Maximizing Spectrum Utilization of Cognitive Radio Networks Using Channel Allocation and Power Control Anh Tuan Hoang and Ying-Chang Liang Institute for Infocomm Research - 21 Heng Mui Keng Terrace, Singapore 119613 Email: {athoang, ycliang}@i2r.a-star.edu.sg Abstract— We consider a cognitive radio network in which a set of base stations make opportunistic unlicensed spectrum access to transmit data to their subscribers As the spectrum of interest is licensed to another (primary) network, power and channel allocation must be carried out within the cognitive radio network so that no excessive interference is caused to any primary user We are interested in spectrum-allocation/power-control schemes that maximize the spectrum utilization of the cognitive network while appropriately protecting primary users While doing so, the control schemes must also meet the required signal to interference plus noise ratio (SINR) of each subscriber of the cognitive network This problem can be formulated as a linear mixed (0-1) integer programming Due to the high complexity in obtaining optimal spectrum-allocation/power-control schemes, we propose a suboptimal scheme that can be obtained at lower complexity while still achieving good spectrum utilization This suboptimal scheme is constructed based on the idea of a dynamic interference graph that captures the interfering effects Numerical studies of our control scheme are presented I I NTRODUCTION The traditional approach of fixed spectrum allocation to licensed networks leads to spectrum underutilization In recent studies by the FCC, it is reported that there are vast temporal and spatial variations in the usage of allocated spectrum, which can be as low as 15% [1] This motivates the concepts of opportunistic unlicenced spectrum access that allows secondary cognitive radio networks to opportunistically exploit the underulizized spectrum In fact, opportunistic spectrum access has been encouraged by both recent FCC policy initiatives and IEEE standadization activities [2], [3] On the one hand, by allowing opportunistic spectrum access, the overall spectrum utilization can be improved On the other hand, transmission from cognitive networks can cause harmful interference to primary users of the spectrum Therefore, important design criteria for cognitive radio include maximizing the spectrum utilization and minimizing the interference caused to primary users In this paper, we consider a cognitive radio network that consists of multiple cells Within each cell, there is a base station (BS) that supports a set of fixed wireless subscribers called customer premise equipments (CPEs) The spectrum of interest is divided into a set of non-overlapping channels To serve each CPE, a BS needs to use exactly one of the available channels The spectrum is actually licensed to a set of primary users (PUs) For the cognitive radio network, two operational constraints must be met: the total amount of interference caused by all opportunistic transmissions to each PU must not exceed a predefined threshold, • for each CPE, the received signal to interference plus noise ratio (SINR) must exceed a predefined threshold We define the system utilization as the total number of CPEs that can be supported while meeting the above two constraints We are interested in spectrum-allocation/powercontrol schemes that maximize the utilization of the cognitive radio network We note that in order to implement such a system, there should be a mechanism that enables secondary users (BSs and CPEs) to sense the spectrum and detect the presence of primary users This is a challenging problem in itself and is beyond the scope of this paper Here, we simply assume that the positions and operating bandwidth of all PUs are known The utilization maximizing problem can be structured as a linear mixed (0-1) integer programming As solving for an optimal solution is NP-hard, we propose a heuristic channelallocation/power-control scheme This heuristic is based on the concepts of a dynamic interference graph that captures not only the pair-wise but also aggregate interference effects when multiple transmissions happen simultaneously on one channel Numerical results are obtained to study the performance of our proposed algorithm Works on channel allocation in cognitive radio networks with opportunistic spectrum access include [4] and [5] In [4], Wang and Liu consider a problem of opportunistically allocating unused licensed channels to a set of cognitive base stations so that the total number of channel usages is maximized The authors then formulate this problem as a graph-coloring problem and propose a number of greedy heuristics for channel allocation In [5], Zheng and Peng consider a problem similar to [4] However, they introduce a reward function that is proportional to the coverage areas of base stations and also allow the interference effect to be channel specific Again, the problem is studied based on a graph-coloring formulation The main drawback of the works in [4], [5] lies in their oversimplified binary interference model, which is simply based on whether or not the coverage areas of two base station overlap This is unrealistic and does not capture the aggregate interference effects when multiple transmissions simultaneously happen on one channel We overcome this by considering the interference effects based ã 1-4244-0063-5/06/$20.00 â2006 IEEE Authorized licensed use limited to: National Taiwan University Downloaded on April 16,2010 at 07:15:35 UTC from IEEE Xplore Restrictions apply 1000 data are transmitted from BSs to CPEs Assuming that a BS needs exactly one channel to serve each CPE, we define the spectrum utilization as the total number of CPEs served Our objective then is to maximize the spectrum utilization of the cognitive radio network while appropriately protecting all primary users We will discuss the requirements for reliable communications between BSs and CPEs and how PUs are protected next PU 900 BS 800 700 600 CPE 500 400 300 B Operational Requirements 200 1) SINR Requirement for CPEs: Note that in our downlink scenario, each CPE is served by one fixed BS Therefore, for the sake of brevity, we use the phrase ”transmission toward CPE i” to refer to the downlink transmission from the BS serving CPE i toward CPE i Let Gcij be the channel power gain from the BS serving CPE j to CPE i on channel c, Gcij includes all path loss and fading effects Let Pic denote the transmit power for the transmission toward CPE i on channel c If channel c is not assigned for the transmission toward CPE i, then Pic = The SINR at CPE i is given by: 100 0 100 200 Fig 300 400 500 600 700 800 900 1000 Deployment of a cognitive radio network on SINR As we that, the problem can not be viewed as a standard graph-coloring problem anymore However intuitive ideas behind some greedy graph-coloring algorithms can still be exploited Works on channel-allocation/power-control problems that model interference effects based on the SINR include [6] and [7] The objective of [6] is to maximize spectrum utilization while that of [7] is to minimize total transmit power to satisfy the rate requirements of all links However, [6] and [7] not consider the scenario of opportunistic spectrum access and there is no issue of protecting primary users In a broader context, our work is related to the class of power control problems for interfering transmissions with the objective of guaranteeing SINR constraints [8]–[11] In fact, similar to [8]–[11], we use Perron-Frobeniuos theorem to check the feasibility of a particular channel allocation The rest of this paper is organized as follows In Section II, we introduce our system model and then define the control problem together with its objective In Section III, we present our channel-allocation/power-control algorithm Numerical results showing the performance of our proposed control scheme will be discussed in Section IV Finally, we conclude the paper in Section V and outline some future research directions II P ROBLEM D EFINITION A System Model We consider the following opportunistic unlicensed spectrum access scenario The spectrum of interest is divided into K channels These channels are licensed to a primary network consisting of M primary users (PUs) In the same area, a secondary cognitive radio network is deployed This cognitive network consists of B cells Within each cell, there is a base station (BS) serving a number of fixed customer premise equipments (CPEs) by opportunistically making use of the K channels As the K channels are licensed only to M primary users, channel allocation and power control must be applied to the cognitive radio network to ensure that each of the M PUs experiences an acceptable level of interference This scenario is depicted in Fig Let N denote the total number of CPEs in the cognitive radio network We consider the downlink situation in which γic = Gcii Pic No + N j=1,j=i Gcij Pjc , ∀i ∈ {1, 2, N }, (1) where No is the noise power spectrum density of each CPE For reliable transmission toward CPE i, we require that γic ≥ γ (2) In practice, γ can be regarded as the minimum SINR to achieve a certain bit error rate (BER) performance at each CPE 2) Protecting Primary Users: Let Πc denote the set of all PUs that use channel c and let Gcpi be the channel gain from the BS serving CPE i to PU p on channel c We require that, for each PU, the total interference from all opportunistic transmissions (BSs toward CPEs) does not exceed a predefined tolerable threshold ζ, i.e., N Pic Gcpi ≤ ζ, ∀p ∈ Πc , ∀c ∈ {1, 2, K} (3) i=1 C Maximizing Spectrum Utilization Let aci be a binary variable denoting whether or not channel c is assigned to the transmission toward CPE i In particular, aci equals one if channel c is assigned to the transmission toward CPE i and is zero otherwise Similar to [6], we can state the problem of maximizing the total number of CPEs served as the following linear mixed (0-1) integer programming K N arg max aci ∈{0,1} subject to: K aci ≤ 1, aci (4) c=1 i=1 ∀i ∈ {1, 2, N }, (5) c=1 Gcii Pic − γ N Gcij Pjc − γNo ≥ (aci − 1)δ, j=1,j=i Authorized licensed use limited to: National Taiwan University Downloaded on April 16,2010 at 07:15:35 UTC from IEEE Xplore Restrictions apply (6) m Pic Gcpi ≤ ζ, ∀p ∈ Πc , III C HANNEL - ALLOCATION /P OWER - CONTROL A LGORITHMS (7) i=1 ≤ Pic ≤ P max , ∀i ∈ {1, 2, N } (8) In (6) δ is a relatively large constant We note that the above problem is NP-hard, therefore, instead of going for an optimal solution, we are interested in heuristic algorithms that can provide good performance D Feasible Assignments Before moving on to present different channelallocation/power-control algorithms in Section III, let us deal with the question of whether it is feasible to assign a particular channel c simultaneously to a set of transmissions toward m CPEs: (i1 , i2 , im ) Here, feasibility means there exists a set of positive transmit power levels P c = (Pic1 , Pic2 , Picm )T such that all the SINR constraints of the m CPEs are met while the interferences caused to PUs not exceed the acceptable threshold If we define an m × vector U c as: Uc = γNo γNo γNo , , c Gci1 i1 Gci2 i2 Gim im T (9) and an m × m matrix F c as: c Frs = 0, γGcir is Gcir ir if r = s , , if r = s, r, s ∈ {1, m} (10) then it can be verified that the SINR constraints of m CPEs (i1 , i2 , im ) can be written compactly as: (I − F c )P c ≥ U c (11) From the Perron-Frobenious theorem [8]–[10], (11) has a positive component-wise solution P c if and only if the maximum eigenvalue of F c is less than one In that case, the Paretooptimal transmit power vector is P c∗ = (I − F c )−1 U c (12) Here Pareto-optimal means that if P c is a positive power vector that satisfies (11), then P c ≥ P c∗ component-wise Due to this fact, the following 2-step procedure can be used to check the feasibility of assigning a particular channel c to the transmissions toward the set of CPEs (i1 , i2 , im ) Two-step Feasibility Check: • • Step 1: Check if the maximum eigenvalue of matrix F c defined in (10) is less than one If not, conclude that the assignment is not feasible, otherwise, continue at Step Step 2: Using (12) to calculate the Pareto-optimal transmit power vector P c∗ Then, check if P c∗ satisfies the constraints for protecting PUs in (7) and the maximum power constraints in (8) If yes, conclude that the assignment is feasible and P c∗ is the power vector that should be used Otherwise, the assignment is not feasible As has been mentioned, we are interested in channelallocation/power-control heuristics that achieve good performance and can be obtained at lower complexity than the optimal algorithm Note that the objective is to maximize the number of CPEs served while guaranteeing protection to legacy primary users We focus on centralized control algorithms in which all channel-allocation/power-control decisions are determined offline before being signaled to BSs and CPEs Although there has been a great interest in distributed power control for wireless interference networks [8]–[11], distributed control is not suitable for control a secondary cognitive system This is because with distributed/online algorithms, it is not possible to give absolute protection to primary users A Main Algorithm: Dynamic Graph Based In this section, for the sake of brevity, when a channel c is allocated to the transmission toward CPE i, we simply say that ”channel c is allocated to CPE i” Our proposed algorithm starts with no CPEs being assigned any channel It then allocates a channel to one CPE at a time, until either all CPEs are served, or there is no more feasible channel assignment At each step, channel assignment and power control must be carried out so that all CPEs that have been allocated channels in prior steps are protected At each step, we construct an interference graph that represents the interference between pairs of unserved CPEs Moreover, this interference graph must also take into account the aggregate interference caused by transmissions that have been allocated channels in previous steps This means our interference graph dynamically changes during the process of channel allocation This is the major difference between our approach and the approach that constructs a fixed interference graph once at the beginning of the channel allocation process [6] We name our approach Dynamic Graph Based and the approach in [6] Fixed Graph Based To implement the Dynamic Graph Based approach, at each step, for each unserved CPE i, we calculate its degree corresponding to a channel c and prior channel-allocation matrix Asgn, as follows • • Deg(i, c, Asgn) = ∞ if it is not feasible to assign channel c to user i while keeping all prior assignments The feasibility can be checked using the two-step procedure presented at the end of Section II-D If it is feasible to assign channel c to CPE i, then Deg(i, c, Asgn) is the total number of unserved CPEs that can not be assigned channel c anymore when this channel is assigned to CPE i Note that we only count those unserved CPEs that can use channel c here The algorithm then picks a CPE-channel pair [i∗ , c∗ ] that minimizes Deg(i, c, Asgn) and assigns channel c∗ to CPE i∗ The channel assignment matrix Asgn and the set of unserved CPEs U nSrv are then updated and the process is repeated The pseudo-codes for our algorithm are given in Algorithm Authorized licensed use limited to: National Taiwan University Downloaded on April 16,2010 at 07:15:35 UTC from IEEE Xplore Restrictions apply Algorithm Dynamic Graph Based 1: Asgn(i, c) ← 0, U nSrv ← {1, 2, N } 2: loop 3: [i∗ , c∗ ] ← arg Deg(i, c, Asgn) i∈U nSrv, c 4: 5: 6: 7: 8: 9: 10: 11: 12: if Deg(i∗ , c∗ , Asgn) = ∞ then break end if Asgn(i∗ , c∗ ) ← 1, U nSrv ← U nSrv \ {i∗ } if U nSrv = ∅ then break end if end loop return Asgn Note that our approach of picking a CPE with the minimum degree to assign a channel is similar to the minimum-degree greedy heuristic in graph-coloring theory [12] within the cell The total number of CPEs is N = 40 The total number of PUs is M = → 40 All CPEs and PUs are randomly deployed across the entire service area with a uniform distribution A sample network is shown in Fig We model an orthogonal frequency division multiple access (OFDMA) system in which the entire bandwidth is divided into 48 subcarriers Each subcarrier is regarded as one channel in our channel-allocation scheme The fading channel is represented by a six-tap channel, with exponential decay factor Although there are 48 channels (subcarriers), we assume that only a subset of them is considered for used by primary and secondary users The number of channels K is set at 4, 8, 16 The path loss exponent is taken to be We assume that each of the M PUs randomly picks and uses one of the channels The noise power spectrum density at each CPE is No = −100dBm The required SINR at each CPE is 15dB The maximum tolerable interference for each PU is 90dBm For each BS, the maximum transmit power on each channel is P max = 50mW B Other Algorithms 1) Power-based Algorithm: In [7], Kulkarni et al consider a problem of allocating subchannels to multiple interfering links so that their rate requirements are met while the total transmit power is minimized Here, a SINR requirement is also set for each link In [7], a power-based subchannel allocation algorithm is proposed The general procedure is the same as our algorithm presented in the above section The only difference is that, at each step, the degree of CPE i on channel c is set equal to the total transmit power of all the nodes We term this approach Min Trans Power In Section IV, we also consider the performance of another power-based algorithm called Min Interf Power This algorithm, at each step, allocates a channel to an unserved CPE such that the total interference power at all PUs and CPEs is minimized 2) Random Algorithm: We also consider a simple random channelallocation/power-control algorithm as follows A channel is assigned to one CPE at a time At each step, we randomly pick an unserved CPE i and a channel c We then check if it is feasible to assign channel c to CPE i while keeping all previous channel assignments using the Two-step Feasibility Check (Section II-D) If it is so, assign channel c to CPE i Otherwise, another pair of unserved CPE and channel is randomly picked again The algorithm stops when all CPEs have been served, or when there is no more feasible channel assignment IV N UMERICAL R ESULTS AND D ISCUSSION A Simulation Model The system model used in our numerical studies is as follows We consider a square service area of size 1000 × 1000m in which a cognitive radio network is deployed The service area is√further divided √ into B adjacent squares, each of size 1000/ B × 1000/ Bm We set B = 4, 9, 16 A BS is deployed at the center of each cell to serve CPEs B Performance of Different Algorithms In Figs 2, 3, 4, and 5, we plot the number of CPEs served versus the number of PUs when each of the algorithms Dynamic Graph Based, Fixed Graph Based, Min Trans Power, Min Interf Power, and Random is employed Here, 500 instances of the network are generated for each scenario in order to obtain the average performance of each algorithm As expected, for all scenarios and all algorithms tested, when the number of PUs increases, the number of CPEs supported decreases This is because less spectrum is available for opportunistic spectrum access As can be seen, our Dynamic Graph Based algorithm consistently outperforms others On the other hand, Random scheme always has the worst performance The performance gain of the Dynamic Graph Base scheme, with respect to the Random scheme, is between 5% and 19% The performance of three schemes Fixed Graph Based, Min Trans Power, and Min Interf Power are comparable to each other When the number of BSs is relatively small while the number of channels is relatively large, there are not much gains of using Fixed Graph Based, Min Trans Power, and Min Interf Power, relative to using the Random scheme (Figs and 3) However, when the number of BSs increases while, at the same time, the number of channels decreases (Figs and 5), the performance gains of Fixed Graph Based, Min Trans Power, and Min Interf Power, relative to Random scheme, are more prominent These effects can be explained as follows When the number of BSs is small while the number of channels is large, there is not much need to reuse each channel To put it another way, there are enough channels to compensate for the sub-optimality effect of random assignment On the other hand, with more BSs and less channels, there is a real need in reducing interference so that each channel can be reused, and this can be achieved with Fixed Graph Based, Min Trans Power, and Min Interf Power Authorized licensed use limited to: National Taiwan University Downloaded on April 16,2010 at 07:15:35 UTC from IEEE Xplore Restrictions apply 40 40 Dynamic Graph Min−Trans−Power Min−Interf−Power Fixed Graph Random 35 Dynamic Graph Min−Trans−Power Min−Interf−Power Fixed Graph Random No of CPEs served No of CPEs served 36 30 25 20 32 28 15 10 10 15 20 25 30 35 25 40 10 15 No of primary users 20 25 30 35 40 No of primary users Fig Performance in terms of no of CPEs served versus no of PUs No of BSs = 4, no of CPEs = 40, no of channels = 16 Fig Performance in terms of no of CPEs served versus no of PUs No of BSs = 9, no of CPEs = 40, no of channels = 16 34 26 Dynamic Graph Min−Trans−Power Min−Interf−Power Fixed Graph Random 32 30 Dynamic Graph Min−Trans−Power Min−Interf−Power Fixed Graph Random 24 No of CPEs served No of CPEs served 22 28 26 24 22 20 18 16 20 14 18 16 10 12 14 16 18 20 No of primary users Fig Performance in terms of no of CPEs served versus no of PUs No of BSs = 9, no of CPEs = 40, no of channels = V C ONCLUSIONS In this paper, we consider the problem of channelallocation/power-control to maximize the spectrum utilization of a cognitive radio network that employs opportunistic spectrum access At the same time, a realistic control framework is formulated to guarantee protection to primary users and reliable communications for cognitive nodes We propose a heuristic channel-allocation/power-control algorithm that is based on constructing a dynamic interference graph Numerical results are obtained to show the performance gain of our proposed algorithm For future research, we are currently extending this work to consider fairness among CPEs At the same time, a joint network-admission/resource-allocation framework is being developed based on the system model of this paper R EFERENCES [1] FCC, “Spectrum policy task force report, FCC 02-155.” Nov 2002 [2] ——, “Facilitating opportunities for flexible, efficient, and reliable spectrum use employing cognitive radio technologies, notice of proposed rule making and order, FCC 03-322.” Dec 2003 [3] IEEE 802.22 Wireless RAN, “Functional requirements for the 802.22 WRAN standard, IEEE 802.22- 05/0007r46,” Oct 2005 12 10 12 14 16 18 20 No of primary users Fig Performance in terms of no of CPEs served versus no of PUs No of BSs = 16, no of CPEs = 40, no of channels = [4] W Wang and X Liu, “List-coloring based channel allocation for openspectrum wireless networks,” in Proceedings of IEEE 62nd Vehicular Technology Conference (VTC’05 Fall), Dallas, Texas, Sep 2005 [5] H Zheng and C Peng, “Collaboration and fairness in opportunistic spectrum access,” in Proceedings of IEEE International Conference on Communications (ICC’05), Korea, May 2005 [6] A Behzad and I Rubin, “Multiple access protocol for power-controlled wireless access nets,” IEEE Transactions on Mobile Computing, vol 3, no 4, pp 307–316, Oct.-Dec 2004 [7] G Kulkarni, S Adlakha, and M Srivastava, “Subcarrier allocation and bit loading algorithms for OFDMA-based wireless networks,” IEEE Transactions on Mobile Computing, vol 4, no 6, pp 652–662, Nov./Dec 2005 [8] G J Foschini and Z Miljanic, “A simple distributed autonomous power control algorithm and its convergence,” IEEE Transactions on Vehicular Technology, vol 42, no 4, pp 641–646, Apr 1993 [9] D Mitra, “An asynchronous distributed algorithm for power control in cellular radio systems,” in Proceedings of 4th WINLAB Workshop on Third Generation Wireless Information Networks, Rutgers University, New Brunswick, NJ, Oct 1993 [10] N Bambos, S C Chen, and G J Pottie, “Radio link admission algorithms for wireless networks with power control and active link quality protection,” in Proc of IEEE INFOCOM, Boston, MA, Nov 1995 [11] ——, “Channel access algorithms with active link protection for wireless communication networks with power control,” IEEE/ACM Transactions on Networking, vol 8, no 5, pp 583–597, Oct 2000 [12] S Sakai, M Togasaki, and K Yamazaki, “A note on greedy algorithms for the maximum weighted independent set problem.” Discrete Applied Mathematics 126, 2-3, pp 313–322, 2003 Authorized licensed use limited to: National Taiwan University Downloaded on April 16,2010 at 07:15:35 UTC from IEEE Xplore Restrictions apply ... served versus no of PUs No of BSs = 4, no of CPEs = 40, no of channels = 16 Fig Performance in terms of no of CPEs served versus no of PUs No of BSs = 9, no of CPEs = 40, no of channels = 16... No of CPEs served No of CPEs served 22 28 26 24 22 20 18 16 20 14 18 16 10 12 14 16 18 20 No of primary users Fig Performance in terms of no of CPEs served versus no of PUs No of BSs = 9, no of. .. channel to serve each CPE, we define the spectrum utilization as the total number of CPEs served Our objective then is to maximize the spectrum utilization of the cognitive radio network while appropriately