A Node Grouping Algorithm for Joint RelaySelection and Resource Allocation in Cooperative

Cognitive Radio NetworksChuan Ma1, Guanding Yu1, Jietao Zhang2

1. Institute of information and communication engineering, Zhejiang University, Hangzhou, China.2. Wireless Research Department, Huawei Technologies Co., Ltd., Shenzhen, China.Email: iammachuan@yahoo.com.cn, yuguanding@zju.edu.cn, jtzhang@huawei.com

Abstract—Compared with traditional wireless networks, cog-nitive radio network (CRN) has a time-variant and unbalancedspectrum distribution. Cooperative relaying technology, whichenables resource-rich users to assist resource-short users, caneffectively improve spectrum utilization as well as system fairnessin CRN. This paper focuses on the R-C-P strategy, i.e. joint relayselection (R), channel assignment (C) and power allocation (P)strategy, for uplink OFDMA cooperative relaying CRN. The R-C-P scheme is formulated as a nonlinear optimization problemwith the objective to improve both throughput and fairness, and aheuristic node grouping algorithm (NGA) is proposed to derive apolynomial-time suboptimal solution to the problem. NGA selectsrelay and allocates resource according to spectrum availabilityand traffic demands of cognitive users, effectively exploiting bothspace and frequency diversity of the system. Simulation resultsshow that, NGA significantly improves system fairness level whilenot reducing the throughput, which has a better performancethan other algorithms.

Index Terms—cooperative relaying; cognitive radio network

I. INTRODUCTION

Cognitive radio [1], which allows cognitive users (CUs)to access the spectrum unoccupied by primary users (PUs),is proposed as a promising technology to promote spectrumefficiency of wireless networks. In traditional cognitive radionetwork (CRN) where exists only direct links, spectrum shar-ing is not efficient due to the diverse spectrum availabilities ofCUs, which hinders the further improvement of network per-formance. Cooperative communication, which enables users torelay each other’s traffic, is regarded as an effective technologyto address this problem.

Cooperative cognitive radio network is studied in manyliteratures [2]-[7], and three types of cooperation mechanismsare proposed: (i) cooperation between PUs and CUs [2], [3].In this case, CUs can relay PUs’ traffic to help complete PUs’transmission as quickly as possible, which in turn offers CUsmore communication opportunities. (ii) Cooperative transmis-sion among CUs [4], [5]. In this case, CUs relay signals foreach other to emulate MIMO system, which can mitigatemultipath fading in wireless environment. (iii) Cooperativerelaying among CUs [6], [7], [8]. In this scenario, spectrum-rich CUs are allowed to assist spectrum-short CUs. Ourresearch focuses on this cooperation mechanism.

[1-5]

[1,2]

[2-6]

1

2 6543

AP

S3

S2

S1[6]

Direct Link

Relay Link

Fig. 1: A simple cooperative relaying scenario in CRN

Literature [6] considers the relay selection scheme in coop-erative relaying CRN, and a simple heuristic algorithm is putforward . In this paper, we study the joint relay selection andresource allocation scheme for uplink cooperative CRN. Themain concerns are as follows:

(1) Joint relay selection, channel assignment and powerallocation (R-C-P) problem. A simple network with three CUs,S1, S2, S3, and a single cognitive access point (AP) is shown inFig.1 to illuminate the cooperation mechanism. The numbersin the brackets denote the available channels, i.e. channelsunoccupied by PUs, at each node. Note that, we use theterms CU and node interchangeably in this paper. AssumeS2 is a resource-rich node, then we select it as the helper toassist other nodes’ transmission. The uplink transmission slotis divided into two subslots: in the first subslot, S1, S2 sendtheir own data to AP directly while S1, S3 send relaying datato S2; In the second subslot, S1, S2 also send their own datato AP directly, and meanwhile, S2 forwards S1, S3’s relayingdata to AP. This paper studies the R-P-C scheme with theobjective to improve both throughout and fairness based onthe described cooperation mechanism.

(2) System fairness. Fairness is an important consideration inR-P-C scheme, and the proposed algorithm should guaranteethat all CUs have equal (or approximately equal) satisfactiondegrees of the traffic demand.

(3) Algorithm complexity. As both throughput and fairnessare considered in the model, the optimal solution has a

978-1-4577-1010-0/11/$26.00 ©2011 IEEE

high complexity. In this paper, we propose a polynomial-timeheuristic algorithm to solve the optimization problem.

The rest of this paper is organized as follows. System modeland problem formulation are introduced in section II, anda heuristic algorithm is proposed in section III. Section IVdescribes the simulation topology and analyzes the simulationresults. Section V concludes this paper.

II. COOPERATIVE RELAYING IN CRN

A. System Model

Consider the uplink of a cooperative CRN with a total of NCUs and K channels. CUs operate in overlay mode to avoidinterference to PUs, i.e. CUs can only access the channelsunoccupied by PUs. Define binary variable aki , i = 1, ...N ,to denote the availability of channel-k (chk) at node-i (Si):aki = 1 indicates that chk is available at Si, and 0 otherwise.ak0 denotes the availability of chk at AP.

CUs can send data to AP directly (one-hop) or relayed byother nodes (two-hop). The uplink slot comprises two subslots,and Fig.2 illustrates one uplink slot in the scenario that Sjhelps Si. The notation Sj(i) in Fig.2 denotes Sj forwardingSi’s data to AP. We assume that CUs are synchronous. Definebinary variables αkij,1, α

kij,2 to denote channel assignment in

subslot 1 and 2 respectively: αkii,1 = 1 denotes that chk isassigned to Si in subslot 1 for sending its own data to AP, and0 otherwise; αkij,1 = 1 (i 6= j) denotes that chk is assignedto Si in subslot 1 for sending data to relay node Sj , and 0otherwise; αkii,2 = 1 denotes that chk is assigned to Si insubslot 2 for sending its own data to AP, and 0 otherwise;αkij,2 = 1 (i 6= j) denotes that chk is assigned to Si in subslot2 for forwarding Sj’s data to AP, and 0 otherwise. Then, thecorresponding transmission rate on chk is Rkij,t = log(1 +P kij,tH

kij,t/N0), where Hk

ij,t denotes power gain of chk, P kij,tdenotes transmission power on chk, and N0 denotes noisepower. We assume that the channel state, including gain andavailability, keeps constant in one slot.

B. Problem Formulation

In this section, we formulate the R-C-P problem intoan optimization problem. The objectives and constraints areelaborated below.

First, channel assignment should satisfy channel availabilityconstraints at each node:

C1: αkii,t ≤ aki · ak0 , ∀i, k, t

αkij,t ≤ aki · akj , ∀i, j 6= i, k, t(1)

To avoid interference, each channel can be used by at mostone link in any subslot, i.e. channel multiplex constraints:

C2:∑i

∑j

αkij,t ≤ 1, ∀k, t (2)

Maximum power constraint of each node:

C3:∑j

∑k

P kij,t · αkij,t ≤ Pi, ∀i, t (3)

Subslot 1 Subslot 2

Slot

Direct

Relay

Si , Sj AP Si , Sj AP

Si Sj Sj (i) AP

Fig. 2: Uplink transmission procedure in one slot

Si’s throughput in one slot consists of two parts: directthroughput and relaying throughput, i.e. θi = θ′i + θ′′i

θ′i =∑k

(Rkii,1 · αkii,1 +Rkii,2 · αkii,2) (4)

θ′′i =∑j,j 6=i

1

2min{

∑k

Rkij,1 · αkij,1,∑k

Rkji,2 · αkji,2} (5)

Define user satisfaction index δi to denote Si’s satisfactionlevel of traffic requirement

δi =θi

2rreqi

(6)

where θi, 2rreqi respectively denote Si’s actual throughput and

throughput demand in one slot. The fairest R-C-P scheme isdefined as: each CU’s actual throughput is in direct proportionto its traffic demand, i.e.

δ1 = δ2 = ... = δN (7)

and Jain index [9] is employed to measure fairness level

Jain Index =(∑δi)

2

N ·∑δ2i

(8)

Jain index is bounded between 0 and 1, and a close-to-onevalue indicates a close-to-fairest scheme.

The objectives of the R-P-C problem are to (1) maximizethe throughput of CU system, and (2) maximize the fairness ofCU system. The mathematical description of the bi-objectiveoptimization problem is

Determine {αkij,t}, {P kij,t}

To Maximize

F1 =

∑i

θi

F2 = Jain Index =(∑δi)

2

N ·∑δ2i

Subject to C1, C2, C3

(9)

Eq.(9) is a multi-objective mixed integer nonlinear program-ming problem (MO-MINLP), which is NP-hard in general[10]. There are several methods to simplify Eq.(9), e.g. com-bine F1 and F2 into a single objective F , relax the integerconstraints on {αkij,t}, etc. However, the simplified problem isstill a nonlinear programming problem, whose optimal solutionhas a high complexity. In next section, we propose a low-complexity heuristic, namely node grouping algorithm (NGA),to derive a suboptimal solution to Eq.(9).

III. NGA: A TWO-PHASE NODE GROUPINGALGORITHM

In this section, we propose a two-phase node groupingalgorithm (NGA) to solve the R-C-P problem in CRN. Themain idea of NGA is: first, single-channel strategy1 is appliedto determine the relay relationship among CUs, and each relaynode forms a group along with the nodes it relays, as shownin Fig.3. In a group, the relay node is called group-masterand other nodes are called group-members. Then, each group-master employs multi-channel strategy2 to assign channels andallocate power within its group.

A. Grouping Algorithm

The node grouping algorithm consists of two phases, aselaborated below.Phase I Single-channel Strategy Phase

In this phase, the single-channel strategy is employed todetermine relay relationship. This phase consists of two steps:group-master selection and group formation.Step 1. Group-master Selection

First, we consider the single-channel assignment problemwithout taking cooperation mechanism into account. The ob-jective of the assignment problem is to minimize total powerconsumption under the constraint that all traffic demands aresatisfied. The assignment problem can be transformed into aminimum weighted bipartite matching problem: take channelset K = {1, 2, . . .K} and node set N = {1, 2, ..N} as thebipartite subsets, and define the weight of edge eki connectingvertex-k of K and vertex-i of N as cki = snrreqi /Hk

i ,where snrreqi is node-i’s equivalent SNR-demand3 in onesubslot, and Hk

i denotes channel-k’s gain at node-i. Note that,cki is proportional to node-i’s minimum transmitting poweron channel-k when its traffic demand is satisfied. Thus, tominimize the weight-sum is equivalent to minimize the totalpower consumption. KM algorithm [11] can be employed tosolve the bipartite matching problem, i.e. the single-channelassignment problem.

Denote ki as the channel that is assigned to node-i. If node-isatisfies the following group-master selection rule, it is calleda potential group-master or a potential relay node; Otherwise,it is called an ordinary node.[Group-master Selection Rule]

log(1 + P0Hkii /N0) > 2rreqi (10)

where P0 denotes the power constraint of each node.Remark 1. Eq.(10) implicates that if node-i transmits onchannel ki with power P0, it can complete its slot trafficdemand in just one subslot, thus it has the potential to helptransmit other nodes’ data in the other subslot.

1Single-channel strategy: each communication process operates on a singlechannel. Three types of processes are considered: (1) Si sends its own datato AP, (2) Sj sends data to Si, and (3) Si forwards Sj ’s data to AP.

2Multi-channel strategy: each communication process operates on multiplechannels and water-filling algorithm is employed for power allocation.

3See Eq.(6), rreqi denotes node-i’s throughput demand in one subslot, thensnrreqi denotes the equivalent SNR-demand: rreqi = log(1 + snrreqi ).

Group

Group-master

Lonely Node

Group Member

Fig. 3: An illustration of node grouping

Step 2. Group FormationSort the potential group-masters in descending order of

Hkvivi to form set V = {vi}, i.e. Hkv1

v1 > Hkv2v2 > ..., and

sort the ordinary nodes in ascending order of Hkuiui/snrrequi

toform set U = {ui}, i.e. Hku1

u1/snrrequ1

> Hku2u2

/snrrequ2> ....

It indicates (1) vi has more surplus resource than vj if i > j,and (2) ui needs more help than uj if i > j. The mainidea of group formulation is to enable the nodes with moresurplus resource to help the nodes needing more help andmeanwhile to minimize the total power consumption. Thegroup formulation procedure is a loop comprising a series ofrepeated rounds, as depicted below:

One-round: starting from u1, each ordinary node uj ∈ U se-quentially searches for its matched group-master and matchedrelay channel pair. Note that, the matched channel pair consistsof two single-channels, say channel-m and channel-n, for thetwo subslots of the relay transmission respectively. uj searchesfor the qualified node and channel pair that satisfy the groupformation rule (see the boldface below). Denote vuj

as thefirst qualified node, and muj ,nuj

as the qualified channelswith maximum gains. Then, uj matches group-master vuj andrelay channel pair muj ,nuj , i.e. uj joins vuj ’s group. If uj failsto match one group-master, it does not join any group. Thisround ends if every uj ∈ U finishes its matching search orevery vi ∈ V is matched.

Repeat: the one-round runs repeatedly until there is no newmatch appears. Then the node groups are formed, as illustratedin Fig.3: each group consists of one group-master and severalgroup-members. The nodes that do not belong to any groupare called lonely nodes.[Group Formation Rule]• vi is not matched by other nodes in this round;• Channels m,n satisfy:

(i) m is available at vi, uj , n is available at vi,AP;(ii) m,n are not matched by other nodes;(iii) Hm

j > 2Gj , Hni > 2Gj .

where Hmj , H

ni denote the gains of channel-m and channel-n

respectively, and Gj denotes the gain of uj’s direct channelwhich is assigned in step 1.Remark 2. Rule(ii) assures that each group accepts at most onegroup-member in each round, which prevents the groups frombeing overcrowded. Rule(iii) indicates that the total powerconsumption of uj’s transmission assisted by vi on m and nis smaller than that of uj’s transmission on the direct channel.The proof is omitted due to space limitations.

Phase II Multi-channel Strategy PhaseIn this phase, multi-channel strategy and water-filling algo-

rithm [12] are employed to assign the remaining channels andallocate power at each node. This phase consists of two steps:remaining channel assignment and power allocation.Step 3. Remaining Channel Assignment

In this step, we repeatedly apply single-channel strategyto assign the remaining channels, i.e. channels unselected inphase I. Note that, the relay relationship determined in phase Iis not changed in this step. First, each group-member sequen-tially selects a pair of relay channels according to Rule(iii) ofGroup Formation Rule. This selection round runs repeatedlyuntil no new match appears or all channels are assigned, thuseach group-member gets multiple relay channels. Then, indescending order of traffic demands, each node sequentiallyselects the best available channels for direct transmission. Thisselection round runs repeatedly until all channels are assigned,thus, each node gets multiple direct channels.Step 4. Power Allocation

In this step, we study the power allocation strategy based onthe relay selection and channel assignment scheme determinedabove. It is easily comprehensible that, for lonely nodes,single-user water-filling algorithm is optimal since lonelynodes have only direct links. However, for group-master andgroup-member nodes, the power allocation strategy is farmore complicated. We propose the following power allocationscheme for group-masters and group-members.

Consider a group Ci = {vi, ui,1, . . . , ui,Ni}, wherein vi

is the group-master and ui,j is the j-th group-member. De-note li,1, li,2 as vi’s direct link for subslots 1 and 2; de-note li,j as ui,j’s direct link, and li,j,1,li,j,2 as ui,j’s relaylinks. Note that, each link contains multiple channels. Denotechi,1, chi,2, chi,j , chi,j,1,chi,j,2 as the corresponding single-channels assigned in phase I. Allocate power on each linkaccording to the power allocation rule (see the boldfacebelow), and then employ water-filling algorithm to furtherallocate power on multiple channels at each link.[Power Allocation Rule]• Total power on li,1 is P0, and total power on li,2 is P0

Ni+1• Total power on li,j,2 is

Pi,j =

snrreqi,j

Hi,j,2∑j

snrreqi,j

Hi,j,2

· NiP0

Ni + 1(11)

• Total power on li,j,1 is Hi,j,2

Hi,j,1Pi,j , and total power on li,j

is P0 − Hi,j,2

Hi,j,1Pi,j

where snrreqi,j denotes ui,j’s SNR-demand, and Hi,j,1, Hi,j,2

denotes the gain of chi,j,1,chi,j,2 respectively.Remark 3. Eq.(11) is based on the fairest scheme defined inEq.(7), which takes into account both channel qualities andtraffic demands.

B. Complexity AnalysisSuppose there are N CUs and K channels in the network,

N < K. Step 1 has a complexity of O(N2K), which is KM al-

-4 -3 -2 -1 0 1 2 3 4-4

-3

-2

-1

0

1

2

3

4

CU Location

Fig. 4: Simulation topology

gorithm complexity [13]. The complexities of step 2 and 3 areO(N2K2), O(NK2) respectively. Step 4 comprises N water-filling operations, having a complexity of O(NK logK).So, the total complexity of the proposed algorithm NGA isO(N2K2), which is bounded between O(K2) and O(K4).Therefore, NGA has a polynomial time complexity and thuscan operate efficiently in practical application.

IV. PERFORMANCE EVALUATION

In this section, we evaluate the performance of the proposednode grouping algorithm NGA. The simulation is based on thefollowing topology: one square area is divided into 4×4 grids.AP is set in the center of the area and N CUs are randomlydistributed in each grid. Fig.4 illustrates the scenario whereN = 8. Each CU moves randomly within its grid in differentslots. A total of 512 channels are adopted in the simulationand PUs can randomly occupy part of them. Path loss andmultipath fading are considered in the channel model. Thepath gain is expressed as Gij = d−αij , where dij denotes thedistance between the two nodes, and α is the path loss factorset to be 4 in the simulation. COST-207 [14] typical urbanmodel is adopted to formulate the fading channel gain Fij .Then the channel gain is given by Hij = GijFij . The channelgains keep constant in each slot but vary in different slots.

In the simulation, the proposed algorithm NGA is comparedwith another two algorithms: (1) non-cooperative algorithm(NCA). This algorithm does not apply cooperative mechanismand each node sends data to AP directly. (2) Cooperativealgorithm with uniform power allocation (CA-UPA). Thisalgorithm adopts the relay selection strategy of NGA, but doesnot take fairness into account and each group-master allocatespower uniformly within its group. Algorithm performances areevaluated based on two metrics: average aggregate throughputper CU and average aggregate Jain index.

Fig.5 presents the simulation results of 100 slots basedon the parameters that CU population is 160 and the ratioof maximum to minimal SNR-demand is 4. Fig.5(a) showsthat, compared with NCA and CA-UPA, NGA improves thethroughput by about 20% and 5% respectively. Fig.5(b) showsthat, compared with NCA and CA-UPA, NGA improvesthe fairness level by about 90% and 30% respectively. The

0 20 40 60 80 1003.2

3.4

3.6

3.8

4

4.2

4.4

4.6

4.8

5

Slot

Avara

ge T

hro

ug

hp

ut

per

CU

Proposed

UPA

NCA

NCA

UPA

Proposed

(a) Throughput

10 20 30 40 50 60 70 80 90 1000.2

0.3

0.4

0.5

0.6

0.7

0.8

0.9

1

Slot

Avera

ge J

ain

In

dex

Proposed

UPA

NCA

NCA

UPA

Proposed

(b) Fairness

Fig. 5: Aggregate performance vs. time

results indicate that NGA has a better performance than otheralgorithms in terms of both throughput and fairness.

Fig.6 and Fig.7 depicts algorithm performances in thescenarios with diverse numbers of users and ratios of max-imum to minimal SNR-demand respectively. It can be seenthat NGA performs better than other algorithms in all thesescenarios, in terms of both throughput and fairness. Twosubfigures need to be further discussed. First, Fig.6(a) showsthat, system throughput of NGA gradually decreases when thenumber of users increases. This is because that when userpopulation increases, the total number of available channelsper user decreases, which lessens the efficiency of the water-filling algorithm and thus leads to the gradually decrease insystem throughput. In addition, Fig.7(b) shows that when thedifference of user traffic demands increases, system fairnesslevel declines. The explanation for this phenomenon is asfollows: when the difference of user traffic demands becomeslarger, it gets harder to satisfy the users with higher trafficdemands; however, the users with smaller traffic demands canalways be satisfied easily. Thus, the demand satisfaction levelsbecomes more and more unbalanced among users, leading tothe degradation of system fairness level.

V. CONCLUSION

This paper studies the joint relay selection, channel as-signment and power allocation strategy for cooperative CRN.The R-C-P strategy is modeled as a nonlinear optimizationproblem. We propose a low-complexity heuristic algorithm,namely node grouping algorithm, to derive a suboptimalsolution to the problem. The grouping algorithm selects relaysand allocates resource according to users’ spectrum availabil-ities and traffic demands, effectively exploiting the space andfrequency diversity of the system. Simulation results showthat, the proposed algorithm outperforms other algorithms interms of both throughput and fairness.

ACKNOWLEDGMENT

This work is supported in part by the National Basic Re-search Program of China (973 Program) (No.2009CB320405),the Zhejiang Provincial Natural Science Foundation of China(No.Y1110368), the National Natural Science Foundation ofChina (No.60802012), and Huawei Collaborative ResearchFunding under the contract YBWL2008046.

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CU Population per Grid

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(a) Throughput

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0.8

0.9

1

1.1

CU Population per Grid

Avara

ge J

ain

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dex

NCA

UPA

Proposed

(b) Fairness

Fig. 6: Performance vs. number of CUs per grid

2 4 6 8 10

2

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Ratio of Max SNR−requirement to Min SNR−requirementA

vera

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Ratio of Max SNR−requirement to Min SNR−requirement

Avara

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UPA

Proposed

(b) Fairness

Fig. 7: Performance vs. ratio of max to min SNR-demand

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