RESEARCH OpenAccess Optimalresourceallocationforcognitive ... · PU’s spectrum on a condition that the QoS of the pri-marytransmissionisnotaffected.Therefore,thetransmit power of

Lan et al. EURASIP Journal onWireless Communications andNetworking (2015) 2015:239 DOI 10.1186/s13638-015-0465-4

RESEARCH Open Access

Optimal resource allocation for cognitiveradio networks with primary user outageconstraintPeng Lan1, Lizhen Chen1, Guowei Zhang2 and Fenggang Sun1*

Abstract

In this paper, we investigate the problem of power allocation in cognitive underlay networks, where a secondary user(SU) is allowed to coexist with a primary user (PU). We consider three transmission models for the secondary link:(i) one-way transmission with relay assisted, (ii) two-way transmission with a direct link, and (iii) two-way transmissionwith relay assisted. In conventional interference-limited cognitive networks, the instantaneous channel stateinformation (CSI) of a PU is required to suppress SU’s transmit power to guarantee the quality of service (QoS) of thePU, which increases the feedback burden in practice. To tackle this issue, in this article we take primary outageprobability as a new criterion to measure the QoS of the PU, where only the statistical CSI of the PU is required. Firstly,we derive the primary outage constraints for the three models, respectively. Then, with the newly obtainedconstraints, we formulate optimization problems to maximize the channel rate of the SU. Finally, we derive theoptimal solutions for power allocation with respect to different parameters, respectively. Simulation results verify theperformance improvement of the proposed schemes.

Keywords: Cognitive radio, Cooperative communication, Power allocation, Quality of service, Two-way networks

1 IntroductionIn cognitive underlay networks, a secondary user (SU) isallowed to share the spectrum with a primary user (PU)as long as the quality-of-service (QoS) requirement of theprimary transmission is guaranteed [1]. The main advan-tage of cognitive underlay systems lies in its efficient uti-lization of radio spectrum, which makes it as a promisingsolution to tackle the spectrum scarcity problem [2]. How-ever, the transmit power of the SU needs to be strictly con-trolled to satisfy PU’s QoS, which consequently degradesSU’s performance. To tackle this issue, power allocationand cooperative relaying techniques are considered as twopotential ways to improve SU’s performance.Cooperative relaying has been widely studied to extend

the coverage, enhance the reliability, as well as the capacityof wireless systems [3–5]. One-way relaying transmissionoften operates in a half-duplex mode that can providemore spatial diversity but suffers from a substantial loss

*Correspondence: [email protected] of Information Science and Engineering, Shandong AgriculturalUniversity, Daizong Road No.61, 271018 Tai’an, Shandong, ChinaFull list of author information is available at the end of the article

in spectral efficiency as compared to direct transmission.Fortunately, two-way relaying transmission has been pro-posed to overcome the spectral efficiency loss [6–8].Combining cooperative relaying and cognitive systemscan provide a promising solution to improve SU’s per-formance. In this article, we consider underlay cogni-tive relay networks involving three different transmissionmodels for secondary transmission as shown in Fig. 1.In the one-way transmission model, a secondary trans-mitter (denoted as S1) transmits signals to a secondaryreceiver (denoted as S2) with the help of a secondaryrelay (SR). In the two-way transmission model, two sec-ondary transceivers (denoted as S1 and S2, respectively)exchanges their signals either in a direct link or in two-wayrelaying link.To protect the PU while optimizing the SU’s perfor-

mance, various power allocation (PA) strategies have beeninvestigated for underlay cognitive relay networks [9, 10].Subject to average/peak interference power constraint forPU, an optimal PA strategy was proposed in [9] to achievethe ergodic capacity for SU in cognitive one-way relay net-works. With power limit for SU being further considered,

© 2015 Lan et al. Open Access This article is distributed under the terms of the Creative Commons Attribution 4.0 InternationalLicense (http://creativecommons.org/licenses/by/4.0/), which permits unrestricted use, distribution, and reproduction in anymedium, provided you give appropriate credit to the original author(s) and the source, provide a link to the Creative Commonslicense, and indicate if changes were made.

http://crossmark.crossref.org/dialog/?doi=10.1186/s13638-015-0465-4-x&domain=pdf

mailto: [email protected]

http://creativecommons.org/licenses/by/4.0/

Lan et al. EURASIP Journal onWireless Communications and Networking (2015) 2015:239 Page 2 of 13

Fig. 1 System model of cognitive underlay networks with three secondary transmission modes. a One-way transmission with relay assisted(OWT-RA), b two-way transmission with a direct link (TWT-DL), and c two-way transmission with relay assisted (TWT-RA)

the authors in [11] proposed optimal PA schemes tomaximize the ergodic/outage capacity of SU. In [12], PAschemes were proposed under the joint constraints ofoutage probability requirement for PU and average/peaktransmit power limit for SU. With relay selection, the sec-ondary transmission can be further enhanced. Joint PAand relay selection was investigated in [13] to maximizethe system throughput with limited interference to PU. In[14], the transmit power limit for SU was also taken intoconsideration. For amplify-and-forward (AF) cognitiverelay networks with multiple SUs, joint relay assignmentand PA was proposed in [15]. In cognitive two-way net-

works, closed-form solutions for optimal PA were derivedin [16] under the joint peak interference constraint for PU.For cognitive two-way relaying networks, optimal PA andrelay selection scheme were studied in [17], where a pairof secondary transceivers communicate with each otherassisted by a set of two-way AF relays. Further, the prob-lem of relay selection and PA for the two-way relayingcognitive radio networks was investigated in [10], wherethe relays select between the AF and decode-and-forward(DF) protocols to maximize SU’s sum rate.In the aforementioned works [9, 10], SU’s transmit

power is controlled to keep the interference of PU under


a predefined limit. In such interference-limited cognitivenetworks, the instantaneous channel state information(CSI) of PU is required to be known at SU to protectPU. Since a secondary network is typically not coordi-nated with a primary network and no dedicated feedbackchannel is available from PU to SU, the instantaneous CSIof PU can hardly be obtained, and unreliable CSI resultsin violation of the interference constraint. To deal withthis critical obstacle, Zou et al. investigated the prob-lem of relay selection to maximize the received signal-to-interference-noise ratio (SINR) at SU under a novelindependent primary outage constraint for PU [18], inwhich only the statistical CSI of PU is required at SU.The work in [18] restrained the transmit powers of sec-ondary transmitter and secondary relay under individualprimary outage constraint for PU. In [19], the authorsintroduced a new cooperative transmission scheme foroverlay cognitive radio in which the secondary networkexploits the primary retransmissions without requiringglobal CSI. Further in [20], the primary outage constraintdue to secondary transmitter and secondary relay wasjointly considered for the first time, and a closed-formsolution for optimal PA and relay selection was derived inDF cognitive relay networks.In this article, we investigate the problem of power

allocation to maximize the achievable rate of SU in cogni-tive networks. Three secondary transmission models areconsidered: (i) one-way transmission with relay assisted(OWT-RA), (ii) two-way transmission with a direct link(TWT-DL), and (iii) two-way transmission with relayassisted (TWT-RA). We first derive the joint primary out-age constraints for the three models, respectively. Withthese constraints, optimization problems for power allo-cation are formulated and optimal solutions are derived.Simulation results are provided to verify the performanceimprovement of our proposed schemes compared withthe equal resource allocation schemes.To be more specific, the main contributions of this

article are described as follows.

• We derived the joint primary outage constraints forthree secondary transmission models, OWT-RA,TWT-DL, and TWT-RA, respectively. Compared tothe traditional interference-limited constraint for PU,the key advantage is that only the statistical CSI of PUis required at SU, which is more practical.

• We proposed power allocation schemes forOWT-RA, TWT-DL, and TWT-RA to maximize theachievable rate of SU, respectively. In addition, wealso proposed power allocation schemes to ensurefairness for TWT-DL and TWT-RA.

• For comparison, we provided correspondinglow-complexity equal resource allocation (ERA)schemes for each model. Simulation results show that

our proposed schemes outperform greatly thecorresponding ERA scheme. The reason is thatprimary outage constraint due to secondarytransmission is considered jointly in our proposedschemes, while it is considered individually in theERA schemes.

The rest of this article is organized as follows. Systemmodel and the joint primary outage constraint of the threetransmit models are, respectively, described in Sections 2and 3. Then, the proposed power allocation schemes ofdifferent models are provided in Sections 4, 5, and 6,respectively. Simulation results are given in Section 7.Section 8 concludes the article.

2 System and channel modelIn this article, we consider underlay cognitive networkswith three secondary transmission models as shown inFig. 1, in which primary system and secondary systemcoexists simultaneously. In the primary system, a primarytransmitter (PT) sends data to a primary destination (PD).The secondary system is a cooperative relay system whichconsists of a pair of transceivers (denoted as S1 and S2)and/or M SRs, in which SRi (for i = 1, . . . ,M) denotesthe ith relay. The M relays are considered to be in a clus-ter, so that they are assumed to be approximately at thesame position. This assumption simplifies the analysis andcan represent a number of practical scenarios [19, 21, 22].Time division multiple access (TDMA)-based protocol isused for the secondary transmissions, and three differ-ent transmission models for the secondary system areconsidered in this article.Model 1—one-way transmission with relay assisted

(OWT-RA)In the OWT-RA model as shown in Fig. 1a, S1 is the

transmit node and S2 is the receive node. The secondarytransmission between S1 and S2 is assisted by SRs (i.e. S1→ SR → S2). The whole transmission process is dividedinto two phases equally. In the first phase, S1 broadcastsits message and SRs receive. In the second phase, the bestrelay is selected to amplify the received signal and forwardit to S2.Model 2—two-way transmission with a direct link

(TWT-DL)In the TWT-DL model, S1 and S2 transmit to each

other without the assistance of SRs (i.e. S1 ↔ S2). Thetransmission procedure is shown in Fig. 1b. The wholesecondary transmission process is divided into two phasesequally, where S1 transmits to S2 in the first phase and S2transmits to S1 in the second phase.Model 3—two-way transmission with relay assisted

(TWT-RA)In TWT-RA model, S1 and S2 exchange information

with the help of SRs (i.e. S1 ↔ SR ↔ S2) when no direct


link between S1 and S2 is available. The two-way sec-ondary transmission is completed in three equal phases,as shown in Fig. 1c. S1 and S2 transmit to SRs in thefirst and second phases, respectively. In the third phase, adecode-and-forward (DF) protocol is considered, the bestSR decodes the signals received from S1 and S2 and jointlyencodes the signal through XOR operation and forwardsthe signal to S1 and S2.In the primary transmission, assume that PT transmits

signal xP(E(|xP|2) = 1

)to PD with fixed power PPT and

a data rate RP ; in the meantime, S1 and/or S2 intends toreuse this time resource to transmit their signals xS1 andxS2

(E(|xS1|2) = 1 and/or E

(|xS2|2) = 1)to each other

with powers PS1 and PS2, respectively. The channels areinvariant during the transmission phases. The channelgain between any transmitter i ∈ {S1, S2, SR, PT} and anyreceiver j ∈ {S1, S2, SR, PD} is denoted as hi−j. Assum-ing all links are independent and identically distributed(i.i.d.), zero-mean Rayleigh flat fading channels with vari-ance 1

/σ 2i−j, where σ 2

i−j is defined as σ 2i−j = dγ

i−j, di−jis the distance between transmitter i and receiver j, andγ is the path-loss exponent [19]. It is assumed that SUhas the instantaneous CSI of the secondary transmis-sion links and the links from PT to SU, which can beobtained by a pilot-aided channel estimation or CSI feed-back [14, 23]. Moreover, the two SUs are assumed to knowthe average CSI between themselves and PD and also theaverage CSI between PT and PD. The thermal noises ofreceivers nj( j ∈ {S1, S2, SR, PD}) are modeled as addi-tive white Gaussian noises (AWGN) with mean zero andvariance N0.

3 The primary outage constraintIn cognitive underlay networks, SU is allowed to sharePU’s spectrum on a condition that the QoS of the pri-mary transmission is not affected. Therefore, the transmitpower of SU must be allocated appropriately to satisfythe primary QoS requirement. Traditionally, SU’s trans-mit power is limited by the peak/average interferenceconstraint for PU [9, 10]. Specifically, SU can accessPU’s licensed spectrum as long as the induced interfer-ence from SU to PU is below the threshold. In such aninterference-limited network, the instantaneous CSI ofthe link from SU to PU is required. However, this CSI canhardly be obtained, since the secondary network is typ-ically not coordinated with the primary network and nodedicated feedback channel is available from PU to SU.To tackle this issue in this article, we use the primary

outage probability as a metric to quantify the QoS ofthe primary transmission. Specifically, we consider thatthe primary outage probability should be kept below apredefined threshold PoutPri,Thr. The main advantage isthat only the statistical CSI of the link from SU to PUis required, which is more practical. In the following,

we derive the primary outage constraints for the threetransmission models, OWT-RA, TWT-DL, and TWT-RA, respectively.According to the SINR at PD during the transmission

phases, the conditional outage probability of PU due to thetransmission of node n (n ∈ {S1, S2, SR}) can be expressedas

Pout (PU|n) = Pr(log2

(1 + rnPD

)< RP

), (1)

where rnPD = PPT|hPT−PD|2Pn|hn−PD|2+N0

= P̂PT|hPT−PD|2P̂n|hn−PD|2+1

(n ∈ {S1, S2, SR})is the SINR at PDwhen node n (n ∈ {S1, S2, SR}) transmitssignals. P̂PT and P̂n are the equivalent transmit pow-ers with normalized noise power, which are defined asP̂PT = PPT/N0 and P̂n = Pn/N0, respectively. Notethat |hPT−PD|2 and |hn−PD|2 follow independent exponen-tial distributions with parameters 1/σ 2

PT−PD and 1/σ 2n−PD

respectively. Using the joint probability density function(PDF) of |hPT−PD|2 and |hn−PD|2, the conditional outageprobability (1) can be derived as

Pout (PU |n )

= 1 − P̂PTσ 2PT−PD

P̂nσ 2n−PD

(2RP − 1

) + P̂PTσ 2PT−PD

exp(− 2RP − 1P̂PTσ 2

PT−PD

).

(2)

In order to derive the primary outage probability routPri,the probability of node n transmits signals is required.Since TDMA protocol is used for secondary transmissionas described in Section 2, therefore, the secondary trans-mission is divided into k equal phases, where k is decidedby which transmission model is adopted (e.g., k = 2 forthe OWT-RA and TWT-DL models, k=3 for the TWT-RA model). Let Pt (n) represents the probability that thenode n transmits signals, we have Pt (n) = 1

k . Using thetotal probability formula, the primary outage probabilitycan be expressed as

PoutPri =∑

n∈{S1,S2,SR}Pt(n)Pout (PU |n )

=∑

n∈{S1,S2,SR}

1kPout (PU |n ) ,

(3)

which should satisfy the constraint PoutPri ≤ PoutPri,Thr.

3.1 The primary outage constraint for the OWT-RAmodelIn the OWT-RA model, S1 and SR transmit in two sepa-rate equal phases, i.e., Pt (n) = 1

2 , n ∈ {S1, SR}. Assumethe ith relay is selected to forward, the primary outage canbe denoted as

PoutPri = Pt (S1)Pout (PU |S1 ) + Pt (SRi)Pout (PU |SRi )

= 12Pout (PU |S1 ) + 1

2Pout (PU |SRi ) (4)

≤ PoutPri,Thr.


Substitute (2) into (4), the primary outage constraint canbe derived as

gP̂S1(i)λS1 + g

+ gP̂RSiλSRi + g

≥ 2ρ, (5)

where ρ = (1 − PoutPr i,Thr

)exp( 2RP−1

P̂PTσ 2PT−PD

), g =P̂PTσ 2

PT−PD, and λn = σ 2n−PD

(2RP − 1

), n ∈ {S1, SR}. P̂SRi

is the equivalent transmit power of the ith relay, and P̂S1(i)is the equivalent transmit power of S1 corresponding tothe ith relay.For the underlay cognitive networks, the QoS of PU

should be conservatively guaranteed, that is, PoutPri,Thrshould take a small value or at least no larger than 0.5[12]. Therefore, ρ > 0.5 always holds. Moreover, since theupper bound of g

P̂S1(i) λS1+g + gP̂RSiλSRi+g is 2, the secondary

transmission is enabled only when ρ < 1. Otherwise, thepowers P̂S1(i) and P̂SRi should be set to zero, and the sec-ondary transmission is not available. Based on the aboveanalysis, the constraint 0.5 < ρ < 1 will always besatisfied for SU power allocation in this model.

3.2 The primary outage constraint for the TWT-DL modelIn the TWT-DL model, the secondary transmission isdivided into two equal phases, i.e., Pt (n) = 1

2 , n ∈{S1, S2}. The primary outage constraint can be denoted as

PoutPri = Pt (S1)Pout (PU |S1 ) + Pt (S2)Pout (PU |S2 )

= 12Pout (PU |S1 ) + 1

2Pout (PU |S2 ) . (6)

With the similar analysis with the OWT-RA model, wederive the primary outage constraint as

gP̂S1λS1 + g

+ gP̂S2λS2 + g

≥ 2ρ, (7)

where g, ρ, and λn, n ∈ {S1, S2} follow the similar defini-tion as in the OWT-RA model.

3.3 The primary outage constraint for the TWT-RAmodelIn the TWT-RA model, the secondary transmission iscompleted in three equal phases, i.e., Pt (n) = 1

3 , n ∈{S1, S2, SR}. Assume that the ith relay is selected, theprimary outage constraint can be expressed as

PoutPri= Pt (S1)Pout (PU |S1 ) + Pt (S2)Pout (PU |S2 )

+ Pt (SRi)Pout (PU |SRi )

= 13Pout (PU |S1 ) + 1

3Pout (PU |S2 ) + 1

3Pout (PU |SRi ) .

(8)

With the similar analysis with the OWT-RA model, wederive the primary outage constraint as

gP̂S1(i)λS1 + g

+ gP̂S2(i)λS2 + g

+ gP̂SRiλSRi + g

≥ 3ρ, (9)

where P̂S1(i) and P̂S2(i) denote the equivalent transmitpowers of S1 and S2 corresponding to the ith relay.

4 Power allocation for the OWT-RAmodelIn this section, the problem of power allocation is studiedto maximize the achievable rate of SU for the OWT-RAmodel.The secondary transmission is divided into two phases,

and the received signal at SRi in the first phase can beexpressed as

ySRi =√PS1(i)hS1−SRi xS+√

PPThPT−SRi xP +nSRi . (10)

In the second phase, the signal received at S2 can beexpressed as

yS2 = √PSRiGihSRi−S2ySRi+

√PPThPT−S2xP+nS2, (11)

where Gi denotes the normalization gain of SRi

Gi =√

1PS1(i)

∣∣hS1−SRi

∣∣2 + PPT∣∣hPT−SRi

∣∣2 + N0. (12)

Based on (10), (11), and (12), the received SINR at S2after the two transmission phases is then given as

rS2 = G2i PS1(i) |hS1−SRi |2PSRi |hSRi−S2|2

G2i PSRi |hSRi−S2|2

(PPT|hPT−SRi |2 + N0

) + PPT|hPT−S2|2 + N0.

(13)

By defining GS1−SRi = |hS1−SRi |2P̂PT|hPT−SRi |2+1

and GSRi−S2 =|hSRi−S2|2

P̂PT|hPT−S2|2+1, (13) can be rewritten as

rS2=P̂S1(i)GS1−SRi P̂SRiGSRi−S2

P̂S1(i)GS1−SRi + P̂SRiGSRi−S2 + 1. (14)

4.1 Equal resource allocationAs noted in Section 3, the equivalent powers P̂S1(i) andP̂SRi must satisfy the primary outage constraint (5). A sim-ple but not optimal way to meet the constraint withoutcoordination between S1 and SRi would be g

P̂S1(i) λS1+g ≥ρ and g

P̂SRiλSRi+g ≥ ρ [18], and the equivalent transmit

powers P̂S1(i) and P̂SRi should satisfy⎧⎪⎪⎪⎪⎪⎪⎪⎨⎪⎪⎪⎪⎪⎪⎪⎩

P̂ERAS1(i)= g(1−ρ)

ρλS1

= σ 2PT−PDP̂PT

σ 2S1−PD(2RP−1)

(1

1−PoutPr i,Thr exp(− 2RP−1

P̂PTσ 2PT−PD

)− 1

)P̂ERASRi

= g(1−ρ)

ρλSRi

= σ 2PT−PDP̂PT

σ 2SRi−PD(2RP−1)

(1

1−PoutPr i,Thr exp(− 2RP−1

P̂PTσ 2PT−PD

)− 1

) .

(15)

We denote this scheme as the equal resource alloca-tion (ERA) scheme. From (15), the powers of S1 and SRiare dominantly determined by the QoS requirement of


PU and the average channel gain of the links from PTto PD and from itself to PD. The static property allowsthe ERA scheme to allocate powers individually with lowcomplexity. However, the only concern of the ERA schemeis to guarantee the primary transmission while the sec-ondary transmission is ignored; therefore, it can not reachan optimal performance. Next, we will jointly allocatethe transmit power between S1 and SR by taking intoconsideration the primary outage constraint (5).

4.2 Optimal power allocationIn the OWT-RA model, the SINR of S2 is the benchmarkto quantify the SU’s performance; therefore, the aim of thepower allocation is to maximize the SU’s SINR as shownin (14). The optimization problem can be formulated as(P̂optS1(i)

, P̂optSRi

)= arg max

P̂S1(i) , P̂SRi

P̂S1(i)GS1−SRi P̂SRiGSRi−S2

P̂S1(i)GS1−SRi + P̂SRiGSRi−S2 + 1,

(16)subject to

gP̂S1(i)λS1 + g

+ gP̂SRiλSRi + g

≥ 2ρ, (17a)

P̂S1 ≥ 0 , P̂S2 ≥ 0. (17b)

This above problem is convex since its objective func-tion (16) is concave and its constraint (17a) is convex and(17b) is linear. Using the Lagrange multiplier method, theoptimal power allocation problem of (16) and (17) can begiven as

L(̂PS1(i) , P̂SRi , λ) = 1P̂S1(i)GS1−SRi

+ 1P̂SRi GSRi−S2

+ 1P̂S1(i)GS1−SRi P̂SRiGSRi−S2

+λ

(g

P̂S1(i) λS1 + g+ g

P̂SRiλSRi + g− 2ρ

),

(18)

where λ ≥ 0 represents the Lagrange multiplier. By apply-ing the Karush-Kuhn-Tucker (KKT) optimality conditions[24], we can obtain

λ

(g

P̂S1(i)λS1 + g+ g

P̂SRiλSRi + g− 2ρ

)= 0, (19a)

∂L∂P̂S1(i)

= 0 and∂L

∂P̂SRi

= 0. (19b)

The direct calculation of (19a) and (19b) yields the opti-mal solutions of the equivalent powers P̂optS1(i)

and P̂optSRias

From the derived solution (20), the optimal powers of S1and SR can be allocated. Different from the ERA schemein (15), the powers of S1 and SRi are decided not onlyby the QoS requirement of PU and the average channelgain of the links from PT to PD and from itself to PD butalso by the instantaneous channel gain of the secondarylink. Moreover, the average channel gains of the interfer-ence links from S1 and SR to PD are jointly considered inour schemes. To be more specific, if the average channelgain of one interference link is dominantly stronger thatthe another, without loss of generality, we assume λS1 islarger than λSRi . According to (20), the proposed schemewill suppress the transmit power of S1 but allocate morepower to SRi without violating the primary outage con-straint. However, the ERA scheme only suppresses thepower of S1 when λS1 is larger than λSRi . Therefore, theproposed scheme can reach a better trade-off betweenS1 and SR than the ERA scheme, which can enhance thesecondary transmission obviously.It is noted that the power of S1 varies with respect to

different SRs. Since the secondary transmission is com-pleted via relaying, the performance of the secondary linkis dominantly affected by SR. In addition to power allo-cation, we can also enhance the secondary transmissionby relay selection. To be more specific, once the optimalpower allocation for all relays has been calculated, therelay with the highest SINR is selected as the best, i.e.,

iopt = argmaxi

⎛⎝ P̂optS1(i)GS1−SRi P̂

optSRi

GSRi−S2

P̂optS1(i)GS1−SRi + P̂optSRi

GSRi−S2 + 1

⎞⎠ .

(21)

5 Power allocation for the TWT-DLmodelIn the cognitive TWT-DL network, since S1 and S2 areboth transceivers and exchange information with eachother, the achievable rate of S1 and S2 can be, respectively,defined as

CS1 = 12log2

(1 + αP̂S1

)andCS2 = 1

2log2

(1 + βP̂S2

),

(22)

in which the two intermediate parameters of Eq. (22) aregiven as α = |hS1−S2|2

P̂PT|hPT−S2|2+1and β = |hS1−S2|2

P̂PT|hPT−S1|2+1.

In the TWT-DL model, we enhance the secondarytransmission by power allocation, and the two differentgoals are as follows: (1) to maximize the sum achievable

⎧⎪⎪⎨⎪⎪⎩P̂optS1(i)

= 2(1−ρ)g√

2(1−ρ)gGSRi−S2+(2ρ−1)λSRi(2ρ−1)λS1

√2(1−ρ)gGSRi−S2+(2ρ−1)λSRi+

√2(1−ρ)gλS1λSRiGS1−SRi+(2ρ−1)λS1

P̂optSRi= 2(1−ρ)g

√2(1−ρ)gGS1−SRi+(2ρ−1)λS1

(2ρ−1)λSRi√

2(1−ρ)gGS1−SRi+(2ρ−1)λS1+√

2(1−ρ)gλS1λSRiGSRi−S2+(2ρ−1)λSRi

(20)


rate and (2) to maximize the achievable rate of the weakerlink which is referred as to guarantee fairness.In the former goal, the sum achievable rate CSum is

denoted as

CSum = CS1 + CS2. (23)

In the latter goal, to guarantee fairness, the achievablerate of S1 and S2 is expected to be the same. The sumachievable rate of S1 and S2 is decided by the weaker one.We denote the corresponding sum achievable rate for thiscase as CFair, which can be expressed as

CFair = 2min (CS1, CS2) . (24)

5.1 Equal resource allocationSimilar with the ERA scheme for the cognitive OWT-RAnetwork as described in Section 4, the equivalent transmitpowers P̂S1 and P̂S2 for the ERA scheme of the cognitiveTWT-DL network should satisfy⎧⎪⎪⎪⎪⎪⎨⎪⎪⎪⎪⎪⎩

P̂ERAS1 = g(1−ρ)

ρλS1

= σ 2PT−PDP̂PT


(1

1−PoutPri,Thr exp(

− 2RP−1P̂PTσ 2

PT−PD

)− 1

)P̂ERAS2 = g(1−ρ)

ρλS2

= σ 2PT−PDP̂PT


(1

1−PoutPri,Thr exp(

− 2RP−1P̂PTσ 2

PT−PD

)− 1

) ,

(25)

respectively. The ERA scheme in the TWT-DL also allo-cates powers individually. However, when consideringthe primary outage constraint, it is more meaningful toimprove the SU’s performance based on the joint primaryoutage constraint for S1 and S2. The SU performancedesires further improvement through jointly allocating thetransmission powers of S1 and S2.

5.2 Optimal power allocation for data rate maximization(DRM)

For the cognitive TWT-DL networks, the optimal equiv-alent power allocation to maximize the achievable rate ofSU can be obtained by solving the following optimizationproblem(

P̂optS1 , P̂optS2

)= arg max

P̂S1, P̂S2CSum, (26)

subject to

gP̂S1λS1 + g

+ gP̂S2λS2 + g

≥ 2ρ, (27a)

P̂S1 ≥ 0 , P̂S2 ≥ 0. (27b)

According to (22) and (23), the goal in (26) to maximizeCSum is equivalent to maximizing αP̂S1+βP̂S2+αβP̂S1P̂S2.For computation simplicity, by assuming P̃S1 = λS1

g P̂S1+1,

P̃S2 = λS2g P̂S2 + 1, α̃ = λS2

βg − 1, and β̃ = λS1αg − 1, the

optimization problem can be further simplified as(P̃optS1 , P̃optS2

)= arg max

P̃S1, P̃S2g(̃PS1, P̃S2

)= P̃S1P̃S2 + α̃P̃S1 + β̃P̃S2.

(28)

subject to1P̃S1

+ 1P̃S2

≥ 2ρ, (29a)

P̃S1 ≥ 1 , P̃S2 ≥ 1. (29b)

Without considering the power limits (29b), to obtainthe optimal solution, the constraint (29a) should satisfywith equality, which can be easily proved by contradiction.Take the equality 1

P̃S1+ 1

P̃S2= 2ρ into (28), the objec-

tive problem g(̃PS1, P̃S2

)can be further converted to a

function with variable P̃S1 as

g(̃PS1

) =(̃α + 1

2ρ

)P̃S1 +

(β̃ + 1

2ρ

)2ρ

(2ρP̃S1 − 1

) + 12ρ

(̃β + 1

2ρ

).

(30)

Take the partial derivative of g(̃PS1

)with respect to P̃S1,

we can obtain

dg(̃PS1

)dP̃S1

= α̃ + 12ρ

− β̃ + 12ρ(

2ρP̃S1 − 1)2 . (31)

Take the limit P̃S1 ≥ 1 into account, we can see thatwhen 2β̃ρ+1

2α̃ρ+1 < (2ρ − 1)2, the partial derivative dg(̃PS1)dP̃S1

>0and Eq. (30) is a monotonously increase function withP̃S1. Therefore, g

(̃PS1

)can be maximized by maximiz-

ing P̃S1 = 12ρ−1 and P̃S2 = 1, i.e., P̂S1 = 2(1−ρ)g

(2ρ−1)λS1 andP̂S2 = 0. In this case, the two-way transmission is retro-graded as a one-way transmission, i.e., S1 → S2. Similarly,if 2α̃ρ+1

2β̃ρ+1 ≤ (2ρ − 1)2, the two-way transmission is retro-graded as a one-way transmission from S2 to S1 with pow-ers P̂S1 = 0 and P̂S2 = 2(1−ρ)g

(2ρ−1)λS2 . With the above analysis,

if min[2β̃ρ+12α̃ρ+1 ,

2α̃ρ+12β̃ρ+1

]≤ (2ρ − 1)2, the sum achievable

rate can be maximized by max[α

2(1−ρ)g(2ρ−1)λS1 ,β

2(1−ρ)g(2ρ−1)λS2

].

Specifically, if αβ

>λS1λS2

, the link of S1 → S2 is enabled

with powers(P̂optS1 , P̂optS2

)=

[2(1−ρ)g

(2ρ−1)λS1 , 0]. Otherwise, if

αβ

≤ λS1λS2

, the link of S2 → S1 is enabled with powers(P̂optS1 , P̂optS2

)=

[0, 2(1−ρ)g

(2ρ−1)λS2

].

For the case min[2β̃ρ+12α̃ρ+1 ,

2α̃ρ+12β̃ρ+1

]> (2ρ − 1)2, we can-

not solve the optimization problem (28) with constraints(29a) and (29b) using the monotone property. Notice thatthe objective function is concave and the feasible regionthat meets every constraint in (28) forms a convex set.Thus, the solution to its Lagrange function also solves


the maximization problem. The optimal power allocationproblem (28) without considering the power limits (29b)can be formulated as

L(̃PS1, P̃S2, λ

) = P̃S1P̃S2+α̃P̃S1+β̃P̃S2+λ

(2ρ − 1

P̃S1− 1

P̃S2

),

(32)

where λ ≥ 0 represents the Lagrange multiplier. Byapplying the KKT optimality conditions, we can obtain

λ

(2ρ − 1

P̃S1− 1

P̃S2

)= 0, (33a)

∂L∂P̃S1

= 0 and∂L

∂P̃S2= 0. (33b)

The direct calculation of (33a) and (33b) yields theoptimal solutions

P̃optS1 = 12ρ

⎛⎝1 +√2β̃ρ + 12α̃ρ + 1

⎞⎠ , (34a)

P̃optS2 = 12ρ

(1 +

√2α̃ρ + 1β̃ρ + 1

). (34b)

Integrated from the above analysis, the optimal solu-tions for the original problem (26) with constraints (27a)and (27b) can be written as(

P̂optS1 , P̂optS2

)

=

⎧⎪⎪⎪⎪⎨⎪⎪⎪⎪⎩

(g

λS1(̃PoptS1 − 1), g

λS2(̃PoptS2 − 1)

), min

[2β̃ρ+12α̃ρ+1 ,

2α̃ρ+12β̃ρ+1

]> (2ρ − 1)2(

2(1−ρ)g(2ρ−1)λS1 , 0

), min

[2β̃ρ+12α̃ρ+1 ,

2α̃ρ+12β̃ρ+1

]≤ (2ρ − 1)2 and α

β>

λS1λS2(

0, 2(1−ρ)g(2ρ−1)λS2

), min

[2β̃ρ+12α̃ρ+1 ,

2α̃ρ+12β̃ρ+1

]≤ (2ρ − 1)2 and α

β≤ λS1

λS2

(35)

5.3 Optimal power allocation for data rate fairness (DRF)In the TWT-DL model, the transceivers S1 and S2exchange information with each other. It is reasonable toconsider fairness between the two transceivers. The prob-lem of power allocation for SU with data rate fairness isformulated as(

P̂optS1 , P̂optS2

)= arg max

P̂S1, P̂S2CFair, (36)

with constraints (27a) and (27b).To ensure fairness, the two transceivers should have the

same rate, which is proved as follows. Assume that P∗S1 and

P∗S2 reach the optimal solution in (36) and CS1 = CS2.

Without loss of generality, assume CS1 > CS2. For thiscase, it is obvious that there must exist a smaller powerP′S1 satisfying CS1 = CS2, which can obtain the same

data rate of SU, however, with less interference to PU andlower transmit power of SU. Therefore, the power alloca-tion (P′

S1 , P∗S2) is superior to that of the allocation (P∗

S1,P∗S2), which means that to obtain the optimal solution,

CS1 = CS2 should be satisfied, and the objective function(36) can be further rewritten as:(

P̂optS1 , P̂optS2

)= arg max

P̂S1, P̂S2(CS1 = CS2) . (37)

To obtain the optimal solution, the constraint (27a)should satisfy with equality, which can be easily provedby contradiction. The optimal equivalent power allocationfor this case should satisfy

P̂optS1 = γ P̂optS2 , (38)

where the parameter γ is denoted as γ = βα. Thus, by

substituting (38) into (27a), the optimal power can becalculated as

P̂optS2 = g (γ λS1 + λS2) (1 − 2ρ)

4γρλS1λS2

+√[

g (γλS1 + λS2)(1 − 2ρ)]2 + 16γ λS1λS2g2ρ (1 − ρ)

4γρλS1λS2(39)

and P̂optS1 can be achieved as shown in (38).

6 Power allocation for the TWT-RAmodelIn the cognitive TWT-RA network, assume that the sig-nal is severely attenuated between the two transceivers;thus, the direct link is not considered for transmission.The two-way transmission is completed with the helpof secondary relays. The TDMA protocol is used, andthe secondary transmission process is divided into threephases equally.The received signals at the ith SR during the first and

second phases can be generally expressed as

ySRi =√PSm(i)hSm−SRi xSm + √

PPThPT−SRi xp + nSRi ,

(40)

where m = 1 when S1 transmits signals and m = 2 whenS2 transmits signals. Based on (40), the SINR at the ith SRin the first and second phases can be derived as

rSm−SRi = |hSm−SRi |2PPT|hPT−SRi |2 + N0

PSm(i) . (41)

In the third phase, after the cancelation of self-interference, the received signal at Sm, (m = 1, 2) corre-sponding to ith SR can be denoted as

ySmi =√PSRi,(m)

hSRi−SmxSm + √PPThPT−Smxp + nSm,

(42)


where PSRi =2∑

m=1PSRi,(m)

is the total transmit power of SR

and PSRi,(m)is the transmit power of SR that allocates to

Sm, (m = 1, 2). The SINR of Sm can be expressed as

rSRi−Sm = |hSRi−Sm|2PPT|hPT−Sm|2 + N0

PSRi,(m). (43)

Let αSm−SRi = |hSm−SRi |2P̂PT|hPT−SRi |2+1

and αSRi−Sn =|hSRi−Sn|2

P̂PT|hPT−Sn|2+1for m, n = 1, 2 and m = n. The achievable

rate of S1 is defined as

CS1(i) = 13min

{log2

(1 + αS1−SRi P̂S1(i)

),

log2(1 + αSRi−S2P̂SRi,(1)

)}.

(44)

Similarly, we have the achievable rate for S2 as

CS2(i) = 13min

{log2

(1 + αS2−SRi P̂S2(i)

),

log2(1 + αSRi−S1P̂SRi,(2)

)}.

(45)

6.1 Equal resource allocationWith the similar analysis as the ERA schemes in theOWT-RA and TWT-DL networks, the ERA scheme in theTWT-RA network allocates powers of P̂S1, P̂S2, and P̂SRindividually, which should satisfy the outage constraint(9). A simple way is to let g

P̂S1(i) λS1+g = ρ, gP̂S2(i) λS2+g = ρ,

and gP̂SRiλSRi+g = ρ, and the equivalent transmit powers of

the ERA scheme are P̂ERAS1(i)= g(1−ρ)

ρλS1, P̂ERAS2(i)

= g(1−ρ)

ρλS2, and

P̂ERASRi= g(1−ρ)

ρλSRiwith P̂ERASRi,(1) = P̂ERASRi,(2) = 1

2 P̂ERASRi

.

6.2 Optimal power allocation scheme for data ratemaximization (DRM)

In this section, we consider the power allocation to max-imize the sum achievable rate for the cognitive TWT-RAnetworks.The sum achievable rate with respect to the ith relay is

given as

CSi,Sum = CS1(i) + CS2(i) . (46)

The optimal power allocation is to maximize the sumachievable rate CSi,Sum. It is obvious from Eqs. (44) and(45) that the achievable rate of Sm(m = 1, 2) is deter-mined by the minimal value of the two-hop links: Sm →SRi and SRi → Sn (m, n = 1, 2 and m = n).Therefore, the two links should achieve the same SINR,i.e., αSm−SRi P̂Sm(i) = αSRi−SnP̂SRi,(n)

. We have P̂SRi,(1) =β1iP̂S1(i) , P̂SRi,(2) = β2iP̂S2(i) , and P̂SRi = P̂SRi,(1) + P̂SRi,(2) =β1iP̂S1(i) + β2iP̂S2(i) , where β1i = αS1−SRi

αSRi−S2and β2i = αS2−SRi

αSRi−S1.

Based on the above analysis, the optimal power alloca-tion can be allocated by solving the following optimizationproblem

(P̂optS1(i)

, P̂optSRi, P̂optS2(i)

)= arg max

P̂S1(i) ,̂PSRi ,̂PS2(i)CSi,Sum, (47)

subject tog

P̂S1(i)λS1 + g+ g

P̂S2(i)λS2 + g+ g

P̂SRiλSRi + g≥ 3ρ,

(48a)P̂SRi = β1iP̂S1(i) + β2iP̂S2(i) . (48b)

Using the Lagrange multiplier method, the optimalpower allocation problem (47) with the constraints of(48a) and (48b) can be written as

L =2∑

m=1log2

(1 + αSm−SRi P̂Sm(i)

)+ λ1

(̂PSRi − β1iP̂S1(i) − β2iP̂S2(i)

)+ λ2

(g

P̂S1(i)λS1 + g+ g

P̂S2(i)λS2 + g

+ gP̂SRiλSRi + g

− 3ρ),

(49)

where λ1 and λ2 represent nonnegative dual variables.The Lagrange dual function can be obtained by

maxP̂S1(i) ,̂PS2(i) ,̂PSRi

L(λ1, λ2, P̂S1(i) , P̂S2(i) , P̂SRi), (50)

and the dual problem can be written as

minλ1,λ2≥0

maxP̂S1(i) ,̂PS2(i) ,̂PSRi

L(λ1, λ2, P̂S1(i) , P̂S2(i) , P̂SRi). (51)

It is noteworthy that solving a dual problem is not alwaysequivalent to solving the primal problem. It has beenproven from duality theory that the optimal duality gapd = D∗ − f ∗ ≥ 0 always holds [25], where D∗ and f ∗denote the primal and dual optimal values, respectively.The optimal duality gap d = 0 when the primal problemis convex. For the problem of our interest, the objectivefunction (47) is concave, and constraints (48a) and (48b)are convex; therefore, the primal and dual problems havethe same optimal solutions.According to [26], the dual problem in (51) can be fur-

ther decomposed into the following sequentially iterativesub-problems:Sub-problem 1—power allocation: Given the dual vari-

ables λ1 and λ2, the optimal powers that maximize (50)can be obtained by solving

∂L∂P̂S1(i)

= 0,∂L

∂P̂S2(i)

= 0, and∂L

∂P̂SRi

= 0. (52)


After direct calculation and some simplification, weobtain the equivalent powers for Sm (m ∈ {1, 2}) and SRias

P̂Sm(i) = 3

√−qm

2+

√(qm2

)2 +(pm

3

)3+ 3

√−qm

2−

√(qm2

)2 +(pm

3

)3,

(53)

P̂SRi =(

1λSRi

(

√λ2λ1

gλSRi − g))+

, (54)

where (·)+ = max(·, 0), um = 1αSm−SRi

+ 2 gλSm

−1

λmβmi, vm =

(g

λSm

)2 + 2 gαSm−SRiλSm

+ (λm−2)gλmβmiλSm

, wm =(1

αSm−SRi− 1

λmβmi

) (g

λSm

)2 + λmλm

1αSm−SRiβmi

gλSm

, pm = vm −u2m3 , qm = wm + 2u3m

27 − umvm3 , andm( = m) ∈ {1, 2}.

Sub-problem 2—dual variables update: To solve theminimization problem in (51), i.e., to find the optimal dualvariables λ1 and λ2 for the given P̂S1(i) , P̂S2(i) , and P̂SRi ,a gradient-type search is guaranteed to converge to theglobal optimum, since the dual function is always convex[24]. Here, we use a subgradient update method. The basicidea of the subgradient method is to design a step-sizesequence to update λ1 and λ2 in the subgradient direc-tion. For the problem of our interest, the update may beperformed as follows:

λ1(k + 1) = (λ1(k) − ξ1(k)J1)+, (55a)λ2(k + 1) = (λ2(k) − ξ2(k)J2)+, (55b)

where ξ1 and ξ2 denote the update step sizes for λ1 and λ2,respectively, k is the iteration index, and

J1 = P̂SRi − β1iP̂S1(i) − β2iP̂S2(i) , (56a)

J2 = gP̂S1(i)λS1 + g

+ gP̂S2(i)λS2 + g

+ gP̂SRiλSRi + g

− 3ρ.

(56b)Through the subgradient method, the powers for all

relays can be allocated.Once the power allocation is completed as described

above, the relay selection is performed to maximize thesum achievable rate, i.e.,

iopt = argmaxi

CSi,Sum. (57)

6.3 Optimal power allocation scheme for data ratefairness (DRF)

To guarantee the fairness between S1 and S2, the sumachievable rate with respect to the ith relay can be denotedas

CSi,Fair = 2 ∗ min{CS1(i) ,CS2(i)

}. (58)

We will now determine the optimal equivalent powervalues P̂S1(i) , P̂S2(i) , P̂SRi,(1) , and PSRi,(2) that lead to the fair-ness between S1 and S2, i.e., CS1(i) = CS2(i) and thenmaximize the system achievable rate CSi,Fair.In order to guarantee the primary QoS requirement,

the constraint (9) should be satisfied with equality; other-wise, the achievable rate of SU can be further improvedthrough increasing the powers at S1, S2, and SR. Also,the links of S1 → SR, SR → S2, S2 → SR, andSR → S1 should have the same SINR to guarantee fair-ness, i.e., αS1−SRi P̂S1(i) = αS2−SRi P̂S2(i) = αSRi−S2P̂SRi,(1) =αSRi−S1P̂SRi,(2) . For simplicity, define αS1−SRi

αS2−SRi= αi,

αS1−SRiαSRi−S1

=βi, and

αS1−SRiαSRi−S2

= γi, which equals to P̂S2(i) = αiP̂S1(i) ,P̂SRi,(2) = βiP̂S1(i) , P̂SRi,(1) = γiP̂S1(i) , and P̂SRi = P̂SRi,(2) +P̂SRi,(1) = (βi + γi) P̂S1(i) . By replacing P̂S2(i) and P̂SRi withP̂S1(i) into (9), the best power allocation for S1 should besatisfied with

gλS1P̂S1(i) + g

+ gαiλS2P̂S1(i) + g

+ g(βi + γi) λSRi P̂S1(i) + g

= 3ρ.

(59)

Equation (59) is the univariate cubic equation aboutP̂S1(i) which can be solved by Cardano’s formula. Oncethe best power allocation for S1 is solved, the best powerallocation for SR and S2 can also be achieved.After the optimal power is allocated for all the relays,

the relay which can maximize the sum achievable rate toguarantee the fairness is selected, i.e.,

iopt = argmaxi

CSi,Fair. (60)

7 Simulation resultsIn this section, we evaluate the performance of the pro-posed power allocation schemes through Monte-Carlosimulations and compare them with the traditional ERAschemes [18]. We assume throughout that the channelcoefficients are i.i.d. and follow Rayleigh distribution. Thefollowing parameters are used throughout this section:

γ = 4, dPT−PD = dS1−SRi = dS2−SRi = 12dS1−S2 = 1,

dS1−PD = dPT−S2 = 4, dPT−S1 = dPT−SR = dSR−PD =dS2−PD = 3, N0 = −50 dBW, and RP = 1.5 bit/s/Hz.

Figure 2a–c describes the SU achievable rate versusthe PU transmit power PPT with the PU outage thresh-old PoutPri,Thr = 10−3 for the OWT-RA, TWT-DL, andTWT-RA networks, respectively. As can be seen from thefigure, all the proposed power allocation schemes greatlyoutperform the traditional ERA schemes in the three dif-ferent networks. It is also observed that there exists acutoff point when PPT changes. The reason is that the QoSof the PU will not be guaranteed when the power PPT istoo small, and thus, there will be no chance for the sec-ondary transmissions. When PPT is higher than the cutoff


Fig. 2 SU achievable rate versus PU transmit power PPT for a thecognitive OWT-RA network, b the cognitive TWT-DL network, andc the cognitive TWT-RA network

value, the SU transmission is enabled and the achievablerate of the SU improves with the increase of PPT. AfterPPT increases further to a certain level, a performanceceiling is achieved. This phenomenon can be explained asfollows: with the increase of PPT, more interference can betolerated by the PU, hence, more transmission power canbe allowed for the SU. However, when PPT becomes largeenough, the interference from the PU becomes the dom-inant factor which will affect the performance improve-ment of the SU. Besides, in the two-way transmissionnetworks, such as the cognitive TWT-DL and TWT-RAnetworks, as shown in Fig. 2b, c, both the DRM and DRFschemes show the obvious improvement as compared tothe corresponding ERA schemes. In addition, the DRFscheme tends to provide a lower achievable rate than theDRM scheme. That is because for the DRF scheme, toguarantee the fairness, the achievable rate of the SU isdetermined by the weaker link. As for the relay-assistednetworks, such as the cognitive OWT-RA and TWT-RAnetworks, except for power allocation, the SU’s achievablerate can be further improved by relay selection for morediversity gain is provided, as shown in Fig. 2a, c.Figure 3a–c describes the SU achievable rate versus the

PU outage threshold PoutPri,Thr with PPT = 0 dBWfor the three different networks as mentioned above. Itis observed that all the proposed schemes provide bet-ter performance than the corresponding ERA schemes.With the increase of PoutPri,Thr, the SU’s achievable ratecan be improved for the reason that larger PoutPri,Thrimplies the lower QoS requirement of the PU, whichwill allow for larger transmit power at SU. The perfor-mance difference among the proposed schemes and thecorresponding ERA schemes becomes apparent with theincrease of PoutPri,Thr, which verifies the effectiveness ofour proposed schemes. Fig. 3b, c show the improvementof the proposed power allocation schemes in the two-way transmission networks (e.g., the cognitive TWT-DLand TWT-RA networks). Except for the power allocation,the effect of the relay selection is illustrated in Fig. 3a, cfor the relay-assisted networks (e.g., the cognitive OWT-RA and TWT-RA networks), which shows that with relayselection, the achievable rate of the SU can be greatlyimproved.Figure 4a–c describes the SU achievable rate versus

the distance dPT−PD between PT and PD with PU out-age threshold PoutPri,Thr = 10−3 and PPT = 0 dBWfor the three different networks as mentioned above. Wecan see from the figure that all the proposed powerallocation schemes provide better performance than thecorresponding ERA schemes. When the primary linkfrom PT to PD is in poor condition, i.e., dPT−PD islarge, the primary QoS requirement can hardly be guar-anteed; therefore, SU must suppress its powers to pro-tect PU and degrade SU’s performance as a result.


Fig. 3 SU achievable rate versus PU outage threshold PoutPri,Thr fora the cognitive OWT-RA network, b the cognitive TWT-DL network,and c the cognitive TWT-RA network

Fig. 4 SU achievable rate versus PU parameter σ 2PT−PD for a the

cognitive OWT-RA network, b the cognitive TWT-DL network, andc the cognitive TWT-RA network


With the decrease of dPT−PD, the SU’s performance canbe improved accordingly. The performance differenceamong the proposed schemes and the correspondingERA schemes becomes apparent with the decrease ofdPT−PD, which verifies the effectiveness of our proposedschemes. In addition to power allocation, the effect ofthe relay selection is illustrated in Fig. 4a, c, manifest-ing the improvement of SU’s performance through relayselection.

8 ConclusionsIn this article, we studied the problem of power allocationfor underlay cognitive networks involving three differ-ent secondary transmission models: (i) OWT-RA, (ii)TWT-DL, and (iii) TWT-RA, respectively. Since sec-ondary network is typically not coordinated with pri-mary network, the instantaneous CSI of PU can hardlybe obtained. To tackle this issue, we adopted pri-mary outage constraint to measure the QoS of pri-mary transmission, where only the statistical CSI of PUrequired. We first derived the joint primary outage con-straints due to the secondary transmission for the threetransmission models. We then proposed power alloca-tion schemes to maximize the received SINR for thecognitive one-way relay network, while in cognitive two-way scenarios, two power allocation criterions are con-sidered: (i) fairness based and (ii) sum achievable ratemaximization based, respectively. In order to furtherimprove the SU’s performance, relay selection was alsoconsidered in the relay-assisted transmission networks(e.g., OWT-RA and TWT-RA networks). The perfor-mance of the proposed schemes was illustrated for dif-ferent operating conditions and shown to yield greatenhancement compared to that of the correspondingERA schemes.

Competing interestsThe authors declare that they have no competing interests.

Authors’ contributionsPL contributed in the conception of the study and design of the study andwrote the manuscript. FS carried out the simulation and revised themanuscript. LC participated in the design of the study. GZ helped perform theanalysis with constructive discussions and helped to draft the manuscript. Allauthors read and approved the final manuscript.

AcknowledgementsThis work was supported in part by the Shandong Province High SchoolScience & Technology Fund Planning Project (J12LN02) and the Research Fundfor the Doctoral Program of Higher Education of China (20123702120016).

Author details1College of Information Science and Engineering, Shandong AgriculturalUniversity, Daizong Road No.61, 271018 Tai’an, Shandong, China.2Administration Center of Shandong Academy of Information &Communication Technology, Xinluo Street No. 1768, High-tech Zone, 250101Jinan, China.

Received: 15 September 2015 Accepted: 16 October 2015

References1. Q Zhao, BM Sadler, A survey of dynamic spectrum access. IEEE Signal

Process Mag. 24(3), 79–89 (2007)2. S Haykin, Cognitive radio: brain-empowered wireless communications.

IEEE J. Select. Areas. Commun. 23(2), 201–220 (2005)3. M Gastpar, M Vetterli, in On the capacity of wireless networks: The relay case.

INFOCOM 2002. Twenty-First Annual Joint Conference of the IEEEComputer and Communications Societies. Proceedings. IEEE, vol. 3 (IEEENew York, 2002), pp. 1577–1586

4. G Kramer, M Gastpar, P Gupta, Cooperative strategies and capacitytheorems for relay networks. IEEE Trans. Inf. Theory. 51(9), 3037–3063(2005)

5. Q Zhang, J Jia, J Zhang, Cooperative relay to improve diversity incognitive radio networks. IEEE Commun. Mag. 47(2), 111–117 (2009)

6. B Rankov, A Wittneben, Spectral efficient protocols for half-duplex fadingrelay channels. IEEE J. Select. Areas. Commun. 25(2), 379–389 (2007)

7. R Zhang, Y-C Liang, CC Chai, S Cui, Optimal beamforming for two-waymulti-antenna relay channel with analogue network coding. IEEE J. Select.Areas. Commun. 27(5), 699–712 (2009)

8. C Sun, C Yang, Energy efficiency analysis of one-way and two-way relaysystems. EURASIP J. Wirel. Commun. Netw. 2012(1), 1–18 (2012)

9. A Ghasemi, ES Sousa, Fundamental limits of spectrum-sharing in fadingenvironments. IEEE Trans. Wirel. Commun. 6(2), 649–658 (2007)

10. A Alsharoa, F Bader, M-S Alouini, Relay selection and resource allocationfor two-way df-af cognitive radio networks. IEEE Wirel. Commun. Lett.2(4), 427–430 (2013)

11. X Kang, Y-C Liang, A Nallanathan, HK Garg, R Zhang, Optimal powerallocation for fading channels in cognitive radio networks: Ergodiccapacity and outage capacity. IEEE Trans. Wirel. Commun. 8(2), 940–950(2009)

12. X Kang, R Zhang, Y-C Liang, HK Garg, Optimal power allocation strategiesfor fading cognitive radio channels with primary user outage constraint.IEEE J. Select. Areas Commun. 29(2), 374–383 (2011)

13. L Li, X Zhou, H Xu, GY Li, D Wang, A Soong, Simplified relay selection andpower allocation in cooperative cognitive radio systems. IEEE Trans. Wirel.Commun. 10(1), 33–36 (2011)

14. L Lu, Y Li, G Wu, Optimal power allocation for cr networks with direct andrelay-aided transmissions. IEEE Trans. Wirel. Commun. 12(4), 1–11 (2013)

15. M Naeem, U Pareek, DC Lee, A Anpalagan, Power allocation and relayassignment for shared-band nonregenerative relaying in cognitive radiosystems. IEEE Trans. Veh. Technol. 62(6), 2853–2859 (2013)

16. X Kang, Optimal power allocation for bi-directional cognitive radionetworks with fading channels. IEEE Wirel. Commun. Lett. 2(5), 567–570(2013)

17. P Ubaidulla, S Aissa, Optimal relay selection and power allocation forcognitive two-way relaying networks. IEEE Wirel. Commun. Lett. 1(3),225–228 (2012)

18. Y Zou, J Zhu, B Zheng, Y-D Yao, An adaptive cooperation diversityscheme with best-relay selection in cognitive radio networks. IEEE Trans.Signal Process. 58(10), 5438–5445 (2010)

19. SB Mafra, RD Souza, JL Rebelatto, EM Fernandez, H Alves, Cooperativeoverlay secondary transmissions exploiting primary retransmissions.EURASIP J. Wirel. Commun. Netw. 2013(1), 1–12 (2013)

20. P Lan, F Sun, L Chen, P Xue, J Hou, Power allocation and relay selection forcognitive relay networks with primary qos constraint. IEEE Wirel.Commun. Lett. 2(6), 583–586 (2013)

21. I Krikidis, J Thompson, JS McLaughlin, N Goertz, Amplify-and-forward withpartial relay selection. IEEE Commun. Letters. 12(4), 235–237 (2008)

22. DB Costa, S Aissa, Performance analysis of relay selection techniques withclustered fixed-gain relays. IEEE Signal Proc. Lett. 17(2), 201–204 (2010)

23. J-p Hong, B Hong, TW Ban, W Choi, On the cooperative diversity gain inunderlay cognitive radio systems. IEEE Trans. Commun. 60(1), 209–219(2012)

24. S Boyd, L Vandenberghe, Convex Optimization. (Cambridge universitypress, Cambridge, 2009)

25. DT Ngo, C Tellambura, HH Nguyen, Resource allocation for ofdma-basedcognitive radio multicast networks with primary user activityconsideration. IEEE Trans. Veh. Technol. 59(4), 1668–1679 (2010)

26. AG Marques, X Wang, GB Giannakis, Dynamic resource management forcognitive radios using limited-rate feedback. IEEE Trans. Signal Process.57(9), 3651–3666 (2009)

Documents

RESEARCH OpenAccess Optimalresourceallocationforcognitive ... · PU’s spectrum on a condition that the QoS of the pri-marytransmissionisnotaffected.Therefore,thetransmit power of