STAR, Singapore ( qchen@i2r. a-star.edu.sg). Y.-C. Liang is with the Institute for Infocomm Research, A*STAR, Singapore ( ycliang@i2r.a-star.edu.sg).. otani and W.-C. Wong are with the Department of Electrical and Computer Engineering, National University of Singapore, Singapore ( motani@nus.edu.sg; elewwcl@nus.edu.sg). Color versions of one or more of the figures in this paper are available online at Digital Object Identifier /TVT I. INTRODUCTION IN conventional spectrum management, most of the spectrum bands are exclusively allocated to particular services, which may potentially exhaust limited frequency resources as wireless applications grow. In contrast to spectrum scarcity, the utilization of the allocated spectrum bands is usually very low. easurement results have shown that only 2% of the allocated spectrum is used, on the average, in the U.S. 1]. Furthermore, although the allocated users are active, there still exists an abundance of spectrum access opportunities at the slot level. This condition motivates the development of cognitive radio (CR) 2], 3], where secondary users (SUs) are allowed to use the spectrum bands that were originally assigned to primary users (PUs). One feasible approach is opportunistic spectrum access (OSA), envisioned by the Defense Advanced Research Projects Agency Next-Generation Communications (DARPA XG) Program 4], which allows SUs to utilize the unused channels when PUs are detected to be inactive. This mechanism is also called listening before transmission, where the listening function is fulfilled by spectrum sensing at the physical (PHY) layer, and the transmission function refers to packet scheduling at the medium access control (AC) layer. Obviously, the introduction of spectrum sensing brings more challenges for the AC protocol design under cognitive radio network (CRN) compared with conventional networks. Several existing works 5] 7] focus on the spatial OSA, and the main issue that is addressed is to coordinate the channel allocation or spectrum reuse in some particular areas or locations (e.g., cellular-based networks), whereas PUs states are considered static or slowly varying in time. Other solutions, e.g., 8] and 9], address the temporal OSA, where the unused time slots of PUs can be accessed by SUs in real time. In 8], Liang et al. studied the performance tradeoff between sensing time and the achieved throughput of SUs and demonstrated the existence of an optimal spectrum sensing time that yields the maximum achievable throughput for SUs under the constraint that PUs are adequately protected. Although this policy can guarantee the maximum throughput of a secondary link pair, it considers only the point-to-point transmission model. In 9] and 10], a AC protocol based on the framework of partially observable arkov decision processes (PODPs) is developed to exploit the optimal sensing and access strategy for CRNs. However, its complexity exponentially grows with the number of channels, /$ IEEE

2 CHEN et al.: TWO-LEVEL AC PROTOCOL STRATEGY FOR OPPORTUNISTIC SPECTRU ACCESS IN CRNs 2165 and the assumption that PUs usage statistics remain unchanged simplifies the AC protocol design. oreover, SUs schedule the packets and coordinate their access based on the following two different models: 1) the guaranteed-access model and 2) the random-access model. ost of the previous works, e.g., 11] 19], applied the guaranteed-access model into CRNs by using an exclusive common control channel (CCC) or central coordinator to schedule SUs packets in a sequential manner. In 13], each frame of the control channel is divided into the report and the negotiation phases. In the report phase, two different channel spectrum sensing policies were proposed to detect the available subchannels and report the obtained information. Then, in the negotiation phase, SUs exchange data following the p-persistent carrier-sensing multiple access (CSA) protocol to compete for the channel and get the permission to utilize all the available subchannels in the next frame. In addition, the authors considered only the perfect spectrum sensing case. In fact, this CCC may not be always available in practice, and it also easily suffers from the control channel saturation problem 20]. To the best of our knowledge, fewer studies considered the random-access model for packet scheduling under CRNs 21], 22]. The difficulty is that, in a CR environment, SUs not only compete for the channel with other SUs but need to vacate the channel to avoid interference to PUs as well. Huang et al. 21] proposed the following three random-access schemes with different sensing, transmission, and backoff mechanisms for SUs: 1) virtual transmit if busy (VX); 2) VAC; and 3) keep sensing if busy (KS). Considering the scenario of one PU band and one SU, the authors investigated the capacity of SUs and derived closed-form expressions of performance metrics for each scheme. However, because they assume that the PUs packet arrival process and spectrum sensing performed at SUs are independent of each other, the spectrum sensing technique is unhelpful in increasing the SUs access opportunities. Therefore, the relevant achievable performance is pessimistic. In this paper, we consider the AC protocol design problem for CRNs based on the random-access model and the imperfect spectrum sensing assumption, where all the SUs share a single transmission channel with PUs, and no additional CCC is needed. To protect the operation of the primary network and optimize the system performance of the secondary network, we propose a two-level OSA strategy here. The first level performs spectrum sensing, which is arranged at the beginning of each AC frame before data transmission. Limited by the interference constraint from PUs, SUs must maintain their detection probabilities at a target threshold. Furthermore, because an SU s packet transmission probability depends on its detection and false-alarm probabilities, the actual traffic rate can be controlled by adjusting the spectrum sensing time. The second level is similar to the function of conventional AC protocols. Based on the slotted ALOHA and CSA (e.g., 23] and 24]), respectively, we develop two AC protocols called the slotted cognitive radio ALOHA (CR-ALOHA) and cognitive-radiobased carrier-sensing multiple access (CR-CSA) to deal with the packet scheduling of SUs under a CR environment. These two protocols can easily be implemented, and closed-form expressions of our network metrics can also be derived to compare with each other. oreover, due to the property of discrete Fig. 1. System model of a CRN. channel access time, we design an appropriate frame structure to support our proposed two-level OSA strategy and develop a framework to evaluate the performance of the secondary network for each protocol in terms of normalized throughput and average packet delay. To measure the protection effects on the primary network, we define the interference factor as the outage probability that SUs would interfere with PUs in an arbitrary frame and also define the agility factor as the ability that SUs can rapidly vacate the channel once PUs have become active. Thus, we study the tradeoff between the achievable performance of the secondary network and the protection effects on the primary network and accordingly design the optimal frame length. Conversely, we also consider the effects of the spectrum utilization of the primary network on the performance of the secondary network. This paper is organized as follows. Section II introduces the system model and our proposed access strategy for CRNs. In Sections III and IV, we propose the slotted CR-ALOHA and CR-CSA and analyze their performances, respectively. The evaluation results, performance-protection tradeoffs, and effects of PUs activities are shown in Section V. Finally, conclusions are drawn in Section VI. A. System odel II. SYSTE ODEL The system model considered in this paper is shown in Fig. 1. The primary network consists of one primary transmitter (denoted by P t ) and several primary receivers (denoted by P r s), where P t can broadcast signals to P r s over a single channel using the licensed spectrum band. The secondary network consists of N number of fixed or mobile SUs (denoted by U i, i =1,...,N), which are located within P t s coverage range (the range that P t can be detected at U i s by spectrum sensing), and are self organized into a wireless local area network (WLAN). Each U i can directly communicate with other SUs or secondary access points (SAPs); thus, the synchronization problem can be solved by the coordination function of SAPs when U i dynamically joins the secondary network. In addition, the primary and the secondary networks operate independent

3 2166 IEEE TRANSACTIONS ON VEHICULAR TECHNOLOGY, VOL. 60, NO. 5, JUNE 2011 Fig. 2. AC frame structure of our proposed two-level OSA strategy. of each other, and there is no message exchange between PUs and SUs. According to OSA, SUs can use P t s channel only when P t is detected to be inactive. Once P t has woken up, U i s must vacate the channel within a certain duration, i.e., T v s. Therefore, U i s are forced to suspend their access and periodically detect the P t s states within T v. This policy results in the discrete channel access time under a CRN in contrast to the continuous access time under conventional networks. To support OSA, a relevant frame structure is designed, as shown in Fig. 2. Each frame with the length T f (T f T v ) consists of a duration of T s for spectrum sensing and T d for data transmission. T s is arranged at the beginning of each frame, and T d can accommodate up to transmission periods (TPs) that are indexed by j, j =1. The advantage of this small data piece structure is that more than one SU can compete for channel access in the same frame duration, which reduces the waiting (or response) time and transmission failure cost of each SU and, furthermore, improves the system performance of the whole secondary network. In addition, we assume that all packets have the same size; thus, each TP consists of a fixed packet transmission time T and a propagation delay T p. Therefore, we have T f = T s T d = T s (T T p ). B. Spectrum Sensing ethods Compared with the traditional networks, PUs and SUs in a CR environment are usually unknown to each other, and the PUs information (e.g., modulation technique and location) seems to be a black box for SUs. Obviously, if SUs are located outside the carrier-sensing range (CSR) of PUs, it is impossible for them to know the PUs ON/OFF states only by the carrier sense technique. Thus, we must consider using the spectrum sensing technique to perform PU detection at each SU in every frame. In general, the following three techniques are widely used: 1) matched filter; 2) energy detection; and 3) cyclostationary feature detection. In this paper, we adopt the energy detection technique 8], 25] due to its simplicity. An energy detector computes the power (denoted by Y i )of the received signal from P t at U i and compares Y i with a predetermined threshold ɛ.ify i ɛ, P t is deemed to be active, and vice versa. Let t be the spectrum sensing time, f s be the sampling frequency, and γ be the received signal-to-noise ratio (SNR) from P t at U i. Considering the complex-valued phaseshift keying (PSK) signal and circularly symmetric complex Gaussian (CSCG) noise case, the detection probability P d for each SU is approximately given by 8] ( ( ) ) ɛ tf s P d (t) =Q γ 1 (1) 2γ 1 σ 2 u where σu 2 is the variance of the received Gaussian noise, and Q( ) is the complementary function of a standard Gaussian variable, i.e., Q(x) =(1/ 2π) x exp( s2 /2)ds. To protect the operation of the primary network, the overall detection probability that all the SUs know the existence of P t when P t is active is given by Pd N, which should be set larger than a threshold based on the application requirement. Assume that U i s are located outside P t s CSR; thus, the primary network would not affect the secondary network. However, U i can still interfere with the receiving of neighboring P r s that are located within U i s CSR. Therefore, to protect the primary network, U i s detection probability P d should not be less than a certain threshold. Then, the corresponding falsealarm probability P f is given by ( P f (t) =Q 2γ 1Q 1 (P d ) ) tf s γ. (2) Based on (1) and (2), we see that P f is a monotonically decreasing function of t for fixed P d and γ. The spectrum sensing time t varies in the domain of dom t = {t 0 <t T s }, whereas the minimum P f (which is denoted by P f,min ) is attained at t = T s. C. Traffic odel and Assumptions The traffic model and its underlying assumptions are characterized as follows. Wellens et al. 26] introduced time-frequency models of spectrum use for various applications. First, because the exponential distribution can provide a good approximation for the packet service time 27], we assume that the run and burst lengths of aggregated arrivals in the primary network follow exponential distributions with the parameters λ r and λ b, respectively. oreover, in the secondary network, each U i is assumed to be an independent Poisson source with an average packet generation rate of λ i packets per TP; thus, the lengths of packet-generating intervals follow the exponential distribution with mean 1/λ i. Suppose that all the λ i s are equal to λ; then, the total traffic rate is G = Nλ. Second, a positive acknowledgment scheme is adopted. If a packet is successfully transmitted, U i will receive a positive acknowledgment. Otherwise, after a time-out period, it knows this failure and uniformly chooses a time to retransmit within a fixed back-off window of size 0, 2 X]. LetT a be the length of an acknowledgment packet; then, the time-out period is given by T T a 2T p. At any instant, each U i has at most one packet that waits for transmission, regardless of whether it is newly generated or backlogged. oreover, we consider that the channel error problem has been solved by an error correction mechanism that is performed at the PHY layer. Last, we make the following assumption. Assumption 1: Suppose that all packets that were sent by SUs are of constant length, which assumed to be T =1; then, we normalize that α = T p /T, β = T s /T, a = T a /T, l = T d /T, f = T f /T, and δ = X/T, respectively. Therefore, the length of TP is equal to 1α, and the total frame length is given by f = β (1 α).

4 CHEN et al.: TWO-LEVEL AC PROTOCOL STRATEGY FOR OPPORTUNISTIC SPECTRU ACCESS IN CRNs 2167 D. Spectrum Access Scheme To protect the operation of the primary network and optimize the system performance of the secondary network, we propose a two-level OSA strategy as follows. At the first level, spectrum sensing is periodically executed by U i to detect P t s activity before its packet transmission. Using energy detection, P d is set according to the protection requirement. If P t is detected to be active, U i will be blocked for transmission in the current frame; otherwise, it will attempt to transmit. Thus, the packet transmission probability for each U i is determined by both P d and P f. Furthermore, because P f is monotonically decreasing with t for a given P d, the actual traffic rate of SUs is eventually determined by t. Therefore, we can choose an appropriate t to achieve better performance of the secondary network. The second level aims at the packet scheduling of SUs, which is similar to the function of conventional AC protocols. In this paper, the slotted CR-ALOHA and CR-CSA are proposed to solve the channel access contention problem. The details will be given in the following sections. E. PUs Activities and Performance Parameters We use H 0 and H 1 to denote the events that P t is inactive and active, respectively, during the spectrum sensing duration and use P H0 and P H1 to denote the occurrence probabilities of H 0 and H 1, respectively. To compute their values, we directly map the active and inactive states of P t to the operation and repair states of a one-unit system 28], where one unit means that the system is collectively viewed and the failure of any component should be interpreted as the failure of the whole system. Thus, in reliability analysis, interval reliability is defined as the probability that, at a specified time, the system operates and will continue to operate for at least a given interval, and serving reliability is defined as the probability that either the system operates at a specified time, or if it is not operating, it will be repaired within a given interval. Considering that both the run and burst lengths of P t follow the exponential distributions, we have { PH0 = λ b e λrβ /(λ r λ b ) (3) P H1 =1 P H0. Obviously, P H0 and P H1 are related to the length of spectrum sensing duration β. Based on our proposed spectrum access scheme, we know that U i sends only when it detects that P t is inactive, which may result in incorrect sensing cases of false alarm and missed detection. Although the sensing result is correct, there still exists the possibility (denoted by H 2 ) that this result is inconsistent with the fact that, when P t keeps inactive during β, later on, it wakes up during the data transmission time T d of the current frame. Let P H3 be the probability that P t is inactive during the whole frame; thus, we have P H3 = λ b e λ rf /(λ r λ b ). (4) Then, the probability of H 2 (which is denoted by P H2 )is given by P H2 = P H0 P H3. (5) Obviously, the secondary network interferes with the primary network in the following two aspects: 1) missed detection under H 1 and 2) transmission under H 2. Note that the case P t is active at the beginning of the spectrum sensing duration but later on turns to be inactive before the end of the sensing duration exists. However, the corresponding occurrence probability is negligible; thus, we can ignore this case and focus only on cases H 1 and H 2. To measure these effects, we define a new parameter, i.e., interference factor (denoted by IF), which is the outage probability that SUs would interfere with PUs in an arbitrary frame, and use subscripts 1 and 2 to distinguish the aforementioned two cases. First, we consider the case of missed detection under H 1. Based on (1) and (3), we have IF 1 = ( 1 Pd N ) PH1. (6) For the second case of transmission under H 2, based on (2) and (5), we have IF 2 = ( 1 Pf N ) PH2. (7) Combining (6) and (7) yields IF = IF 1 IF 2. (8) Based on (8), we see that, for fixed P d and N, IF depends only on P f and f. oreover, because P f is a monotonically decreasing function of t, IF is a monotonically increasing function of t and is also a monotonically increasing function of f. In addition, we consider another parameter called the agility factor (which is denoted by AF ), which refers to the U i s ability to rapidly vacate the channel once P t has turned active from an inactive state. Based on our designed frame structure, we define that AF = T f /T v, which varies in (T s /T v, 1] due to the condition of T s <T f T v. By definition, the smaller the value of AF is, the quicker the channel is vacated, and vice versa. Obviously, AF is related to the configuration of the frame length. Therefore, we take this parameter into account to design the optimal frame length. III. SLOTTED CR-ALOHA AND ITS PERFORANCE A. Slotted CR-ALOHA The slotted CR-ALOHA is developed from the conventional slotted ALOHA, which differs in the discrete channel access time and the constraint of protecting the primary network. We assume that, for each frame, the data transmission duration l is slotted, and the slot size is equal to the TP length of 1α. As showninfig.3,theslotted CR-ALOHA operates as follows. 1) If U i detects that the channel is available in the current frame, any packet that arrives in the th slot of the previous frame or the spectrum sensing duration of this frame will be transmitted in the first slot; otherwise, if

5 2168 IEEE TRANSACTIONS ON VEHICULAR TECHNOLOGY, VOL. 60, NO. 5, JUNE 2011 Fig. 3. Operation scheme of the slotted CR-ALOHA. The box with solid lines indicates the inactive P t case, and the box with dash lines indicates the active case. a packet arrives in the jth slot (j ), it will start to transmit at the beginning of the (j 1)th slot. 2) If the channel is unavailable, any packet arrival within this frame up to the ( 1)th slot will be blocked to the end of this frame and then uniformly retransmit within a backoff window, as mentioned in Section II-C. 3) The current transmission is successful when there is only one packet that was transmitted; otherwise, a collision occurs, and the packets involved will be retransmitted after corresponding separate random delays to avoid continuously repeated conflicts. 4) Any arrival in the th slot of one frame will be processed in the next frame. For the conventional slotted ALOHA, the normalized throughput S, defined as the fraction of time that can successfully transmit SUs packets, is given by S = Ge G, and the maximum S is equal to when G =1. However, in a CR environment, P t s activities will definitely degrade S, which will be shown as follows. B. Throughput Analysis Based on the operation scheme of the slotted CR-ALOHA, a packet that can successfully be transmitted by U i must satisfy the following three conditions if the capture effect is ignored: 1) U i can access the channel in the current frame; 2) no collision occurs between P t s transmission and U i s transmission; and 3) no collision occurs between U i and any other SU s packets. Let C i, i =1, 2, 3, denote the aforementioned conditions. Obviously, C 2 and C 3 are independent of each other, conditioned on C 1. First, we consider C 1.ForH 0, U i can access the channel with a probability of 1 P f, because no false alarm occurs. oreover, if U i cannot detect P t s activeness under H 1, U i can still access with a probability of 1 P d.letv 0 and V 1 be the probabilities of both cases, respectively; then, we have { V0 =1 P Pr{C 1 } = f, H 0 (9) V 1 =1 P d, H 1. Based on (2) and (9), we see that V 1 is constant and V 0 is monotonically increasing with t; thus, we have V 0 (t) =1 Q( 2γ 1Q 1 (P d ) ) tf s γ. (10) For notational simplicity, we use V 0 or V 0 (t) as the intermediate variable for analyzing the performance in the remainder part. Because U i s independently detect P t, the number of SUs that can access the channel in one frame (which is denoted by n) follows a binomial distribution, whose occurring probability is given by ( ) N Pr{n SUs can access} = (Pr{C 1 }) n (1 Pr{C 1 }) N n n { ( N ) = n V n 0 (1 V 0 ) N n, H ) 0 V n 1 (1 V 1 ) N n, H 1 ( N n 0 n N. (11) Accordingly, we use G(n) to denote the actual traffic rate that corresponds to n SUs; thus, we have G(n) =nλ, with the probability given by (11). Then, we consider C 2. Because we have assumed that U i s are located outside P t s CSR, P t s transmission has no influence on U i s transmission, but U i can still interfere with P r s reception. In this case, the transmission by SUs under H 1 is not encouraged, and the achieved performance should be ignored. Therefore, we have { 1, H0 Pr{C 2 } = (12) 0, H 1. Last, C 3 occurs if and only if no other SU s packet waits at the beginning of the current slot. In particular, when a packet transmits in the first slot of this frame, its vulnerable period (defined as the time slots during which, if other packet sends, the ongoing transmission and the current transmission would overlap) lasts from the th slot of the prior frame to the end of the spectrum sensing duration in this frame. Based on the condition that n SUs satisfy C 1, we obtain Pr{C 3 } = 1α β e (n 1)λ(1αβ) l β l (1 α) l β e (n 1)λ(1α). (13) Let C denote the event that a packet is successfully transmitted by U i. Combining the results in (11) (13), we have Pr{C n SUs can access} = Pr{C 2 C 3 H 0 }P H0 Pr{C 2 C 3 H 1 }P H1 (14) where the second term is equal to zero due to Pr{C 2 H 1 } =0 given by (12). Then, we use S(n, t) to denote the achieved throughput that corresponds to n SUs and spectrum sensing time t, and the average achievable S(t) is given by S(t)=E {S(n, t)} N = G(n)Pr{C n SUs can access} Pr{n SUs can access} n=0 =NλV 0 1 V 0 V 0 e λ(1α)] N 1 λ b e λ rβ λ r λ b {1 (1 α β) 1 e ] } (N 1)λV 0β l β NλV 0 1 V0 V 0 e λ(1α)] N 1 λb e λ rβ (15) λ r λ b

6 CHEN et al.: TWO-LEVEL AC PROTOCOL STRATEGY FOR OPPORTUNISTIC SPECTRU ACCESS IN CRNs 2169 where E is the expectation operator, and the last equation holds for small λ and β. Therefore, the optimization problem of S can be expressed as max V 0 S(t) s.t. V 0 dom V 0 = {V 0 0 <V 0 1 P f,min } (16) where dom V 0 is obtained from (2) and (10) as t varies in its domain 0,T s ]. Let S max denote the maximum S(t) and V0 denote the optimal V 0 for S max. Solving (16), the extremum of S is achieved as ds/dv 0 =0; thus, we obtain that V 0 =(1/N 1 e λ(1α) ]) 1/G due to e λ(1α) =1 λ(1 α) when α and λ are relatively small. If 1/G dom V 0, V0 =1/G, because S (V 0 ) > 0 and S (V 0 ) < 0. Otherwise,if1/G > 1 P f,min, S is a monotonically increasing function of V 0 ; thus, S max is obtained at V0 =1 P f,min. Using (10), the optimal sensing time t for S max, which is denoted by t, is given by 1 t f s γ Q 1 (1 1/G) 2γ 1Q 1 (P = 2 d ) ] 2 1/G dom V 0 (17) T s, otherwise. oreover, combining (10) and (15), for large N and small α, we have S max = NλV 0 (t )λ b e (N 1)λV 0(t ) λ r β /(λ r λ b ) λ b G e G λ r β /(λ r λ b ) (18) where G = NλV 0 (t ) is the optimal traffic rate adjusted by our proposed two-level OSA strategy. Compared to the conventional slotted ALOHA, we note that S max under the slotted CR-ALOHA decreases by a fraction P H0 due to the existence of P t. C. Delay Analysis In this section, we analyze the average packet delay D for the slotted CR-ALOHA, which refers to the average interval from the instant that a packet is originally generated until the instant that it is successfully transmitted. We make the following assumption. Assumption 2: The packet-processing time is negligible, including the sum check and acknowledgment generation time. Let R 0 and R 1 be the average duration between two consecutive transmissions of the same packet due to collision and being blocked, respectively. According to Assumptions 1 and 2, we have R 0 =12α a δ ω (19) where ω is the average length of the pretransmission delay, which refers to the interval from the instant that the SU attempts to transmit until the instant that it senses that the channel is idle for transmission. Theorem 1: If a packet can be transmitted, its average pretransmission delay ω is given by ω = β 2 2β(1 α)l(1 α)/2(l β), and lim α,β 0 ω =1/2. Proof: Although the number of arrivals that were generated by SUs follows a Poisson distribution, the arriving instants of these packets would still be uniformly distributed over the time axis. Therefore, the average pretransmission delay ω can be calculated as follows: 1) If the packet arrives in the th slot of one frame, the probability density function (pdf) of the arrival instant is given by f(x) =1/(1 α), and thus, the average pretransmission time for this case (denoted by ω 1 ) consists of the residual time of the current frame and the spectrum sensing duration of the next frame, i.e., ω 1 = 1α 0 (1 α x)f(x)dx β =(1α)/2β; 2) if the packet arrives in the spectrum sensing duration, the pdf of the arrival instant is f(x) =1/β, and we have ω 2 = β 0 (β x)f(x)dx = β/2; and 3) if a packet arrives in the jth slot (j ), wehave ω 3 = 1α 0 (1 α x)f(x)dx =(1α)/2. Based the aforementioned analysis, ω is given by ω = (1 α)ω 1 l β βω 2 l β (l 1 α)ω 3 l β = β2 2β(1 α)l(1 α). (20) 2(l β) Furthermore, as α and β go to zero, we have lim α,β 0 ω = 1/2. Now, we consider R 1. Due to blocking, R 1 consists of the average blocking time t b and the average retransmission delay δ. It is easily derived that t b =(l β)/2; thus, we have R 1 = t b δ = l β δ. (21) 2 Therefore, the average number of collisions is given by G(n)/S(n, t) 1, and the average number of being blocked is (G G(n))φ/S(n, t), where φ = δ/r 1 denotes the fraction of the unblocked time during R 1. Therefore, the average packet delay D(t) is expressed as { ] G(n) D(t) =E S(n, t) 1 R 0 G G(n)] φ R 1 }1αω S(n, t) = e λ(1α) (R 0 φr 1 ) 1 V 0 V 0 e λ(1α)] N P H0 e 2λ(1α) φr 1 1 V0 V 0 e λ(1α)] N1 (αaδ) V 0 P H0 e λrβ (λ r λ b )R 0 (1/V 0 1)δ] 1 V 0 V 0 e λ(1α)] N 1 / λ b (α a δ) (22) where the last equation holds due to e λ(1α) 1 V 0 V 0 e λ(1α) ] 1. Similarly, the optimization problem of D can be written as min V 0 D(t) s.t. V 0 dom V 0. (23) Let D min denote the minimum D(t) and V 0 denote the optimal V 0 for D min. Because D(t) as given in (22) is

7 2170 IEEE TRANSACTIONS ON VEHICULAR TECHNOLOGY, VOL. 60, NO. 5, JUNE 2011 differentiable, the extremum of D is obtained as dd(t)/dv 0 = 0. When G 4(1 R 0 /δ), we obtain 2 V 0 = G Δ = V 0. (24) G 2 4G(1 R 0 /δ) If V 0 dom V 0,wehaveV 0 = V 0, because D (V 0 ) < 0, and D (V 0 ) > 0. Otherwise,ifV 0 > 1 P f,min, D(t) is a monotonically decreasing function of V 0. Therefore, D min is achieved at V 0 =1 P f,min. Then, the corresponding optimal sensing time t for D min (denoted by t ) is eventually given by t = { 1 f s γ Q 1 (1 V 2 0 ) 2γ1Q 1 (P d ) ] 2, V 0 dom V 0 T s, otherwise. (25) Based on (22) and (25), for large N and small α and λ, we have D min =e G λ r β (λ r λ b )R 0 (G/G 1)δ] /λ b (αaδ) (26) where G = NλV 0 (t ) is the corresponding optimal traffic rate for D min. D. Optimal Sensing Time t In (17) and (25), we have derived the optimal t for S max and D min, respectively. oreover, based on (24), we know that V 0 < 1/G due to R 0 >δ; furthermore, we have t t. In other words, S max and D min cannot simultaneously be achieved, and there exists a range defined as R(t) ={t t t t }, within which increasing S will result in the increasing of D, and vice versa. In fact, the back-off window size is chosen as a large value to avoid continuous collisions, i.e., δ is much greater than 12α a ω; thus, we have R 0 /δ 1 and V 0 1/G. Furthermore, we note that t = t and R(t) converges to a point. IV. COGNITIVE-RADIO-BASED CARRIER-SENSING ULTIPLE ACCESS AND ITS PERFORANCE A. CR-CSA Protocol In the previous section, we assume that the data transmission duration l of each frame is divided into slots of length TP. Now, in CR-CSA, we assume that l is divided into minislots of length σ, which is called the slot time (ST) in the IEEE distributed coordination function (DCF). The concepts of slot and minislot are different due to the differences of the operation schemes. CR-CSA requires that each packet starts to transmit at the beginning of the following ST. To improve the utilization of the channel access time, we assume that one slot or TP is equal to the integral number (denoted by m) of minislots, i.e., 1 α = mσ. oreover, because the carrier-sensing time is relatively short compared to the spectrum sensing time, we neglect it in the following analysis. As shown in Fig. 4, the details of CR-CSA are described as follows. 1) If U i detects that P t is inactive during the current frame, any arrival during the th slot of the previous frame Fig. 4. Operation scheme of CR-CSA. The box with solid lines indicates the inactive P t case, and the box with dash lines indicates the active case. or the spectrum sensing duration of this frame will be transmitted in the first slot; otherwise, if it arrives in the jth slot (j ), the following conditions hold. If the channel is idle, it will be transmitted at the beginning of the next ST. If the channel is busy, U i keeps sensing until the channel again becomes idle (i.e., the end of the current transmission) and then attempts to transmit. 2) If U i detects that P t is active, any arrival within the current frame up to the ( 1)th slot will be blocked to the end of this frame, and then, U i chooses a uniformly distributed back-off time to retransmit. 3) The current transmission will be successful if there are no other packets transmitting during this TP; otherwise, it fails and will be retransmitted after a random delay to avoid continuously repeated conflicts. 4) Any attempt during the th slot of one frame must wait to be processed in the next frame. The difference between the slotted CR-ALOHA and CR-CSA is obvious: SUs transmit only from the beginning of a slot under the slotted CR-ALOHA, and thus, they need not sense the channel. However, under CR-CSA, SUs become more aggressive to transmit, because they keep sensing until the channel becomes idle. B. Throughput Analysis We define idle period (IP) as the duration within which the channel is available but no packet is transmitted or waits to be transmitted, busy period (BP) as the duration occupied by U i s, and useful period (UP) as the successful transmission time within one BP. According to the CR-CSA scheme, BP always starts from the instant when an arrival comes in an IP. If any other packet arrives during the current transmission, this BP continues; otherwise, it terminates at the end of the current transmission, and a new IP immediately follows. Obviously, IP and BP alternately distribute themselves over the time axis, except when there are unavailable frames. Based on Section III-B, we know that a packet that was successfully transmitted must satisfy the three conditions of C i s. Based on the renewal theory, the normalized throughput S(t) for CR-CSA is obtained as S(t) =P H0 U B I (27) where I, B, and U are the expected lengths of IP, BP, and UP, respectively. Then, we compute them as follows. First, let Z(τ) be the probability that U i has no packet that was generated within a duration τ. Then, it is easily verified that Z(τ) =1 V 0 V 0 e λτ e λv0τ. oreover, we use

8 CHEN et al.: TWO-LEVEL AC PROTOCOL STRATEGY FOR OPPORTUNISTIC SPECTRU ACCESS IN CRNs 2171 Y to denote the length of an arbitrary IP, and the cumulative distribution function (cdf) of Y is given by F Y (y)=1 Pr{Y > y}=1 Z N (y)=1 e GV 0y. (28) Furthermore, the mean value of I is given by I = 0 ydf Y (y) 1 GV 0. (29) Second, we consider the total number of packets (denoted by K) that were transmitted in one BP. Let z be the probability that no SUs transmit in one TP; thus, we have z = Z N (1 α) = 1 V 0 V 0 e λ(1α)] N e GV 0 (1α). (30) Therefore, the probability that the next TP belongs to the current BP is given by 1 z. In particular, when a BP processes in the last slot of one frame, it continues only when there exists any packet that waits at the end of the current transmission. If the next frame is available, the waiting packets will be processed in the first slot of the next frame. Conversely, if the next frame is unavailable, the waiting packets will be blocked for transmission or insist to proceed but interfere with P t s transmission. In the second case, once the channel has again become available, the packets that accumulate at the end of the last unavailable frame will be processed in the first slot of this frame. However, we see that BP continues with the same probability of 1 z, regardless of which case occurs, i.e., BP can jump over the unavailable frames and, without interruption, proceeds in the available frames. Therefore, K is geometrically distributed with mean 1/z, and Pr{K = k} = z(1 z) k 1, k =1, 2,... (31) Now, we use B j and U j, j =0, 1,...,, to distinguish the expected lengths of BP and UP, beginning within the jth slot of one frame, respectively. Then, their values are calculated as follows. 1) BP starts in the spectrum sensing duration j =0. When a packet arrives at time x within the spectrum sensing duration β, it will be transmitted in the first slot of this frame. The next slot transmits only if any packet waits at the end of the current slot, and this process continues, unless BP terminates. However, due to the frame length limitation, at most TPs can be accommodated in one frame, and any larger than th TP will be processed in the next available frames. In addition, the (i 1)th TP, i =1, 2,... must wait an extra spectrum sensing time β to detect the channel states. Obviously, the first TP is successfully transmitted only when no other packets wait at the end of β. Similarly, the next TP is successful if and only if one packet waits at the beginning of this transmission. For the (i 1)th case, successful transmission must satisfy the following two conditions: 1) There must exist a packet that waits at the end of the previous TP such that the current BP can continue, and 2) only one packet accumulates at the beginning of the current TP, i.e., no collision would occur. Lemma 1: For j =0, the average length of a BP and a UP are given by (32) and (33), shown at the bottom of the page, respectively. Proof: See Appendix A. 2) BP starts in the jth slot of one frame, j =1,..., 1. Suppose that the first packet arrives during the jth slot of one frame. Then, it starts to transmit at the beginning of the following ST, which produces a false-busy period (FP) with a length of (x β)/σ σ (x β), referring to the unused idle time slots in this BP. If no other packets accumulate at the end of this FP, it will successfully be transmitted. In particular, when K> j, the( j 1)th TP will proceed in the next available frame, which results in a FP of j(1 α) (x β)/σ σ, lasting from the end of the ( j)th TP to the end of the frame. Lemma 2: For 0 <j<, the average length of a BP and UP are given by (34) and (35), shown at the bottom of the next page, respectively. Proof: See Appendix B. 3) BP starts in the th slot of one frame. In this case, the interval from the arrival of the first packet to the end of the current frame is a FP. oreover, the first TP will proceed in the next available frame. Lemma 3: For j =, the average length of a BP and UP are given by (36) and (37), shown at the bottom of the next page, respectively. Proof: See Appendix C. Theorem 2: Based on the CR-CSA scheme, the average length of a BP and a UP are given by (38) and (39), shown at the bottom of the next page, respectively, where θ = β/f is the fraction of spectrum sensing duration per frame. Proof: Because the packet arrival process is random, we have B = U = β l β B 0 1α l β B 1 1α l β B (40) β l β U 0 1α l β U 1 1α l β U. (41) B 0 = 1α z U 0 = 1 e GV 0β GV 0 β β(1 z) 1 (1 z) β 2 GV 0(1 α)e GV 0(1α) 1 e GV 0(1α) (32) ] 1 z 1 (1 z) 1 (1 z) GV 0(1 α β)e GV 0(1αβ) (1 z) 1 e GV 0(1α) 1 (1 z) (33)

9 2172 IEEE TRANSACTIONS ON VEHICULAR TECHNOLOGY, VOL. 60, NO. 5, JUNE 2011 Substituting the equations from Lemmas 1 3 into (40) and (41), we see that (38) and (39) hold. Last, substituting (29), (38), and (39) into (27), we obtain the expression of S(t) for CR-CSA. Note that the closed-form expression of t for S(t) cannot easily be obtained, but we can find its value by a numerical method. In addition, if α, β, and σ are relatively small and is large enough, we see that S(t) P H 0 (1 GV 0 ) e GV = GV 0λ b e GV0 λrβ (1 GV 0 ) 0 1/GV0 (GV 0 e GV 0 )(λr λ b ). (42) C. Delay Analysis Similar to the analysis for the slotted CR-ALOHA in Section III-C, we determine the average packet delay D for CR-CSA. Due to the different operation schemes, we must recalculate the value of R 0. Thus, the pretransmission time ω is derived as follows. 1) If a packet arrives in the spectrum sensing duration, its average waiting time is β/2. 2) If a packet arrives in the jth TP (j =1,..., 1) of one frame when the channel is idle, its average waiting time is σ/2; otherwise, when the channel is busy, its average waiting time equates to (1 α)/2. 3) If a packet arrives in the th TP of one frame, its average waiting time is (1 α)/2β. Therefore, we obtain ω = β2 2β(1 α)(1α) 2 (l 1 α) σi(1α)b BI. 2(l β) (43) B j = 1α z β(1 z) j 1 (1 z) σ (1 α σ)(1 z) j 2 2 U j = 1 e GV 0σ GV 0(1 α)e GV 0(1α) GV 0 σ 1 e GV 0(1α) (1 z) j 1 (1 z) P H 0 (1 z) j ( ) 1α β 1 GV 0 e GV0(1αβ) 1 (1 z) j 1 z 1 (1 z) ] P H0 (1 z) j ] GV 0(1 α β)e GV 0(1αβ) 1 e GV 0(1α) ( ) 22α β 1 GV 0 e GV 0(22αβ) (1 α) 1 e ] (35) GV 0(1α) (34) B = 1α z β 1 (1 z) 1α 2 U = e GV 0β 1 e GV 0(1α) ] V 0 P H0 GV 0 (1 α) GV 0(1 α β)e GV 0(1αβ) 1 e GV 0(1α) GV 0(1 α)e GV 0(1α) 1 e GV 0(1α) ] 1 1 (1 z) P H 0 ] 1 z 1 1 (1 z) (36) (37) B = 1α z β β(1 z) θ 2 1 (1 z) ] { σ (1 θ) 2 2β (1α σ) ] } 1 (1 z) 2z (38) U = GV 0(1 α)e GV ] 0(1α) 1 1 e GV 0(1α) z 1 θ(1 z) (1 θ)(1 z) GV 0(1 α β)e GV 0(1αβ) 1 (1 z) z 1 e GV 0(1α) θ(1 z) 1 (1 z) (1 θ)p H 1 P H0 (1 z) ] z θ { (l 1 α)(1 e GV 0 σ ) 1 e GV0β e GV 0β 1 e ] GV 0(1α) V 0 P H0 β GV 0 σ GV 0 P H0 ( 1α β 1 GV 0 ) e GV 0(1αβ) 1 e GV 0(1α) ( ) 22α β 1 GV 0 e GV 0(22αβ) 1 z (1 z) } (39) z

10 CHEN et al.: TWO-LEVEL AC PROTOCOL STRATEGY FOR OPPORTUNISTIC SPECTRU ACCESS IN CRNs 2173 Obviously, the value of ω in (43) is less than the value in (20). Substituting (43) into (19), we can obtain the corresponding R 0 for CR-CSA. According to Little s law, because the expected traffic rate in any available frame is given by N ( N ) n=1 n nλv n 0 (1 V 0 ) N n = GV 0, D(t) for CR-CSA can be derived as ] GV0 D(t)= S(t) 1 R 0 (G GV 0)φ R 1 1α ω (44) S(t) where S(t) corresponds to the normalized throughput of CR-CSA given by (27). Therefore, we can obtain the theoretical value of t by a numerical method. V. S IULATION RESULTS We develop an event-driven network simulator to evaluate the performance of our proposed CR-ALOHA and CR-CSA. The simulator is written in ATLAB, closely following all the details of the protocols for each SU, as described in Sections III-A and IV-A. Suppose that the bandwidth of the channel and the sampling frequency f s are both chosen as 6 Hz. To protect the primary network, U i s are required to vacate the channel within 100 ms, i.e., T v = 100 ms. We assume that, for the worst case, the received SNR γ from P t at U i is given by 13 db and the overall detection probability is larger than 0.9. These configurations consist with the sensing requirement of wireless microphones in the IEEE Draft Standard 29]. Fig. 5. S versus t for the slotted CR-ALOHA. A. Performance of the Slotted CR-ALOHA We design the frame structure for SUs as follows. The packet size is 2000 b, the channel bit rate is 1 b/s, and the propagation delay is ignored; thus, the length of TP is standardized to 2 ms. The maximum spectrum sensing duration T s equates to one TP length of 2 ms (i.e., β =1), which ensures that P f is small enough as the actual sensing time t goes to T s according to (2). oreover, we assume that T d consists of 49 TPs; therefore, the total frame length T f is 100 ms, and f = 50. Note that the constraint T f T v is satisfied here. Suppose that the traffic rate λ of each U i is given by 0.02 and the parameters λ r and λ b used to simulate that P t s traffic are given by 0.01 and 0.99, respectively. Thus, we obtain P H0 =0.98 and P H1 =0.02 by (3), i.e., the average occupancy by the primary network is 2% in our interested frequency band 1]. Next, we validate the accuracy of the analytical results derived in Section III. In Figs. 5 and 6, we plot the curves of normalized throughput S and average packet delay D versus the spectrum sensing time t for different numbers of SUs N, respectively. In these figures, it is clearly shown that the simulation results (dashed line) perfectly match with the theoretical results (solid line). Here, theoretical S and D are obtained by (15) and (22), respectively. Then, we consider the effects of spectrum sensing time t on the achievable normalized throughput S and average delay D. As shown in Fig. 5, for N =25and 50 as G 1, S monotonically increases with t, and the corresponding S max is achieved at t = T s.forn = 100 as G>1 and 1/G dom V 0, S first monotonically increases with t until t = t, which is attained by Fig. 6. D versus t for the slotted CR-ALOHA. (17), and then, further increase of t will decrease S. oreover, in Fig. 6, for N =25and 50, D monotonically decreases with t. For N = 100 and 1/G dom V 0, D initially decreases with t until t = t, which is attained by (25), and then, D later monotonically increases with t. The curvilinear trend of D is similar to S, which means that D s decrease corresponds with S s increase, and vice versa. This phenomenon can be explained by the fact that the longer the sensing time t, the larger the packet transmission probability V 0. When G 1, a larger V 0 increases the transmission opportunity and achieves better performance. However, when G>1, a larger V 0 aggravates the system burden and results in more collisions such that the performance degrades. We also observe that S max and D min are achieved at the same t, which validates the conclusion that t = t and R(t) converges at a point in Section III-D. Last, we plot S max and D min versus the number of SUs N in Figs. 7 and 8, respectively. The simulation results (dashed line) closely match with the theoretical results (solid line) obtained by (18) and (26). Then, we compare the performance of the slotted CR-ALOHA under the optimal t (t = t or t ) and maximum t (t = T s ). Here, the optimal t is obtained by our proposed two-level OSA strategy, and the maximum t means

11 2174 IEEE TRANSACTIONS ON VEHICULAR TECHNOLOGY, VOL. 60, NO. 5, JUNE 2011 Fig. 7. S max versus N for the optimal t and maximum t (slotted CR-ALOHA). Fig. 9. S versus t for CR-CSA. Fig. 8. D min versus N for the optimal t and maximum t (slotted CR-ALOHA). that U i sends its packets without traffic control, unless it has detected P t to be active, which is used by several existing protocols. As shown in Fig. 7, S max keeps the same value for both cases and increases with N until N =50. However, when N>50, the former case can still maintain a stable large value, but in the latter case, S max dramatically degrades as N increases. oreover, for both cases shown in Fig. 8, we see that D min monotonically increases with N. However, D min for the optimal t keeps linearly increasing rather than exponentially increasing compared with the maximum t case. This phenomenon vigorously validates the dominance of our proposed two-level OSA strategy. Note that there exists a small gap between the simulation results and the theoretical results for the maximum t. The reason is that, in this case, the collisions increase with the increase of number N, which eventually results in the back-off and retransmission at SUs. Thus, the actual input traffic rate for each SU will be less than its theoretical value of λ under the assumption of Poisson distribution. Therefore, D min of the simulation results is accordingly smaller than the theoretical results, as shown in Fig. 8. Fig. 10. D versus t for CR-CSA. B. Performance of CR-CSA In a similar way, we evaluate the performance of CR-CSA analyzed in Section IV. We set each ST to 20 μs, as configured in the IEEE DCF. As shown in Figs. 9 and 10, the simulation results (dashed line) perfectly match with the theoretical results, which are obtained by (27) and (44). oreover, in the cases of N =25 and 50, S monotonically increases, and D monotonically decreases with t in its domain. However, as N = 100, we see that the maximum S and minimum D are attained at the same point within domain t. This condition validates that the optimal performance of CR-CSA can be achieved at the same t, i.e., t = t. Furthermore, S max and D min versus the number of SUs N for the optimal t and maximum t are plotted in Figs. 11 and 12, respectively. Simulation results (dashed line) perfectly match with the theoretical results (solid line) obtained by the numerical method. Obviously, when N 50, both the optimal t and maximum t can achieve the same performance due to t = t = T s. However, if N continues to increase, S max in the former case still maintains a stable large value, and the corresponding D min also keeps linearly increasing, which

12 CHEN et al.: TWO-LEVEL AC PROTOCOL STRATEGY FOR OPPORTUNISTIC SPECTRU ACCESS IN CRNs 2175 Fig. 11. S max versus N for the optimal t and maximum t (CR-CSA). primary network. Based on the definition of interference factor given in (8), we know that IF increases with t or f. oreover, if the optimal t has been adopted, IF only depends on f, and its value varies in the range of 0, 0.382] as f changes from 2 to 50. As shown in Figs. 13 and 14, the normalized throughput S monotonically increases, and the average delay D monotonically decreases with IF for both the slotted CR-ALOHA and CR-CSA, which shows that the performance improvement of the secondary network results in more interference on the primary network. In other words, we can sacrifice the performance of the primary network to improve the performance of the secondary network or restrain SUs transmissions to protect more PUs, because they exist in the same spectrum band. Therefore, we conclude that the achievable performance of secondary network depends on the interference requirement of protecting the primary network. D. Tradeoff Between Performance and Agility According to the definition of agility factor, we know that a smaller value of AF leads to more rapidly vacating the channel to PUs but degrades the performance of SUs as well. Similar to the tradeoff between performance and interference, there also exists a tradeoff between performance and agility, which is shown in Figs. 15 and 16 for the slotted CR-ALOHA and CR-CSA, respectively. We observe that S max monotonically increases and D min monotonically decreases with AF, and meanwhile, the optimal performance is achieved at AF =1 for different numbers of N. Therefore, we conclude that the achievable performance of the secondary network depends on the agility requirement of protecting the primary network. Fig. 12. D min versus N for the optimal t and maximum t (CR-CSA). outperforms the latter case. This phenomenon is similar to the slotted CR-ALOHA. Then, we compare the performance between the slotted CR-ALOHA and CR-CSA. Based on Figs. 5, 6, 9, and 10, given the same t, CR-CSA always performs better than the slotted CR-ALOHA for both S and D. oreover, given the same N, the performance of S max and D min for CR-CSA is much better than the slotted CR-ALOHA, as shown in Figs. 8, 9, 11, and 12. This performance advantage is because the packets of the secondary network can more efficiently be scheduled into the channel and accordingly wait less time for transmission under the scheduling operation of CR-CSA compared with the slotted CR-ALOHA. oreover, compared to the performance of normalized throughput under the slotted CR-ALOHA and CR-CSA with the performance under the VX scheme 21], we can easily see that the values of S max in Figs. 7 and 11 are much greater than in 21], which shows the advantages of our proposed protocols. C. Tradeoff Between Performance and Interference We study the tradeoff between the performance achieved by the secondary network and the resulting interference on the E. Optimal Frame Length Now, we take into account the influence of the total frame length f. Based on the aforementioned analysis, we know that parameters IF and AF are both monotonically increasing functions of f. Therefore, a longer frame length f achieves higher S max and lower D min for both the slotted CR-ALOHA and CR-CSA, which has been validated in Figs This case can be explained by the following two reasons: 1) Periodic spectrum sensing takes up data transmission time, which reduces the channel utilization, particularly when the frame is very short, and 2) for a longer frame length, more SUs are allowed to compete for channel access rather than being blocked, which increases the transmission opportunities and finally improves the system performance. oreover, we know that the performance of the secondary network depends on both IF and AF. In fact, these two parameters are usually predefined by the application requirement. In our simulation, T v is set at 100 ms; therefore, the optimal frame length that satisfies the requirement of AF (denoted by f AF ) should be chosen as f AF =50. On the other hand, if the primary network requires that IF 0.2, we can calculate that the optimal frame length that satisfies the IF requirement (denoted by f IF ) is given by f IF =23. Considering both effects of interference and agility, the optimal f should be chosen as the minimum value of f IF and f AF, i.e., f =23.

13 2176 IEEE TRANSACTIONS ON VEHICULAR TECHNOLOGY, VOL. 60, NO. 5, JUNE 2011 Fig. 13. Tradeoff between performance and interference for the slotted CR-ALOHA. Fig. 14. Tradeoff between performance and interference for CR-CSA. Fig. 15. Tradeoff between performance and agility for the slotted CR-ALOHA. In particular, we observe that, when each frame contains only one TP, i.e., f =2,theS max for N =25is greater than for N =50 or N = 100, as shown in Fig. 13. This case is because the item in the right side of (15) cannot be neglected when l = β =1. Thus, the value of optimal t obtained from (17) is inaccurate for this special case. However, as the frame length f increases, the curve of S(t) in (15) becomes concave, and t, indeed, can achieve the maximum S. oreover, this

14 CHEN et al.: TWO-LEVEL AC PROTOCOL STRATEGY FOR OPPORTUNISTIC SPECTRU ACCESS IN CRNs 2177 Fig. 16. Tradeoff between performance and agility for CR-CSA. Fig. 17. Effects of P H0 on the slotted CR-ALOHA. Fig. 18. Effects of P H0 on CR-CSA. phenomenon proves the fact that, for f =2(short frame length) and larger N (heavy traffic rate), the system performance is really poor. Thus, we design the frame structure that one frame duration contains TPs, as mentioned in Section II-A. In addition, when N 50, the curves of S max in Figs are very close to each other. Furthermore, the performance curves sharply vary at the beginning of increasing f, but later on, they more gently change, and the performance finally

15 2178 IEEE TRANSACTIONS ON VEHICULAR TECHNOLOGY, VOL. 60, NO. 5, JUNE 2011 approaches a stable value, regardless of f s increase. This phenomenon is due to the maximum achievable performance constraints of the slotted CR-ALOHA or CR-CSA. F. Effects of the PUs Activities According to Section II-E, we know that PUs activities are related to their traffic parameters λ r and λ b. To consider the effects of the spectrum utilization of the primary network on the performance of the secondary network, we change the values of λ r and λ b to ensure that P H0 (the probability that P t is detected to be inactive in one frame) varies in the range 0.1, 1]. Intuitively, given a smaller P H0, U i s would more possibly be blocked for transmission. Conversely, given a larger P H0, U i s obtain more opportunities to compete for the channel, and the performance would be improved. Thus, we plot the S max and D min versus P H0 for the slotted CR-ALOHA and CR-CSA in Figs. 17 and 18, respectively. We see that S max linearly increases and D min monotonically decreases with the increase of P H0 for both the slotted CR-ALOHA and CR-CSA. This phenomenon validates the fact that P t s activities, indeed, have an influence on the performances of SUs and the spectrum utilization of the primary network determines the maximum achievable performance of the secondary network. oreover, in the beginning of the range P H0, because P t frequently occupies the current channel, the performance of U i s is really disappointing, regardless of whether N is equal to 25, 50, or 100, as shown in Figs. 17 and 18. In this case, to achieve better performance, SUs must consider shifting to another channel with a higher P H0. In fact, how we can choose a good channel is another key technique for CRNs, and we will consider it as our future work. VI. CONCLUSION In this paper, we have proposed a two-level OSA strategy and developed two random-access AC protocols called the slotted CR-ALOHA and CR-CSA for CRNs. A suitable frame structure has been designed, and closed-form expressions of network metrics, i.e., normalized throughput and average packet delay, have been derived, respectively. For various frame lengths and numbers of SUs, the optimal performance of SUs can be achieved at the same spectrum sensing time, and the maximum achievable performance of the secondary network is affected by the spectrum utilization of the primary network. oreover, using the interference and agility factors, we have shown that there exists a tradeoff between the achieved performance of the secondary network and the effects of protection on the primary network; therefore, the optimal frame length can accordingly be designed. APPENDIX A PROOF OF LEA 1 In this case, because the BP starts at time x during β and it consists of exact k TPs, the length of this BP and the UP are given by B 0 k,x = β x k(1 α) (k 1)/ β and U 0 k,x =z1 N 1 (k 1 (k 1)/ )N(1 z 2 )z2 N 1 /(1 z) (k 1)/ N(1 z 3 )z N 1 3 /(1 z), respectively, where z 1 = Z(β x), z 2 = Z(1 α), and z 3 = Z(1 α β). By removing the conditions of k and x, B 0 and U 0 are given by B 0 = 1 β U 0 = 1 β β 0 β 0 k=1 k=1 β xk(1α) k 1 z1 N 1 N(1 z 2)z2 N 1 1 z ] β z(1 z) k 1 dx ( k 1 (45) ) k 1 k 1 N(1 z3 )z N 1 ] 3 z(1 z) k 1 dx 1 z (46) respectively. It is easily verified that k=1 z(1 z)k 1 =1, k=1 kz(1 z)k 1 =1/z, and k=1 (k j 1)/ z(1 z) k 1 =(1 z) i /1 (1 z) ]; therefore, (32) and (33) in Lemma 1 hold. APPENDIX B PROOF OF LEA 2 In a similar way, we obtain B j and U j, j =1,..., 1, as B j = 1 1α I j = 1 1α βj(1α) β(j 1)(1α) k=1 k= j1 j(1α) βj(1α) β(j 1)(1α) k=1 k= j1 x β σ ( kj 1 σ (x β)k(1α) kj 1 x β σ β ] z(1 z) k 1 ] σ z(1 z) k 1 dx (47) ( ) kj 1 z4 N 1 k 1 N(1 z 2)z 2 N 1 ] z(1 z) k 1 1 z P H0 ) N(1 z3 )z N z P H 0 N(1 z 5 )z5 N 1 ] z(1 z) k 1 dx 1 z (48)

16 CHEN et al.: TWO-LEVEL AC PROTOCOL STRATEGY FOR OPPORTUNISTIC SPECTRU ACCESS IN CRNs 2179 respectively, where the variables z 4 and z 5 are given by z 4 = Z( (x β)/σ σ (x β)) and z 5 = Z(β (j 1)(1 α) (x β)/σ σ). oreover, we note that (1 α)(1 e GV 0σ )/(GV 0 σ) and βi(1α) β(j 1)(1α) zn 1 4 dx = βi(1α) β(j 1)(1α) N(1 z 5 )z N 1 5 dx 1 α β 1/(GV 0 )]e GV 0(1αβ) 2 2α β 1/(GV 0 )]e GV 0(22αβ). Based on (47) and (48), it follows that Lemma 2 is proved. APPENDIX C PROOF OF LEA 3 The proof process is similar to Lemmas 1 and 2. In this case, we obtain B and U B = 1 1α U = 1 1α βl k=1 βl (1α) βl k=1 βl (1α) β l x k(1 α) ] k 1 β z(1 z) k 1 dx (49) { z N 1 6 V 0 (N 1) (1 z 6 )z6 N 2 (1 V 0 ) ] ( ) k 1 P H0 k N(1 z 2)z2 N 1 1 z ( ) k 1 P H0 } N(1 z 3)z3 N 1 1 z z(1 z) k 1 dx. (50) respectively, where z 6 = Z(l x β). Solving (49) and (50), we see that (36) and (37) are verified. REFERENCES 1] U.S. Fed. Commun. Comm., Spectrum Policy Task Force Report, Nov Online]. 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17 2180 IEEE TRANSACTIONS ON VEHICULAR TECHNOLOGY, VOL. 60, NO. 5, JUNE 2011 Qian Chen (S 09) received the B.Eng. and.eng. degrees in computer science and engineering from Xi an Jiao Tong University, Xi an, China, in 2003 and 2006, respectively. He is currently working toward the Ph.D. degree with the Department of Electrical and Computer Engineering, National University of Singapore, Singapore. He is currently a Research Fellow with the Institute for Infocomm Research, A STAR, Singapore. His research interests include cognitive radio networks, mobile ad hoc and sensor networks, and medium-access-control (AC) layer protocols. Ying-Chang Liang (F 11) received the Ph.D. degree in electrical engineering from Jilin University, Changchun, China, in From December 2002 to December 2003, he was a Visiting Scholar with the Department of Electrical Engineering, Stanford University, Stanford, CA. He is currently a Principal Scientist with the Institute for Infocomm Research, A STAR, Singapore, and holds a joint appointment with Nanyang Technological University, Singapore. His research interests include cognitive radio, dynamic spectrum access, reconfigurable signal processing for broadband communications, space time wireless communications, wireless networking, information theory, and statistical signal processing. Dr. Liang is currently an Associate Editor for the IEEE TRANSACTIONS ON VEHICULAR TECHNOLOGY. He was an Associate Editor for the IEEE TRANSACTIONS ON WIRELESS COUNICATIONS from 2002 to 2005 and the Lead Guest Editor of the IEEE JOURNAL ON SELECTED AREAS IN COUNICATIONS Special Issue on Cognitive Radio: Theory and Applications and Special Issue on Advances in Cognitive Radio Networking and Communications. He is the Lead Guest Editor of the EURASIP Journal on Advances in Signal Processing Special Issue on Advanced Signal Processing for Cognitive Radio and a Guest Editor of the Elsevier Computer Networks Journal Special Issue on Cognitive Wireless Networks. He received the Best Paper Award at the IEEE Vehicular Technology Conference Fall, in 1999 and the IEEE International Symposium Personal, Indoor, and obile Radio Communications in 2005 and from the EURASIP Journal on Wireless Communications and Networking in He also received the Institute of Engineers Singapore Prestigious Engineering Achievement Award in ehul otani ( 98) received the B.S. degree from Cooper Union, New York, NY, the.s. degree from Syracuse University, Syracuse, NY, and the Ph.D. degree from Cornell University, Ithaca, NY, all in electrical and computer engineering. He is currently a Visiting Fellow with Princeton University, Princeton, NJ, and an Associate Professor with the Electrical and Computer Engineering Department, National University of Singapore, Singapore. Previously, he was a Research Scientist with the Institute for Infocomm Research, Singapore, for three years and a Systems Engineer with Lockheed artin, Syracuse, for over four years. His research interests are in the area of wireless networks. Recently, he has been working on research problems which sit at the boundary of information theory, communications, and networking, including the design of wireless ad hoc and sensor network systems. Dr. otani received the Intel Foundation Fellowship for work related to his Ph.D. research, which focused on information theory and coding for code division multiple access systems. He has served on the organizing committees of ISIT, WiNC, and ICCS, and the technical program committees of obicom, Infocom, ICNP, SECON, and several other conferences. He participates actively in the IEEE and the Association for Computing achinery and has served as the secretary of the IEEE Information Theory Society Board of Governors. He is currently an Associate Editor for the IEEE TRANSACTIONS ON INFORATION THEORY and an Editor for the IEEE TRANSACTIONS ON COUNICATIONS. Wai-Choong (Lawrence) Wong (S 93) received the B.Sc. (first-class honors) and Ph.D. degrees in electronic and electrical engineering from Loughborough University, Loughborough, U.K. From November 2002 to November 2006, he was the Executive Director of the Institute for Infocomm Research, A STAR, Singapore. From 1980 to 1983, he was a ember of Technical Staff with AT&T Bell Laboratories, Crawford Hill, NJ. He is currently a Professor with the Department of Electrical and Computer Engineering, National University of Singapore (NUS), Singapore, where he is also the Deputy Director (Strategic Development) with the Interactive and Digital edia Institute. Since joining NUS in 1983, he has served in various positions at the department, faculty, and university levels, e.g., the Head of the Department of Electrical and Computer Engineering from January 2008 to October 2009, the Director of the NUS Computer Centre from July 2000 to November 2002, and the Director of the Centre for Instructional Technology from January 1998 to June He is a coauthor of the book Source-atched obile Communications. His research interests include wireless networks and systems, multimedia networks, and source-matched transmission techniques, for which he has more than 200 publications and is the holder of four patents. Dr. Wong received the 1989 IEEE arconi Premium Award, the 1989 NUS Teaching Award, the 2000 IEEE illennium Award, the 2000 e-nnovator Award, Open Category, and the Best Paper Award at the 2006 IEEE International Conference on ultimedia and Expo.