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Abstract—In this paper, we propose a novel framework of cognitive radio assisted cooperation (CRAC) for downlink transmissions in orthogonal ...
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IEEE JOURNAL ON SELECTED AREAS IN COMMUNICATIONS, VOL. 30, NO. 9, OCTOBER 2012

CRAC: Cognitive Radio Assisted Cooperation for Downlink Transmissions in OFDMA-Based Cellular Networks Yang Cao, Tao Jiang, Chonggang Wang, and Lei Zhang

Index Terms—Cognitive radio, cooperative relay, downlink transmission, OFDMA-based cellular networks, resource allocation.

I. I NTRODUCTION

R

ECENTLY, cooperative networking has received significant attention as an emerging network design strategy since the future cellular networks are eager for higher capacity and larger coverage due to tremendously growing end user demands and wireless terminal amount. One of ways is to deploy more base stations (BSs) as taken in traditional cellular networks. In contrast, cooperative relaying aided cellular

Manuscript received February 1, 2011; revised July 20, 2011. This work was supported by the National Science Foundation of China with Grant 61172052 and Grand 60872008, the Program for New Century Excellent Talents in University of China under Grant NCET-08-0217, the Science Found for Distinguished Young Scholars of Hubei in China with Grant 2010CDA083, the Project-sponsored by SRF for ROCS, SEM, the National & Major Project with Grant 2012ZX03003004, the Research Fund for the Doctoral Program of Higher Education of the Ministry of Education of China under Grant 200804871142, and 863 Program by the Ministry of Science and Technology of the People’s Republic of China with Grant 2009AA011803. Y. Cao, T. Jiang, and L. Zhang are with Wuhan National Laboratory For Optoelectronics, Department of Electronics and Information Engineering, Huazhong University of Science and Technology, Wuhan, 430074, P. R. China (e-mail: [email protected], [email protected], [email protected]). C. Wang is with the InterDigital Communications, USA (e-mail: [email protected]). Digital Object Identifier 10.1109/JSAC.2012.121004.

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Abstract—In this paper, we propose a novel framework of cognitive radio assisted cooperation (CRAC) for downlink transmissions in orthogonal frequency-division multiple access (OFDMA) - based cellular networks. In the proposed CRAC framework, relay stations are deployed in each cell and have spectrum sensing capability. In turn, they can access unoccupied white space to opportunistically obtain additional sub-channels to assist relaying information for cellular users. One of promising novelties is that the proposed CRAC considers joint resource allocation which includes transmission mode selection, relay station allocation, and transmit power/sub-channel allocation, to cost-effectively provide services and applications. Specifically, we first formulate the joint resource allocation as a sum utility maximization problem with power constraints on the base station and relay stations, which is a mixed integer programming problem. Then, we leverage dual decomposition method and derive a centralized optimal solution. Extensive simulation results are presented and demonstrate that the proposed CRAC can achieve a significant performance improvement in terms of the downlink network throughput while maintaining comparable fairness among cellular users in contrast to the traditional relaybased cooperation approach.

BS

Fig. 1.

2

C1

CU

An example of motivation.

network, as a more advanced system, introduces using relay stations (RSs) to increase the capacity and the coverage, which provides better quality of service (QoS) to especially for cellular users (CUs) at the cell edge [1]. Moreover, cooperative relaying can also reduce overall cost compared with traditional non-relay approach [2]. However, the performance gain of adopting cooperative relaying in cellular networks could be minor due to the following two major reasons (we use downlink transmission case for illustration): • Bottleneck link between the RS and CU: Generally, the BS-to-RS link is line-of-sight as the BS and the RS are both placed at some height above the ground, while the BS-to-CU and the RS-to-CU links are non-line-of-sight. Therefore, the BS-to-RS link has better quality than the BS-to-CU and RS-to-CU links most of the time. As a result, the performance gain of the cooperative relaying is constrained by the quality of the weaker link, i.e., the compound BS/RS-to-CU link [1]. • Half-duplex cooperation: Obviously, direct transmissions of BS-to-RS/CU and RS-to-CU can not be scheduled simultaneously. As depicted in Fig. 1 (a), the BS and RS are scheduled sequentially to transmit at two different time-slots over the same sub-channel C1 . Such timedivision multiplexing basically leads to 50% throughput reduction of the transmission from BS to CU and may offset potentially achievable benefit from cooperative diversity [3].

c 2012 IEEE 0733-8716/12/$31.00 

CAO et al.: CRAC: COGNITIVE RADIO ASSISTED COOPERATION FOR DOWNLINK TRANSMISSIONS IN OFDMA-BASED CELLULAR NETWORKS

Motivated by the above observation, we propose a novel framework to leverage cognitive radio technique at the RS to make possible of concurrent BS-to-RS/CU and RS-to-CU transmissions in this paper, and in turn overall downlink network throughput can be improved in contrast to traditional cooperative relaying. The target system, based on the orthogonal frequency-division multiple access (OFDMA), is a cooperative cellular network assisted by cognitive radio technique. For simplicity, the proposed novel framework is called as cognitive radio assisted cooperation (CRAC) and its work-flow could be summarized as follows. Each RS is equipped with cognitive radio and can opportunistically access sub-channels in the white space, i.e., the frequency band that is temporarily not occupied by primary users (PUs) [4]. Note that, here PUs refer to primary users in other networks operating in different frequency bands. With the additional white space sub-channels (WSSs), full-duplex cooperation can be established. As illustrated in Fig. 1 (b), the BS employs its dedicated band sub-channel (DBS) C1 for direct communications to the CU and RS, while RS uses orthogonal sub-channel C2 in the white space (i.e., WSS) to relay transmissions to the CU. As a result, the BS-to-RS/CU and RS-to-CU transmissions can be delivered simultaneously. In turn, the overall achievable rate from the BS to the CU is improved. Moreover, if the white space lies in the ultrahigh-frequency (UHF) band (54 − 862 MHz) that has better propagation capability than the commonly used cellular band (e.g. 2000 MHz and higher frequency band), the RS-to-CU links have much better qualities to overcome the bottleneck effect. In short, such cognitive cooperative relaying in the proposed CRAC can potentially greatly improve the system performance. Therefore, the major contributions in this paper could be summarized as follows: •





A novel CRAC framework is proposed for the downlink transmissions in OFDMA-based cellular network, where RS leverages cognitive radio technique to occupy white space sub-channels for relaying transmissions to CU. We propose a centralized optimization framework to maximize the network utility in the proposed CRAC framework. Joint resource allocation that includes transmission mode selection, relay station allocation and transmit power/sub-channel allocation is considered to costeffectively provide services and applications. A mathematical formulation of the joint resource allocation is established, then, we derive its optimal solution via the employing of dual decomposition method. Conducted simulation results show that the proposed CRAC can significantly improve the network throughput while maintaining comparable fairness among CUs comparing with the traditional relay-based cooperation.

The rest of this paper is organized as follows. In Section II, we present the proposed CRAC framework in detail. In Section III, we formulate problem of the joint resource allocation. In Section IV, we derive an optimal solution employing the dual decomposition method. Simulation results are presented in Section V. Related works are deeply discussed in Section VI, followed by conclusions in Section VII.

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II. P ROPOSED CRAC F RAMEWORK A. Elements in The CRAC Framework As shown in Fig. 2, the proposed CRAC framework considers an OFDMA-based cellular cell and some overlapping PU networks. The cell consists of a single BS, multiple CUs and serval RSs. RSs are deployed at some predefined locations inside the cell to aid BS-to-CU communications with cooperative relaying. In the proposed CRAC, each RS is equipped with two radios which can transmit and receive data simultaneously over different sub-channels. Specifically, one radio uses DBSs and the other one as a cognitive radio uses WSSs. Moreover, the transmit power budget of RSs is constrained due to their low cost setup and/or limited energy source. Each PU network has an access point and some PUs. The cellular cell and PU networks operate over different frequency band. For PU networks, CUs and RSs look like secondary users because they opportunistically access the band of PU networks using cognitive techniques. For the sake of clarity, we mainly consider the downlink transmission case in this paper, and the CRAC framework could also be extended to the uplink transmission case. Without loss of generality and for simplicity, we make some assumptions as follows: 1) Cellular network We assume that the RS adopts the decode-and-forward (DF) protocol with the same codebook as that of the BS. One RS may serve multiple CUs over different sub-channels simultaneously, and the downlink transmissions to a CU could occur over multiple DBSs. Moreover, we suppose that each DBS and WSS have the same bandwidth, and each transmission from the BS to a CU over one DBS could be assisted with one RS that relays the BS-to-CU transmission over one sub-channel (DBS in half-duplex cooperation or WSS in full-duplex cooperation). The frame level synchronization throughout the whole cellular network is assumed in this paper. As the network operates in a slow fading environment, the accurate channel estimation is possible so that the full channel side information (CSI) is available at the BS, and the CSI keeps static during an OFDMA frame. Moreover, a subchannel could only be assigned to one CU, meaning that there is no sharing or intra-cell sub-channel reuse. 2) PU network We assume that some PU networks are overlapped with the cellular cell. Multiple RSs can perform independent or cooperative spectrum sensing to locate and exploit WSS while preventing the PUs from excessive interference [5]. Each PU network operates over an orthogonal licensed channel, which spans over some WSSs and has a certain protection area. We define that, if the RS-to-CU link is within the protection area of a PU network, it can utilize the PU channel only when the PU network is idle. Otherwise, the RS-to-CU link can always utilize the PU channel when its transmit power is not so high. Due to the geographical diversity, different RS-toCU links may experience different WSS availabilities. This diversity can be well exploited by CRAC to produce more transmission opportunities. We suppose that the PU network state (active / idle) remains the same during an OFDMA frame.

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IEEE JOURNAL ON SELECTED AREAS IN COMMUNICATIONS, VOL. 30, NO. 9, OCTOBER 2012

Channel 1 Channel 2 Access Point

Primary User

Base Station

Channel 3

Channel 4

Relay Station

Cellular User Channel 5

Fig. 2.

Proposed CRAC framework.

B. Operations of Elements 1) BS operations With the purpose of reducing the cost of updating infrastructure, the BS does not have any functionality of the cognitive radio, and it solely uses the DBSs. In the proposed CRAC framework, there is a built-in centralized resource scheduler at the BS, which allocates resources to cater for downlink data streams of all CUs in the cell at the beginning of each OFDMA frame. The resource scheduler jointly considers the selection of transmission modes, the assignment of sub-channels, RSs and transmit power, with the knowledge of CSI of BS-to-RS, BS-to-CU and RS-to-CU links over all sub-channels obtained during the current OFDMA frame. The scheme of obtaining optimal resource allocation policy will be discussed in the next two sections. 2) RS operations As stated above, each RS is equipped with two radios that can transmit and receive data over DBSs and WSSs simultaneously. During the spectrum sensing duration at the beginning of each OFDMA frame, the RS performs spectrum sensing and channel probing to obtain CSI of RS-to-CU links over WSS and DBS. After that, the RS operates under three transmission modes according to the scheduling of the BS. As depicted in Fig. 3, there are three transmission modes for downlink data streams and accordingly three OFDMA frame structures. • Direct transmission. The RS keeps idle over the DBS C1 during the current OFDMA frame when the data stream is over a certain DBS C1 . • Half-duplex cooperation. When the data stream is over a certain DBS C1 , the RS assists the data stream transmission over the same DBS C1 . In the first-half frame, the RS receives and decodes the data stream from the BS. In the second-half frame, the RS encodes and forwards the received data stream to the corresponding CU, while the BS keeps idle over the DBS C1 . • Full-duplex cooperation. Similarly, the RS assists the data stream transmission over an additional WSS C2 .

Therefore, the RS decodes and forwards the data stream symbol by symbol over the WSS C2 , while the BS still occupies the DBS C1 . 3) CU operations The CU could receive data streams over DBSs and WSSs simultaneously with two independent radios working over two different frequency bands. As shown in Fig. 3, when the data stream over one DBS is assisted by a RS, the CU combines the two copies of the data stream in two time-slots (see Fig. 3(b)) or over two sub-channels (see Fig. 3(c)) with the maximumratio-combining [6]. In sum, the proposed CRAC framework aims to improve the network throughput through efficient scheduling of resources (transmit power, sub-channels, RSs and etc.), which will be addressed in detail in the following two sections. III. P ROPOSED O PTIMIZATION F RAMEWORK FOR CRAC In this section, we propose an optimization framework for the proposed novel CRAC. Denote Φ, Ω, ψ and ξ as the set of CUs, RSs, DBSs and WSSs, respectively. m ∈ Φ = {1, 2, · · · , K} represents the index of a CU as well as the index of the combined data stream1 received at a CU. r ∈ Ω = {1, 2, · · · , J} represents a RS. cD ∈ ψ = {1, 2, · · · , N } and cW ∈ ξ = {N + 1, N + 2, ..., N + SG} represent a DBS and a WSS, respectively. Moreover, suppose that S PU networks coexist with the cellular cell, and each PU channel spans over G WSSs (K, J, N , S, G ∈ N+ ). A. PU Channel Availabilities Denote Q(t) = {Qs (t)}S as the state of the PU network during the OFDMA frame t, where Qs (t) is a binary value. Qs (t) = 1 means that the PU network over the channel s is active. Otherwise, Qs (t) = 0. According to a finite state ergodic Markov chain, Q(t) evolves. Depending on the current locations of the RS and the CU, as well as 1 Here, a combined data stream is defined as a combination of all data streams received at the CU from BS and RSs over multiple sub-channels.

CAO et al.: CRAC: COGNITIVE RADIO ASSISTED COOPERATION FOR DOWNLINK TRANSMISSIONS IN OFDMA-BASED CELLULAR NETWORKS

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OFDMA Frame OFDMA Frame

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(a) direct transmission

OFDMA Frame

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BSRS/CU

C1

BS-RS/CU

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(b) half-duplex cooperation

(c) full-duplex cooperation

* For (c), the time offset between two copies of the data stream results from the DF delay. Fig. 3.

OFDMA frame structure for three transmission modes.

the PU network state, a RS-to-CU link could access a subset of PU channels potentially during an OFDMA frame. Since each RS could relay data streams for all CUs in the cell, the maximum amount of possible RS-to-CU links is JK. Therefore, we define the PU channel availability matrix s V(t) = {Vr,m (t)}S×JK as ⎧ ⎨ 0, when the link of rth RS to s mth CU over channel s is available, Vr,m (t) = ⎩ 1, otherwise.

(1)

B. Achievable Rate As mentioned above, each data stream operates in one and only one of three transmission modes shown in Fig. 3 over one DBS. For simplicity, the noises are modeled as independent and identically distributed (i.i.d.) circularly symmetric complex Gaussian noise CN (0, N0 W ), where W is the bandwidth of a DBS or a WSS, and N0 is the power density of the noises. 1) Direct transmission mode cD For convenience, we first define R1 (m, cD , PBS ) as the achievable rate function over the DBS cD ∈ ψ, which is cD allocated to the combined data stream m, where PBS denotes the transmit power at the BS over the DBS cD . With the spectral efficiency formulation (in b/s/Hz) [7], we have  cD ) R1 (m, cD , PBS

= log2

P cD · |hm,cD | 1 + BS ΓN0 W

2

 ,

(2)

where Γ is the gap to Shannon capacity, which is mainly determined by modulation techniques and the target bit-error rate, and hm,cD denotes the channel gain from the BS to the mth CU over the DBS cD . For simplicity, Γ is set to one in this paper. 2) Half-duplex cooperation mode cD , r, PrcD ) as the achievSimilarly, we define R2 (m, cD , PBS able rate function over the DBS cD ∈ ψ that is allocated to the combined data stream m, where RS r ∈ Ω is assigned to be the relay over the DBS cD with the allocated power PrcD . In the half-duplex cooperation mode, the BS and RS transmit over the same DBS in a two time-slots sharing manner. Therefore,

according to [1], the achievable rate is cD cD R(m,  cD , PBS , r, Pr )  2 cD 1 2PBS · |hr,cD | = min log2 1 + , 2 ΓN0 W   2 2 cD 2PBS · |hm,cD | + 2PrcD · |hr,m,cD | , log2 1 + ΓN0 W (3) where the coefficient 1/2 before the right part of the formucD lation and the coefficient 2 before PBS and PrcD account for the fact that the half-duplex cooperation operates over two time-slots, respectively. hr,cD , hm,cD and hr,m,cD denote the channel gain from the BS to the rth RS, BS to the mth CU and rth RS to the mth CU over the DBS cD , respectively. 3) Full-duplex cooperation mode cD , r, cW , PrcW ) as the Similarly, we define R3 (m, cD , PBS achievable rate function over the DBS cD ∈ ψ and the WSS cW ∈ ξ that are allocated to the combined data stream m. RS r ∈ Ω is assigned to be the relay with the allocated power PrcW over the WSS cW ∈ ξ. In the full-duplex cooperation mode, the BS and RS transmit over different sub-channels in parallel. Therefore, the achievable rate is cD cW R(m,  cD , PBS , r, cW , Pr )  2 cD P · |hr,cD | , = min log2 1 + BS ΓN0 W   2 2 cD PBS · |hm,cD | + PrcW · |hr,m,cW | log2 1 + , ΓN0 W

(4) where hr,cD and hm,cD denote the channel gain from the BS to the rth RS and BS to the mth CU over the DBS cD , respectively. hr,m,cW is the channel gain from the rth RS to the mth CU over the WSS cW . Since the direct data transmission and the relay data transmission are conducted simultaneously in the long run with the full-duplex cooperation mode, (4) does not have the coefficient of 1/2. C. Objective Function To find the proper tradeoff between the network throughput and the fairness among CUs, the sum utility maximization framework is employed as the objective function in this paper. Obviously, the utility function is a concave and increasing function of the achievable rate for the data stream of each CU and reflects the satisfaction of the CU. For convenience, we define Um (·) as the utility function of achievable rate of the combined data stream m. Moreover,

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IEEE JOURNAL ON SELECTED AREAS IN COMMUNICATIONS, VOL. 30, NO. 9, OCTOBER 2012

r,cD r,cD ,cW three 0-1 indicators αcmD , βm and γm are defined, in cD which αm indicates whether combined data stream m is r,cD assigned DBS cD for the direct transmission or not, βm denotes whether combined data stream m is operating in the half-duplex cooperation mode with rth RS and DBS cD , or r,cD ,cW not, and γm represents whether combined data stream m is operating in the full-duplex cooperation mode with rth RS, DBS cD and WSS cW , or not. Thus, the achievable rate of the combined data stream m can be expressed as cD λm = R1 (m, cD , PBS )αcmD cD ∈ψ cD r,cD + R2 (m, cD , PBS , r, PrcD )βm cD ∈ψ r∈Ω cD r,cD ,cW + R3 (m, cD , PBS , r, cW , PrcW )γm , cD ∈ψ cW ∈ξ r∈Ω

Where, ∀m ∈ Φ. Therefore, the optimization objective function is

Um (λm ), max

(5)

(6)

m∈Φ

constraints are given as follows. 1) DBS allocation constraints As mentioned above, each DBS can only be assigned to one data stream which operates with one of the three modes, ⎛ ⎞



r,cD r,cD ,cW ⎠ ⎝αcmD + βm + γm ≤ 1, ∀cD ∈ ψ. m∈Φ

cW ∈ξ r∈Ω

r∈Ω

(7) 2) WSS allocation constraints Obviously, each WSS can be assigned to assist only one DBS,



r,cD ,cW γm ≤ 1, ∀cW ∈ ξ. (8) m∈Φ cD ∈ψ r∈Ω

Moreover, each assigned WSS should be available to its corresponding RS-to-CU link. Define mapping function s = f (cW ) as that WSS cW is spanned over by PU channel s, we have 

 r,cD ,cW f (cW ) · Vr,m γm = 0, ∀cW ∈ ξ. (9) m∈Φ cD ∈ψ r∈Ω

3) Power constraints

cD PBS ≤ P¯BS ,

(10)

cD ∈ψ



PrcD +

cD ∈ψ



PrcW ≤ P¯RS , ∀r ∈ Ω.

(11)

cW ∈ξ

IV. D ERIVED O PTIMIZATION Obviously, the optimization problem of (6) is a mixed integer programming problem. According to [10], the optimization problem of (6) can be treated as a spectrum balancing problem in an OFDMA system with a large number of sub-channels, which could be solved optimally via convex optimization techniques. Therefore, the Lagrangian dual decomposition method is adopted to obtain the optimal solution of (6).

A. Cross-layer Optimization via Dual Decomposition For the ease of utilizing the Lagrangian dual decomposition, we introduce an auxiliary value, i.e., the application layer demand of each CU denoted by dm (∀m ∈ Φ). Then, we rewrite (6) as

Um (dm ), (12) max m∈Φ

s.t. (7) - (11), and ∀m, λm ≥ dm . Obviously, the objective of (12) is maximized when λm = dm ∀m because Um is a concave and increasing function. As a result, (6) and (12) have the same solution. Introducing Lagrange multiplier vector θ, the dual function can be written as  max [Um (dm ) + θm (λm − dm )] , m∈Φ (13) g(θ) = s.t. (7) − (11), where, θm (m ∈ Φ) is the element of θ. The dual function (13) can be separated into two maximization sub-problems. The first sub-problem is a utility maximization problem, corresponding to a rate adaption problem in the application layer,

[Um (dm ) − θm dm ]. (14) gappl (θ) = max dm ,∀m

m∈Φ

The second problem is a joint RSs, transmit power, subchannels allocation and transmission modes selection problem in the physical layer,  max θm λm , m∈Φ gphy (θ) = (15) s.t. (7) − (11). Due to the fact that the sum utility maximization problem of (12) has zero duality gap when the number of sub-channels go to infinity [10], it can be solved by minimizing the dual objective as min g(θ), (16) s.t. θ 0. According to [11], the problem of (16) could be solved with updating θ via the sub-gradient method. Note that, the dual variable θ can be considered as the price of achievable rate. When the CU demand exceeds the achievable rate, θm grows. Otherwise, θm decreases. Compared with the sub-problem (15), it is easier to solve the sub-problem (14). According to [9], we could define the utility function of each combined data stream as    k1 1 − e−k2 x , if x ≥ 0, (17) U (x) = −∞, if x < 0, where, k1 determines the upper-bound of the utility function. k2 reflects the average demand level of the CU and it should be carefully tuned according to application layer requirements and fairness rules. B. Power Constraints Elimination via Dual Decomposition In this sub-section, we give a solution of (15). For simplicity, we assume that the transmit power over each DBS ¯ o o and PBS ≤ PNBS . at the BS is equal and predefined as PBS Then, introduce a Lagrange multiplier vector μ in the power

CAO et al.: CRAC: COGNITIVE RADIO ASSISTED COOPERATION FOR DOWNLINK TRANSMISSIONS IN OFDMA-BASED CELLULAR NETWORKS

a(μ) =

⎧ ⎪ ⎨

max

⎪ ⎩

θm λm +

m∈Φ



θm λm −

m∈Φ

s.t.(7), (8),

r∈Ω

 μr

cD ∈ψ

2 Ă

2

N

Ă

N 1

Ă

cD

Ă

cT

\

Ă

V Fig. 4. Equivalent CRAC problem and weighted bipartite matching. Not all links are shown here.

constraint (11), the dual function is written as (18), where, μr (r ∈ Ω) is the element of μ. Since μr P¯r is constant in (18) when μr is given, we r∈Ω

rewrite (18) as (19), which is termed as the CRAC problem. Obviously, the CRAC problem (19) is equivalent to the dual problem (18). Since (18) has zero duality gap [10], it can be solved by minimizing the dual objective function as min a(μ), s.t .μ 0,

P¯r −

μr

r∈Ω

1 1



s.t.(7), (8).



max



(20)

where we remove the constraint (9) by setting the channel gain to zero when the link over a WSS is not available due to the PU activities. Similarly, we solve this dual problem via updating μ with the sub-gradient method, where the dual variable μ could be considered as the price of relay power. C. Derived Solution of CRAC Problem As depicted in Fig. 4, we transform the CRAC problem to an equivalent weighted bipartite matching problem. Then, we give the following proposition: Proposition 1: The optimal solution of the equivalent weighted bipartite matching problem is also the optimal solution of the CRAC problem. Proof: For convenience, we construct a bipartite graph A = (ψ × σ, E), where ψ is the set of DBS, σ is the combined set of DBS and WSS, σ = ψ ∪ ξ. Moreover, cT denotes a DBS when cT ∈ [1, N ] and denotes a WSS

 PrcD



cD ∈ψ



PrcD



r∈Ω

μr



cW ∈ξ

cW ∈ξ

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 PrcW

(18)

 PrcW

,

(19)

when cT ∈ [N + 1, N + SG]. The edge set E corresponds to |ψ| |σ| edges connecting all possible pairs of subchannels in two vertex sets. Each edge (cD , cT ) carries four attributes, (wcD ,cT , mcD ,cT , rcD ,cT , PcD ,cT ), where weight wcD ,cW is mapped from the effective achievable rate of the data stream mcD ,cT assisted by the RS rcD ,cT with transmit power PcD ,cT over sub-channel set {cD , cT }. Note that, the effective achievable rate accounts for the price of achievable rate and relay power, i.e., θ and μ. Through this mapping, the maximum matching process represents the comprehensive assignment of RSs, sub-channels and transmit power, as well as the transmission mode selection. Moreover, constraints (7) (8) in CRAC problem (19) are also inherent in the matching process. As a result, the optimal solution of the weighted bipartite matching problem is also the optimal solution of the CRAC problem. In the following, we obtain four attributes in three cases. Case 1: cD = cT ∈ [1, N ]. In this case, the transmission mode can be direct transmission or half-duplex cooperation (dotted links in Fig. 4). Define the effective achievable rate functions o ), (21) g1 (m) = θm R1 (m, cD , PBS o g2 (m, r, PrcD ) = θm R2 (m, cD , PBS , r, PrcD ) − μr PrcD , (22)

then, we have wcD ,cT

  cD = max max g1 (m), maxc g2 (m, r, Pr ) . (23) m

m,r,Pr D

To maximize g1 (m), search m ∈ Φ and pick out the optimal m. ˆ Moreover, the optimal (m, ˆ rˆ, PˆrcD ) is picked out cD to maximize g2 (m, r, Pr ). When max g1 (m) ≥ maxc g2 (m, r, PrcD ), direct transm

m,r,Pr D

mission mode is better for the data stream than the half-duplex cooperation mode. Thus, we have mcD ,cT = arg max g1 (m), m

(24)

and rcD ,cT = 0, PcD ,cT = 0. Otherwise, we have (mcD ,cT , rcD ,cT , PcD ,cT ) = arg maxc g2 (m, r, PrcD ). (25) m,r,Pr D

Case 2: cD = cT ∈ [1, N ] (dotted links in Fig. 4). Obviously, it is impossible to match between two different DBSs in this case. Therefore, we set wcD ,cT , mcD ,cT , rcD ,cT and PcD ,cT to zero. Case 3: cT ∈ [N + 1, N + SG]. Obviously, the transmission mode is full-duplex cooperation with DBS cD and WSS cT

IEEE JOURNAL ON SELECTED AREAS IN COMMUNICATIONS, VOL. 30, NO. 9, OCTOBER 2012

1

(solid links in Fig. 4). Define the effective achievable rate function =

o θm R3 (m, cD , PBS , r, cT , PrcT )



0.9

μr PrcT ,

0.7

and (mcD ,cT , rcD ,cT , PcD ,cT ) = arg maxc

m,r,Pr T

g3 (m, r, PrcT ).

Network utility

m,r,Pr T

(27)

(28)

The optimal (m, ˆ rˆ, PˆrcT ) is picked out to maximize cT g3 (m, r, Pr ). So far, some good polynomial-time algorithms have been proposed to optimally solve the bipartite matching problem, e.g., the Hungarian algorithm [12]. Obviously, the whole algorithm is polynomial time since the computation complexity of the graph construction is O (|ψ| |σ| |Φ| |Ω|).

In conducted computer simulations, a cell centered at the BS with a radius of 1000 meters. J = 4 fixed RSs are located at (±353.5, ±353.5), i.e., on a circle with the radius equal to 500 meters. CUs are uniformly distributed inside the cell. The channels between the BS, RSs and CUs are selected as the COST-231 model [8], including the path loss, large-scale shadowing and small-scale fading. Suppose that the BS and RSs are both placed at some height above the ground, thus, the fading has a LOS component. The cell area is overlapped with S = 3 PU networks. The protection radius of each PU network is set to 1000 meters. Each PU network operates over one PU channel that spans over G = 3 OFDMA subchannels. The state of each PU channel is modeled as a Markov ON-OFF process. The bandwidth of a sub-channel (DBS or WSS) is W = 200kHz. There are N = 30 DBSs centered around 2000MHz, while WSSs are centered around 700MHz. The transmit power constraints of BS and RS are 25dBm and 19dBm, respectively. The white noise power density is −174dBm/Hz. The parameters of the utility function are determined via setting the satisfactory throughput of each CU to 7.0Mbps. The satisfactory throughput achieves a utility value that is 90% of the maximum achievable utility. For comparisons, we consider three different schemes as follows. • BL-1: It is the baseline scheme that only uses direct transmission mode without cooperative relaying. • BL-2: It is the baseline scheme that uses both direct transmission mode and half-duplex cooperation mode (i.e. traditional cooperative relaying). • CRAC: It is the optimal scheme in the CRAC framework. The CRAC scheme adopts the optimization framework proposed in Section III and the optimal solution derived in Section IV. The following performance metrics are considered and calculated in the simulation for the comparison of performances between the CRAC scheme and baseline schemes as described above.

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Network utility: It is defined as the sum of K CUs’ utilities. The network utility reflects the satisfaction of the CUs, which ranges between 0 and 1. Network throughput: It is defined as the sum of K CUs’ throughput in the cell. Throughput gain: It is defined as the ratio of the network throughput of a scheme to that of the BL-1 scheme. If the gain of a scheme considered is bigger than 100%, it means that the scheme achieves better performance than the BL-1 scheme. Fairness: Jain’s fairness index [13] is adopted as the fairness metric, which is defined as  2 K λ m m=1 (29) f= K K m=1 λ2m where λm is the achievable rate of the mth CU. The Jain’s fairness index ranges between 1/K and 1.0. When it approaches 1.0, the system is fairer.

B. Performance Comparisons In this sub-section, the number of CUs is set to K = 4. The probabilities of that a PU network transforms from ON (active) to OFF (idle) and vice versa are 0.2, 0.2, respectively. Therefore, the PU traffic load is ρ = 0.5. Performance comparisons among different schemes are depicted in Fig. 5. In summary, we have • Cooperative relaying schemes (including the BL-2 and CRAC) can achieve a higher network utility than the non-cooperative scheme (e.g., the BL-1). Moreover, the network utility of the CRAC scheme is the highest among all three schemes. • The network throughput could be moderately improved by the BL-2 scheme with traditional cooperative relaying up to 10% compared with the BL-1 scheme. However, the CRAC scheme can greatly improve the network throughput up to 76.5% even when the PU traffic load is

CAO et al.: CRAC: COGNITIVE RADIO ASSISTED COOPERATION FOR DOWNLINK TRANSMISSIONS IN OFDMA-BASED CELLULAR NETWORKS

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heavy (ρ = 0.5) due to its capability of exploiting white space with the optimal resource allocation. • Better fairness can be obtained with the BL-2 scheme, compared with the BL-1 scheme. However, the CRAC scheme achieves the best fairness among all schemes. Obviously, the performance of the CRAC scheme significantly outperforms other two baseline schemes. C. Impact of The Cell Population As shown in Fig. 6, it is obvious that the network utilities of three schemes decrease as the cell population grows. The major reason is that each CU has less resource in average as the number of CUs become larger. Similarly, the network throughput of the three schemes increases as the cell population climbs due to the user diversity gain, which is shown in Fig. 7. In addition, Fig. 8 show that the fairness of three schemes becomes worse as the cell population goes up. How-

CRAC(4CUs) CRAC (6CUs) CRAC (8CUs) BL−2 (4CUs) BL−2 (6CUs) BL−2 (8CUs)

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Fig. 9. Throughput gain versus PU traffic load with the CRAC and BL-2 schemes with three different number of CUs.

ever, the CRAC scheme still achieves much better performance in network utility, network throughput and fairness than the other two baseline schemes with different cell populations. D. Impact of the PU Traffic Load In Fig. 9, it shows some curves of throughput gain versus PU traffic load with the CRAC and the BL-2 schemes under three different number of CUs. It is obvious to observe that the throughput gain of the CRAC scheme decreases as the PU traffic load varies from 0 (lightest) to 1 (heaviest) with different number of CUs. When the PU traffic load is 0, the resulted throughput gain is the upper-bound performance of the CRAC scheme. When the number of CUs is K = 4, we find that the upper-bound of the throughput gain is only slightly higher than that of the PU traffic load ρ = 0.5 by 6.25%. It is also obviously observed that the CRAC scheme still has larger throughput gain than that of the BL-2 scheme when the PU traffic load ρ = 1. All results show the

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robustness of the CRAC scheme to the change of the PU traffic load, which is because that the spatial diversity offers more abundant transmission opportunities in the cognitive radio environment [16]. Moreover, we find that the throughput gain of the CRAC scheme outperforms that of the BL-2 scheme under different number of CUs with the varying of the PU traffic load. VI. R ELATED W ORKS A. Resource Allocation in Relay-aided Cellular Networks Recently, the resource allocation in relay-aided cellular networks has been investigated. To maximize network sum utility, a joint optimization of the tone assignment, relay strategy selection and power allocation in each tone of OFDMA cellular networks was proposed in [9]. The problem of sub-channels assignment and power allocation for multihop OFDMA networks was deeply studied in [14]. A network coding assisted cooperation scheme was proposed in [15], in which full-duplex cooperation is adopted with the assumption of the existence of dedicated sub-channels for the RS-toCU links. With the assumption of that the sub-channels are pre-assigned, authors proposed a joint optimization of relay selection and power allocation in [3], in which a related convex optimization problem is formulated and provides an extremely tight upper bound on the system performance. B. Cognitive Radio in Relay-aided Cellular Networks Some works have been done to combine the cognitive radio and the relay-aided cellular network to implement network goals in a coordinated way. In [16], a joint relay selection and spectrum allocation were formulated and solved in the context of the cooperative relaying in cognitive radio cellular networks. A distributed resource scheduling scheme was proposed in the relay-assisted cognitive cellular network [17], where only white spaces channels could be utilized. A network architecture was proposed in [18] to enable the spectrum sharing between a primary TV broadcast system and a secondary cellular broadband system. In this framework, a cellular base station spends a part of its power to cooperate with the TV system to obtain the access right of the TV bands with favorable propagation properties. Obviously, the CRAC framework proposed and demonstrated in this paper differs all above existing approaches by introducing cognitive radio to the wireless relay station in cooperative cellular networks that operate on the legacy frequency band. Moreover, we develop an optimization framework for the joint resources allocation, then, derive an optimization to cost-effectively provide services and applications.

VII. C ONCLUSIONS In this paper, we proposed a novel CRAC framework for downlink transmissions in OFDMA-based cellular networks. A centralized optimal solution via employing the dual decomposition method was derived for the CRAC framework. Extensive simulation results showed a significant performance gain of the CRAC framework comparing with the traditional cooperative relaying in terms of the network utility, network throughput and fairness. R EFERENCES [1] J. Laneman, D. Tse, and G. Wornell, “Cooperative diversity in wireless networks: Efficient protocols and outage behavior,” IEEE Trans. Inf. Theory, vol. 50, no. 12, pp. 3062-3080, Dec. 2004. [2] Y. Yang, H. Hu, J. Xu, and G. Mao, “Relay technologies for WiMAX and LTE-advanced mobile systems,” IEEE Commun. Mag., vol. 47, no. 10, pp. 100-105, Oct. 2009. [3] S. Kadloor and R. Adve, “Relay selection and power allocation in cooperative cellular networks,” IEEE Trans. Wireless Commun., vol. 9, no. 5, pp. 1676-1685, May 2010. [4] I. Akyildiz, W. Lee, M. Vuran, and S. Mohanty, “NeXt generation/dynamic spectrum access/cognitive radio wireless networks: a survey,” Computer Networks, vol. 50, no. 13, pp. 2127-2159, May 2006. [5] J. Shen, T. Jiang, S. Liu and Z. Zhang, “Maximum channel throughput via cooperative spectrum sensing in cognitive radio networks,” IEEE Trans. Wireless Commun., vol. 8, no. 10, pp. 5166-5175, Oct. 2009. [6] J. Proakis, Digital Communications, McGraw-Hill, 3rd edition, 1995. [7] A. Goldsmith and S. Chua, “Variable-rate variable-power MQAM for fading channels,” IEEE Trans. Commun., vol. 45, no. 10, pp. 1218-1230, 1997. [8] “Multi-hop relay system evaluation methodology.” [Online]. Available: http://ieee802.org/16/relay/docs/80216j-06 013r3.pdf [9] T. Ng and W. Yu, “Joint optimization of relay strategies and resource allocations in cooperative cellular networks,” IEEE J. Sel. Areas Commun., vol. 25, no. 2, pp. 328-339, Feb. 2007. [10] W. Yu and R. Lui, “Dual methods for nonconvex spectrum optimization of multicarrier systems,” IEEE Trans. Commun., vol. 54, no. 7, pp. 1310-1322, July 2006. [11] S. Boyd, L. Xiao, and A. Mutapcic, “Subgradient methods,” lecture notes of EE364b, Stanford University, Spring Quarter 2007-2008. [12] C. Papadimitriou and K. Steiglitz, Combinatorial Optimization: Algorithms and Complexity. Prentice Hall, 1982. [13] R. Jain, The Art of Computer Systems Performance Analysis: Techniques for Experimental Design, Measurement, Simulation and Modeling. New York: Wiley, 1991. [14] S. Kim, X. Wang, and M. Madihian, “Optimal resource allocation in multi-hop OFDMA wireless networks with cooperative relay,” IEEE Trans. Wireless Commun., vol. 7, no. 5, pp. 1833-1838, May 2008. [15] H. Xu and B. Li, “XOR-assisted cooperative diversity in OFDMA wireless networks: optimization framework and approximation algorithms,” in Proc. IEEE INFOCOM, 2009, pp. 2141-2149. [16] J. Jia, J. Zhang, and Q. Zhang, “Cooperative relay for cognitive radio networks,” in Proc. IEEE INFOCOM, 2009, pp. 2304-2312. [17] R. Wang, V. Lau, and Y. Cui, “Decentralized Fair Scheduling in TwoHop Relay-Assisted Cognitive OFDMA Systems,” IEEE J. Sel. Topics Signal Process., vol. 5, no. 1, pp. 171-181, Jan. 2011. [18] J. Sachs, I. Mari, A. Goldsmith, “Cognitive cellular networks within the TV spectrum”, in Proc. IEEE DySPAN, 2010.