Multi-Channel MAC Protocol for Full-Duplex Cognitive Radio Networks with Optimized Access Control and Load Balancing

Transcription

1 Multi-Channel MAC Protocol for Full-Dulex Cognitive Radio etworks with Otimized Access Control and Load Balancing Le Thanh Tan and Long Bao Le arxiv:.3v [cs.it] Feb Abstract In this aer, we roose a multi-channel full-dulex Medium Access Control MAC rotocol for cognitive radio networks MFDC MAC. Our design exloits the fact that fulldulex FD secondary users SUs can erform sectrum sensing and access simultaneously, and we emloy the randomized dynamic channel selection for load balancing among channels and the standard backoff mechanism for contention resolution on each available channel. Then, we develo a mathematical model to analyze the throughut erformance of the roosed MFDC MAC rotocol. Furthermore, we study the rotocol configuration otimization to maximize the network throughut where we show that this otimization can be erformed in two stes, namely otimization of access and transmission arameters on each channel and otimization of channel selection robabilities of the users. Such otimization aims at achieving efficient selfinterference management for FD transceivers, sensing overhead control, and load balancing among the channels. umerical results demonstrate the imacts of different rotocol arameters and the imortance of arameter otimization on the throughut erformance as well as the significant erformance gain of the roosed design comared to traditional design. Index Terms MAC rotocol, sectrum sensing, otimal sensing, throughut maximization, full-dulex cognitive radios. I. ITRODUCTIO Design of MAC rotocols for efficient sharing of white saces and aroriate rotection of transmissions from rimary users PUs on licensed frequency in cognitive radio networks CRs is an imortant research toic. In the traditional design and analysis of a half-dulex HD MAC rotocol [], [], [3], [], [], SUs tyically emloy a twostage sensing/access rocedure due to the HD constraint [3], [], []. This constraint also requires SUs be synchronized during the sectrum sensing stage, which could be difficult to achieve in ractice. Moreover, sohisticated design and arameter configuration of cognitive MAC rotocols can result in significant erformance enhancement while aroriately rotecting SUs [], []. Furthermore, different multi-channel cognitive MAC rotocols were roosed consering either different sectrum sensing and access methods [], []. By emloying the advanced FD transceiver, each SU can transmit and receive data simultaneously on the same frequency band []. Practical FD transceivers, however, suffer from self-interference, which is caused by ower leakage from the transmitter to the receiver. The self-interference may indeed lead to serious communication erformance degradation of FD wireless systems. Emloyment of FD transceivers for more efficient sectrum access design in cognitive radio networks has been very under exlored in the literature. The cognitive MAC design in one recent work [] allows SUs to The authors are with IRS-EMT, University of Quebec, Montréal, Québec, Canada. s: {lethanh,long.le}@emt.inrs.ca. erform sensing and transmission simultaneously; however, the work [] assumes simultaneous sectrum access of the SU and PU networks. This design is, therefore, not alicable to the hierarchical sectrum access in the CRs where PUs should have higher sectrum access riority comared to SUs. In this aer, we roose a novel MFDC MAC rotocol that allows concurrent sectrum sensing and transmission on each channel as well as efficient access and load balancing among the channels. In our design, each SU adots the randomized channel selection to choose its channel, which is slowly udated over time for load balancing. Moreover, SUs emloy the standard -ersistent CSMA mechanism for contention resolution on the selected channel, and the winning SU follows a two-stage rocedure for sectrum sensing and access. Secifically, the winning SU erforms simultaneous sensing and transmission during the first stage and transmission only in the second stage. This design enables aroriate rotection of PUs and efficient exloitation of white saces on all the channels. We develo a mathematical model for throughut erformance analysis of the roosed MFDC-MAC rotocol consering the imerfect sensing and self-interference effects. Moreover, we study the otimal configuration of different rotocol arameters for sectrum sensing, access, and load balancing i.e., channel access robabilities to achieve the maximum throughut. Extensive numerical results are then resented to illustrate the imacts of different rotocol arameters on the throughut erformance and the significant throughut gains of the roosed MFD-MAC rotocol with resect to conventional designs. The remaining of this aer is organized as follows. Section II describes the system and PU activity models. MAC rotocol design and throughut analysis are erformed in Section III. We discuss the rotocol otimization in Section IV. Section V demonstrates numerical results followed by concluding remarks in Section VI. A. System Model II. SYSTEM AD PU ACTIVITY MODELS We conser a network setting where airs of SUs oortunistically exloit white saces on M frequency channels for data transmission. We assume that each SU is equied with one full-dulex transceiver, which can erform sensing and transmission simultaneously. However, any SU suffers from self-interference from its transmission during sensing i.e., transmitted signals are leaked into the received signal. At channel, we denote I as the average self-interference ower, which is assumed to be modeled as I = ζ P sen, ξ [] where P sen, is the SU transmit ower, ζ and ξ ξ are

2 I Fig.. DIFS Channel is available DATA DATA FD C RTS Collision... Active sensing SU DIFS RTS SIFS CTS SIFS RTS/CTS exchange C I U Contention and access cycle T T eva Collision C DATA FD Successful channel reservation U DATA Channel is not available Sensing stage Tx stage Sensing stage Tx stage T T eva Active sensing SU Idle I DATA SIFS ACK Data Transmission... DATA Contention and access cycle Contention hase T ove PU activity t PU activity t Data hase T T T PU activity h h S h h h h Timing diagram of the roosed full-dulex MAC rotocol.... time Case h, h! Case h, h! Case 3 h, h! redetermined coefficients which cature the self-interference cancellation quality. We design an asynchronous MAC rotocol where no synchronization is required between SUs and PUs as well as among SUs. We assume that different airs of SUs can overhear transmissions from the others i.e., a collocated network. In the following, we refer to air i of SUs simly as SU i. B. Primary User Activity We assume that the PU s le/busy status follows two indeendent and entical distribution rocesses. In articular, each channel is available and busy for the secondary access if the PU is in the le and busy states, resectively. Let H and H denote the events that the PU is le and active, resectively. To rotect the PU, we assume that SUs must sto their transmission and evacuate from the channel within the maximum delay of T eva, which is referred to as channel evacuation time. Let τac and τ denote the random variables which reresent the durations of channel active and le states on channel, resectively. We assume that τac and τ are larger than T eva with high robability. We denote robability density functions of τac and τ as f τac t and f τ t, resectively. In addition, let P H = τ and P H τ + τ ac = P H resent the robabilities that the channel is available and busy, resectively. III. MULTI-CHAEL FULL-DUPLEX COGITIVE MAC PROTOCOL In this section, we describe our roosed MFDC-MAC rotocol and conduct its throughut analysis consering imerfect sensing and self-interference of the FD transceiver. A. MFDC MAC Protocol Design In our MFDC-MAC rotocol, each SU randomly selects one channel by using a randomized channel selection mechanism where channel is selected with robability. In this aer, we conser the general heterogeneous scenario where the statistical arameters τac and τ of different channel can be different. This channel selection is reeated once after a redetermined long eriod, which is an order of magnitude larger than the average contention/access time to transmit one data frame acket on each channel e.g., every K max data frames. After channel selection, each SU emloys the following single-channel contention, sectrum sensing, and transmission to exloit the white sace. Secifically, SUs choosing the same channel is assumed to emloy the -ersistent CSMA rincile [9] for contention resolution where each SU attemts to cature the channel with a robability after the channel is sensed to be le during the standard DIFS interval DCF Interframe Sace. If a articular SU deces not to transmit with robability of, it will carrier sense the channel and attemt to transmit again in the next slot with robability. To comlete the reservation, the four-way handshake with Request-to-Send/Clear-to-Send RTS/CST exchanges [9] is emloyed to reserve the available channel for transmission in the next hase. After each successful transmission of duration T, an acknowledgment ACK from the SU s receiver is transmitted to its corresonding transmitter to notify the successful recetion of a acket. Furthermore, the standard small interval, namely SIFS Short Interframe Sace, is used before the transmissions of CTS, ACK, and data frame as in the standard. MAC rotocol [9]. Then, the data hase after the channel contention hase comrises two stages where the winning SU erforms concurrent sensing and transmission in the first stage with duration, called FD sensing stage and transmission only in the second stage with duration T, called transmission stage. Here, the SU exloits the FD communication caability of its transceiver to realize concurrent sensing and transmission the first stage where the sensing outcome at the end of this stage i.e., an le or active channel status determines its further actions as described in the following. If the sensing outcome indicates an available channel then the SU transmits data in the second stage; otherwise, it remains silent for the remaining eriod of the data hase with duration T,. We assume that the duration of the SU s data hase T is smaller than the channel evacuation time T eva so timely evacuation from the busy channel can be realized. Therefore, our design allows to rotect the PU with evacuation delay at most T if the carrier sensing before the contention hase and the sectrum sensing in the data hase are erfect. Furthermore, we assume that the SU transmits at ower levels P sen, and P dat during the FD sensing and transmission stages, resectively where the transmit ower P sen, will be chosen to effectively mitigate the self-interference and achieve good sensing-throughut tradeoff. The timing diagram of the roosed MFDC MAC rotocol is illustrated in Fig.. B. Throughut Analysis We now analyze the saturation throughut. Recall that for each channel, the PU is active and le with the corresonding dfs of τac and τ are f τac τ ac and fτ τ. Moreover, we assume that the received PU s signal ower at the SU s receiver for channel is P. The throughut is a function of following arameters: robability of transmission, sensing

3 3 time,, frame length T, and SU transmit ower P sen, for each channel. For brevity, we ignore the deendence of throughut on and T in the following. To calculate the throughut of the MFDC MAC rotocol, denoted as T, we conser all ossible cases where each case is reresented by the corresonding sets of users selecting different channels each set of users is { for one channel. We now define the set Ω = ω k ={n k,,..., n k,,..., n k,m }: } M = n k, = where its k-th element ω k has its comonents n k, reresenting the number of users who select channel. The robability for the set ω k is M = sec nk,. Then, the network throughut can be exressed as T P sec, T S, P Ω M sen = sec nk, {n k, } k= = M T,, P sen, n k, I n k, >, = where T,, P sen, n k, I n k, > reresents the throughut contributed by channel given that n k, users select this channel; and I. denotes the indicator function. Moreover, is the multinomial coefficient {n k, } which is defined as = = {n k, } n k,, n k,,..., n k,m n k,!n k,!...n k,m!. Furthermore, the throughut of channel T,, P sen, n k, can be calculated as T,, P sen, n k, = B T ove, + T. where T ove, reresents the time overhead required for one successful channel reservation on channel i.e., successful RTS/CTS exchanges, B bits/hz denotes the average number of bits transmitted er one unit of system bandwth for one contention/access CA cycle on channel. To comlete the throughut analysis, we derive the quantities T ove, and B, which are conducted in the following. Derivation of T ove, : The average time overhead for one successful channel reservation can be written as T ove, = T cont, + SIF S + P D + ACK, 3 where ACK is the length of an ACK message, SIF S is the length of a short interframe sace, and P D is the roagation delay where P D is usually small comared to the slot size σ, and T cont, denotes the average time overhead due to le eriods, collisions, and successful transmissions of RTS/CTS messages in one CA cycle. To calculate T cont,, we define some further arameters as follows. Denote T coll as the duration of the collision and T succ as the required time for successful RTS/CTS transmission. These quantities can be calculated as follows [9]: { Tsucc = DIF S + R + SIF S + C + P D T coll = DIF S + R + P D, where DIF S is the length of a distributed interframe sace, R and C denote the lengths of the RTS and CTS messages, resectively. As being shown in Fig., there can be several le eriods and collisions before one successful channel reservation. Let Tle, i denote the i-th le duration between two consecutive RTS/CTS exchanges on channel, which can be collisions or successful exchanges. Then, Tle i can be calculated based on its robability mass function mf, which is derived as follows. In the following, all relevant quantities are defined in terms of the number of time slots. With n k, SUs oining the contention resolution on channel, let P succ,, P coll, and P le, denote the robabilities that a articular generic slot corresonds to a successful transmission, a collision, and an le slot, resectively. These robabilities can be calculated as follows: P succ, = n k, n k, P le, = n k, P coll, = P succ, P le,, where is the transmission robability of an SU in a generic slot. In general, the interval T cont,, whose average value is T cont, given in 3, consists of several intervals corresonding to le eriods, collisions, and one successful RTS/CTS transmission. Hence, this quantity can be exressed as T cont, = coll, i= Tcoll + Tle, i + T coll, + le, + T succ, where coll, is the number of collisions before the successful RTS/CTS exchange on channel and coll, is a geometric random variable RV with arameter P coll, /P le, where P le, = P le,. Therefore, its mf can be exressed as f coll, X x = Pcoll, P le, x P coll, P le,, x =,,,... 9 Also, T le, reresents the number of consecutive le slots on channel, which is also a geometric RV with arameter P le, with the following mf f T le, X x = P le, x P le,, x =,,,... Therefore, T cont, the average value of T cont, can be written as follows [9]: T cont, = coll, T coll + T le, coll, + + T succ, where T le, and coll, can be calculated as T le, = coll, = n k, n k, n k, n k, n. k, 3 These exressions are obtained by using the mfs of the corresonding RVs given in 9 and, resectively [9]. Derivation of B : To calculate B, we conser all ossible cases that cature the activities of SUs and status changes of the PU in the data hase of duration T. Because the PU s activity is not synchronized with the SU s transmission, the PU can change its active/inactive status any time. We assume that there can be at most one transition between the le and active states of the PU during the interval T. This is consistent with the assumtion on the slow status changes of the PU as described in Section II-B since T < T eva. Furthermore, we assume that the carrier sensing of the MFDC-MAC rotocol

4 is erfect; therefore, the PU is le at the beginning of the data hase. ote that the PU may change its status during the SU s sensing or access stage, which requires us to conser different ossible events in the data hase. We use h kl k, l {, } to reresent events caturing status changes of the PU in the FD sensing stage and transmission stage where i = and i = reresent the le and active states of the PU, resectively. For examle, if the PU is le during the FD sensing stage and becomes active during the transmission stage, then we reresent this event as h, h where sub-events h and h reresent the status changes in the FD sensing and transmission stages, resectively. Moreover, if the PU changes from the le to the active state during the FD sensing stage and remains active in the remaining of the data hase, then we reresent this event as h, h It can be verified that we must conser the following three cases with the corresonding status changes of the PU during the FDC-MAC data hase to analyze B. Case : The PU is le for the whole FDC-MAC data hase i.e., there is no PU s signal in both FD sensing and transmission stages and we denote this event as h, h. The average number of bits in bits/hz transmitted during the data hase in this case is denoted as B,. Case : The PU is le during the FD sensing stage but the PU changes from the le to the active status in the transmission stage. We denote the event corresonding to this case as h, h where h and h cature the subevents in the FD sensing and transmission stages, resectively. The average number of bits in bits/hz transmitted during the data hase in this case is reresented by B,. Case 3: The PU is first le then becomes active during the FD sensing stage and it remains active during the whole transmission stage. Similarly we denote this event as h, h and the average number of bits in bits/hz transmitted during the data hase in this case is denoted as B,3. Then, we can calculate B as follows: B = B, + B, + B,3. Theoretical derivation for B,, B,, and B,3 is given in the online technical reort [] due to the sace constraint. IV. MFDC MAC PROTOCOL COFIGURATIO FOR THROUGHPUT MAXIMIZATIO In this section, we study the otimal configuration of the roosed MFDC MAC rotocol to achieve the maximum secondary throughut while satisfactorily rotecting the PU. A. Problem Formulation We are interested in determining suitable configuration for P sec, TS, and P sen to maximize the secondary throughut, T P sec, T S, P sen. Suose that the PU requires that the average detection robability be at least P d. Then, the throughut maximization roblem can be stated as follows: P: max T P sec, T S, P sen, P sec, T S, P sen s.t. ˆP d ε,, P d, P sen, P max,, T, M, = sec = where { } is the robability of channel selection P sec = sec, Psen, is the SU s transmit ower on channel and P max is the maximum ower for SUs, and, is uer bounded by T. In fact, the first constraint on ˆP d ε,, imlies that the sectrum sensing should be sufficiently reliable to rotect the PU. Moreover, the SU s transmit ower P sen, must be aroriately set to achieve good tradeoff between the network throughut and self-interference mitigation. To solve roblem, we roose the two-ste aroach where we solve the following two subroblems P and P3 in the two stes, resectively. In the first stage, we otimize the arameters for each indivual channel and n k, contending SUs on this channel to achieve maximum throughut of each channel, i.e., T,, P sen, n k,. This roblem can be resented as P: max T,, P sen, n k,,,p sen, s.t. ˆP d ε,, P d, P sen, P max,, T After solving roblem P with otimal results T T S, n k,, Psen, n k, n k, for all channels and ossible cases with different n k, contending SUs. Then, the network throughut with given T S, P sen only deends on the channel selection robabilities in P sec. Problem P3 maximizes the throughut with resect to P sec as P3: max T P sec P sec s.t. M = sec =. Here, T P sec can be written as T P sec = Ω k= = M sec nk, B {n k, } where M B ω k = B {n k, } = I n {n k, } k, > = T T S, n k,, Psen,n k, n k,. 9 Due to the decomosed structure of the throughut exression T P sec, T S, P sen in, it can be seen that the roosed two-ste aroach does not loose otimality. B. Configuration for MFDC MAC Protocol Configuration for Sensing and Access Stages: We will solve roblem P in the following. In the following analysis, we assume the exonential distribution for τ ac and τ where τ ac and τ denote the corresonding average values of these active and le intervals on channel. Secifically, let f τ x t

5 denote the df of τx x reresents ac or in the df of τac or τ, resectively then f τ x t = τ x ex t τ x. We assume a homogeneous case with same frame length T. We are interested in determining suitable configuration for,, and P sen, to maximize the secondary throughut, T,, P sen, n k,. To gain insights into the arameter configuration of the MFDC MAC rotocol, we first study the otimization with resect to the sensing time, for a given P sen,. For a fixed,, we would need to set the sensing detection threshold ε so that the detection robability constraint is met with equality, i.e., ˆP d ε,, = P d as in [3], []. Since the detection robability is smaller in Case 3 i.e., the PU changes from the le to active status during the FD sensing stage of duration, comared to that in Case and Case i.e., the PU remains le during the FD sensing stage consered in the revious section, we only need to conser Case 3 to maintain the detection robability constraint. The average robability of detection for the FD sensing in Case 3 can be exressed as ˆP d = TS, P, d tf τ t t, dt, where t denotes the duration from the beginning of the FD sensing stage to the instant when the PU changes to the active state, and f τ t A is the df of τ conditioned on event A caturing the condition t,, which is given as f τ t A = f τ t Pr {A} = τ ex t τ ex, τ. ote that P, d t is derived in Aendix A and f τ t is given in. We conser the following single-variable otimization roblem for a given P sen, : max <, T T,, P sen, n k,. 3 We characterize the roerties of function T,, P sen, n k, with resect to, for given P sen, in Proosition in technical reort [], whose details are omitted due to the sace constraint. In fact, we rove that there exists the otimal solution for TS,, P sen, to maximize the throughut T,, P sen, n k,. Therefore, we can determine the otimal values,, P sen, by using bi-section search of P sen, for given corresonding otimal, on each channel with the corresonding number of contending SUs. Configuration for Channel Selection Probabilities: We now solve roblem P3 by emloying the olynomial otimization technique for details of this technique, lease see []. Let us define the variables X { } = X,..., X M, X M+,..., X M+ Ω as follows: X i = { sec i if i M M = sec nk, if k = i M Ω Then, roblem P3 can be transformed into the linear rogram P: Throughut T, bits/s/hz Throughut vs P sen, and, P sen, db T * 3 ms,.9 db =.3.., s Fig.. Throughut versus SU transmit ower P sen and sensing time for =., =, ξ =.9, ζ =. and P dat = db. max X s.t. T X = Ω k= X M+kB ω k X i, i {,..., M + Ω } M i= X i = 3 where B ω k is the constant, which is given in 9. Recall that B ω k can be determined from the otimal solution of Problem P in ste. To solve roblem P in ste, standard methods in [] such as cutting-lane method, branch and bound, branch and cut, branch and rice can be emloyed. We use the branch and bound method [] to solve this roblem. V. UMERICAL RESULTS To obtain numerical results, we take key arameters for the MAC rotocol from Table II in []. All other arameters are chosen as follows unless stated otherwise: mini-slot is σ = µs; samling frequency for sensing is f s = MHz; bandwth of PU s QPSK signal is MHz; P d =.; the SR of PU signals at SUs γ P = P = db; varying selfinterference arameters ζ and ξ. Without loss of generality, the noise ower is normalized to one; hence, the SU transmit ower, P sen becomes P sen = SR s ; and P max = db. For one secific channel, we investigate the effect of selfinterference on the throughut erformance and the singlechannel throughut erformance versus SU transmit ower P sen and sensing time for different cases with varying self-interference arameters. Detailed results are shown in the online technical reort [] due to the sace constraint. We now investigate the multichannel scenario where we conser a network consisting of = SUs and 3 channels with following } arameter settings: τ = τ = τ 3 = ms, { τ ac, τ ac, τ ac 3 =,, ms. Moreover, we set =. and P dat = db. Fig. illustrates the throughut erformance versus SU transmit ower P sen, and sensing time, for channel for the case with ξ =.9 and ζ =.. The otimal configuration of SU transmit ower Psen, =.9 db and sensing time TS, = 3 ms is shown to achieve the maximum throughut T TS,, P sen, =.3, which is again indicated by a star symbol. To investigate the imacts of channel selection robabilities, we also conser the above network with following arameter settings: τ = τ = τ 3 = ms, { τ ac, τ ac, τ ac} 3 = {,, } ms, ξ =.9, ζ =. and P dat = db. Fig. 3 demonstrates the throughut erformance versus channel selection robabilities for channels and {, }. The otimal configuration of channel selection robabilities is

6 Throughut T, bits/s/hz. Throughut vs and T *.3,. =.3. 3 Throughut T, bits/s/hz... Throughut vs ζ Proosed Alg. Alg. Alg ζ Fig. 3. Throughut versus SU transmit ower and for =, ξ =.9, ζ =. and P dat = db. Throughut T, bits/s/hz 9 3 Throughut vs =,.,.,., Fig.. Throughut versus SU transmit ower and for =, ξ =.9, ζ =. and P dat = db., =.3 and, =., which is again indicated by a star symbol i.e., the robability of channel selection for the last channel is, 3 =,, =.3. We can observe that the SUs choose a more busy channel with lower channel selection robability at otimality, which is quite intuitive. To better observe the relationshi of throughut vs channel selection robabilities, we show the throughut erformance versus channel selection robabilities for channels and {, } in Fig.. We set the network arameters as follows: τ = τ = τ 3 = ms, { τ ac, τ ac, τ ac} 3 = {,, } ms, ξ =.9, ζ =., and P dat = db. This figure shows that the throughut curve for each value of first increases to the maximum value which is indicated by the asterisk and then decreases as we increase. We now conser the scenario with SUs and channels. We set τ = ms, τ ac = τ ac = ms, varying τ, ξ =, ζ =.3, and P dat = db. We would like to comare our roosed design with other two schemes called Algs. and which do not otimize the channel selection robabilities. TABLE I THROUGHPUT VS τ, τ MX=X τ ms Alg. T Alg. T Proosed.3.3. Alg. T T % 9..3 T % 9.9. Fig.. Throughut versus ζ for M = 3 3, ξ =.9, τ = ms, τ ac, τ ac, τ ac 3 =,, ms and Pdat = db. In Alg., we use equal channel selection robabilities for different channels, i.e., =. In Alg., a fixed channel assignment is used, i.e, each channel is assigned to one corresonding set of SUs where each set has the same number of SUs. For the channels with { τ } i = {,, } ms, we obtain the corresonding throughut values of { T i } = {.99,.,.993}, resectively. So the total throughut is the sum of two throughut values for the two channels. ote that we also erform otimization of sensing and access arameters for each channel in calculating the throughut of Algs. and. The results shown in Table I demonstrate that our roosed algorithm outerforms Algs. and. Moreover, the throughut gains between our roosed algorithm and Algs. and which are T and T, resectively are about %, which is quite significant. We now conser the scenario with 3 SUs and 3 channels. We set τ 3 = ms, τ ac = τ ac = τ ac 3 = ms, varying τ and τ, ξ =.9, ζ =. and P dat = db. We will also comare our roosed design with Algs. and. For the channels with { τ } i = {,, } ms, we obtain the corresonding throughut values of { T i } = {.9,., 3.}. Again, the total throughut for Alg. is the sum of throughut values achieved for the three channels. The results summarized in Table II show that our roosed design again outerforms Algs. and. ote that for the case of τ = τ = τ 3, all algorithms achieve the same throughut because all the channels have the same statistics and we do not need to otimize the load balancing. In Fig., we comare our roosed design with Algs. and for varying self-interference arameters. Here, we conser the network of SUs and 3 channels where ξ =.9, τ = ms, τ ac, τ ac, τ ac 3 =,, ms and P dat = db. Again, our roosed design leads to higher throughut than those under Algs. and. Moreover, the throughut gas between our design and Algs. and become larger with lower self-interference cancellation quality. These results confirm that otimal configuration of the MAC rotocol and load balancing arameters is indeed imortant to achieve the largest throughut erformance. VI. COCLUSIO In this aer, we have roosed the MFDC MAC rotocol for CRs, analyzed its throughut erformance, and studied its otimal arameter configuration. The design and analysis have taken into account the FD communication caability and

7 TABLE II THROUGHPUT VS τ, τ MX=3X3 τ, τ ms,,,,, Alg. T Alg. T , sec.,..3,..,..3, ,.3333 Proosed T Alg. T % T %....3 the self-interference of the FD transceiver. In addition, we roosed the mechanism of channel selection to effectively balance the load among channels. Finally, we have resented extensive numerical results to demonstrate the imacts of selfinterference and rotocol arameters of sensing, access and load balancing strategies on the throughut erformance. APPEDIX A FALSE ALARM AD DETECTIO PROBABILITIES We derive the detection and false alarm robabilities for FD sensing and two PU s state-changing events h and h in this aendix. Here, we conser only one secific channel, so we omit index in all the arameters for simlicity. Assume that the transmitted signals from the PU and SU are circularly symmetric comlex Gaussian CSCG signals while the noise at the secondary receiver is indeendently and entically distributed CSCG C, [3]. Under FD sensing, the false alarm robability for event h can be derived using the similar method as in [3], which is given as P f [ = Q ɛ + IP sen ] fs, where Q x = + ex t / dt; f x s,, ɛ, IP sen are the samling frequency, the noise ower, the detection threshold and the self-interference, resectively; is the FD sensing duration. The detection robability for event h is given as d = Q P ɛ t +IP sen fs γ P S, t γ P S + + t where t is the interval from the beginning of the data hase to the instant when the PU changes its state, γ P S = P +IP sen is the signal-to-interference-lus-noise ratio SIR of the PU s signal at the SU. REFERECES [] C. Cordeiro, and K. Challaali, C-MAC: A cognitive MAC rotocol for multi-channel wireless networks, in IEEE DySPA. [] J. Park, P. Pawelczak, and D. Cabric, Performance of oint sectrum sensing and mac algorithms for multichannel oortunistic sectrum access ad hoc networks, IEEE Trans. Mobile Comut., vol., no.,., July. [3] Y. C. Liang, Y. H. Zeng, E. C. Y. Peh, and A. T. Hoang, Sensingthroughut tradeoff for cognitive radio networks, IEEE Trans. Wireless Commun., vol., no.,. 3 33, Aril. [] L. T. Tan and L. B. Le, Distributed MAC rotocol for cognitive radio networks: Design, analysis, and otimization, IEEE Trans. Veh. Technol., vol., no., , Oct.. [] L. T. Tan and L. B. Le, Channel assignment with access contention resolution for cognitive radio networks, IEEE Trans. Veh. Technol., vol., no.,. 3, Aril. [] W. Cheng, X. Zhang, H. Zhang, Full-dulex sectrum-sensing and mac-rotocol for multichannel non-time-slotted cognitive radio networks, IEEE J. Sel. Areas Commun., vol. 33, no.,. 3, Aril. [] M. Duarte, C. Dick, and A. Sabharwal, Exeriment-driven characterization of full dulex wireless systems, IEEE Trans. Wireless Commun., vol., no.,. 9 3, Dec.. [] L. T. Tan and L. B. Le, Multi-Channel MAC rotocol for full dulex cognitive radio networks with otimized access control and load balancing, technical reort. Online: htt:// [9] F. Cali, M. Conti, and E. Gregori, Dynamic tuning of the IEEE. rotocol to achieve a theoretical throughut limit, IEEE/ACM Trans. etw., vol., no.,. 99, Dec.. [] J. B. Lasserre, Global otimization with olynomials and the roblem of moments, SIAM J. Otim., vol., no. 3,. 9,. [] H. D. Sherali, and C. H. Tuncbilek, A global otimization algorithm for olynomial rogramming roblems using a reformulationlinearization technique, Journal of Global Otimization, vol., no.,., 99.