A two phase channel and power allocation

The 17th Annual IEEE International Symposium on Personal, Indoor and Mobile Radio Communications (PIMRC’06) A TWO-PHASE CHANNEL AND POWER ALLOCATION SCHEME FOR COGNITIVE RADIO NETWORKS Anh Tuan Hoang and Ying-Chang Liang Institute for Infocomm Research 21 Heng Mui Keng Terrace, Singapore 119613 {athoang, ycliang}@i2r.a-star.edu.sg A BSTRACT 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 For such a cognitive network, we propose a two-phase channel/power allocation scheme that improves the system throughput, defined as the total number of subscribers that can be simultaneously served In the first phase of our scheme, channels and power are allocated to base stations with the aim of maximizing their total coverage while keeping the interference caused to each primary user below a predefined threshold In the second phase, each base station allocates channels to their active subscribers based on a maximal bipartite matching algorithm Numerical results show that our proposed resource allocation scheme yields significant improvement in the system throughput 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% [3] This motivates the concepts of opportunistic unlicenced spectrum access that allows secondary cognitive radio networks to opportunistically exploit the underulized spectrum In fact, opportunistic spectrum access has been encouraged by both recent FCC policy initiatives and IEEE standadization activities [4, 6] 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) supporting a set of fixed users called customer premise equipments (CPEs) We consider the downlink scenario The spectrum of interest is divided into a set of nonoverlapping channels Each CPE can be either active or idle and a BS needs exactly one channel to serve each active CPE The spectrum is 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 throughput as the total number of active CPEs that can be simultaneously served Note that in order to implement the above system, there should be a mechanism for secondary users, i.e., BSs and CPEs, to sense the spectrum and detect the presence of primary users This is a challenging problem and is beyond the scope of this paper Here, we simply assume that the positions and operating channels of all PUs are known We propose a Two-phase Resource Allocation (TPRA) scheme that improves the system throughput and can be implemented with a reasonable complexity In the first phase of our scheme, channels and power are allocated to BSs with the aim of maximizing their total coverage while keeping the total interference caused to each PU below a predefined threshold The coverage of a particular BS is the number of CPEs that can be supported by the BS using at least one of its allocated channels In the second phase of TPRA, each BS allocates channels within its cell so that the number of active CPEs served is maximized This is done by solving a related maximal bipartite matching problem Numerical results show that our proposed TPRA scheme yields significant improvement in the system throughput Works on channel allocation in cognitive radio networks include [10] and [11] In [10], Wang and Liu consider a problem of opportunistically allocating licensed channels to a set of cognitive base stations so that the total number of channel usages is maximized In [11], Zheng and Peng consider a problem similar to [10] 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 Both problems in [10] and [11] are studied based on graph-coloring frameworks There are two significant differences between our work and [10] and [11] Firstly, instead of looking at the total number of channel usages or the coverage area of base stations, we are interested in the number of subscribers that are actually served While doing so, we take into account the fact that subscribers are not always active Secondly, a major drawback of the works in [10, 11] lies in their oversimplified binary interference model, which is based on whether or not the coverage areas of two base stations overlap This is unrealistic and does not capture the aggregate interference effects when multiple transmissions simultaneously happen on one channel Our model overcomes this by considering the interference effects based on received SINR The 17th Annual IEEE International Symposium on Personal, Indoor and Mobile Radio Communications (PIMRC’06) B Operational Requirements 1000 PU 1) SINR Requirement for CPEs 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 Let Pic denote the transmit power for the transmission toward CPE i on channel c, ≤ Pic ≤ P max If channel c is not assigned for the transmission toward CPE i, then Pic = The SINR at CPE i is given by: 900 BS 800 700 600 CPE 500 400 300 200 100 0 100 200 300 400 500 600 700 800 900 γic = 1000 Gcii Pic No + Figure 1: Deployment of a cognitive radio network Works on channel-allocation/power-control problems that model interference effects based on received SINR include [2] and [7] The objective of [2] is to maximize spectrum utilization while that of [7] is to minimize total transmit power to satisfy the rate requirements of all links However, [2] 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 transmission links with SINR constraints [1, 5, 9] In fact, similar to [1, 5, 9], 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 the control problem In Section III., we present the TPRA scheme Numerical results showing the performance of our proposed control scheme will be discussed in Section IV Finally, in Section V., we conclude the paper and outline the future research II A P ROBLEM D EFINITION System Model We consider an opportunistic spectrum access scenario depicted in Fig The spectrum of interest is divided into K channels that are licensed to a primary network of M primary users (PUs) In the same area, a 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 Channel allocation and power control must be applied to the cognitive radio network to ensure that each PU experiences an acceptable level of interference Let N denote the total number of CPEs We consider the downlink scenario in which data are transmitted from BSs to CPEs Moreover, we assume that each CPE is only active and requires data transmission with probability pa , < pa ≤ Assuming that a BS needs exactly one channel to serve each active CPE, we define the system throughput as the total number of active CPEs that can be simultaneously served Our objective then is to find a channel/power allocation scheme that achieves good average system throughput while appropriately protecting all primary users 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 the minimum SINR required 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 does not exceed a predefined threshold ζ, i.e., N Pic Gcpi ≤ ζ, ∀p ∈ Πc , ∀c ∈ {1, 2, K} (3) i=1 C Feasible Assignments Before moving on, let us address 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 , c c Gi1 i1 Gi2 i2 Gim im T (4) 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} (5) then the SINR constraints of m CPEs (i1 , i2 , im ) can be written compactly as: (I − F c )P c ≥ U c (6) From the Perron-Frobenious theorem [1, 5, 9], (6) 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 (7) The 17th Annual IEEE International Symposium on Personal, Indoor and Mobile Radio Communications (PIMRC’06) Here Pareto-optimal means that if P c is a positive power vector that satisfies (6), 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: channels on which it can only transmit at low power to cover nearby CPEs Based on the above intuition, we propose the following procedure to allocate channels/powers to BSs We process K channels one at a time For channel c, let Γcpb denote the channel gain from base station b to primary user p and define: • Step 1: Check if the maximum eigenvalue of F c defined in (5) is less than one If not, the assignment is not feasible, otherwise, continue at Step • Step 2: Using (7) to calculate the Pareto-optimal transmit power vector P c∗ Then, check if P c∗ satisfies the constraints for protecting PUs in (3) and the maximum power constraints, i.e P c∗ ≤ P max If yes, conclude that the assignment is feasible and P c∗ is the power vector to use Otherwise, the assignment is not feasible If it is feasible to assign channel c to the transmissions toward CPEs (i1 , i2 , im ), we simply say the set (i1 , i2 , im ) is feasible on channel c c Γc∗ b = maxc {Γpb } III A T WO -P HASE R ESOURCE A LLOCATION Motivations We are interested in channel/power allocation schemes that can simultaneously serve a good number of active CPEs while protecting all PUs from excessive interference To protect PUs, all BSs have to coordinate their transmit powers on each channel That requires a global control mechanism On the other hand, CPEs in the network can switch between active and idle states frequently In that case, it is preferable that changes in CPEs’ states are dealt with locally, within each cell This will reduce the amount of recalculations and signaling/updates involved These observations motivate our Two-Phase Resource Allocation (TPRA) scheme B The Two-Phase Resource Allocation Scheme 1) Phase - Global Allocation: In this phase, channels and transmit powers are allocated to BSs so that the interference caused to each PU is below a tolerable threshold At the same time, we aim to cover as many CPEs as possible When talking about coverage here, we not care whether a CPE is active or idle That will be taken care of in the second phase of the TPRA scheme Consider a particular channel c For each BS, the higher power it transmits on c, the more CPEs it can cover However, the higher the transmit power of the BS, the more interference it causes to PUs and other cells This interference reduces the number of CPEs that can be covered using channel c in other cells We note that it is extremely hard to fully characterize the above dual effects of varying base stations transmit powers on the number of CPEs being covered in the whole network Therefore, we rely on the following intuition for making our channel/power allocation decisions A BS that is near any PU using channel c should only transmit at low power to reduce interference On the other hand, a BS that is faraway from all PUs using channel c can transmit at higher power Each BS can use a set of channels on which it can transmit at high power to cover faraway CPEs The same BS can use a set of p∈Π (8) We the following: • Sort the base stations in the ascending order of Γc∗ b , i.e., c∗ form (b1 , b2 , bB ) where Γc∗ bn ≤ Γbm , ∀1 ≤ n < m ≤ B The base stations will be processed one at a time in this order • For base station bn , determine a particular CPE in that bn should cover This is done as follows Given the set (i1 , i2 , in−1 ) of CPEs being covered by (b1 , b2 , bn−1 ), let V cn be the set of all CPEs in the cell of bn such that (i1 , i2 , in−1 , i) is feasible on channel c (see the two-step feasibility check in Section II-C.) Then in is the CPE that has the weakest channel gain from bn , i.e., in = arg {Gcii } (9) i∈V cn It can happen that the set V cn is empty Then, with some little abuse of notation, we set in = to indicate that no CPE is covered by bn • After processing all BSs in the order b1 , b2 , bB , we obtain a set of CPEs (i1 , i2 , iB ) Using (7), determine the transmit power to serve each of these CPEs, i.e., (Pic1 , Pic2 , PicB ) • Finally, based on (Pic1 , Pic2 , PicB ), determine the N × K coverage matrix C, where C(i, c) = indicates that CPE i can be served by the corresponding BS on channel c This can be checked based on (2) It can happen that when sorting BSs based on Γc∗ b , there are ties among BSs In that case, the BSs with less number of CPEs covered so far (can be checked from coverage matrix C) will be processed first 2) Phase - Local Allocation Based on the coverage matrix C obtained in the first phase, channel allocation can be carried out within each cell, in a manner independent to what happens in the rest The procedure is as follows • First, determine all active CPEs in the cell • Next, form a bipartite graph that represents the coverage of the cell This is done by representing the set of active CPEs as a set of vertices, which are connected to another set of vertices representing the available channels Note that an edge exists between the vertex representing CPE i and the vertex representing channel c if and only if C(i, c) = This is demonstrated in Fig • Now, the problem of maximizing the number of active CPEs served is equivalent to the problem of maximizing the number of disjoint edges in the resulting bipartite graph Two edges in a graph are disjoint if they not share any end This is called the maximal bipartite matching problem The 17th Annual IEEE International Symposium on Personal, Indoor and Mobile Radio Communications (PIMRC’06) CPEs 100% Channels TPRA NOCA Random PCSA 90% 80% 3 Figure 2: Representing the coverage within one cell as a bipartite graph Edges with the same color represent the same channel % of CPEs covered 70% 60% 50% 40% 30% 20% There are a host of algorithms for finding the maximal matching of a bipartite graph In this paper, we obtain maximal bipartite matching based on Berge’s Theorem of finding alternating augmenting paths [8] C 10% 10 15 20 25 30 35 40 45 50 55 60 No of primary users Figure 3: Percentage of CPEs being covered vs no of PUs No of BSs = 4, no of CPEs = 300, no of channels = 16 Other Channel/Power Allocation Schemes To relatively evaluate the performance of our proposed TPRA scheme, let us consider the following other resource allocation schemes 1) Random Allocation In this so called Random scheme, the two-phase approach is still followed However, the decisions in each phase are made in random manners In the first phase, for each channel c, the base stations are processed one at a time following a random order, e.g., (b1 , b2 , bB ) For base station bn , instead of picking a CPE to cover according to (9), we just arbitrarily choose any CPE i with i ∈ V cn In the second phase, for each cell, no maximal bipartite matching is carried out Instead, active CPEs in the cell are processed one at a time according to a randomly chosen order For each active CPE, we assign the first free channel This continues until all active CPEs of the cell are served or no more channel is available 2) Non-overlapping Allocation In this scheme, the K channels are first partitioned into B disjoint groups, each consists of ⌊K/B⌋ channels Each of the base stations is then assigned one group of channels to support its active CPEs Channel groups are formed and assigned as follows Pick an arbitrary order of the base stations, e.g., (b1 , b2 , bB ), and let them to choose their ⌊K/B⌋ channels one at a time in this order This means bn cannot pick the channels chosen by b1 , b2 , bn−1 Among all channel left, each of the channel c chosen by bn must satisfy: c∗ Γc∗ bn < Γbm , ∀1 ≤ n < m ≤ B (10) Each BS can assign channels to its active CPEs based on the simple allocation procedure of the Random scheme discussed above We call this the Non-overlapping Channel Allocation (NOCA) scheme 3) Allocation Based on An Interference Graph In [2], Behzad and Rubin propose the power control scheduling algorithm (PCSA) that improves the system throughput while also guaranteeing the SINR constraints of all transmission links In the PCSA scheme, an interference graph, which captures the pairwise interference effects among all transmissions, is first constructed After that, the problem of channel allocation to maximize the number of noninterfering links can be converted into the problem of finding a maximum independent set of the interference graph In Section IV., we will test the performance of PCSA under two scenarios In the first scenario, we reapply the algorithm every time there is a change in state of any CPE We call this PCSA G (PCSA Global) In the second scenario, we apply the algorithm to the whole network once, and after that, the changes in CPEs’ states are only dealt with locally We call this PCSA L (PCSA Local) IV N UMERICAL R ESULTS AND D ISCUSSION A Simulation Model 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 cells, each is a square of size 500 × 500m A BS is deployed at the center of each cell to serve CPEs within the cell The total number of CPEs is N = 300 and each CPE is active with probability pa = 0.1 We vary M , the total number of PUs, from 10 to 60 All CPEs and PUs are randomly deployed across the entire service area with a uniform distribution A sample network is shown in Fig The number of channels available is K = 16 We assume a free-space path loss model with the path-loss exponent of We assume that each PU randomly picks and uses one of the K channels The noise power spectrum density at each CPE is No = 100dBm The required SINR for 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 Performance Analysis As the number of active CPEs served is closely related to how many CPEs in the network are covered, let us look at the percentage of CPEs being covered first In Fig 3, we plot the percentage of CPEs being covered versus the number of PUs when four schemes TPRA, NOCA, Random, and PCSA are employed As expected, when the number of PUs increases, the coverage of each of the four schemes decreases The 17th Annual IEEE International Symposium on Personal, Indoor and Mobile Radio Communications (PIMRC’06) 25 26 PCSA_G TPRA NOCA Random PCSA_L 22 No of active CPEs served No of active CPEs served 20 TPRA NOCA Random 24 15 10 20 18 16 14 12 10 10 15 20 25 30 35 40 45 50 55 60 No of primary users 10 15 20 25 30 35 40 45 50 55 60 No of primary users Figure 4: Number of active CPEs being served versus no of PUs No of BSs = 4, no of CPEs = 300, probability of a CPE being active = 0.1, no of channels = 16 Figure 5: Number of active CPEs being served versus no of PUs No of BSs = 4, no of CPEs = 300, probability of a CPE being active = 0.1, no of channels = 24 The coverage of TPRA is best because in this scheme (first phase), we deliberately seek to cover faraway CPEs On the other hand, the coverage of PCSA is worst This is because when using the interference graph approach, PCSA tends to only cover nearby CPEs to minimize interference The coverage of NOCA is close to that of TPRA This is because in NOCA scheme, base stations employ non-overlapping channel groups and therefore, can transmit at high power to reach faraway CPEs The coverage of Random scheme is significantly worse than that of TPRA, but still much better than that of PCSA Next, in Fig 4, we plot the average number of active CPEs served versus the number of PUs for TPRA, NOCA, Random, and PCSA G and PCSA L Clearly, as PCSA G is allowed to respond globally to changes in CPEs’ states, its performance outperforms the rest We present the throughput of PCSA G here just to show what can be achieved if we can tolerate the computational and signaling costs of always carrying out global control As can be seen in Fig 4, our TPRA scheme consistently outperforms NOCA and Random schemes The gain of TPRA, relative to NOCA, is higher when the number of PUs is small This is because when the number of PUs is small, there is more chance for channel reuse but NOCA is not flexible enough to take advantage of that The gain of TPRA, relative to Random, is higher when the number of PUs increases This is because Random scheme does not take PUs into account when carrying out allocation It is also interesting to see how PCSA performs when it is subject to the local update constraint, i.e PCSA L The throughput of PCSA L is much worst than all the other schemes This is because, as shown in Fig 3, the coverage of PCSA is very low compared to that of other schemes In Fig 5, the number of channels is increased from 16 to 24 The performance trends are similar to those of Fig We have results for other sets of system parameters and the trends are also similar to what have been discussed 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 the TPRA scheme that achieves good system performance while can be implemented at reasonable complexity Numerical results show that our proposed scheme achieves significant performance gain, relative to other schemes For future research, we are currently extending this work to consider fairness among CPEs as well as their QoS At the same time, a joint network-admission/resource-allocation framework is being developed based on the system model of this paper V C ONCLUSIONS In this paper, we consider the problem of channelallocation/power-control to 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Resource Allocation (TPRA) scheme B The Two- Phase Resource Allocation Scheme 1) Phase - Global Allocation: In this phase, channels and transmit powers are allocated to BSs so that the interference caused... A BS that is near any PU using channel c should only transmit at low power to reduce interference On the other hand, a BS that is faraway from all PUs using channel c can transmit at higher power. .. called Random scheme, the two- phase approach is still followed However, the decisions in each phase are made in random manners In the first phase, for each channel c, the base stations are processed