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Throughput-oriented channel assignment for opportunistic spectrum access networks
Mathematical and Computer Modelling 53 (2011) 2108–2118
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Mathematical and Computer Modelling journal homepage: www.elsevier.com/locate/mcm
Throughput-oriented channel assignment for opportunistic spectrum access networks Haythem Ahmad Bany Salameh ∗ Telecommunications Engineering Department, Hijjawi Faculty for Engineering Technology, Yarmouk University, Irbid 21163, Jordan
article
info
Article history: Received 23 December 2009 Received in revised form 22 June 2010 Accepted 30 June 2010 Keywords: Spectrum scarcity Channel assignment Integer programming Opportunistic spectrum access
abstract Cognitive radio (CR) is a revolutionary technology in wireless communications that enhances spectrum utilization by allowing opportunistic and dynamic spectrum access. One of the key challenges in this domain is how CR users cooperate to dynamically access the available spectrum opportunities in order to maximize the overall perceived throughput. In this paper, we consider the coordinated spectrum access problem in a multiuser single-transceiver CR network (CRN), where each CR user is equipped with only one half-duplex transceiver. We first formulate the dynamic spectrum access as a rate/power control and channel assignment optimization problem. Our objective is to maximize the sum-rate achieved by all contending CR users over all available spectrum opportunities under interference and hardware constraints. We first show that this problem can be formulated as a mixed integer nonlinear programming (MINLP) problem that is NP-hard, in general. By exploiting the fact that actual communication systems have a finite number of available channels, each with a given maximum transmission power, we transfer this MINLP into a binary linear programming problem (BLP). Due to its integrality nature, this BLP is expected to be NP-hard. However, we show that its constraint matrix satisfies the total unimodularity property, and hence our problem can be optimally solved in polynomial time using linear programming (LP). To execute the optimal assignment in a distributed manner, we then present a distributed CSMA/CA-based random access mechanism for CRNs. We compare the performance of our proposed mechanism with reference CSMA/CA channel access mechanisms designed for CRNs. Simulation results show that our proposed mechanism significantly improves the overall network throughput and preserves fairness. © 2010 Elsevier Ltd. All rights reserved.
1. Introduction Spectrum measurements by the FCC Spectrum Policy Task Force [1] challenges for the first time the common belief of spectrum scarcity by indicating significant temporal and geographical variations in the utilization of the licensed spectrum, ranging from 15% to 85% [2]. To exploit the highly under-utilized portions of the spectrum (a.k.a, white spaces, spectrum holes, etc.), the FCC is considering revising its static spectrum allocation policies to allow for opportunistic spectrum access (OSA). For this purpose, cognitive radios (programmable radio platforms) have been proposed as a revolutionary technology in wireless communications for opportunistic and dynamic access to the limited radio spectrum without impacting spectrum-licensed primary-radio (PR) users. CRs are smart, programmable radios that are capable of channelinterference sensing, environment learning, and dynamic spectrum access [2].
∗
Corresponding address: Department of Telecommunication Engineering, Yarmouk University, Irbid 21163, Jordan. Tel.: +962 797708510. E-mail addresses: [email protected], [email protected].
0895-7177/$ – see front matter © 2010 Elsevier Ltd. All rights reserved. doi:10.1016/j.mcm.2010.06.044
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A CRN should dynamically utilize spectrum opportunities (idle PR channels) and adapt its operating parameters according to the surrounding environment such that the PRN’s performance is not negatively affected. Specifically, CR users should frequently sense their operating frequency channels for active PR users, and should vacate these channels if a PR signal is detected. Thus, to enable an efficient OSA, the operation of a CRN should address two essential issues: (1) identifying spectrum opportunities (i.e., idle PR channels that are potentially available for CR transmissions), and (2) providing an efficient reuse of such opportunities (achieving the maximum possible CRN throughput). While several studies have focused on the first issue based on channel sensing in a cooperative or non-cooperative manner, the second issue is still a challenging problem in a multi-user CRN. Thus, in this paper, we tackle the following question: ‘‘given the available spectrum opportunities at different CR users, what is the optimal channel assignment strategy in a multi-user single-transceiver CRN that efficiently utilizes those opportunities and achieves the maximum possible network throughput’’? 1.1. Related work Recently, several attempts were made to develop channel assignment/access mechanisms for CRNs (e.g., [3–13]). The spectrum access mechanism in [3] jointly optimizes the multi-channel power/rate assignment, assuming a given power mask on CR transmissions. DDMAC [4] is a spectrum-sharing protocol for CRNs that attempts to maximize the number of simultaneous CR transmissions through a novel probabilistic channel assignment algorithm that exploits the dependence between the signal’s attenuation model and the transmission distance while considering the prevailing traffic and interference conditions. DDMAC assumes a given rate demand per a CR user. AS-MAC [5] is a spectrum-sharing protocol for CRNs that coexist with a GSM network. CR users select channels based on the CRN’s control exchanges and GSM broadcast information. Explicit coordination with the PRNs is required. In [8], the authors developed a spectrum aware channel access protocol for CRNs (CMAC). CMAC enables opportunistic access and sharing of the available white spaces in the TV spectrum by adaptively allocating the spectrum among contending users. In [11], the interference temperature model [14] is used to select an optimal bandwidth/power assignment for CR users. COMAC [12] is a distributed MAC protocol for opportunistic CRNs. It improves spectrum utilization while statistically guaranteeing the performance of PR users. Specifically, COMAC ensures a statistical (soft) guarantee on the performance of PRNs. In [13], the authors developed a power control approach for CR systems based on spectrum sensing side information. The objective of such an approach is to mitigate the interference to a PR user from CR transmissions. Three spectrum-sharing techniques were proposed and compared in [15]: spreadingbased underlay, interference avoidance overlay, and spreading-based underlay with interference avoidance. The metric of interest in the comparison was pout . Most of these schemes were designed assuming that each CR user is equipped with multiple transceivers, which may not be true for low-cost CR systems. In addition, these schemes are often based on a purely greedy strategy of using the best idle channel for a given CR transmission.1 As reported in [4], employing a greedy strategy in a CRN may result in a significant reduction in the achievable network throughput. Therefore, new distributed channel assignment algorithms and MAC protocols are needed for single-transceiver CRNs. These solutions should provide a better spectrum utilization. 1.2. Contribution In this paper, we first investigate the spectrum access problem under hardware, interference, maximum transmission power, and received SINR constraints. Our design goal is to maximize the sum-rate achieved by all CR users, with respect to both channel assignment and transmission rate. The transmission rate in our setup depends on the PHY-layer implementation. Hence, unlike the case in previous works, our treatment is not restricted to the information-theoretic capacity,2 and can be applied to any arbitrarily given rate–SINR function. Specifically, the contribution of this paper is as follows. We first show that the joint rate/power control and channel assignment problem can be formulated as a mixed integer nonlinear programming (MINLP). To make this formulation more amenable for further processing, we note that actual communication systems only have a finite number of available channels, each associated with a maximum transmission power. Based on this fact, we transfer our MINLP to a BLP that only contains binary variables (i.e., we transfer our problem to rate/channel selection problem). This transformation applies to any arbitrarily given rate–SINR relationship. Then, we show that this BLP has a unimodular constraint matrix, and hence it can be optimally solved in polynomial time. Finally, we present a decentralized channel access protocol that realizes the optimal channel assignment in a distributed manner. Our proposed protocol is novel in three aspects. First, it is designed assuming a single-transceiver per CR user, and thus represents more realistic scenarios. Second, it employs an optimal channel assignment algorithm that cooperatively maximizes the achieved sum-rate, and thus can exploit the available spectrum more efficiently. Third, it does not assume any predefined rate–SINR relationship, and thus can be applied to any arbitrarily given rate–SINR function. To evaluate the performance of our proposed spectrum access mechanism, we conduct simulations over a CRN assuming a Rayleigh fading channel model. Our simulation results show that compared to typical CRN spectrum access schemes, our scheme significantly improves network throughput by up to 35% and preserves fairness. 1 The best channel is often defined as the one that supports the highest rate. We refer to this approach as the greedy approach. 2 The information-theoretic capacity is a logarithmic function of the received signal-to-interference-plus-noise ratio (SINR).
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Rate R4 R3 R2 R1 SINRth1 SINRth2
SINRth4
SINR
Fig. 1. Rate/SINR relationship.
1.3. Organization The rest of the paper is organized as follows. The system model is presented in Section 2. In Section 3, we formulate and solve the optimal channel assignment problem. The proposed spectrum access mechanism that employs the optimal assignment is described in Section 4. Section 5 presents the simulation results comparing our proposed solution with a baseline mechanism. Section 6 concludes the paper. 2. Network model We consider a distributed CRN that coexists with M licensed PRNs over a finite area. The PRNs are licensed on different, non-overlapping frequency bands. We assume that all the PRN bands have the same Fourier bandwidth BW . In reality, a PRN may occupy multiple, non-contiguous, unequal frequency bands. Such a PRN can be easily represented in our setup by using multiple equal-bandwidth virtual PRNs, each operating over its own carrier frequency. For the ith PRN, we denote its carrier frequency by fi . Each CR user is equipped with one half-duplex transceiver, and can only transmit (or receive) on one channel only. Without loss of generality, we assume that the bandwidth BW of a channel is sufficient to support at least one CR transmission. This is an acceptable assumption in many wireless systems that are built to operate in the unlicensed bands, including IEEE 802.11/a/b/g-compliant devices. To avoid corrupting the transmissions of licensed PR users, CR users continuously identify potential spectrum holes (idle PR channels) and opportunistically exploit them for their transmissions.3 Within a given neighborhood, multiple CR transmissions may contend for access to one of the available channels. Let C (t ) and N (t ) respectively denote the set of all C (t ) idle channels and the set of all N (t ) CR transmission requests in a given neighborhood at a given time t. Note that the set of available channels C (t ) is time varying (i.e., heavily depends on the PR activities) and can be identified based on channel sensing information. Because our focus is to obtain an optimal channel assignment at a given time t (i.e., in current snapshot), in what follow, we drop the time subscript (t) for notational convenience. We say the jth CR transmission (j ∈ N ) is successful if the following condition is met: ‘‘It is possible to find an (i) idle channel i from the set C such that the received SINR of the selected channel i (SINRj ) is greater than the SINR threshold (µ∗i ) that is required at the CR receiver of the jth transmission to achieve a target bit error rate over channel i’’. Formally, for (i)
transmission j and channel i, the transmission rate, denoted by Rj , ∀j ∈ N and i ∈ C , is obtained as follows: (i)
Rj =
(i)
f (SINRj ) Mbps, 0,
(i)
if SINRj ≥ µ∗i otherwise
(1)
where f (.) is any arbitrary rate–SINR function (e.g., Shannon’s equation, staircase function, etc.) that is decided by the PHYlayer implementation. It is worth mentioning that, in practice, this rate–SINR function takes the shape of a staircase, as shown in Fig. 1. Finally, to resolve collision between CR transmissions, we enforce an exclusive channel occupancy policy on CR transmissions, whereby a channel i assigned to a CR transmission j cannot be simultaneously assigned to another CR transmission in the same vicinity (inline with the CSMA/CA mechanism). 3. Optimal channel assignment 3.1. Maximum sum-rate single-transceiver problem Given the set of CR transmission requests N , the set of idle channels C , the maximum transmission powers over idle channels, our objective is to maximize the sum of rate of all CR transmissions over all channels in the current snapshot (i.e., a given time t), subject to the following constraints: a. A CR transmitter (receiver) can transmit (receive) over only one channel at a given time. 3 The FCC recently adopted three principal methods that can be used to determine the list of idle channels that is potentially available for CR transmissions at a given time and in a given geographical location [16].
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b. An idle channel cannot be assigned to more than one CR transmission in the same locality. c. A CR user can potentially access channel i if and only if the received SINR over channel i exceeds the pre-specified threshold µ∗i . (i) (i) d. For a CR transmission j and idle channel i, the transmission power Pj is limited to Pmax . If channel i is occupied by a (i)
(i)
PR user, Pj = 0, where Pmax is the smaller of the FCC regulatory maximum transmission power over channel i and the maximum power supported by the CR’s battery. Observation 1. In general, the transmission rate is an increasing function of the transmission power. Thus, for a CR transmission j and a channel i, the maximum achievable transmission rate is achieved when transmission j uses the (i) maximum possible transmit power (Pmax ) over that channel. 3.2. Problem formulation Our objective is to maximize the sum of rate of all CR transmissions over all channels in current snapshot, by the means (i) of optimal channel/rate assignment. Before formulating the problem, we define a binary variable xj as follows: (i)
xj =
1, 0,
if channel i is assigned to transmission j otherwise.
(2)
Hence, the maximum sum-rate single-transceiver problem is stated as follows:
−−
Maximizex(i) ,R(i) ,P (i) j
j
j
(i) (i)
R j xj
j∈N i∈C
Subject to
− j∈N −
(i)
xj ≤ 1, (i)
xj ≤ 1,
i∈C
∀i ∈ C (3)
∀j ∈ N
(i)
(i)
SINRj − µ∗i ≥ (xj − 1)Γ (i)
0 ≤ Pj
(i) ≤ Pmax ,
∀i ∈ C and ∀j ∈ N (i)
where Γ is a relatively large constant ≫1 and Pj
is the transmit power of the jth transmission over channel i. Recall that
(i)
(i)
SINRj is a function of Pj . 3.3. Solution An observation of the objective function of (3) and the constraints shows that this formulation, in general, constitutes a mixed integer nonlinear programming (MINLP) problem, which belongs to the class of NP-hard problems (i.e., computing the optimal solution for such problem grows exponentially with the size of the network) [4,17,18]. However, by exploiting the fact that actual communication systems have a finite number of available channels, each associated with a pre-specified maximum transmission power, we transfer this MINLP into a unimodular BLP that can be solved in polynomial time. Formally, given the set of idle channels and the associated maximum transmission powers over these channels, a CR (i) (i) transmission can compute the maximum achievable rates rj over each idle channel (see Observation 1). For all SINRj < µ∗i , (i)
where j ∈ N and i ∈ C , we set rj following BLP problem: Maximizex(i) j
−−
= 0. Given rj(i) , ∀j ∈ N and i ∈ C , the MINLP problem can be transformed into the
(i) (i)
r j xj
j∈N i∈C
Subject to
− j∈N
−
(i)
xj ≤ 1, (i)
xj ≤ 1,
∀i ∈ C
(4)
∀j ∈ N .
i∈C
Let A and b denote the linear constraint matrix and the right hand side of (4), respectively. Due to its integrality nature, the BLP in (4) is expected to be NP-hard. However, we show that its constraint matrix satisfies the total unimodularity property (see Lemma 1), and hence our problem can be optimally solved in polynomial time using linear programming (LP) (see Lemma 2). Lemma 1. The constraint matrix A of the formulation in (4) is totally unimodular (refer to Appendix A for the concept of unimodularity). Proof. Refer to Appendix B.
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Lemma 2. The BLP in (4) can be solved in polynomial time using standard LP methods (i.e., it has a polynomial-time complexity). Proof. Because the objective function of (4) is a linear function, the constraints are linear, A is unimodular, and b is integer, our BLP in (4) satisfies the unimodularity property (i.e., unimodular BLP). It is well known that for a unimodular BLP, the optimal solution of its linear program relaxation is the optimal solution of the original unimodular BLP [19]. Therefore, the optimal solution of the BLP in (4) can be exactly found in polynomial time using the standard LP techniques. Consequently, finding the optimal solution of (4) has a polynomial-time complexity. Remark 1. According to our treatment, CR users adopt a binary-level transmission power strategy, in which the transmission power over channel i, ∀i ∈ M is given by: (i)
Pt
(i) Pmax , 0,
=
if channel i is idle; if channel i is occupied by a PR user.
(5)
It is worth mentioning that most of previously proposed spectrum access/sharing protocols and algorithms for CRNs were designed assuming the binary-level transmission power strategy given in (5) (e.g., [8,11,20–22]). This strategy ensures a non-overlapping (collision-free) channel occupancy between CR and PR users. 4. Proposed channel access mechanism 4.1. Overview Based on the optimal channel assignment algorithm presented in Section 3, we now describe the proposed channel access protocol for CRNs. This protocol uses contention-based handshaking for exchanging control information. Our protocol is designed to (1) ensure exclusive channel occupancy policy (i.e., non-overlapping local channel occupancy between CR users) and (2) realize the optimal channel assignment in a distributed manner. It is worth mentioning that providing a reliable mechanism for exchanging control information (e.g., transmitter–receiver handshake, sensing information exchange, etc.) is a challenging problem in designing MAC protocols for CRNs [2]. To deal with this challenge, many techniques for providing such a reliable control channel for CR users have been proposed in the literature, including (1) pre-specified common control channel (CCC) approach, (2) dynamic local control channel approach, and (3) hopping-based control channel approach [2]. For our purposes, we assume that the common control channel approach is in place for exchanging control information between CR users, where a common control channel is available to all CR users. This channel is pre-specified but is not necessarily dedicated (i.e., licensed) to the CRN. For example, it can be one of the unlicensed ISM bands. It may, for example, be one of the unlicensed ISM bands. Note that the existence of a common control channel is a characteristic of many MAC protocols proposed for CRNs (e.g., [3–5,7,8,10,23,24]). 4.2. Channel contention 4.2.1. Admission control phase According to the optimal channel assignment, the set of idle channels C and the instantaneous SINR information of all contending CR users in a given neighborhood should be known to all CR users in that neighborhood before assigning channels and transmission rates. Given the set C , the issue of announcing the SINR information of all contending users can be handled during the ‘‘admission phase’’ by introducing a contention period known as the access window (AW). The AW consists of C fixed-duration access slots (AS), where the size of the AW is dynamically adjusted based on the number of available channels C (Fig. 2 illustrates the concept of AW admission control). A series of control packet exchanges take place during these slots, in which communicating CR users announce their instantaneous SINR information. It is worth mentioning that the use of an AW for contention was previously proposed in MACA-P and POWMAC protocols [25,26]. However, in both protocols, the objective was not to facilitate the channel assignment mechanism, but to resolve collisions between control and data packets and address single-channel transmission power control. 4.2.2. Operation details A CR user that has packets to transmit and that is not aware of any already established AW in its neighborhood can asynchronously initiate an AW. Each AS consists of the sum of an RTS duration, a CTS duration, and a maximum backoff interval. Control packets are sent at the maximum (known) transmission power imposed on the control channel. Upon receiving an RTS packet from a CR user, say A, that is initiating an AW, other CR users in the network synchronize their time reference with A’s AW. Suppose that a CR user D is aware of A’s AW, and has a data packet to transmit. D contends for the control channel in the next AS of D’s AW as follows. To prevent synchronized RTS attempts, D first backs off for a random duration of time (T ) that is uniformly distributed in the interval [0, Tmax ]; Tmax is a system-wide backoff counter. After this backoff time and if no carrier is sensed over the control channel, user C sends its control packet in the current AS. After all the control packets have been exchanged, the optimal channel assignment/rate allocation of Section 3 is executed at every communicating CR user. In the rest of this paper, we refer to the channel access mechanism that uses our optimal assignment as OPT-MAC.
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Contension Window (Announcing SINR info.)
AW
AS1
AS2
ASc1 t
Start Assignment Process Fig. 2. Example that illustrates the concept of dynamic AW in CRNs with C = C1 .
Remark 2. In our study, we consider the coordinated spectrum access problem in a single-hop CRN, where all CR users can hear each other. The primary advantage of our scheme is that it is based on passive learning. This is because in OPT-MAC, CR users when not transmitting/receiving (i.e., during admission control phase) always listen to the control channel in order to overhear control packet exchanges, including those not destined to them. Contending CR users use the control information to extract instantaneous SINR information and idle channel lists. Thus, our MAC protocol does not introduce any additional control message overhead beyond the two-way handshake, which is indeed needed for any CSMA/CA-based multi-channel CRN MAC protocol. Claim 1. The OPT-MAC protocol and any CSMA/CA-based multi-channel CRN MAC protocol have comparable overheads (i.e., a two-way handshake is needed to send one data packet). 5. Performance evaluation We compare the performance of our proposed protocol (OPT-MAC) with two CSMA-based CRN MAC protocols: COMAC [12] and DDMAC [4]. As mentioned in Section 1.1, COMAC employs a greedy channel assignment strategy of using the best idle channel for a given CR transmission. On the other hand, DDMAC attempts to maximize the CRN throughput through a probabilistic channel assignment algorithm that exploits the dependence between the signal’s attenuation model and the transmission distance while considering the prevailing traffic and interference conditions. In our evaluation, we study the network performance under two different rate–SINR relationships: the information-theoretic capacity (i.e., Shannon’s equation) and a staircase-like function4 similar to the one shown in Fig. 1. Our results are based on simulation experiments conducted using CSIM programs (CSIM is a C-based process-oriented discrete-event simulation package [27]). Our performance metrics are the CRN sum-rate, and the fairness. We use the fairness index in [28] to quantify the fairness of a scheme according to the sum-rate of all CR users in the network. A Rayleigh fading signal propagation model to describe the channel gain between any two CR users is considered. Specifically, for a transmitter–receiver separation d, the received power over the ith channel is given by: Pr
(i)
(i)
(i)
= Po
where Po =
d
−n
do (i)
(i) (i) Pt (i) Gt Gr l2i (i) (4π do )2 (i) power, Gt
ξ (i) ,
d ≥ do (i)
(6)
is the path loss of the close-in distance do (i) = max{ 2Dl , D, li }, D is the antenna length, Pt (i) is the 2
i
(i)
transmission is the antenna gain at the transmitter, Gr is the antenna gain at the receiver, li is the wavelength of fi , n is the path loss exponent, and ξ (i) is a normalized random variable that represents the power gain of the fading process. For Rayleigh fading, ξ (i) is exponentially distributed; Pr(ξ (i) ≤ y) = 1 − e−y [29]. 5.1. Simulation setup We consider N pairs of one-hop transmitter–receiver CR users in a 100 m × 100 m area. To simplify our simulation, we assume that all CR users are within the transmission range of each other, so that any control packet sent from a CR can be heard by all other CR users. The locations of the CR transmitters and receivers are randomly assigned within the simulation region. We assume that there are M = 11 channels, each has 2.5 MHz of bandwidth and licensed to one PRN. The carrier
4 A staircase-like rate–SINR function typically characterizes practical multi-rate systems.
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Table 1 Rate–SINR relationship. Rate index
Rate (Mbps)
SINRth
R1 R2 R3 R4 R5 R6 R7 R8
1 4.5 6 7 8.5 9.5 10.5 11
1 5 7 10 15 20 25 31
120 120 100
CRN Sum-rate (Mbps)
CRN Sum-rate (Mbps)
100 Opt-MAC,µ*=3
80
Opt-MAC,µ*=9
60
COMACµ*=3 COMAC,µ*=9
40
OPT-MAC,µ*=3
80
OPT-MAC,µ*=9
60
COMAC,µ*=3 COMAC,µ*=9
40
DDMAC,µ*=3 DDMAC,µ*=3
DDMAC,µ*=9
20
20 DDMAC,µ*=9
0
2
4
6
8 10 12 14 Number of CR Links (N)
16
(a) Assuming Shannon capacity formula.
18
0
2
4
6
8 10 12 14 Number of CR Links (N)
16
18
(b) Assuming staircase formula. Fig. 3. CRN sum-rate vs. number of CR links N.
frequency of the ith PRN is fi = 900 + i MHz, for i = 1, . . . , M. CR users can opportunistically access the 11 channels. We set µ∗i = µ∗ , ∀i ∈ M . For the simulated staircase rate–SINR function, the values of the different supported rates and their corresponding SINR thresholds are summarized in Table 1. Note that for both the information-theoretic and the staircase rate–SINR functions, the achieved rate is 0 if the received SINR < µ∗ . We divide the time into slots, each of length 100 ms. A 2-state Markov model that alternates between two states: IDLE and BUSY is considered to determine the status of a PR channel at any given time. A BUSY (IDLE) state indicates that some (no) PR user is transmitting over the given channel. For channel i, denote the average IDLE and BUSY durations of the PR activity by λi and µi , respectively. At any given time (i) λi . We set µi = 100 ms and λi = λ, ∀i ∈ {1, . . . , M }. Accordingly, slot, the ith PRN is idle with probability PB = λ +µ (i)
i
i
PB = PB , ∀i ∈ M . The locations of the CR transmitters and receivers are randomly assigned within the simulation region. We set the maximum transmission power of a CR user to Pmax = 1 W, the thermal noise power density to 10−21 W/Hz for all channels, the path loss exponent to n = 4, and the antenna length to D = 5 cm. The results presented below are based on the average of 30 randomly generated topologies, with a simulation time of 5000 time slots for each topology. 5.2. Simulation results We first compare the achieved sum-rate of all CR links for OPT-MAC, COMAC, and DDMAC protocols. The CRN sum-rate is plotted as a function of the number of active CR links in Fig. 3. In Fig. 3(a) (Fig. 3(b)), we consider Shannon’s equation (the staircase function) to compute the achieved rates over idle channels for each active CR link. Fig. 3 shows that as the number of CR users increases, OPT-MAC significantly outperforms COMAC and DDMAC, irrespective of the employed rate–SINR relationship. Specifically, OPT-MAC improves the overall achieved sum-rate by up to 35% compared to COMAC and up to 25% compared to DDMAC. This improvement is mostly attributed to the employed proper channel assignment. Fig. 4 shows the achievable sum-rate as a function of PR activities (PB ). Fig. 4 reveals that the throughput gain of OPT-MAC over COMAC and DDMAC is smaller at larger PB . This is expected since the larger the value of PB , the lower the chances of finding idle channels, which consequently reduces the performance gain (similar behavior was observed when staircase rate–SINR function is used). Fig. 5 shows the achievable sum-rate as a function of SINR threshold (µ∗ ). This figure reveals that the throughput gain of OPT-MAC over COMAC and DDMAC is larger at larger µ∗ .
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140 Opt-MAC,µ*=3
120 CRN Sum-rate (Mbps)
Opt-MAC,µ*=9
100
COMACµ*=3 COMAC,µ*=9
80
DDMAC µ*=3
60
DDMAC µ*=9
40 20 0 0.1
0.2
0.3
0.4
0.5 PB
0.6
0.7
0.8
0.9
Fig. 4. CRN sum-rate vs. PB , assuming Shannon capacity formula.
120
125
OPT-MAC, N=10
Opt-MAC, N=10
120
Opt-MAC, N=18
OPT-MAC, N=18
115
COMAC, N=10
CRN Sum-rate (Mbps)
CRN Sum-rate (Mbps)
COMAC, N=10
115
COMAC, N=18 DDMAC, N=10
110
DDMAC, N=18
105
COMAC, N=18
110
DDMAC, N=10 DDMAC, N=18
105
100
100 95
95 90
1
2
3
4
5 µ*
6
7
8
90
9
(a) Assuming Shannon capacity formula.
1
2
3
4
5 µ*
6
7
8
9
(b) Assuming staircase formula.
Fig. 5. CRN sum-rate vs. SINR threshold, assuming Shannon formula.
1 0.99
Fairness Index
0.98
OPT-MAC,µ*=3 COMAC,µ*=3
0.97 0.96 0.95 0.94 0.93 0.92
2
4
6
8
10 N
12
14
16
18
Fig. 6. Fairness index vs. number of CR links (N) for µ∗ = 3 (DDMAC depicted similar behavior as OPT-MAC).
In Fig. 6, we study the impact of the channel assignment strategy on fairness. We set mu∗ = 3. It is clear that all protocols achieve comparable fairness (other values of µ∗ depicted similar fairness behavior). This can be attributed to the fact that, in
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10 9
Channel Usage (%)
8 OPT-MAC
7
COMAC
6 5 4 3 2 1 0
0
1
2
3
4
5 6 7 8 Channel Number
9
10
11
12
Fig. 7. Channel usage (%) for µ∗ = 3 and N = 18 (DDMAC depicted similar behavior as OPT-MAC).
all protocols, CR users contend over the control channel using a variant of the CSMA/CA mechanism. Finally, Fig. 7 depicts, for µ∗ = 3, the channel usage, defined as the fraction of time in which a specific channel is used for CR transmissions. For all protocols, channel usage is roughly evenly distributed among all channels, irrespective of the number of CR links.5 6. Conclusions In this paper, we proposed a solution to solve the joint rate control and channel assignment problem for the coordinated channel access in opportunistic CRNs. Our solution improves the CRN throughput through an optimal channel assignment process. The assignment process dynamically assigns channels to CR transmissions with the objective of maximizing the achieved CRN sum-rate and subject to interference and SINR constraints. In order to realize our solution in a distributed manner, we developed a CSMA/CA-based MAC protocol (OPT-MAC) for CRNs with access window (AW). The purpose of the AW is to announce CR transmission requests, idle channel list, and SINR information; and resolve contention between CR transmissions. We compared the performance of OPT-MAC with that of two multi-channel CSMA/CA-based CRN MAC (i.e., COMAC and DDMAC) protocols. We showed that our protocol achieves about 35% (25%) increase in throughput over the COMAC (DDMAC) protocol, while preserves fairness. In summary, OPT-MAC provides better spectrum utilization by achieving a larger network throughput. Appendix A A.1. Concept of unimodularity Definition 1. A matrix B is said to be totally unimodular if the determinant of every square submatrix (minor) of B is in the set {−1, 0, 1} [30]. The following theorem provides sufficient but not necessary conditions for a matrix of 0’s and 1’s to be totally unimodular. Theorem 1. An m × n matrix B is totally unimodular if its rows can be partitioned into two disjoint matrices B1 and B2, with the following properties [30]:
• Every entry in B is 0 or 1. • Every column of B contains at most two 1’s. • Every column of B1 and B2 contains at most one non-zero element. Appendix B B.1. Proof of total unimodularity of the constraint matrix
T
To prove this, we partition the matrix A into two disjoint matrices A1 (N × CN) and A2 (C × CN), (i.e., A = A1A2 ), where A1 and A2 correspond to the first and second constraints in (4), respectively. The matrices A1 and A2 can be written as: 5 Other values of µ∗ depicted similar channel-usage behavior.
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C 1 . . . 1 0 . . . 0 A1 = 0 . . . 0 . ..
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0...0
...
...
C
1...1
0...0
...
C
0...0
.. .
1...1 .. .
... .. .
...
...
...
0...0
0 . . . 0
0 . . . 0 0 . . . 0 .. . C 1 . . . 1 N ×CN
(7)
and
C
C
10 . . . 0 C 010 . . . 0 C A2 = 0010 . . . 0 .. . C 0...1
10 . . . 0
...
C
010 . . . 0
...
C
0010 . . . 0
.. .
... .. .
C
0...1
...
C 10 . . . 0 C 010 . . . 0 C . 0010 . . . 0 .. . C 0...1 C ×CN
(8)
Note that A, A1, and A2 satisfy all the sufficient conditions of total unimodularity given in Theorem 1. Therefore A is totally unimodular. References [1] FCC, spectrum policy task force report, ET docket no. 02-155, Nov. 2002. [2] H. Bany Salameh, M. Krunz, Channel access protocols for multihop opportunistic networks: Challenges and recent developments, in: Networking over Multi-hop Cognitive Networks, IEEE Network 23 (4) (2009) 14–19 (special issue). [3] T. Shu, S. Cui, M. Krunz, Medium access control for multi-channel parallel transmission in cognitive radio networks, in: Proceedings of the IEEE GLOBECOM Conference, 2006, pp. 1–5. [4] H. Bany Salameh, M. Krunz, O. Younis, Distance- and traffic-aware channel assignment in cognitive radio networks, in: Proceedings of IEEE SECON’08, 2008, pp. 10–18. [5] S. Sankaranarayanan, P. Papadimitratos, A. Mishra, S. Hershey, A bandwidth sharing approach to improve licensed spectrum utilization, in: Proceedings of the IEEE DySPAN Conf., 2005, pp. 279–288. [6] A. Sabharwal, A. Khoshnevis, E. Knightly, Opportunistic spectral usage: Bounds and a multi-band CSMA/CA protocol, IEEE/ACM Transactions on Networking 15 (3) (2007) 533–545. [7] L. Ma, X. Han, C.-C. Shen, Dynamic open spectrum sharing MAC protocol for wireless ad hoc networks, in: Proceedings of the IEEE DySPAN Conf., 2005, pp. 203–213. [8] Y. Yuan, P. Bahl, R. Chandra, P. Chou, J. Ferrell, T. Moscibroda, S. Narlanka, Y. Wu, Knows: Kognitive networking over white spaces, in: Proceedings of the IEEE DySPAN Conf., 2007, pp. 416–427. [9] H. Bany Salameh, M. Krunz, O. Younis, Dynamic spectrum access protocol without power mask constraints, in: Proceedings of the IEEE INFOCOM Conference, 2009, pp. 2322–2330. [10] H. Bany Salameh, M. Krunz, O. Younis, Cooperative adaptive spectrum sharing in cognitive radio networks, IEEE/ACM Transactions on Networking (2010). [11] T.C. Clancy, Achievable capacity under the interference temperature model, in: Proceedings of the IEEE INFOCOM Conference, 2007, pp. 794–802. [12] H. Bany Salameh, M. Krunz, O. Younis, MAC protocol for opportunistic cognitive radio networks with soft guarantees, IEEE Transactions on Mobile Computing 8 (6) (2009) 1339–1352. [13] K. Hamdi, W. Zhang, K.B. Letaief, Power control in cognitive radio systems based on spectrum sensing side information, in: Proceedings of the IEEE ICC Conference, 2007, pp. 5161–5165. [14] S. Haykin, Cognitive radio: Brain-empowered wireless communications, IEEE Journal on Selected Areas in Communications 23 (2) (2005) 201–220. [15] R. Menon, R. Buehrer, J. Reed, Outage probability based comparison of underlay and overlay spectrum sharing techniques, in: Proceedings of the IEEE DySPAN Conf., 2005, pp. 101–109. [16] Second Report and Order and Memorandum Opinion and Order, ET Docket No. 04-186; FCC 08-260, 2008. [17] A. Hoang, Y. Liang, Maximizing spectrum utilization of cognitive radio networks using channel allocation and power control, in: Proceedings of Vehicular Technology Conference, VTC, 2006, pp. 1–5. [18] E. Arikan, Some complexity results about packet radio networks, IEEE Transactions on Information Theory 30 (4) (1984) 681–685. [19] R. Garfinkel, G. Nemhauser, Integer Programming, Wiley, New York, 1972. [20] W. Wang, X. Liu, List-coloring based channel allocation for open-spectrum wireless networks, in: Proceedings of the IEEE Vehicular Tech. Conference, 2005, pp. 690–694. [21] S. Huang, X. Liu, Z. Ding, Opportunistic spectrum access in cognitive radio networks, in: Proceedings of the IEEE INFOCOM Conference, 2008, pp. 1427–1435. [22] J. Jia, Q. Zhang, X. Shen, HC-MAC: a hardware-constrained cognitive MAC for efficient spectrum management, IEEE Journal on Selected Areas in Communications 26 (1) (2008) 106–117. [23] Q. Zhao, L. Tong, A. Swami, Decentralized cognitive MAC for dynamic spectrum access, in: Proceedings of the IEEE DySPAN Conf., 2005, pp. 224–232. [24] P. Pawelczak, R. Prasad, L. Xai, I. Niemegeers, Cognitive radio emergency networks - requirements and design, in: Proceedings of the IEEE DySPAN Conf., 2005, pp. 601–606.
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[25] A. Acharya, A. Misra, S. Bansal, MACA-P: a MAC for concurrent transmissions in multi-hop wireless networks, in: Proceedings of the First IEEE PerCom 2003 Conference, 2003, pp. 505–508. [26] A. Muqattash, M. Krunz, POWMAC: a single-channel power control protocol for throughput enhancement in wireless ad hoc networks, IEEE Journal on Selected Areas in Communications 23 (5) (2005) 1067–1084. [27] Mesquite Software Incorporation, www.mesquite.com. [28] R. Jain, The Art of Computer System Performance Analysis, John Wiley & Sons, New York, 1991. [29] T.S. Rappaport, Wireless Communications-Principles and Practice, 2nd ed., Prentice-Hall Press, 2001. [30] I. Heller, C.B. Tompkins, An extension of a theorem of dantzig’s, in: H.W. Kuhn, A.W. Tucker (Eds.), Linear Inequalities and Related Systems, Annals of Mathematics Study (38) (1956), 247–254.
Contents lists available at ScienceDirect
Mathematical and Computer Modelling journal homepage: www.elsevier.com/locate/mcm
Throughput-oriented channel assignment for opportunistic spectrum access networks Haythem Ahmad Bany Salameh ∗ Telecommunications Engineering Department, Hijjawi Faculty for Engineering Technology, Yarmouk University, Irbid 21163, Jordan
article
info
Article history: Received 23 December 2009 Received in revised form 22 June 2010 Accepted 30 June 2010 Keywords: Spectrum scarcity Channel assignment Integer programming Opportunistic spectrum access
abstract Cognitive radio (CR) is a revolutionary technology in wireless communications that enhances spectrum utilization by allowing opportunistic and dynamic spectrum access. One of the key challenges in this domain is how CR users cooperate to dynamically access the available spectrum opportunities in order to maximize the overall perceived throughput. In this paper, we consider the coordinated spectrum access problem in a multiuser single-transceiver CR network (CRN), where each CR user is equipped with only one half-duplex transceiver. We first formulate the dynamic spectrum access as a rate/power control and channel assignment optimization problem. Our objective is to maximize the sum-rate achieved by all contending CR users over all available spectrum opportunities under interference and hardware constraints. We first show that this problem can be formulated as a mixed integer nonlinear programming (MINLP) problem that is NP-hard, in general. By exploiting the fact that actual communication systems have a finite number of available channels, each with a given maximum transmission power, we transfer this MINLP into a binary linear programming problem (BLP). Due to its integrality nature, this BLP is expected to be NP-hard. However, we show that its constraint matrix satisfies the total unimodularity property, and hence our problem can be optimally solved in polynomial time using linear programming (LP). To execute the optimal assignment in a distributed manner, we then present a distributed CSMA/CA-based random access mechanism for CRNs. We compare the performance of our proposed mechanism with reference CSMA/CA channel access mechanisms designed for CRNs. Simulation results show that our proposed mechanism significantly improves the overall network throughput and preserves fairness. © 2010 Elsevier Ltd. All rights reserved.
1. Introduction Spectrum measurements by the FCC Spectrum Policy Task Force [1] challenges for the first time the common belief of spectrum scarcity by indicating significant temporal and geographical variations in the utilization of the licensed spectrum, ranging from 15% to 85% [2]. To exploit the highly under-utilized portions of the spectrum (a.k.a, white spaces, spectrum holes, etc.), the FCC is considering revising its static spectrum allocation policies to allow for opportunistic spectrum access (OSA). For this purpose, cognitive radios (programmable radio platforms) have been proposed as a revolutionary technology in wireless communications for opportunistic and dynamic access to the limited radio spectrum without impacting spectrum-licensed primary-radio (PR) users. CRs are smart, programmable radios that are capable of channelinterference sensing, environment learning, and dynamic spectrum access [2].
∗
Corresponding address: Department of Telecommunication Engineering, Yarmouk University, Irbid 21163, Jordan. Tel.: +962 797708510. E-mail addresses: [email protected], [email protected].
0895-7177/$ – see front matter © 2010 Elsevier Ltd. All rights reserved. doi:10.1016/j.mcm.2010.06.044
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A CRN should dynamically utilize spectrum opportunities (idle PR channels) and adapt its operating parameters according to the surrounding environment such that the PRN’s performance is not negatively affected. Specifically, CR users should frequently sense their operating frequency channels for active PR users, and should vacate these channels if a PR signal is detected. Thus, to enable an efficient OSA, the operation of a CRN should address two essential issues: (1) identifying spectrum opportunities (i.e., idle PR channels that are potentially available for CR transmissions), and (2) providing an efficient reuse of such opportunities (achieving the maximum possible CRN throughput). While several studies have focused on the first issue based on channel sensing in a cooperative or non-cooperative manner, the second issue is still a challenging problem in a multi-user CRN. Thus, in this paper, we tackle the following question: ‘‘given the available spectrum opportunities at different CR users, what is the optimal channel assignment strategy in a multi-user single-transceiver CRN that efficiently utilizes those opportunities and achieves the maximum possible network throughput’’? 1.1. Related work Recently, several attempts were made to develop channel assignment/access mechanisms for CRNs (e.g., [3–13]). The spectrum access mechanism in [3] jointly optimizes the multi-channel power/rate assignment, assuming a given power mask on CR transmissions. DDMAC [4] is a spectrum-sharing protocol for CRNs that attempts to maximize the number of simultaneous CR transmissions through a novel probabilistic channel assignment algorithm that exploits the dependence between the signal’s attenuation model and the transmission distance while considering the prevailing traffic and interference conditions. DDMAC assumes a given rate demand per a CR user. AS-MAC [5] is a spectrum-sharing protocol for CRNs that coexist with a GSM network. CR users select channels based on the CRN’s control exchanges and GSM broadcast information. Explicit coordination with the PRNs is required. In [8], the authors developed a spectrum aware channel access protocol for CRNs (CMAC). CMAC enables opportunistic access and sharing of the available white spaces in the TV spectrum by adaptively allocating the spectrum among contending users. In [11], the interference temperature model [14] is used to select an optimal bandwidth/power assignment for CR users. COMAC [12] is a distributed MAC protocol for opportunistic CRNs. It improves spectrum utilization while statistically guaranteeing the performance of PR users. Specifically, COMAC ensures a statistical (soft) guarantee on the performance of PRNs. In [13], the authors developed a power control approach for CR systems based on spectrum sensing side information. The objective of such an approach is to mitigate the interference to a PR user from CR transmissions. Three spectrum-sharing techniques were proposed and compared in [15]: spreadingbased underlay, interference avoidance overlay, and spreading-based underlay with interference avoidance. The metric of interest in the comparison was pout . Most of these schemes were designed assuming that each CR user is equipped with multiple transceivers, which may not be true for low-cost CR systems. In addition, these schemes are often based on a purely greedy strategy of using the best idle channel for a given CR transmission.1 As reported in [4], employing a greedy strategy in a CRN may result in a significant reduction in the achievable network throughput. Therefore, new distributed channel assignment algorithms and MAC protocols are needed for single-transceiver CRNs. These solutions should provide a better spectrum utilization. 1.2. Contribution In this paper, we first investigate the spectrum access problem under hardware, interference, maximum transmission power, and received SINR constraints. Our design goal is to maximize the sum-rate achieved by all CR users, with respect to both channel assignment and transmission rate. The transmission rate in our setup depends on the PHY-layer implementation. Hence, unlike the case in previous works, our treatment is not restricted to the information-theoretic capacity,2 and can be applied to any arbitrarily given rate–SINR function. Specifically, the contribution of this paper is as follows. We first show that the joint rate/power control and channel assignment problem can be formulated as a mixed integer nonlinear programming (MINLP). To make this formulation more amenable for further processing, we note that actual communication systems only have a finite number of available channels, each associated with a maximum transmission power. Based on this fact, we transfer our MINLP to a BLP that only contains binary variables (i.e., we transfer our problem to rate/channel selection problem). This transformation applies to any arbitrarily given rate–SINR relationship. Then, we show that this BLP has a unimodular constraint matrix, and hence it can be optimally solved in polynomial time. Finally, we present a decentralized channel access protocol that realizes the optimal channel assignment in a distributed manner. Our proposed protocol is novel in three aspects. First, it is designed assuming a single-transceiver per CR user, and thus represents more realistic scenarios. Second, it employs an optimal channel assignment algorithm that cooperatively maximizes the achieved sum-rate, and thus can exploit the available spectrum more efficiently. Third, it does not assume any predefined rate–SINR relationship, and thus can be applied to any arbitrarily given rate–SINR function. To evaluate the performance of our proposed spectrum access mechanism, we conduct simulations over a CRN assuming a Rayleigh fading channel model. Our simulation results show that compared to typical CRN spectrum access schemes, our scheme significantly improves network throughput by up to 35% and preserves fairness. 1 The best channel is often defined as the one that supports the highest rate. We refer to this approach as the greedy approach. 2 The information-theoretic capacity is a logarithmic function of the received signal-to-interference-plus-noise ratio (SINR).
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Rate R4 R3 R2 R1 SINRth1 SINRth2
SINRth4
SINR
Fig. 1. Rate/SINR relationship.
1.3. Organization The rest of the paper is organized as follows. The system model is presented in Section 2. In Section 3, we formulate and solve the optimal channel assignment problem. The proposed spectrum access mechanism that employs the optimal assignment is described in Section 4. Section 5 presents the simulation results comparing our proposed solution with a baseline mechanism. Section 6 concludes the paper. 2. Network model We consider a distributed CRN that coexists with M licensed PRNs over a finite area. The PRNs are licensed on different, non-overlapping frequency bands. We assume that all the PRN bands have the same Fourier bandwidth BW . In reality, a PRN may occupy multiple, non-contiguous, unequal frequency bands. Such a PRN can be easily represented in our setup by using multiple equal-bandwidth virtual PRNs, each operating over its own carrier frequency. For the ith PRN, we denote its carrier frequency by fi . Each CR user is equipped with one half-duplex transceiver, and can only transmit (or receive) on one channel only. Without loss of generality, we assume that the bandwidth BW of a channel is sufficient to support at least one CR transmission. This is an acceptable assumption in many wireless systems that are built to operate in the unlicensed bands, including IEEE 802.11/a/b/g-compliant devices. To avoid corrupting the transmissions of licensed PR users, CR users continuously identify potential spectrum holes (idle PR channels) and opportunistically exploit them for their transmissions.3 Within a given neighborhood, multiple CR transmissions may contend for access to one of the available channels. Let C (t ) and N (t ) respectively denote the set of all C (t ) idle channels and the set of all N (t ) CR transmission requests in a given neighborhood at a given time t. Note that the set of available channels C (t ) is time varying (i.e., heavily depends on the PR activities) and can be identified based on channel sensing information. Because our focus is to obtain an optimal channel assignment at a given time t (i.e., in current snapshot), in what follow, we drop the time subscript (t) for notational convenience. We say the jth CR transmission (j ∈ N ) is successful if the following condition is met: ‘‘It is possible to find an (i) idle channel i from the set C such that the received SINR of the selected channel i (SINRj ) is greater than the SINR threshold (µ∗i ) that is required at the CR receiver of the jth transmission to achieve a target bit error rate over channel i’’. Formally, for (i)
transmission j and channel i, the transmission rate, denoted by Rj , ∀j ∈ N and i ∈ C , is obtained as follows: (i)
Rj =
(i)
f (SINRj ) Mbps, 0,
(i)
if SINRj ≥ µ∗i otherwise
(1)
where f (.) is any arbitrary rate–SINR function (e.g., Shannon’s equation, staircase function, etc.) that is decided by the PHYlayer implementation. It is worth mentioning that, in practice, this rate–SINR function takes the shape of a staircase, as shown in Fig. 1. Finally, to resolve collision between CR transmissions, we enforce an exclusive channel occupancy policy on CR transmissions, whereby a channel i assigned to a CR transmission j cannot be simultaneously assigned to another CR transmission in the same vicinity (inline with the CSMA/CA mechanism). 3. Optimal channel assignment 3.1. Maximum sum-rate single-transceiver problem Given the set of CR transmission requests N , the set of idle channels C , the maximum transmission powers over idle channels, our objective is to maximize the sum of rate of all CR transmissions over all channels in the current snapshot (i.e., a given time t), subject to the following constraints: a. A CR transmitter (receiver) can transmit (receive) over only one channel at a given time. 3 The FCC recently adopted three principal methods that can be used to determine the list of idle channels that is potentially available for CR transmissions at a given time and in a given geographical location [16].
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b. An idle channel cannot be assigned to more than one CR transmission in the same locality. c. A CR user can potentially access channel i if and only if the received SINR over channel i exceeds the pre-specified threshold µ∗i . (i) (i) d. For a CR transmission j and idle channel i, the transmission power Pj is limited to Pmax . If channel i is occupied by a (i)
(i)
PR user, Pj = 0, where Pmax is the smaller of the FCC regulatory maximum transmission power over channel i and the maximum power supported by the CR’s battery. Observation 1. In general, the transmission rate is an increasing function of the transmission power. Thus, for a CR transmission j and a channel i, the maximum achievable transmission rate is achieved when transmission j uses the (i) maximum possible transmit power (Pmax ) over that channel. 3.2. Problem formulation Our objective is to maximize the sum of rate of all CR transmissions over all channels in current snapshot, by the means (i) of optimal channel/rate assignment. Before formulating the problem, we define a binary variable xj as follows: (i)
xj =
1, 0,
if channel i is assigned to transmission j otherwise.
(2)
Hence, the maximum sum-rate single-transceiver problem is stated as follows:
−−
Maximizex(i) ,R(i) ,P (i) j
j
j
(i) (i)
R j xj
j∈N i∈C
Subject to
− j∈N −
(i)
xj ≤ 1, (i)
xj ≤ 1,
i∈C
∀i ∈ C (3)
∀j ∈ N
(i)
(i)
SINRj − µ∗i ≥ (xj − 1)Γ (i)
0 ≤ Pj
(i) ≤ Pmax ,
∀i ∈ C and ∀j ∈ N (i)
where Γ is a relatively large constant ≫1 and Pj
is the transmit power of the jth transmission over channel i. Recall that
(i)
(i)
SINRj is a function of Pj . 3.3. Solution An observation of the objective function of (3) and the constraints shows that this formulation, in general, constitutes a mixed integer nonlinear programming (MINLP) problem, which belongs to the class of NP-hard problems (i.e., computing the optimal solution for such problem grows exponentially with the size of the network) [4,17,18]. However, by exploiting the fact that actual communication systems have a finite number of available channels, each associated with a pre-specified maximum transmission power, we transfer this MINLP into a unimodular BLP that can be solved in polynomial time. Formally, given the set of idle channels and the associated maximum transmission powers over these channels, a CR (i) (i) transmission can compute the maximum achievable rates rj over each idle channel (see Observation 1). For all SINRj < µ∗i , (i)
where j ∈ N and i ∈ C , we set rj following BLP problem: Maximizex(i) j
−−
= 0. Given rj(i) , ∀j ∈ N and i ∈ C , the MINLP problem can be transformed into the
(i) (i)
r j xj
j∈N i∈C
Subject to
− j∈N
−
(i)
xj ≤ 1, (i)
xj ≤ 1,
∀i ∈ C
(4)
∀j ∈ N .
i∈C
Let A and b denote the linear constraint matrix and the right hand side of (4), respectively. Due to its integrality nature, the BLP in (4) is expected to be NP-hard. However, we show that its constraint matrix satisfies the total unimodularity property (see Lemma 1), and hence our problem can be optimally solved in polynomial time using linear programming (LP) (see Lemma 2). Lemma 1. The constraint matrix A of the formulation in (4) is totally unimodular (refer to Appendix A for the concept of unimodularity). Proof. Refer to Appendix B.
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Lemma 2. The BLP in (4) can be solved in polynomial time using standard LP methods (i.e., it has a polynomial-time complexity). Proof. Because the objective function of (4) is a linear function, the constraints are linear, A is unimodular, and b is integer, our BLP in (4) satisfies the unimodularity property (i.e., unimodular BLP). It is well known that for a unimodular BLP, the optimal solution of its linear program relaxation is the optimal solution of the original unimodular BLP [19]. Therefore, the optimal solution of the BLP in (4) can be exactly found in polynomial time using the standard LP techniques. Consequently, finding the optimal solution of (4) has a polynomial-time complexity. Remark 1. According to our treatment, CR users adopt a binary-level transmission power strategy, in which the transmission power over channel i, ∀i ∈ M is given by: (i)
Pt
(i) Pmax , 0,
=
if channel i is idle; if channel i is occupied by a PR user.
(5)
It is worth mentioning that most of previously proposed spectrum access/sharing protocols and algorithms for CRNs were designed assuming the binary-level transmission power strategy given in (5) (e.g., [8,11,20–22]). This strategy ensures a non-overlapping (collision-free) channel occupancy between CR and PR users. 4. Proposed channel access mechanism 4.1. Overview Based on the optimal channel assignment algorithm presented in Section 3, we now describe the proposed channel access protocol for CRNs. This protocol uses contention-based handshaking for exchanging control information. Our protocol is designed to (1) ensure exclusive channel occupancy policy (i.e., non-overlapping local channel occupancy between CR users) and (2) realize the optimal channel assignment in a distributed manner. It is worth mentioning that providing a reliable mechanism for exchanging control information (e.g., transmitter–receiver handshake, sensing information exchange, etc.) is a challenging problem in designing MAC protocols for CRNs [2]. To deal with this challenge, many techniques for providing such a reliable control channel for CR users have been proposed in the literature, including (1) pre-specified common control channel (CCC) approach, (2) dynamic local control channel approach, and (3) hopping-based control channel approach [2]. For our purposes, we assume that the common control channel approach is in place for exchanging control information between CR users, where a common control channel is available to all CR users. This channel is pre-specified but is not necessarily dedicated (i.e., licensed) to the CRN. For example, it can be one of the unlicensed ISM bands. It may, for example, be one of the unlicensed ISM bands. Note that the existence of a common control channel is a characteristic of many MAC protocols proposed for CRNs (e.g., [3–5,7,8,10,23,24]). 4.2. Channel contention 4.2.1. Admission control phase According to the optimal channel assignment, the set of idle channels C and the instantaneous SINR information of all contending CR users in a given neighborhood should be known to all CR users in that neighborhood before assigning channels and transmission rates. Given the set C , the issue of announcing the SINR information of all contending users can be handled during the ‘‘admission phase’’ by introducing a contention period known as the access window (AW). The AW consists of C fixed-duration access slots (AS), where the size of the AW is dynamically adjusted based on the number of available channels C (Fig. 2 illustrates the concept of AW admission control). A series of control packet exchanges take place during these slots, in which communicating CR users announce their instantaneous SINR information. It is worth mentioning that the use of an AW for contention was previously proposed in MACA-P and POWMAC protocols [25,26]. However, in both protocols, the objective was not to facilitate the channel assignment mechanism, but to resolve collisions between control and data packets and address single-channel transmission power control. 4.2.2. Operation details A CR user that has packets to transmit and that is not aware of any already established AW in its neighborhood can asynchronously initiate an AW. Each AS consists of the sum of an RTS duration, a CTS duration, and a maximum backoff interval. Control packets are sent at the maximum (known) transmission power imposed on the control channel. Upon receiving an RTS packet from a CR user, say A, that is initiating an AW, other CR users in the network synchronize their time reference with A’s AW. Suppose that a CR user D is aware of A’s AW, and has a data packet to transmit. D contends for the control channel in the next AS of D’s AW as follows. To prevent synchronized RTS attempts, D first backs off for a random duration of time (T ) that is uniformly distributed in the interval [0, Tmax ]; Tmax is a system-wide backoff counter. After this backoff time and if no carrier is sensed over the control channel, user C sends its control packet in the current AS. After all the control packets have been exchanged, the optimal channel assignment/rate allocation of Section 3 is executed at every communicating CR user. In the rest of this paper, we refer to the channel access mechanism that uses our optimal assignment as OPT-MAC.
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Contension Window (Announcing SINR info.)
AW
AS1
AS2
ASc1 t
Start Assignment Process Fig. 2. Example that illustrates the concept of dynamic AW in CRNs with C = C1 .
Remark 2. In our study, we consider the coordinated spectrum access problem in a single-hop CRN, where all CR users can hear each other. The primary advantage of our scheme is that it is based on passive learning. This is because in OPT-MAC, CR users when not transmitting/receiving (i.e., during admission control phase) always listen to the control channel in order to overhear control packet exchanges, including those not destined to them. Contending CR users use the control information to extract instantaneous SINR information and idle channel lists. Thus, our MAC protocol does not introduce any additional control message overhead beyond the two-way handshake, which is indeed needed for any CSMA/CA-based multi-channel CRN MAC protocol. Claim 1. The OPT-MAC protocol and any CSMA/CA-based multi-channel CRN MAC protocol have comparable overheads (i.e., a two-way handshake is needed to send one data packet). 5. Performance evaluation We compare the performance of our proposed protocol (OPT-MAC) with two CSMA-based CRN MAC protocols: COMAC [12] and DDMAC [4]. As mentioned in Section 1.1, COMAC employs a greedy channel assignment strategy of using the best idle channel for a given CR transmission. On the other hand, DDMAC attempts to maximize the CRN throughput through a probabilistic channel assignment algorithm that exploits the dependence between the signal’s attenuation model and the transmission distance while considering the prevailing traffic and interference conditions. In our evaluation, we study the network performance under two different rate–SINR relationships: the information-theoretic capacity (i.e., Shannon’s equation) and a staircase-like function4 similar to the one shown in Fig. 1. Our results are based on simulation experiments conducted using CSIM programs (CSIM is a C-based process-oriented discrete-event simulation package [27]). Our performance metrics are the CRN sum-rate, and the fairness. We use the fairness index in [28] to quantify the fairness of a scheme according to the sum-rate of all CR users in the network. A Rayleigh fading signal propagation model to describe the channel gain between any two CR users is considered. Specifically, for a transmitter–receiver separation d, the received power over the ith channel is given by: Pr
(i)
(i)
(i)
= Po
where Po =
d
−n
do (i)
(i) (i) Pt (i) Gt Gr l2i (i) (4π do )2 (i) power, Gt
ξ (i) ,
d ≥ do (i)
(6)
is the path loss of the close-in distance do (i) = max{ 2Dl , D, li }, D is the antenna length, Pt (i) is the 2
i
(i)
transmission is the antenna gain at the transmitter, Gr is the antenna gain at the receiver, li is the wavelength of fi , n is the path loss exponent, and ξ (i) is a normalized random variable that represents the power gain of the fading process. For Rayleigh fading, ξ (i) is exponentially distributed; Pr(ξ (i) ≤ y) = 1 − e−y [29]. 5.1. Simulation setup We consider N pairs of one-hop transmitter–receiver CR users in a 100 m × 100 m area. To simplify our simulation, we assume that all CR users are within the transmission range of each other, so that any control packet sent from a CR can be heard by all other CR users. The locations of the CR transmitters and receivers are randomly assigned within the simulation region. We assume that there are M = 11 channels, each has 2.5 MHz of bandwidth and licensed to one PRN. The carrier
4 A staircase-like rate–SINR function typically characterizes practical multi-rate systems.
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Table 1 Rate–SINR relationship. Rate index
Rate (Mbps)
SINRth
R1 R2 R3 R4 R5 R6 R7 R8
1 4.5 6 7 8.5 9.5 10.5 11
1 5 7 10 15 20 25 31
120 120 100
CRN Sum-rate (Mbps)
CRN Sum-rate (Mbps)
100 Opt-MAC,µ*=3
80
Opt-MAC,µ*=9
60
COMACµ*=3 COMAC,µ*=9
40
OPT-MAC,µ*=3
80
OPT-MAC,µ*=9
60
COMAC,µ*=3 COMAC,µ*=9
40
DDMAC,µ*=3 DDMAC,µ*=3
DDMAC,µ*=9
20
20 DDMAC,µ*=9
0
2
4
6
8 10 12 14 Number of CR Links (N)
16
(a) Assuming Shannon capacity formula.
18
0
2
4
6
8 10 12 14 Number of CR Links (N)
16
18
(b) Assuming staircase formula. Fig. 3. CRN sum-rate vs. number of CR links N.
frequency of the ith PRN is fi = 900 + i MHz, for i = 1, . . . , M. CR users can opportunistically access the 11 channels. We set µ∗i = µ∗ , ∀i ∈ M . For the simulated staircase rate–SINR function, the values of the different supported rates and their corresponding SINR thresholds are summarized in Table 1. Note that for both the information-theoretic and the staircase rate–SINR functions, the achieved rate is 0 if the received SINR < µ∗ . We divide the time into slots, each of length 100 ms. A 2-state Markov model that alternates between two states: IDLE and BUSY is considered to determine the status of a PR channel at any given time. A BUSY (IDLE) state indicates that some (no) PR user is transmitting over the given channel. For channel i, denote the average IDLE and BUSY durations of the PR activity by λi and µi , respectively. At any given time (i) λi . We set µi = 100 ms and λi = λ, ∀i ∈ {1, . . . , M }. Accordingly, slot, the ith PRN is idle with probability PB = λ +µ (i)
i
i
PB = PB , ∀i ∈ M . The locations of the CR transmitters and receivers are randomly assigned within the simulation region. We set the maximum transmission power of a CR user to Pmax = 1 W, the thermal noise power density to 10−21 W/Hz for all channels, the path loss exponent to n = 4, and the antenna length to D = 5 cm. The results presented below are based on the average of 30 randomly generated topologies, with a simulation time of 5000 time slots for each topology. 5.2. Simulation results We first compare the achieved sum-rate of all CR links for OPT-MAC, COMAC, and DDMAC protocols. The CRN sum-rate is plotted as a function of the number of active CR links in Fig. 3. In Fig. 3(a) (Fig. 3(b)), we consider Shannon’s equation (the staircase function) to compute the achieved rates over idle channels for each active CR link. Fig. 3 shows that as the number of CR users increases, OPT-MAC significantly outperforms COMAC and DDMAC, irrespective of the employed rate–SINR relationship. Specifically, OPT-MAC improves the overall achieved sum-rate by up to 35% compared to COMAC and up to 25% compared to DDMAC. This improvement is mostly attributed to the employed proper channel assignment. Fig. 4 shows the achievable sum-rate as a function of PR activities (PB ). Fig. 4 reveals that the throughput gain of OPT-MAC over COMAC and DDMAC is smaller at larger PB . This is expected since the larger the value of PB , the lower the chances of finding idle channels, which consequently reduces the performance gain (similar behavior was observed when staircase rate–SINR function is used). Fig. 5 shows the achievable sum-rate as a function of SINR threshold (µ∗ ). This figure reveals that the throughput gain of OPT-MAC over COMAC and DDMAC is larger at larger µ∗ .
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2115
140 Opt-MAC,µ*=3
120 CRN Sum-rate (Mbps)
Opt-MAC,µ*=9
100
COMACµ*=3 COMAC,µ*=9
80
DDMAC µ*=3
60
DDMAC µ*=9
40 20 0 0.1
0.2
0.3
0.4
0.5 PB
0.6
0.7
0.8
0.9
Fig. 4. CRN sum-rate vs. PB , assuming Shannon capacity formula.
120
125
OPT-MAC, N=10
Opt-MAC, N=10
120
Opt-MAC, N=18
OPT-MAC, N=18
115
COMAC, N=10
CRN Sum-rate (Mbps)
CRN Sum-rate (Mbps)
COMAC, N=10
115
COMAC, N=18 DDMAC, N=10
110
DDMAC, N=18
105
COMAC, N=18
110
DDMAC, N=10 DDMAC, N=18
105
100
100 95
95 90
1
2
3
4
5 µ*
6
7
8
90
9
(a) Assuming Shannon capacity formula.
1
2
3
4
5 µ*
6
7
8
9
(b) Assuming staircase formula.
Fig. 5. CRN sum-rate vs. SINR threshold, assuming Shannon formula.
1 0.99
Fairness Index
0.98
OPT-MAC,µ*=3 COMAC,µ*=3
0.97 0.96 0.95 0.94 0.93 0.92
2
4
6
8
10 N
12
14
16
18
Fig. 6. Fairness index vs. number of CR links (N) for µ∗ = 3 (DDMAC depicted similar behavior as OPT-MAC).
In Fig. 6, we study the impact of the channel assignment strategy on fairness. We set mu∗ = 3. It is clear that all protocols achieve comparable fairness (other values of µ∗ depicted similar fairness behavior). This can be attributed to the fact that, in
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10 9
Channel Usage (%)
8 OPT-MAC
7
COMAC
6 5 4 3 2 1 0
0
1
2
3
4
5 6 7 8 Channel Number
9
10
11
12
Fig. 7. Channel usage (%) for µ∗ = 3 and N = 18 (DDMAC depicted similar behavior as OPT-MAC).
all protocols, CR users contend over the control channel using a variant of the CSMA/CA mechanism. Finally, Fig. 7 depicts, for µ∗ = 3, the channel usage, defined as the fraction of time in which a specific channel is used for CR transmissions. For all protocols, channel usage is roughly evenly distributed among all channels, irrespective of the number of CR links.5 6. Conclusions In this paper, we proposed a solution to solve the joint rate control and channel assignment problem for the coordinated channel access in opportunistic CRNs. Our solution improves the CRN throughput through an optimal channel assignment process. The assignment process dynamically assigns channels to CR transmissions with the objective of maximizing the achieved CRN sum-rate and subject to interference and SINR constraints. In order to realize our solution in a distributed manner, we developed a CSMA/CA-based MAC protocol (OPT-MAC) for CRNs with access window (AW). The purpose of the AW is to announce CR transmission requests, idle channel list, and SINR information; and resolve contention between CR transmissions. We compared the performance of OPT-MAC with that of two multi-channel CSMA/CA-based CRN MAC (i.e., COMAC and DDMAC) protocols. We showed that our protocol achieves about 35% (25%) increase in throughput over the COMAC (DDMAC) protocol, while preserves fairness. In summary, OPT-MAC provides better spectrum utilization by achieving a larger network throughput. Appendix A A.1. Concept of unimodularity Definition 1. A matrix B is said to be totally unimodular if the determinant of every square submatrix (minor) of B is in the set {−1, 0, 1} [30]. The following theorem provides sufficient but not necessary conditions for a matrix of 0’s and 1’s to be totally unimodular. Theorem 1. An m × n matrix B is totally unimodular if its rows can be partitioned into two disjoint matrices B1 and B2, with the following properties [30]:
• Every entry in B is 0 or 1. • Every column of B contains at most two 1’s. • Every column of B1 and B2 contains at most one non-zero element. Appendix B B.1. Proof of total unimodularity of the constraint matrix
T
To prove this, we partition the matrix A into two disjoint matrices A1 (N × CN) and A2 (C × CN), (i.e., A = A1A2 ), where A1 and A2 correspond to the first and second constraints in (4), respectively. The matrices A1 and A2 can be written as: 5 Other values of µ∗ depicted similar channel-usage behavior.
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C 1 . . . 1 0 . . . 0 A1 = 0 . . . 0 . ..
2117
0...0
...
...
C
1...1
0...0
...
C
0...0
.. .
1...1 .. .
... .. .
...
...
...
0...0
0 . . . 0
0 . . . 0 0 . . . 0 .. . C 1 . . . 1 N ×CN
(7)
and
C
C
10 . . . 0 C 010 . . . 0 C A2 = 0010 . . . 0 .. . C 0...1
10 . . . 0
...
C
010 . . . 0
...
C
0010 . . . 0
.. .
... .. .
C
0...1
...
C 10 . . . 0 C 010 . . . 0 C . 0010 . . . 0 .. . C 0...1 C ×CN
(8)
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