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Fang et al. EURASIP Journal onWireless Communications and Networking 2013, 2013:129http://jwcn.eurasipjournals.com/content/2013/1/129

RESEARCH Open Access

ARQ-based spectrum sharing withmultiple-access secondary systemShu Fang1*, See Ho Ting2, Qiang Li3, Ashish Pandharipande4 and Mehul Motani5

Abstract

We consider a cognitive radio network in which a multiple-access secondary system coexists with an automatic repeatrequest (ARQ)-based primary system under heavy primary traffic. To achieve spectrum sharing without degrading theperformance of the primary system, the secondary transmitters alternate between cooperation and access modesbased on a credit system. In the cooperation mode, the secondary transmitters serve as potential relays among whichthe best one is selected to help forward the primary packet, thus accumulating credits. These credits will then allowthe secondary transmitters to gain spectrum access by exploiting the ARQ mechanism of the primary system.Our results show that with a cluster of closely located secondary transmitters, the proposed spectrum sharing protocolachieves an equal average throughput for the primary system compared to the case without spectrum sharing, whileproviding access opportunities for the secondary system. Furthermore, by increasing the number of secondarytransmitters or decreasing the distance between secondary transmitters and secondary receiver, an overall higherthroughput can be achieved for the secondary system, without affecting the analytical results for the upper bounds ofprimary throughput under cooperation mode, and secondary throughput under access mode are also derived.

Keywords: Cognitive radios, Spectrum sharing, Automatic repeat request, Relay, Multiple-access

IntroductionSpectrum is a valuable resource in wireless communica-tion systems. Around the world, the frequency spectrumis tightly regulated by fixed spectrum assignment policieswhich partition the spectrum into a large number of fre-quency bands and legally limit the applications, users, andoperators within each band [1]. This leads to an undesir-able situation where some systems may not fully utilizethe allocated spectrum while others suffer from a lack ofbandwidth. Over the past decades, these challenges andrequirements have been extensively studied, giving birthto the notion of cognitive radios [2,3]. Cognitive radio isa technique that improves the utilization of the spectrumby intelligently sharing radio resources among differentusers, which is also considered in the framework of hier-archical spectrum sharing where the users with differentpriorities are allowed to operate over the same portion ofspectrum.

*Correspondence: [email protected] of National key Laboratory on Communications, University ofElectronic Science and Technology of China, Chengdu 611731, ChinaFull list of author information is available at the end of the article

With the development of cognitive radio technologies,dynamic spectrum access [4-6] becomes a promisingapproach to increase the efficiency of spectrum usage. Itallows unlicensed wireless users to dynamically access thelicensed bands allocated to legacy spectrum holders on anegotiated or an opportunistic basis. The key componentof dynamic spectrum access is dynamic spectrum sharing[7-10], which is able to provide efficient and fair spectrumallocation or scheduling solutions between the primaryand secondary users.Three approaches to spectrum sharing between primary

and secondary users have been evaluated [11]: spectruminterweave, spectrum underlay, and spectrum overlay.Spectrum interweave is the original idea of utilizing thespectrum holes left by primary system to establish sec-ondary communication links. Spectrum underlay imposesstrict constraints on the behavior of the secondary usersso that the interference caused to the primary users is lim-ited below a predefined threshold [12]. Spectrum overlaydoes not necessarily impose restrictions on the trans-mission power of secondary users, but rather on whenand where they may transmit opportunistically withoutdegrading the primary performance [13].

© 2013 Fang et al.; licensee Springer. This is an Open Access article distributed under the terms of the Creative CommonsAttribution License (http://creativecommons.org/licenses/by/2.0), which permits unrestricted use, distribution, and reproductionin any medium, provided the original work is properly cited.

Fang et al. EURASIP Journal onWireless Communications and Networking 2013, 2013:129 of 12http://jwcn.eurasipjournals.com/content/2013/1/129

According to spectrum utilization report of FCC [1],there is a large variation in spectrum usage intensity thatsome bands are heavily used, while others have light usage.When the traffic is light that results in spectrum holeswithin this band, it is better to use spectrum interweaveto allow the secondary access. Conversely, when the traf-fic is very heavy in this band, where a spectrum hole canbe hardly found, spectrum underlay and overlay are betterchoices.Cooperative diversity brought about by relay transmis-

sions can effectively combat channel fading and enhancethe throughput. It also has a great potential to be adoptedin cognitive radio networks [14-22]. Both theoretical andexperimental results demonstrate that a relay-assistedcognitive spectrum sharing protocol [16,18] is able toassist the primary system to achieve a better performanceand at the same time allows spectrum access for the sec-ondary system. In [17], multi-relay-based cognitive radionetworks were considered to improve the performanceof secondary users while ensuring the quality of servicefor primary users. Cooperative spectrum sharing proto-col with multiple secondary transmitters was studied in[18]. A two-phase spectrum sharing protocol with cooper-ative decode-and-forward relaying was proposed in [19],and a spectrum sharing protocol with two-way relayingwas proposed in [20]. Cognitive relay networks with mul-tiple primary transceivers under spectrum sharing wasconsidered in [21], where the impact of multiple primarytransmitters and receivers on the outage performance ofcognitive decode-and-forward relay networks was exam-ined. In [22], the outage probability of dual-hop cognitiveamplify-and-forward relay networks subject to Nakagami-m fading is investigated under spectrum sharing environ-ment. In [23], the author analyzed the performance ofthe secondary user in spectrum sharing cognitive relaynetworks with the primary user’s interference, where theperformance loss of the secondary user due to the primaryinterference can compensate by increase in the number ofrelays for the secondary system.Besides the above proposals for spectrum sharing

with cognitive relays, the feedback mechanism of auto-matic repeat request (ARQ)-based primary system hasalso been exploited to gain secondary spectrum access[24-29]. In [24], the secondary user is able to eavesdropon the handshaking signals of the ARQ-based primarysystem and adaptively adjust its input rate such that sec-ondary spectrum sharing is achieved, while maintainingthe target rate for the primary user. The interference thatthe secondary user causes to the primary user and howthis interference impacts the retransmission process ofthe latter were studied in [25]. In [26-29], the authorsaddressed the coexistence problem by taking advantageof the opportunities that arise during ARQ retransmis-sions of the primary system. In [26] and [27], the structure

of primary ARQ retransmissions is exploited to providenontrivial rate for the secondary user while minimizingthe impact on the primary user. In [28], the secondaryuser broadcasts a probing signal and listens to the cor-responding ACK/NACK sent from the primary receiverand then decides whether to access the spectrum. In[29], a cooperation-and-access spectrum sharing protocolwith a single secondary user is proposed where the sec-ondary user alternates between cooperation and accessmodes by exploiting the ARQ ACK/NACK mechanismof the primary system. Although the basic idea of [29]is similar with our proposed spectrum sharing protocol,there are two major differences. One is that we extendthe single secondary transmitter in [29] to multiple sec-ondary transmitters. The other is that they [29] focusedon different retransmission times while our work focuson one retransmission. When the multiple secondarytransmitters are served as potential relays to help for-ward the primary packet, the spectrum sharing protocolis much different from the case in [29] with single sec-ondary transmitter. We also derived the analytical upperbound of system throughput for primary and secondarysystem under cooperation and access mode with multi-ple secondary transmitters. Our results show that witha cluster of closely located secondary transmitter servedas potential relay to help forward the primary packet, anoverall higher throughput can be achieved for the sec-ondary system. The secondary throughput gap betweenthe scheme in [29] and our proposed scheme is given inthis paper. It was noted that even though ARQ retrans-missions may be relatively infrequent, it is still possi-ble to achieve a reasonably good performance for thesecondary user.In this paper, a relay-assisted and ARQ-based spectrum

sharing protocol was proposed where the secondary sys-tem is configured with multiple secondary transmittersand served as relay to help forward the primary packet. Asshown in Figure 1, the primary system consists of a sin-gle primary transmitter (PT) and a single primary receiver(PR). On the other hand, the secondary system consists ofmultiple secondary transmitters (ST) attempting to trans-mit to a single secondary receiver (SR). To achieve sec-ondary spectrum access without degrading the primaryperformance, the multiple secondary users will switchbetween cooperation and access modes based on a creditsystem. The proposed protocol works efficiently underheavy traffic and switches smartly between cooperationmode and access mode to achieve considerable secondarythroughput under heavy traffic mode without degradingthe primary performance. We analyze the throughput forthe primary and secondary systems and derive theoreti-cal upper bounds for primary throughput in cooperationmode and secondary throughput in access mode. Wefind the performance gap between the traditional scheme


PT

STi

STM

......

SR

PR

ST1

(Primary Transmitter) (Primary Receiver)

(Secondary Receiver) (Secondary Transmitter)

h0

h11

h1i

h1M

h21

h2i

h2Mh31

h3i

h3M

h4

Figure 1 Systemmodel for the proposed spectrum sharingprotocol with multiple-access secondary system.

without relay and the proposed scheme with multiple sec-ondary transmitters serving as potential relay. With theproposed spectrum sharing protocol, it is shown that thesecondary system is able to access the spectrum withoutdegrading the primary system performance under heavytraffic and obtain considerable secondary system through-put. With a cluster of closely located secondary transmit-ters, the secondary system throughput increases with thenumber of STs and with decreasing distance between STsand SR.

Systemmodel and protocol descriptionSystemmodelConsider a cognitive radio system with a stop-and-waitARQ-based primary system with relay functionality [30],as depicted in Figure 1. The primary system consists ofa single PT and PR. The secondary system consists of Msecondary transmitters STi where i ∈ M = 1, 2, ...,Mand a single SR as shown in Figure 1. The channelsover links PT→PR, PT→STi, STi →PR, STi →SR, andPT→SR are modeled as Rayleigh flat fading with channelcoefficients denoted by h0, h1i, h2i, h3i, and h4 respectively.We have h0 ∼ CN (0, d−v

0 ), hki ∼ CN (0, d−vki ), k =

1, 2, 3, and h4 ∼ CN (0, d−v4 ), where v is the path-loss

exponent and d0, dki, k = 1, 2, 3, and d4 are the dis-tances between the respective transmitters and receivers.In order to simplify the theoretical analysis, we assumethat the secondary transmitters are closely located andthus we have dki = dk ,∀i ∈ M, k = 1, 2, 3. Wealso denote the instantaneous channel gains for theselinks as γ0 = |h0|2, γki = |hki|2 , k = 1, 2, 3, andγ4 = |h4|2. The transmit power at PT and STi isdenoted as Pp and Ps ∀i, respectively. The target ratesfor the primary and secondary systems are denoted byRp and Rs, respectively. The variances of the additivewhite Gaussian noise at all receivers are assumed to beidentical and are denoted as σ 2.

Protocol descriptionIn cooperation mode, we quantify the improvement inprimary performance due to cooperative relaying fromthe secondary system as credits accumulated by the sec-ondary system. Each complete transmission for a pri-mary packet in cooperation mode is associated with acredit which is tracked and collected by the secondarysystem. When enough credits are accumulated by the sec-ondary system to compensate the possible performanceloss caused by secondary access, the secondary systemturns into access mode.During access mode, one of the secondary transmit-

ters is allowed to access the spectrum along with theARQ-based retransmission from PT.When the secondaryaccess is completed, the system returns to cooperationmode again to collect more credits, so on and so forth.We assume that the transmission of a primary packet

is completed within at most two slots, i.e., the maximumnumber of retransmissions is 1. The secondary systemtransmits each secondary packet only once with a best-effort mechanism. Since the primary system has heavytraffic, PT is backlogged, i.e., it always has a packet totransmit. The secondary system is also assumed to bebacklogged.The details of the proposed spectrum sharing protocol

are described below:

1. In cooperation mode. PT sends a packet to PR in thefirst time slot while PR, STi,∀i ∈ M, and SR attemptto decode this packet. The achievable rate of linkPT→PR is given by

R0 = log2(1 + Ppγ0

σ 2

). (1)

Thus, decoding at PR is successful if R0 ≥ Rp and thecorresponding outage probability of link PT→PR canbe expressed as

O0 = PrR0 < Rp = 1 − e−dv0(2Rp−1)σ2

Pp . (2)

If PR successfully decodes the packet, it sends backan ACK. Otherwise, a NACK is sent from PR.The decoding of the primary packet at STi, i ∈ M issuccessful if R1i ≥ Rp, where R1i denotes theachievable rate of link PT →STi and is given by

R1i = log2(1 + Ppγ1i

σ 2

), (3)

then the corresponding outage probability for linkPT →STi can be written as

O1i = O1 = PrR1i < RP = 1−e−dv1(2Rp−1)σ2

Pp . (4)


We defineA = R1i ≥ Rp|i ∈ M, whereArepresents the set of secondary transmitters that havesuccessfully decoded the primary packet.The secondary transmitters will listen to the ACK orNACK message sent from PR. By overhearing thesemessages, STi, i ∈ A is able to estimate the channelgains γ2i, i ∈ A. If an ACK is overheard, STi,∀i ∈ Adiscards the received primary packet, and PTproceeds to send a new packet. On the other hand, ifa NACK is overheard, each secondary transmitterSTi,∀i ∈ A starts a count-down timer with initialvalue

t2i = 1γ2i

, (5)

where 1 = σ 2

Ps(22Rp − 1

)t0 is the normalization

factor and t0 is a predetermined initial time. The STi,whose count-down timer reduces to zero first, i.e.,STp, p = argmax

i∈A[ γ2i] will broadcast a relay

confirmation message (RCM) to identify its presenceand then relay the primary packet to PR. In fact, it isthe same as selection combining for the primary user.When NACK is heard by PT, it will not retransmitthe packet immediately, but instead, it will wait for apredefined duration to see if a RCM is received fromany potential relay. When the RCM is heard by PTand all other secondary users STi,∀i ∈ A\p, PTwill delegate the retransmission packet andSTi,∀i ∈ A\p will withdraw themselves from therelay contention.The achievable rate R2i between link STi →PR isgiven by

R2i = log2(1 + Psγ2i

σ 2

). (6)

Then the corresponding outage probability for linkSTi →PR can be expressed as

O2i = O2 = PrR2i < Rp = 1−e−dv2(2Rp−1)σ2

Ps . (7)

If STp successfully relays the primary packet to PR,then PR sends back an ACK. If the relayed packet isnot successfully decoded by PR, PT will notretransmit this packet but a new packet will betransmitted as the number of retransmission islimited to one.If a NACK is overheard by STi,∀i ∈ M, and PT afterthe first transmission slot of primary packet, andnone of the secondary transmitters has successfullydecoded the primary packet, i.e., no RCM is heard byPT within a predefined duration, then PT willretransmit the primary packet in the second timeslot. If the packet cannot be decoded at PR after twoslots, an outage for primary transmission is declared.

At the same time, SR keeps track of the creditsaccumulated by secondary system as NC. Eachcomplete transmission for a primary packet incooperation mode is recorded as a credit earned bythe secondary system. The credits accumulated incooperation mode are used to earn accessopportunities for the secondary system in accessmode. When enough credits NC are collected by SR,i.e., NC ≥ NC, where NC is the threshold value, asecondary access start message (SASM) isbroadcasted by SR and the system turns into accessmode. Upon hearing that SASM is sent from SR,STi,∀i ∈ M is able to estimate the channel gainsγ3i,∀i ∈ M.

2. In access mode. When PT transmits a new packet toPR, SR tries to decode the primary packet inanticipation for interference cancelation to beperformed to retrieve the secondary packet. Theachievable rate R4 between link PT →SR is given by

R4 = log2(1 + Ppγ4

σ 2

). (8)

The outage probability for link PT→SR is given by

O4 = PrR4 < Rp = 1 − e−dv4(2Rp−1)σ2

Pp . (9)

If SR fails to decode the primary packet in the firsttransmission slot, we presume that an outage isdeclared for the secondary transmission. Then thesecondary system will operate in cooperation modefor another NC times until it is allowed to access thespectrum again.After the first transmission, an interference signal(INF) is transmitted by SR to corrupt thecorresponding ACK/NACK sent from PR. Since thefailure to receive an ACK/NACK is treated as animplicit NACK, PT retransmits the packet in thesecond transmission slot. At the same time, eachsecondary transmitter STi,∀i ∈ M now starts acount-down timer with initial value

t3i = 2γ3i

, (10)

where 2 = σ 2

Ps(22Rs − 1

)t0 is the normalization

factor. The STi, whose count-down timer reduces tozero first, i.e., STq, q = argmax

i∈M[ γ3i] will send a

secondary packet to SR together with a secondaryaccess confirmation message (SACM) to identify itspresence. All other secondary users STi,∀i ∈ M\q,upon hearing SACM, will withdraw the accesscontention. Therefore, the secondary transmitterwith the best channel gain exploits the primaryretransmission by transmitting to SR simultaneously,with interference cancelation done at SR to retrieve


the secondary packet. The achievable rate R3ibetween link STi →SR is given by

R3i = log2(1 + Psγ3i

σ 2

). (11)

Then the outage probability for link STi →SR isgiven by

O3i = O3 = PrR3i < Rs = 1 − e−dv3(2Rs−1)σ2

Ps .(12)

In access mode, the secondary packet is transmittedalong with the retransmission of the primary packet.Thus the secondary packet is successfully received atSR if R3i > Rs. The secondary packet is successfullydecoded at SR if R3i > Rs and R4 > Rp. Regardlesswhether the secondary packet is successfully decodedat SR or not, the system turns into cooperation modeand SR resets NC to zero.In access mode, since the secondary system transmitsalong with the retransmission of primary packets toachieve spectrum access, the retransmission of theprimary packets will always fail due to the stronginterference from secondary access. Therefore, thesuccessful transmission of primary packets in accessmode is dependent only on the first primarytransmission. As a result, the primary performancewill be severely degraded in access mode.

Throughput and credit analysisThroughput for conventional primary systemwithout relayFor a conventional system based on ARQ mechanism, weconsider the scenario where the packet can be transmittedat most by two transmission slots, i.e., only one retrans-mission. We have the following mutually exclusive eventsfor the transmission of a packet:

Event 1: C1 = primary packet is successfully receivedat PR in the first transmission slot.Event 2: C2 = primary packet is not successfullyreceived at PR in the first transmission slot, but theretransmission of the same packet from PT issuccessfully received at PR.Event 3: C3 = primary packet transmission fails aftertwo transmission slots.

From (2), the probability of the above events are respec-tively given by

PrC1 = 1 − O0, (13)PrC2 = O0(1 − O0), (14)PrC3 = O2

0. (15)

Thus, the throughput ηPbits is denoted as

ηPbits = RPηP, (16)

We define ηP as the average number of packets success-fully delivered per time slot. That is the ratio between howmuch of each packet that can be successfully delivered andthe number of time slots required.

ηP = PrC1 + PrC2PrC1 + 2 PrC2 + 2 PrC3 . (17)

The nominator denotes on average how much of eachpacket can be successfully delivered, and the denominatordenotes the average time slots that are consumed. There-fore, ηP is the actual throughput normalized by the bitrate. In this paper, we focus on analyzing the normalizedthroughput for convenience. Thus, the throughput for theconventional primary system is denoted as

ηP = 1 − O0. (18)

Throughput for the primary system in cooperation modeIn cooperation mode, the secondary system is alwaysready to serve as a relay for the primary system, for whichwe have the following mutually exclusive events:

Event 1: E1 = primary packet is successfully receivedat PR in the first transmission slot.Event 2: E2 = primary packet is not successfullyreceived at PR and STi,∀i ∈ M in the firsttransmission slot, PT retransmits the same packet inthe subsequent slot and it is successfully received atPR.Event 3: E3 = primary packet is not successfullyreceived at PR, but successfully received at one ormore STi, i ∈ M; thus, one ST serves as relay toforward this packet to PR in the subsequent slot andit is successfully received at PR.Event 4: E4 = primary packet transmission fails aftertwo transmission slots.

From (2) and (4), the probability for E1, E2, and E3 aregiven by

PrE1 = 1 − O0, (19)PrE2 = O0O1

M(1 − O0), (20)PrE3 = O0PSR, (21)

where the superscript SR denotes successful relaying, andPSR represents the joint probability that at least one ofthe STi, i ∈ M successfully receives the primary packetand successfully relays the packet to PR. In other words,PSR indicates the probability that k ≥ 1 secondary trans-mitters can successfully receive the primary packet fromPT. Among which, f ≥ 1 secondary transmitters cansuccessfully relay the primary packet to PR.We denote B = STi|i ∈ M,R1i > Rp,R2i > Rp,

where B is the set of secondary transmitters STi, i ∈ Msuccessfully receiving the primary packet and are able


to successfully forward the primary packet to PR in thesubsequent slot. Hence, B ⊆ A. When the first trans-mission from PT to PR fails, the secondary system selectsSTp, p ∈ A with the best channel gain p = argmax

i∈A[ γ2i] to

relay the primary packet. The joint probability PSR can beexpressed as

PSR =M∑k=1

k∑f=1

Pr|A| = k, |B| = f

=M∑k=1

k∑f=1

Pr|B| = f∣∣ |A| = kPr|A| = k,

(22)

and

Pr|B| = f∣∣ |A| = k =

(kf

)(1 − O2)

f O(k−f )2 , (23)

Pr|A| = k =(Mk

)(1 − O1)

kO(M−k)1 . (24)

Then PSR is derived as

PSR =M∑k=1

k∑f=1

(Mk

)(kf

)(1 − O2)

f O(k−f )2 (1 − O1)

kO(M−k)1 .

(25)

Thus, we have

PrE3=O0

M∑k=1

k∑f=1

(Mk

)(kf

)(1−O2)

f O(k−f )2 (1−O1)

kO(M−k)1 .

(26)

E4 represents the outage occurrence, and its probability isgiven by

PrE4 = O0O1MO0 + O0PFR, (27)

where the first term O0O1MO0 denotes the first event that

the primary packet fails in the first transmission from PTto PR and all the secondary transmitters STi,∀i ∈ M alsofail to decode the primary packet, and the retransmissionof the packet from PT to PR fails again. The second termO0PFR denotes the event that the primary packet fails atthe first transmission from PT to PR link and the super-script FR denotes failed relaying. So PFR indicates the jointprobability that k ≥ 1 secondary transmitters can success-fully receive the primary packet from PT. Among which,zero secondary transmitters can successfully relay the pri-mary packet to PR. However, at least one of the secondarytransmitter STi, i ∈ M successfully decodes the primarypacket but fails to relay it to PR, i.e., A ∈ ∅ and B ∈ ∅.Thus, PFR is also the joint probability that denotes the

secondary transmitters successfully receiving the primarypacket but failing to relay, for which we have

PFR =M∑k=1

Pr|A| = k, |B| = 0

=M∑k=1

Pr|B| = 0∣∣ |A| = kPr|A| = k.

(28)

By substituting f = 0 into (25), we have from (28)

PFR =M∑k=1

(Mk

)(1 − O1)

kO(M−k)1 O2

k . (29)

Therefore,

PrE4 = O0O1MO0+O0

M∑k=1

(Mk

)(1 − O1)

kO(M−k)1 O2

k .

(30)

The throughput for primary system under cooperationmode is thus

ηCP = PrE1 + PrE2 + PrE3PrE1 + 2 PrE2 + 2 PrE3 + 2 PrE4

= (1 − O0) + O0[O0PSR − PFR(1 − O0)

]1 + O0

.(31)

Lemma 1. An upper bound of ηCP is given by

η∗CP = lim

M→∞ ηCP

= (1 − O0) + O20

1 + O0.

(32)

Proof. Since PSR + PFR represents the probability thatat least one of the secondary transmitters successfullydecodes the primary packet,

PSR + PFR = 1 − O1M. (33)

From the binomial theorem, PFR in (29) can beexpressed as

PFR= [(1 − O1)O2 + O1]M − OM1 = (O2 − O1O2)

×[(O2−O1O2+O1)

M−1+(O2−O1O2+O1)M−2O1

+ (O2−O1O2+O1)M−3O2

1+. . .+(O2−O1O2+O1)

× OM−21 + OM−1

1

],

(34)

and

PSR = 1 − [(1 − O1)O2 + O1]M . (35)

It is clear that PSR → 1 and PFR → 0 when M → ∞;hence, the upper bound is obtained.


Throughput for primary system in access modeIn access mode, SR transmits an INF signal to corruptthe primary ACK/NACK of the first transmission, andthe failure to receive the ACK/NACK is treated as animplicit NACK. Since the secondary transmitter utilizesthe retransmission of primary packets to achieve spec-trum access, the retransmission of the primary packetswill fail due to the strong interference from secondaryaccess. Thus, whether the primary packets can be success-fully transmitted or not in access mode is determined bythe first transmission slot. There are two mutually exclu-sive events for primary system in access mode as shown inFigure 2:

Event 1: A1 = the primary packet is successfullyreceived at PR in the first transmission, but thecorresponding ACK is corrupted by SR; PT thenretransmits this packet and an ACK is received fromPR.Event 2: A2 = the primary packet is not successfullyreceived at PR in the first transmission and thecorresponding NACK is corrupted by SR; PT thenretransmits this packet but still fails due to the stronginterference from the secondary access and a NACKis received at PR, i.e., a packet loss.

Thus, the probability of the above two events are respec-tively given by

PrA1 = 1 − O0. (36)PrA2 = O0. (37)

The throughput for primary system under access modethus given by

ηAP = PrA12 PrA1 + 2 PrA2

= 1 − O02

.(38)

Credits and penaltiesFrom the above analysis, it is apparent that the through-put for the primary system decreases severely underaccess mode, but improves significantly under coopera-tion mode. The performance loss in access mode incurredby the secondary system is regarded as penalties and theperformance gain collected by the secondary system incooperationmode is regarded as credits. Thus we proposean ARQ-based spectrum sharing protocol to regulate thecredits and the penalties such that secondary spectrumaccess can be achieved without degrading the primaryperformance.In cooperation mode, ‘credits’ is defined as

C= ηCP − ηP (credits/slot) (39)

In access mode, ‘penalties’ is denoted as

P= ηP − ηAP (penalties/slot) (40)

It is apparent that the throughput for the conventional sys-tem ηP is taken as a benchmark in the definition of credits

(a)

(b)Figure 2 The ARQmechanisms in the access mode. (a) An illustration of event A1. (b) An illustration of event A2.


and penalties. For ease of exposition, we define the ratiobetween penalties and credits as

NC = PC

. (41)

To achieve spectrum sharing without degrading theperformance of the primary system, every NC (or lNC)complete transmission for a packet in cooperation modeallows one (or l) access opportunity for the secondarysystem, where l ∈ Z

+. Thus, the overall average through-put for primary system in the proposed spectrum sharingprotocol is given by

ηTP = ηCPNC

NC + 1+ ηAP

1NC + 1

. (42)

Throughput for secondary system in access modeFor the secondary system, if the primary packet is suc-cessfully received at SR in the first transmission, theinterference from PT’s retransmission can be perfectlycanceled out at SR. Otherwise, we assume that the sec-ondary packet fails to be received at SR due to the inter-ference from the primary retransmission. Thus in accessmode, there are three mutually exclusive events for thesecondary system:

Event 1: S1 = the primary packet is successfullyreceived at SR in the first transmission slot, and thesecondary packet is also successfully received at SR inthe second transmission slotEvent 2: S2 = the primary packet is successfullyreceived at SR in the first transmission slot, but thesecondary packet fails to be received at SR in thesecond transmission slotEvent 3: S3 = the primary packet failed to be receivedat SR in the first transmission slot

Thus, the probability of the above three events can bederived as

PrS1 = (1 − O4)(1 − O3

M), (43)

PrS2 = (1 − O4)O3M, (44)

PrS3 = O4. (45)

The throughput for the secondary system under accessmode is thus given by

ηS = PrS12 PrS1 + 2 PrS2 + 2 PrS3

= (1 − O4)(1 − O3

M)2

.

(46)

Lemma 2. An upper bound of the secondary throughputunder access mode with an increasing M is given by

η∗S = lim

M→∞ ηS

= 1 − O42

.(47)

Proof. It is clear that O3M → 0 when M → ∞; hence,

the upper bound is obtained.

Through the proposed credit system, the secondarysystem switches between cooperation and access modes,according to the accumulated credits, continuously. Thus,the overall average throughput for secondary system in theproposed spectrum sharing protocol is given by

ηTS = 1NC + 1

ηS. (48)

Lemma 3. An upper bound of the overall averagethroughput for secondary system with an increasing M isgiven by

η∗TS = lim

M→∞ ηTS

= 1 − O4

2(NC + 1).

(49)

Simulation resultsIn this section, we show the theoretical and simulationresults for the throughput of the primary and secondarysystems in the proposed spectrum sharing protocol. Thetheoretical results are according to the previous analysis,and the simulation results are according to the simu-lated transmission cases. For ease of exposition, as shownin Figure 1, we assume that the distance is the normal-ized distance, which is done with respect to the distancebetween PT and PR, i.e., d0 = 1, dki = 0.5 (k = 1, 2),d4 = 0.5, and the path-loss exponent v = 4.We let the tar-get rates Rp = Rs = 1 and the transmit powers Pp = Ps.We use markers to denote the simulation results and linesto denote the analytical results.Figure 3 shows the throughput for primary system in

cooperation mode under different values M. When M =1, the results are identical with the spectrum sharingprotocol in [29] with one retransmission of the primarysystem. The upper bound for primary throughput is alsoplotted when M → ∞. It is apparent that the theo-retical results agree well with the simulation results. Wecan see that the primary throughput in cooperation modeηCP is always higher than that in the conventional pri-mary system ηP; thus, credits can be accumulated bythe secondary system in cooperation mode. In the lowSNR region, the primary throughput in cooperation modeηCP improves significantly with an increasing number


Figure 3 Theoretical and simulation results for the primary throughput in cooperation mode ηCP and access mode ηTP .

of M due to the cooperation from the secondary sys-tem. On the other hand, in high SNR region, since theoutage probability of the direct primary link PT→PR islow, opportunities for cooperation from secondary systemdecreases, thus increasing M will not improve the perfor-mance significantly in the high SNR region. We can also

observe that withM = 10, the primary throughput undercooperation mode ηCP is very close to the upper boundη∗CP

whenM → ∞.As shown in Figure 3, the primary system throughput in

cooperation mode hits a plateau at about 0.5 in low SNRregion and approaches 1 in the high SNR region. This is

Figure 4 Theoretical and simulation results of the secondary throughput in access mode ηS with different values ofM.


Figure 5 The ratio between penalties and credits log10NC under different values of PS/σ 2.

because in the low SNR region, the direct link PT→PR isweak and withM → ∞ secondary transmitters, the prob-ability that the primary packet is successfully relayed bysecondary users after two slots approaches 1. On the otherhand, in the high SNR region, the direct link PT→PR is so

strong that the primary packet is always successfully deliv-ered after the first transmission. Thus, the improvementdue to cooperation from secondary users is negligible. It isalso observed that the primary throughput in access modeηAP degrades severely because of the secondary access.

Figure 6 Theoretical and simulation results of the overall secondary throughput ηTS with different values ofM.


However, with the proposed ARQ-based spectrum shar-ing protocol, it is apparent that the same overall averagethroughput ηTP = ηP is achieved for the primary sys-tem compared to the case without relay, while providingsecondary spectrum access.Figure 4 shows the throughput for secondary system in

access mode ηS under different SNR values PS/σ 2. We letM = 1, 2, 5, 10,∞ and d3i = 1, 0.5 respectively. It canbe observed that the secondary throughput in the accessmode increases with an increasing M and a decreasingd3i. This is because on one hand, the probability of suc-cessfully receiving the secondary packet at SR improvessignificantly with the increasing M. On the other hand,with the decrease of d3i, the probability of successfultransmission from secondary transmitter to secondaryreceiver also increases. It is also observed that the sec-ondary throughput in access mode approaches the upperbound η∗

S, when d3i is decreased from 1 to 0.5 and M =10. A throughput floor of 0.5 appears in the high SNRregion for secondary system; this is because both the out-age probability of link PT→SR and STi →SR approach 0in the high SNR region indicate that the probability of suc-cessfully decoding the secondary packet in access modeapproaches 1. Therefore, in high SNR region, the through-put floor for secondary system in access mode is 0.5 due tothe two transmissions.Figure 5 shows the ratio log10(NC) under different SNR

values PS/σ 2 in the proposed spectrum sharing protocol.When NC is lower, the access frequency for secondarysystem, i.e., 1/(NC + 1) is higher. From Figure 5 we canobserve that in low SNR region, where ratio NC → 0,the secondary transmitters are able to operate in accessmode for most of the time as 1/(NC + 1) → 1, withoutdegrading the primary performance. On the other hand,in high SNR region where NC 1, the secondary trans-mitters have to operate in cooperation mode for most ofthe time, i.e., NC/(NC + 1) → 1, before they are allowedto switch to access mode.We also observe that an increasein M will cause a decrease in NC. This is because byincreasing M, the primary throughput gain in coopera-tion mode increases. Thus, in order to achieve the sameprimary throughput as in the case without relay, the oper-ating time in access mode can be increased by increasingM. However, as shown in Figure 5, when the SNR ishigh, increasing M will not affect the value of NC signifi-cantly, which validates the observation in Figure 3 wherethe credits due to cooperation from secondary users arenegligible in high SNR region.In Figure 6, we show the overall average throughput for

secondary system ηTS under different PS/σ 2. We observethat ηTS increases with an increasing M. This is becausewith an increase in M, the secondary system collectsmore credits and hence gains more chances to access thespectrum. Furthermore, with an increasing M, a lower

outage probability for link STi →SR can be achieved. Apeak value of the overall average secondary throughputmax(ηTS) for secondary system is achieved inmodest SNRvalues, e.g., around 0 dB for d3i = 1 and around −5 dBfor d3i = 0.5. This is because in the low SNR region,although ST is able to operate for a higher fraction of time1/(NC + 1) in access mode, the corresponding ηS is small.On the other hand, in high SNR region, although a highersecondary throughput ηS is achieved in access mode, thesecondary system has to spendmost of the time in cooper-ationmode.When the distance of STi →SR decreases, thecorresponding max(ηTS) occurs in the lower SNR region.This is because with smaller d3i, the required SNR toachieve the same ηS is lower. At the same time, the accessfraction 1/(NC+1) is larger in lower SNR region than thatin higher SNR.

ConclusionsWe presented an ARQ-based spectrum sharing protocolto achieve spectrum access for multiple secondary trans-mitters coexisting with a primary system. Upon establish-ing a credit system, the secondary transmitters alternatebetween relaying for the primary system and accessing thespectrum for their own use. Credits can be accumulatedby secondary transmitters in cooperation mode, whichin return allow the secondary system to gain spectrumaccess in access mode. Our results show that the pro-posed protocol can achieve secondary spectrum accesswithout degrading the performance of the primary systemcompared to the conventional system without relays. Fur-thermore, the throughput for secondary system improvesas the number of secondary transmitters increases.

Competing interestsThe authors declare that they have no competing interests.

AcknowledgementsThis work is supported by the Singapore Ministry of Education AcademicResearch Fund Tier 2, MOE2009-T2-2-059 and the Fundamental ResearchFunds for the Central Universities of China, ZYGX2012Z004.

Author details1Department of National key Laboratory on Communications, University ofElectronic Science and Technology of China, Chengdu 611731, China. 2Schoolof Electrical and Electronic Engineering, Nanyang Technological University,639801, Singapore. 3Department of Electronics and Information EngineeringHuazhong University of Science and Technology, 1037 Luoyu Road, Wuhan,China. 4Philips Research, High Tech Campus, Eindhoven 5656 AE, TheNetherlands. 5Department of Electrical and Computer Engineering, NationalUniversity of Singapore, 117576, Singapore.

Received: 2 December 2012 Accepted: 18 April 2013Published: 13 May 2013

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doi:10.1186/1687-1499-2013-129Cite this article as: Fang et al.: ARQ-based spectrum sharing with multiple-access secondary system. EURASIP Journal on Wireless Communications andNetworking 2013 2013:129.

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