MAC Protocol for Cognitive Radio Networks
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MAC Protocol for Cognitive Radio Networks



In this paper, we consider the joint optimal sensing ...

In this paper, we consider the joint optimal sensing
and distributed MAC protocol design for cognitive radio
networks. Specifically, we design a synchronized MAC protocol
for dynamic spectrum sharing among multiple secondary
users, which incorporates spectrum sensing for protecting active
primary users. We perform saturation throughput analysis for
the proposed MAC protocol that explicitly captures spectrum
sensing performance. Then, we find its optimal configuration
by formulating a throughput maximization problem subject to
detection probability constraints for primary users. In particular,
the optimal solution of this optimization problem returns the
required sensing time for primary users’ protection and optimal
contention window for maximizing total throughput of the
secondary network. Finally, numerical results are presented to
illustrate a significant performance gain of the optimal sensing
and protocol configuration.



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MAC Protocol for Cognitive Radio Networks MAC Protocol for Cognitive Radio Networks Document Transcript

  • 1 Course Report Student: Le Thanh Tan (LETT25047901) Instructor: Prof. Le Bao Long Semester: Winter 2011 Report Topic: MAC Protocol for Cognitive Radio Networks I. INTRODUCTION Emerging broadband wireless applications have been demanding unprecedented increase in radio spec- trum resources. As a result, we have been facing a serious spectrum shortage problem. However, several recent measurements reveal very low spectrum utilization in most useful frequency bands [1]. To resolve this spectrum shortage problem, the Federal Communications Commission (FCC) has opened licensed bands for unlicensed users’ access. This important change in spectrum regulation has resulted in growing research interests on dynamic spectrum sharing and cognitive radio in both industry and academia. In particular, IEEE has established an IEEE 802.22 workgroup to build the standards of WRAN based on CR techniques [1]. Hierarchical spectrum sharing between primary networks and secondary networks is one of the most popular dynamic spectrum sharing paradigms. For this spectrum sharing paradigm, primary users typically have strictly higher priority than secondary users in accessing the underlying spectrum. Therefore, a proper spectrum sensing mechanism is needed so that secondary users can search for and exploit available spectrum holes (i.e., available frequency bands) [2]. There are several challenging technical issues related to this spectrum discovery and exploitation problem. On one hand, secondary users should spend sufficiently long time for spectrum sensing so that they do not interfere with active primary users. On the other hand, secondary users should efficiently exploit spectrum holes to transmit their data by using an appropriate spectrum sharing mechanism. Even though these aspects are tightly coupled with each other, they are not treated thoroughly in the existing literature. There is a rich literature on spectrum sensing for cognitive radio networks (e.g., see [3] and references therein). Classical sensing based on, for example, energy detection techniques or advanced cooperative sensing strategies [4] where multiple secondary users collaborate with another to improve the sensing performance have been investigated in the literature. In [2], optimization of sensing and throughput tradeoff under a detection probability constraint was investigated. It was shown that the detection constraint is met with equality at optimality. However, this optimization tradeoff was only investigated for a simple scenario with one pair of secondary users. There are also a large number of papers considering MAC protocol design and analysis for cognitive radio networks [5]-[10]. However, these existing works either assumed perfect spectrum sensing or did not explicitly model the sensing imperfection in their design and analysis. In this paper, we make a further bold step in designing, analyzing, and optimizing a MAC protocol for cognitive radio networks considering sensing performance captured in detection and false alarm probabilities. Specifically, the contributions of this paper can be summarized as follows: i) we design a distributed synchronized MAC protocol for cognitive radio networks incorporating spectrum sensing operation; ii) we analyze saturation throughput of the proposed MAC protocols; iii) we perform the throughput maximization of the proposed MAC protocol against its key parameters, namely sensing time and contention window; iv) we present numerical results to illustrate performance of the proposed MAC protocol and the throughput gain due to the optimal protocol configuration.
  • TEL352 Reading Course - Final Report Fig. 1. Typical spectrum sharing model. The remaining of this paper is organized as follows. Section II describes a system model and the design of a synchronized MAC protocol. Throughput analysis and optimization are provided in Section III. Section IV demonstrates numerical results followed by concluding remarks in Section V. II. SYSTEM MODEL AND MAC PROTOCOL DESIGN A. System Model We consider a network setting where N pairs of secondary users opportunistically exploit one particular radio channel (i.e., a frequency band) for their data transmission, which belongs a primary network. Extension to a more general case with multiple channels will be discussed later. We assume that each pair of secondary users can overhear transmissions from other pairs of secondary users (i.e., it is a collocated network). It is further assumed that transmission from each individual pair of secondary users affects one different primary receiver. Note that it is straightforward to extend this assumption to the scenario where each pair of secondary users affects more than one primary receiver and/or each primary receiver is affected by more than one pair of secondary users. The network setting under investigation is shown in Fig. 1. In the following, we will refer to pair i of secondary users as secondary link i or flow i interchangeably. B. Spectrum Sensing We assume that secondary links rely on a distributed synchronized MAC protocol to share the spectrum when it is available. Specifically, time is divided into fixed-size cycles and it is assumed that secondary links can perfectly synchronize with each other (i.e., there is no synchronization error) [8], [11]. It is assumed that each secondary link performs spectrum sensing at the beginning of each cycle and only proceeds to contend with others to capture the channel if the sensing outcome indicates an available channel (i.e., it is not being used by nearby primary users). Detailed MAC protocol design will be elaborated in the next subsection. Let H0 and H1 denote the events that a particular primary user is idle and active, respectively (i.e., the underlying channel is available and busy, respectively). In addition, let Pi (H0) and Pi (H1) = 1−Pi (H0) be the probabilities that secondary link i sees an idle and busy channel, respectively. We assume that secondary users employ an energy detection scheme and let fs be the sampling frequency used in the sensing period whose length is τ for all secondary links. There are two important performance measures, which are used to quantify the sensing performance, namely detection and false alarm probabilities. In particular, detection event occurs when a secondary link successfully senses a busy channel and false 2
  • TEL352 Reading Course - Final Report … One cycle SensingSYN Backoff DATA ACK DATA ACK Backoff time Fig. 2. Timing diagram of the proposed MAC protocol. alarm represents the situation when a spectrum sensor returns a busy state for an idle channel (i.e., a transmission opportunity is overlooked). Assume that transmission signals from primary users are complex-valued PSK signals while the noise at the secondary links is independent and identically distributed circularly symmetric complex Gaussian CN (0, N0) [2]. Then, the detection and false alarm probability for secondary link i can be calculated as [2] Pi d εi , τ = Q εi N0 − γi − 1 τfs 2γi + 1 , (1) Pi f εi , τ = Q εi N0 − 1 τfs = Q 2γi + 1Q−1 Pi d εi , τ + τfsγi , (2) where εi is the detection threshold for an energy detector, γi is the signal-to-noise ratio (SNR) of the PU’s signal at the secondary link, fs is the sampling frequency, N0 is the noise power, τ is the sensing interval, and Q (.) is defined as Q (x) = 1/ √ 2π ∞ x exp (−t2 /2) dt. These probabilities will be used in throughput analysis in the next section. C. MAC Protocol Design We describe our proposed synchronized MAC for dynamic spectrum sharing among secondary flows in this subsection. We assume that each fixed-size cycle of length Tcycle is divided into 3 phases, namely sensing phase, synchronization phase, and data transmission phase. During the sensing phase of length τ, all secondary users perform spectrum sensing on the underlying channel. Then, only secondary links whose sensing results indicate an available channel proceed to the next phase (they will be called active secondary users/links in the following). In the synchronization phase, active secondary users broadcast beacon signals for synchronization purposes. Finally, active secondary users perform contention and transmit data in the data transmission phase. The timing diagram of one particular cycle is illustrated in Fig. 2. We assume that the length of each cycle is sufficiently large such that secondary links can transmit several packets during the data transmission phase. Indeed, the current 802.22 standard specifies the spectrum evacuation time upon the return of primary users is 2 seconds, which is a relatively large interval. Therefore, our assumption would be valid for most practical cognitive systems. During the data transmission phase, we assume that active secondary links perform a standard contention technique to capture the channel similar to that employed by the CSMA/CA protocol. For simplicity, we assume a fixed contention window equal to W is used for random backoff. Extension to the case where exponential backoff [12] is employed will be discussed later. Specifically, each active secondary link starts the contention by choosing a random backoff time uniformly distributed in the range [0, W − 1] and starts decrementing its backoff time counter while carrier sensing transmissions from other secondary links. Let σ denote a mini-slot interval, each of which corresponds one unit of the backoff time counter. Upon hearing a transmission from any secondary link, each secondary link will “freeze” its backoff time counter and reactivate when the channel sensed 3
  • TEL352 Reading Course - Final Report idle again. Otherwise, if the backoff time counter reaches zero, the underlying secondary link wins the contention and transmits one data packet to its intended receiver. The transmitter then waits for an acknowledgment (ACK) from the receiver to indicate a successful reception of the packet. Standard small intervals, namely DIFS and SIFS, are used before backoff time decrements and ACK packet transmission as described in [12]. D. Throughput Maximization Given the sensing model and proposed MAC protocol, we are interested in finding its optimal con- figuration to achieve the maximum throughput subject to protection constraints for primary receivers. Specifically, let NT (τ, W) be the normalized total throughput, which is a function of sensing time τ and contention window W. Suppose that each primary receiver requires that detection probability achieved by its conflicting primary link i to be at least P i d. Then, the throughput maximization problem can be stated as follows: max τ,W NT (τ, W) s.t. Pi d (εi , τ) ≥ ¯Pi d, i = 1, 2, · · · , N 0 < τ ≤ Tcycle, 0 < W ≤ Wmax, (3) where Wmax is the maximum contention window and recall that Tcycle is the cycle interval. In fact, optimal sensing τ would allocate sufficient time to protect primary receivers and optimal contention window would balance between reducing collisions among active secondary links and protocol overhead. III. THROUGHPUT ANALYSIS AND OPTIMIZATION We perform saturation throughput analysis and solve the optimization problem (3) in this section. Throughput analysis for the cognitive radio setting under investigation is more involved compared to standard MAC protocol throughput analysis (e.g., see [11], [12]) because the number of active secondary links participating in contention in each cycle varies depending on the sensing outcomes. Suppose that all secondary links have same packet length. Let Pr (n = n0) and T (τ, φ |n = n0 ) be the probability that n0 secondary links participating in contention and the conditional normalized throughput when n0 secondary links join the channel contention, respectively. Then, the normalized throughput can be calculated as NT = N n0=1 T (τ, W |n = n0 ) Pr (n = n0), (4) where recall that N is the number of secondary links, τ is the sensing time, W is the contention window. In the following, we show how to calculate Pr (n = n0) and T (τ, φ |n = n0 ). A. Calculation of Pr (n = n0) It is noted that only secondary links whose sensing outcomes in the sensing phase indicate an available channel proceed to contention in the data transmission phase. There are two scenarios for which this can happen for a particular secondary link i: • The primary user is not active and no false alarm is generated by the underlying secondary link. • The primary user is active and secondary link i mis-detects its presence. Therefore, secondary link i joins contention in the data transmission phase with probability Pi idle = 1 − Pi f εi , τ Pi (H0) + Pi m εi , τ Pi (H1) , (5) where Pi m (εi , τ) = 1 − Pi d (εi , τ) is the mis-detection probability. Otherwise, it will be silent for the whole cycle and waits until the next cycle. This occurs with probability Pi busy = 1 − Pi idle. We assume that interference of active primary users to secondary users is negligible; therefore, a transmission from 4
  • TEL352 Reading Course - Final Report any secondary link only fails when it collides with transmissions from other secondary links. Now, let Sk denote one particular subset of all secondary links having exactly n0 secondary links. There are Cn0 N = N! n0!(N−n0)! such sets Sk. The probability of the event that n0 secondary links join contention in the data transmission phase can be calculated as Pr (n = n0) = C n0 N k=1 i∈Sk Pi idle j∈SSk Pj busy, (6) where S denotes the set of all N secondary links, and SSk is the set of remaining N − n0 secondary links. If all secondary links have the same SNRp and the same probabilities Pi (H0) and Pi (H1), then we have Pi idle = Pidle and Pi busy = Pbusy = 1 − Pidle for all i. In this case, (6) becomes Pr (n = n0) = Cn0 N (Pidle)n0 (1 − Pidle)N−n0 , (7) where all terms in the sum of (6) become the same. B. Calculation of Conditional Throughput The conditional throughput can be calculated by using the standard technique developed by Bianchi in [12] where we approximately assume a fixed transmission probability φ in a generic slot time. It was shown in [12] that for a fixed contention window W, we have φ = 2/ (W + 1). Suppose there are n0 secondary links participating in contention in the third phase, the probability of the event that at least one secondary link transmits is data packet can be written as Pt = 1 − (1 − φ)n0 . (8) However, the probability that a transmission occurring on the channel is successful given there is at least one secondary link transmitting can be written as Ps = n0φ(1 − φ)n0−1 Pt . (9) The average duration of a generic slot time can be calculated as ¯Tsd = (1 − Pt) Te + PtPsTs + Pt (1 − Ps) Tc, (10) where Te = σ, Ts and Tc represent the duration of an empty slot, the average time the channel is sensed busy due to a successful transmission, and the average time the channel is sensed busy due to a collision, respectively. These quantities can be calculated as [12]    Ts = T1 s = H + PS + SIFS + 2 ∗ PD+ACK+DIFS Tc = T1 c = H + PS + DIFS + PD H = HPHY + HMAC , (11) where HPHY and HMAC are the packet headers for physical and MAC layers, PS is the packet size, which is assumed to be fixed in this paper, PD is the propagation delay, SIFS is the length of a short interframe space, DIFS is the length of a distributed interframe space, ACK is the length of an acknowledgment. Based on these quantities, we can express the conditional normalized throughput as follows: T (τ, φ |n = n0 ) = Tcycle − τ ¯Tsd PsPtPS Tcycle , (12) where ⌊.⌋ denotes the floor function and recall that Tcycle is the duration of a cycle. Note that Tcycle−τ ¯Tsd denotes the average number of generic slot times in one particular cycle excluding the sensing phase. Here, we omit the length of the synchronization phase, which is assumed to be negligible. 5
  • TEL352 Reading Course - Final Report C. Optimal Sensing and MAC Protocol Design Now, we turn to solve the throughput maximization problem formulated in (3). Note that we can calculate the normalized throughput given by (4) by using Pr (n = n0) calculated from (6) and the conditional throughput calculated from (12). It can be observed that the detection probability Pi d (εi , τ) in the primary protection constraints Pi d (εi , τ) ≥ ¯Pi d depends on both detection threshold εi and the optimization variable τ. We can show that by optimizing the normalized throughput over τ and W while fixing detection thresholds εi = εi 0 where Pi d (εi 0, τ) = ¯Pi d, i = 1, 2, · · · , N, we can achieve almost the maximum throughput gain. The intuition behind this can be interpreted as follows. If we choose εi < εi 0 for a given τ, then both Pi d (εi , τ) and Pi f (εi , τ) increase compared to the case εi = εi 0. As a result, Pi idle given in (5) decreases. Moreover, it can be verified that the decrease in Pi idle will lead to the shift of the probability distribution Pr (n = n0) to the left. Specifically, Pr (n = n0) given in (6) increases for small n0 and decreases for large n0 when Pi idle decreases. Fortunately, with appropriate choice of contention window W the conditional throughput T (τ, W |n = n0 ) given in (12) is quite flat for different n0 (i.e., it only decreases slightly when n0 increases). Therefore, the normalized throughput given by (4) is almost a constant when we choose εi < εi 0. In the following, we will optimize the normalized throughput over τ and W while choosing detection thresholds such that Pi d (εi 0, τ) = ¯Pi d, i = 1, 2, · · · , N. From these equality constraints and (2) we have Pi f = Q αi + τfsγi (13) where αi = √ 2γi + 1Q−1 ¯Pi d . Hence, the optimization problem (3) becomes independent of all detection thresholds εi , i = 1, 2, · · · , N. Unfortunately, this optimization problem is still a mixed integer program (note that W takes integer values), which is difficult to solve. In fact, it can be verified even if we allow W to be a real number, the resulting optimization problem is still not convex because the objective function is not concave [13]. Therefore, standard convex optimization techniques cannot be employed to find the optimal solution for the optimization problem under investigation. Therefore, we have to rely on numerical optimization [14] to find the optimal configuration for the proposed MAC protocol. Specifically, for a given contention window W we can find the corresponding optimal sensing time τ as follows: max 0<τ≤Tcycle NT(τ, W) = N n0=1 T (τ, W |n = n0 )Pr (n = n0). (14) This optimization problem is not convex because its objective function is not concave in general. However, there exists an optimal solution τ∗ for this problem because the objective function is bounded from above (because Pr (n = n0) < 1 and conditional throughput are all bounded) and its objective function increases in small τ and decreases in large τ. This second property is formally stated in the following proposition. Proposition 1: The objective function NT(τ) of (14) satisfies the following properties lim τ→Tcycle ∂NT ∂τ < 0, lim τ→0 ∂NT ∂τ = +∞. (15) Proof: Let us start the proof by defining the following quantities: ϕj := − αj+ √ τfsγj 2 2 and cn0 := 6
  • TEL352 Reading Course - Final Report PsPtPS Tcycle . Taking the derivative of NT versus τ, we have ∂NT ∂τ = N n0 cn0 CN n0 k=1   −1 Tsd i∈Sk Pi idle j∈SSk Pj busy+ Tcycle−τ Tsd fs 8πτ ×    i∈Sk γi exp (ϕi ) Pi (H0) l∈Ski Pl idle j∈SSk Pj busy − j∈SSk γj exp (ϕj ) Pj (H0) l∈SSkj Pl busy i∈Sk Pi idle       . (16) From this we have lim τ→Tcycle ∂NT ∂τ = N n0 cn0 CN n0 k=1 −1 Tsd i∈Sk Pi idle j∈SSk Pj busy < 0. (17) Now, let us define the following quantity Kτ:= N n0 cn0 CN n0 k=1    i∈Sk γi exp (ϕi )Pi (H0) l∈Ski Pl idle j∈SSk Pj busy− j∈SSk γj exp (ϕj )Pj (H0) l∈SSkj Pl busy i∈Sk Pi idle   . (18) Then, it can be verified that Kτ > 0. Therefore, we have lim τ→0 ∂NT ∂τ = +∞. (19) Hence, we have completed the proof. In summary, one can find the globally optimal (W∗ , τ∗ ) by finding optimal τ for each W in its feasible range [1, Wmax]. The procedure to find (W∗ , τ∗ ) can be described in the following algorithm. Algorithm 1 OPTIMIZATION OF COGNITIVE MAC PROTOCOL 1: For each W ∈ [1, Wmax], find the optimal τ according to (14), i.e., τ(W) = argmax 0<τ≤Tcycle NT(τ, W) (20) 2: The globally optimal (W∗ , τ∗ ) can then be found as (W∗ , τ∗ ) = argmax W,τ(W) NT(τ(W), W). (21) Numerical studies reveal that this algorithm has quite low computation time for practical values of Wmax and Tcycle. Remark 1: The above analysis and optimization can be extended to the case where exponential backoff with minimum contention window Wmin and maximum backoff stage m is employed. However, transmission probability φ needs to be found as a fixed point solution of two equations [12], which is used to calculate conditional throughput in Section III.B. In this case, Wmin and τ will be optimization variables. Remark 2: We can extend the presented MAC protocol design to the case where there are multiple channels. To exploit spectrum holes in this case, we assume that there is one control channel which belongs to the secondary network (i.e., it is always available) and M data channels whose states (i.e., idle or busy) change over time. We further assume that each secondary user has two transceivers one which is always tuned to the control channel while the remaining one may be switched to different data channels. We can design a multi-channel synchronized MAC protocol for this setting as follows. Each cycle is still divided into 3 phases as before. However, in the sensing phase each secondary link needs to 7
  • TEL352 Reading Course - Final Report 8 16 32 64 128 256 512 1,000 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 Contention window (W) Throughput(NT) Throughput vs contention window N = 2 N = 5 N = 10 N = 15 N = 20 Fig. 3. Normalized throughput versus contention window W for τ = 1ms and different N. 0 0.5 1 1.5 2 2.5 3 3.5 x 10 −3 0.4 0.45 0.5 0.55 0.6 0.65 0.7 0.75 0.8 0.85 0.9 Sensing time (τ) Throughput(NT) Throughput vs sensing time N = 30 N = 20 N = 2 N = 5 N = 10 Fig. 4. Normalized throughput versus the sensing time τ for W = 32 and different N. sequentially perform spectrum sensing on all data channels. Therefore, by the end of the first phase each secondary link i has a list of available channel Ci. In the data transmission phase, active secondary links who find at least one available channel contend on the control channel to choose a data channel for their transmissions. Again, contention is performed by using the CSMA-based random backoff mechanism and secondary links winning the contention exchange RTS/CTS which contains information about one chosen data channel for data transmission as well as the packet length to be transmitted (for other secondary users to update their network allocation vector (NAV)). Note that because all secondary users have one transceiver tuned to the control channel, they always know which channels are being used by other secondary users. Due to the space constraint, analysis and optimization of this multi-channel MAC protocol are not pursued further in this paper. IV. NUMERICAL RESULTS We present numerical results to illustrate throughput performance of the proposed cognitive MAC protocol. We take key parameters for the MAC protocol from Table II in [12]. Other parameters are chosen as follows: cycle time is Tcycle = 100ms; mini-slot (i.e., generic empty slot time) is σ = 20µs; sampling frequency for spectrum sensing is fs = 6MHz; bandwidth of PUs’ QPSK signals is 6MHz. The signal- to-noise ratio of PU signals at secondary links SNRi p are chosen randomly in the range [−15, −20]dB. The target detection probability for secondary links and the probabilities Pi (H0) are chosen randomly in the intervals [0.7, 0.9] and [0.7, 0.8], respectively. In Fig. 3, we show normalized throughput NT versus contention window W for different values of N when the sensing time is fixed at τ = 1ms for one particular realization of system parameters. The maximum throughput on each curve is indicated by a star symbol. This figure indicates that the maximum throughput is achieved at larger W for larger N. This is expected because larger contention window can alleviate collisions among active secondary for larger number of secondary links. It is interesting to 8
  • TEL352 Reading Course - Final Report 0 0.5 1 1.5 x 10 −3 0 0.02 0.04 0.06 0 0.2 0.4 0.6 0.8 1 Sensing time (τ) Throughput vs transmission probability and sensing time Transmission probability (φ) Throughput(NT) 0.2 0.3 0.4 0.5 0.6 0.7 0.8 NT opt (0.0003, 0.0125) = 0.8542 Fig. 5. Normalized throughput versus sensing time τ and transmission probability φ for N = 15. 0 2 4 6 8 x 10 −4 0 0.02 0.04 0.06 0 0.2 0.4 0.6 0.8 1 Sensing time (τ) Throughput vs transmission probability and sensing time Transmission probability (φ) Throughput(NT) 0.2 0.3 0.4 0.5 0.6 0.7 0.8 NT opt (0.0002, 0.0091) = 0.8546 Fig. 6. Normalized throughput versus sensing time τ and transmission probability φ for N = 20. observe that the maximum throughput can be larger than 0.8 although Pi (H0) are chosen in the range [0.7, 0.8]. This is due to a multiuser gain because secondary links are in conflict with difference primary receivers. In Fig. 4 we present the normalized throughput NT versus sensing time τ for a fixed contention window W = 32 and different number of secondary links N. Again, the maximum throughput is indicated by a star symbol on each curve. This figure confirms the fact that the normalized throughput NT increases when τ is small and decreases with large τ as being proved in Proposition 2. In addition, the normalized throughput NT is not a concave function of τ for large N. Moreover, for a fixed contention window optimal sensing time indeed decreases with the number of secondary links N. Finally, the multi-user diversity gain can also be observed in this figure. To illustrate the joint effect of contention window W and sensing time τ, we show the normalized throughput NT versus τ and transmission probability φ for N = 15 and N = 20 in Fig. 5 and Fig. 6, respectively. Recall that the transmission probability can be calculated from contention window W as φ = 2/(W + 1). We show the globally optimal parameters (φ∗ , τ∗ ) which maximize the normalized throughput NT of the proposed cognitive MAC protocol by a star symbol in these two figures. These figures reveal that the performance gain due to optimal configuration of the proposed MAC protocol is very significant. Specifically, while the normalized throughput NT tends to be less sensitive to the transmission probability φ, therefore the contention window W, it decreases significantly when the sensing time τ is deviated from the optimal value τ∗ . Therefore, the proposed optimization approach would be 9
  • TEL352 Reading Course - Final Report very useful in achieving the largest throughput performance for the secondary network. V. CONCLUSION In this paper, we have designed, analyzed, and optimized a MAC protocol for cognitive radio networks that explicitly take into account spectrum sensing performance. Specifically, we have derived the normal- ized throughput of the proposed MAC protocol as a function of sensing time, contention window and other system parameters. Then, we have showed how to choose detection thresholds for energy spectrum sensors, sensing time, and contention window to maximize the normalized throughput subject to protection constraints for primary receivers. In addition, we have presented numerical results to confirm important theoretical findings in the paper and show the significant performance gain achieved by the optimal configuration for proposed MAC protocol. Finally, several potential extensions including consideration of exponential backoff and multi-channel scenario have been discussed. REFERENCES [1] C. Stevenson, G. Chouinard, L. Zhongding, H. Wendong, S. Shellhammer, W. Caldwell, “IEEE 802.22: The first cognitive radio wireless regional area network standard,” IEEE Commun. Mag., vol. 47, no. 1, pp. 130–138, Jan. 2009. [2] L. Ying-Chang, Z. Yonghong, E. C. Y. Peh and H. Anh Tuan, “Sensing-throughput tradeoff for cognitive radio networks”, IEEE Trans. Wireless Commun., vol. 7, no. 4, pp. 1326-1337, April 2008. [3] T. Yucek and H. Arslan, “A survey of spectrum sensing algorithms for cognitive radio applications,” IEE Commun. Surveys and Tutorials, vol. 11, no. 1, pp. 116–130, 2009. [4] J. Unnikrishnan and V. V. Veeravalli, “Cooperative sensing for primary detection in cognitive radio,” IEEE J. Sel. Areas Signal Processing, vol. 2, no. 1, pp. 18–27, Feb. 2008. [5] H. Kim and K. G. Shin, “Efficient discovery of spectrum opportunities with MAC-layer sensing in cognitive radio networks,” IEEE Trans. Mobile Computing, vol. 7, no. 5, pp. 533-545, May 2008. [6] H. Nan, T.-I. Hyon, and S.-J. Yoo, “Distributed coordinated spectrum sharing MAC protocol for cognitive radio,” in IEEE DySPAN’2007. [7] C. Cordeiro, and K. Challapali, “ C-MAC: A cognitive MAC protocol for multi-channel wireless networks,” in IEEE DySPAN’2007. [8] Y.R. Kondareddy, and P. Agrawal, “Synchronized MAC protocol for multi-hop cognitive radio networks,” in Proc. IEEE ICC’2008. [9] A. C.-C. Hsu, D.S.L. Weit, and C.-C.J. Kuo, “A cognitive MAC protocol using statistical channel allocation for wireless ad-hoc networks,” in Proc. IEEE WCNC’2007. [10] H. Su, and X. Zhang, “Cross-layer based opportunistic MAC protocols for QoS provisionings over cognitive radio wireless networks,” IEEE J. Sel. Areas Commun., vol. 26, no. 1, pp. 118–129, Jan. 2008. [11] J. Shi, E. Aryafar, T. Salonidis and E. W. Knightly, “Synchronized CSMA contention: Model, implementation and evaluation”, in IEEE INFOCOM, pp. 2052-2060, 2009. [12] G. Bianchi, “Performance analysis of the ieee 802.11 distributed coordination function”, IEEE J. Sel. Areas Commun., vol. 18, no. 3, pp. 535-547 Mar. 2000. [13] S. P. Boyd and L. Vandenberghe, Convex optimization, Cambridge University Press, Cambridge, UK ; New York, 2004. [14] S. Kameshwaran and Y. Narahari, “Nonconvex piecewise linear knapsack problems,” European J. Operational Research, vol. 192, no. 1, pp. 56-68, 2009. 10