Cooperative Cognitive Radio Protocol ExploitingPrimary Retransmissions in Nakagami-𝑚 Fading

Samuel Baraldi Mafra, Evelio M. G. FernandezFederal University of Parana (UFPR)

Curitiba-PR, Brazilmafrasamuel@gmail.com, evelio@eletrica.ufpr.br

Richard Demo Souza, Joao Luiz RebelattoFederal University of Technology-Parana (UTFPR)

Curitiba-PR, Brazil{richard, jlrebelatto}@utfpr.edu.br

Abstract—We consider a cooperative overlay cognitive net-work, where the secondary exploits the primary retransmissions.We show that by using cooperation, the secondary rate canbe considerably increased when compared to other schemes,without causing major impact on the primary performance. Thebest configuration for the proposed scheme is that in which thesecondary nodes are close to the primary transmitter.

I. INTRODUCTION

The term cognitive radio was introduced by Mitola [1] in1999 to designate intelligent communication networks, whichcan learn about the surrounding environment and are adaptableto changes. Furthermore, Haykin [2] defined cognitive radioas an intelligent wireless communication system able to adaptcertain parameters (such as transmit-power, carrier-frequency,etc) with two main goals: highly reliable communications andefficient utilization of the radio spectrum.

Cognitive radio network can be divided into interweave,underlay, and overlay protocols [3], [4]. In the interweaveprotocol, the unlicensed users (also referred as secondaryusers) monitor the radio spectrum and communicate overspectrum holes without causing interference to the licensedusers (primary users). In the underlay protocol, the secondaryusers are allowed to transmit simultaneously to the primaryusers whereas the interference they cause is below a giventhreshold. Thus, the secondary transmitter power is limitedby the interference level accepted by the primary user. In theoverlay protocol (the one with the best performance, as shownin [4]), the secondary users know, a priori, the primary usermessage. With this knowledge and using advanced commu-nication techniques, the secondary can transmit concurrentlywith the primary.

In [5], Tannious and Nosratinia proposed an overlay proto-col where the secondary exploits the primary retransmissions.In many cases, there is an excess of mutual information aftera retransmission with respect to the minimum mutual infor-mation required to correctly decode the message, such that theprimary link can tolerate a certain amount of interference with-out losing performance. Nevertheless, it is still possible thatthe secondary communication interferes on the primary abovean acceptable threshold. In [5], the authors proposed a solutionto eliminate the excess secondary interference on the primary,which requires the knowledge of all the channels (secondary-secondary, secondary-primary and primary-primary) by the

secondary transmitter. Note that this global channel knowledgeis much difficult to achieve in practice. In [6], it is considered asimilar scenario, but assuming that the nodes in the secondarynetwork are provided with multiple antennas, which enables toconsiderably decrease the interference on the primary, withoutthe need of global channel knowledge. However, this strategymay not be applied in situations where the size or cost of thedevices limit the installation of multiple antennas.

An alternative to multiple antennas is to consider coop-erative communications [7]–[9], where one or more nodeshelp the communication between source and destination byacting as relays, achieving spatial diversity even in a networkcomposed of single antenna devices. In [7], Laneman et alpresented two cooperative communications protocols: amplify-and-forward (AF) and decode-and-forward (DF). In the AFprotocol, the relay amplifies the received signal and forwardsit to the destination. In the DF protocol, the relay tries todecode the source message and then re-encodes and forwardsit to the destination. The DF protocol can be divided intothe fixed DF (FDF), selective DF (SDF) and incrementalDF (IDF) protocols. In the FDF protocol, the relay alwaysforwards the message to the destination. In the SDF protocolthe message is forwarded only if its decoding at the relaywas successful. Finally, in the IDF protocol (which requires afeedback channel), similarly to the SDF protocol, the messagealso needs to be correct decoded by the relay, however, theforwarding occurs only when requested by the destination.

In this paper, we consider the same scenario as in [5], [6],but with a cooperative secondary network, operating accordingto the SDF and IDF protocols. Our main objective is toincrease the secondary rate, without significantly harming theperformance of the primary, and without requiring global chan-nel knowledge nor the use of multiple antennas. We presentthe outage probability and throughput of the proposed scheme,and show through numerical results that the use of cooperationin the secondary network can increase its throughput withoutconsiderably harming the primary performance.

The remainder of this paper is organized as follows. Sec-tion II describes the system model and the proposed protocol,whose outage probability and throughput are presented inSection III. Section IV presents some numerical results, whileSection V concludes the paper.

978-1-4673-0762-8/12/$31.00 ©2012 IEEE 771

II. SYSTEM MODEL

We consider a primary network composed of a transmitter𝑇𝑝 and a destination 𝐷𝑝. The secondary network consist of asecondary transmitter 𝑇𝑠, a relay 𝑅𝑠 and a secondary destina-tion 𝐷𝑠, as depicted in Fig. 1. The channel coefficient betweentransmitter 𝑖 and receiver 𝑗 is denoted by ℎ𝑖𝑗 and follows aNakagami-𝑚 distribution1 [10] with fading parameter 𝑚𝑖𝑗 andaverage power 𝜆𝑖𝑗 . In our notation 𝑖, 𝑗 ∈ {𝑝, 𝑠, 𝑟}, where 𝑝represents the primary transmitter or receiver, 𝑠 the secondarytransmitter or receiver and 𝑟 the relay. The average power isdefined as 𝜆𝑖𝑗 =

1(𝑑𝑛𝑖𝑗)𝛼

, where 𝑑𝑛𝑖𝑗 =𝑑𝑖𝑗

𝑑𝑝𝑝is the normalized

distance between the transmitter 𝑖 and the receiver 𝑗 withrespect to the distance between 𝑇𝑝 and 𝐷𝑝 (𝑑𝑝𝑝), and 𝛼 isthe path-loss exponent. The secondary network operates at thesame frequency band and time slot allocated to the primarynetwork.

𝑇𝑝𝐷𝑝

𝐷𝑠 𝑅𝑠 𝑇𝑠

Fig. 1. System model with a primary transmitter 𝑇𝑝, primary receiver 𝐷𝑝,secondary transmitter 𝑇𝑠, relay 𝑅𝑠 and secondary receiver 𝐷𝑠.

The received signal at node 𝑗 is given by

𝑦𝑖𝑗 =√

𝑃𝑖ℎ𝑖𝑗𝑥𝑖 + 𝑧𝑗 , (1)

where 𝑃𝑖 is the transmit power, 𝑥𝑖 is the transmitted messageand 𝑧𝑗 is additive white Gaussian noise with variance 𝑁0

2per dimension, where 𝑁0 is the noise power spectral densityassumed to be 𝑁0 = 1.

The outage probability is the probability that a failureoccurs in the communication between nodes 𝑖 and 𝑗 [11].Moreover, an outage can be defined as the event that themutual information is lower than the attempted rate ℛ𝑘,where 𝑘 ∈ {𝑝, 𝑠}. Assuming a unitary bandwidth, the outageprobability is given by [7]:

𝒫𝑜𝑢𝑡 = 𝒫{log2(1 + ∣ℎ𝑖𝑗 ∣2𝑃𝑖) < ℛ𝑘}, (2)

where 𝒫{𝑎} is the probability of event 𝑎. The expectedthroughput 𝒯𝑘 is the rate of error-free information transfer:

𝒯𝑘 = ℛ𝑘(1− 𝒫𝑜𝑢𝑡). (3)

1The Nakagami-𝑚 distribution is a general distribution, that fits severaltypes of fading. The Rayleigh distribution, for example, corresponds to 𝑚 =1. For 𝑚 > 1 there is some line-of-sight between the transmitter and receiver.

A. Proposed Protocol

The proposed protocol works as follows.

∙ 𝑇𝑝 broadcasts a packet, which can be received by both 𝐷𝑝

and 𝐷𝑠, due to the broadcast nature of the wireless chan-nel. If 𝐷𝑝 successfully decodes such a packet, a positiveacknowledgment (ACK) is broadcasted back, allowing 𝑇𝑝

to send a new packet. However, if 𝐷𝑝 does not receivethe packet correctly, a negative acknowledgment (NACK)is sent back, requesting a retransmission.

∙ Upon hearing a NACK, 𝐷𝑠 verifies if it could decodethe packet broadcasted by 𝑇𝑝. If yes, then 𝐷𝑠 sendsa “clear to send” (CTS) to 𝑇𝑠, enabling the secondarytransmission.

∙ The secondary communication occurs in two steps2: Inthe first step, upon receiving a CTS, 𝑇𝑠 broadcasts itsmessage to 𝑅𝑠 and 𝐷𝑠. In the second step, 𝑅𝑠 forwardssuch a message to 𝐷𝑠. If 𝑅𝑠 does not decode the messagefrom 𝑇𝑝 or 𝑇𝑠, it does not cooperate. Note that both𝑅𝑠 and 𝐷𝑠 can eliminate the primary interference onreceiving the packet transmitted by 𝑇𝑝.

∙ Both receivers decode their corresponding messages.

III. OUTAGE PROBABILITY AND THROUGHPUT

In this section we determine the outage probability andthroughput for three different situations: First we consider anetwork where the secondary network is inactive; then weanalyze the performance of primary and secondary links whenthe proposed cooperative secondary network is active; andfinally we present the performance of the secondary network inthe case of a non-cooperative secondary network, as proposedin [5].

A. Inactive Secondary Network

Defining 𝒫{𝑂𝑖𝑛𝑖} as the outage probability of the initialtransmission of the primary user, then [12], [13]:

𝒫{𝑂𝑖𝑛𝑖} = 𝒫{log2(1 + ∣ℎ𝑝𝑝∣2𝑃𝑝) < ℛ𝑝}

=Ψ(𝑚𝑝𝑝,

(𝑚𝑝𝑝(2(ℛ𝑝)−1))

(𝜆𝑝𝑝𝑃𝑝)

)Γ(𝑚𝑝𝑝)

, (4)

where 𝜆𝑝𝑝 denotes the average energy of channel ℎ𝑝𝑝,𝑚𝑝𝑝 is the associated Nakagami parameter and 𝑃𝑝 isthe transmit power of the primary. Moreover, Ψ(𝑎, 𝑏) =∫ 𝑏

0𝑦𝑎−1 exp (−𝑦)𝑑𝑦 is the incomplete gamma function and

Γ(𝑎) =∫∞0

𝑦𝑎−1 exp (−𝑦)𝑑𝑦 is the complete Gamma func-tion.

Considering that only one retransmission is allowed, anoutage occurs in the primary network when the accumulatedmutual information after two transmissions (the transmissionplus the retransmission) is lower than the attempted rate ℛ𝑝.We assume that the primary link employs an incrementalredundancy (IR) strategy and that the channels remain constant

2The communications of the secondary transmitter and relay must occurduring the interval of the primary retransmission.

772

during the two transmissions. The outage probability of theprimary after a retransmission is then given by

𝒫{𝑂𝑟𝑒𝑓} = 𝒫{2 log2(1 + ∣ℎ𝑝𝑝∣2𝑃𝑝) < ℛ𝑝}

=

Ψ

(𝑚𝑝𝑝,

(𝑚𝑝𝑝(2

(ℛ𝑝2

)−1))

(𝜆𝑝𝑝𝑃𝑝)

)Γ(𝑚𝑝𝑝)

. (5)

The expected throughput 𝒯𝑟𝑒𝑓 depends on whether thesuccessfully received packets required retransmission or not,that is

𝒯𝑟𝑒𝑓 = ℛ𝑝𝒫{𝑂𝑖𝑛𝑖}+ ℛ𝑝

2𝒫{𝑂𝑟𝑒𝑓 , 𝑂𝑖𝑛𝑖}

= ℛ𝑝𝒫{𝑂𝑖𝑛𝑖}+ ℛ𝑝

2𝒫{𝑂𝑖𝑛𝑖}𝒫{𝑂𝑟𝑒𝑓 ∣𝑂𝑖𝑛𝑖}

= ℛ𝑝𝒫{𝑂𝑖𝑛𝑖}+ ℛ𝑝

2𝒫{𝑂𝑖𝑛𝑖} ⋅

(1− 𝒫{𝑂𝑟𝑒𝑓}

𝒫{𝑂𝑖𝑛𝑖}), (6)

where 𝒫{𝑎} = 1 − 𝒫{𝑎}. Moreover, in (6) we used the factthat:

𝒫{𝑂𝑟𝑒𝑓 ∣𝑂𝑖𝑛𝑖} = 1− 𝒫{𝑂𝑟𝑒𝑓 ∣𝑂𝑖𝑛𝑖}= 1− 𝒫{𝑂𝑖𝑛𝑖∣𝑂𝑟𝑒𝑓}𝒫{𝑂𝑟𝑒𝑓}

𝒫{𝑂𝑖𝑛𝑖}= 1− 𝒫{𝑂𝑟𝑒𝑓}

𝒫{𝑂𝑖𝑛𝑖} . (7)

B. Proposed Cooperative Secondary Network

In this case, it is necessary to analyze the overall systemperformance when the cooperative secondary network is ac-tive. First, consider the probability that the secondary receiveris not able to decode the primary message:

𝒫{𝑂𝑝𝑠} = 𝒫{log2(1 + ∣ℎ𝑝𝑠∣2𝑃𝑝) < ℛ𝑝}. (8)

Defining 𝒫{𝑈𝑑} as the probability that the secondary isactive (i. e. the initial transmission of the primary failed andthe secondary receiver decoded the primary message), then:

𝒫{𝑈𝑑} = 𝒫{𝑂𝑖𝑛𝑖} ⋅ (1− 𝒫{𝑂𝑝𝑠}). (9)

The outage probability of the primary in the presence ofsecondary 𝒫{𝑂𝑝} can then be written as:

𝒫{𝑂𝑝} = 𝒫{𝑂𝑝∣𝑈𝑑} ⋅ 𝒫{𝑈𝑑}︸ ︷︷ ︸(𝐴)

+𝒫{𝑂𝑝∣𝑈𝑑} ⋅ 𝒫{𝑈𝑑}︸ ︷︷ ︸(𝐵)

, (10)

where term (A) is the probability that an outage occurred inthe primary link and that the secondary correctly decoded theprimary message, while in (B) the primary link is in outageand the secondary could not decode the primary message.Moreover, the term (A) in (10) can be written as:

𝒫{𝑂𝑝∣𝑈𝑑}𝒫{𝑈𝑑} = 𝒫{𝑂𝑝∣𝑂𝑖𝑛𝑖, 𝑂𝑝𝑠}𝒫{𝑂𝑖𝑛𝑖, 𝑂𝑝𝑠}= 𝒫{𝑂𝑝}𝒫{𝑂𝑖𝑛𝑖∣𝑂𝑝}𝒫{𝑂𝑝𝑠∣𝑂𝑝}. (11)

Since the occurrence of an outage in the first transmission isa necessary requirement in order to an outage in the primarylink occurs after the retransmission, we can rewrite (11) as:

𝒫{𝑂𝑝∣𝑈𝑑}𝒫{𝑈𝑑} = 𝒫{𝑂𝑝}𝒫{𝑂𝑝𝑠∣𝑂𝑝}= 𝒫{𝑂𝑝∣𝑂𝑝𝑠}𝒫{𝑂𝑝𝑠}, (12)

where the first term is the probability that the mutual infor-mation of the primary link after the first transmission plus themutual information of the retransmission (in the presence ofinterference from 𝑇𝑠) is less than the attempted rate ℛ𝑝.

The term (B) in (10) can be rewritten as:

𝒫{𝑂𝑝∣𝑈𝑑}𝒫{𝑈𝑑} = 𝒫{𝑂𝑝, 𝑈𝑑}

= 𝒫{𝑂𝑝, 𝑂𝑖𝑛𝑖, 𝑂𝑝𝑠}= 𝒫{2 log2(1 + ∣ℎ𝑝𝑝∣2𝑃𝑝) < ℛ𝑝}⋅ 𝒫{log2(1 + ∣ℎ𝑝𝑠∣2𝑃𝑝) < ℛ𝑝}. (13)

Thus, we can write the throughput of the primary in thepresence of the secondary as:

𝒯𝑝 = ℛ𝑝𝒫{𝑂𝑖𝑛𝑖}+ ℛ𝑝

2𝒫{𝑂𝑝∣𝑂𝑖𝑛𝑖}

= ℛ𝑝𝒫{𝑂𝑖𝑛𝑖}+ ℛ𝑝

2𝒫{𝑂𝑝∣𝑂𝑖𝑛𝑖, 𝑂𝑝𝑠} ⋅ 𝒫{𝑂𝑝𝑠}

+ℛ𝑝

2𝒫{𝑂𝑝∣𝑂𝑖𝑛𝑖, 𝑂𝑝𝑠} ⋅ 𝒫{𝑂𝑝𝑠}

= ℛ𝑝 ⋅ (1− 𝒫{𝑂𝑖𝑛𝑖})+

ℛ𝑝

2

(𝒫{log2(1 + ∣ℎ𝑝𝑝∣2𝑃𝑝) < ℛ𝑝 ≤ (log2(1 + ∣ℎ𝑝𝑝∣2𝑃𝑝)

+1

2log2

(1 +

∣ℎ𝑝𝑝∣2𝑃𝑝

1 + ∣ℎ𝑠𝑝∣2𝑃𝑠

)+

1

2log2

(1 +

∣ℎ𝑝𝑝∣2𝑃𝑝

1 + ∣ℎ𝑟𝑝∣2𝑃𝑟

)})

⋅ 𝒫{log2(1 + ∣ℎ𝑝𝑠∣2𝑃𝑝) ≥ ℛ𝑝} )

+ℛ𝑝

2(𝒫{log2(1 + ∣ℎ𝑝𝑝∣2𝑃𝑝) < ℛ𝑝 ≤ 2 log2(1 + ∣ℎ𝑝𝑝∣2𝑃𝑝)}

⋅ 𝒫{log2(1 + ∣ℎ𝑝𝑠∣2𝑃𝑝) < ℛ𝑝}), (14)

where 𝑃𝑠 corresponds to the transmission power of 𝑇𝑠.The first term in (14) represents the case where the first

primary transmission was successful; the second term corre-sponds to the case where a retransmission is requested and𝐷𝑠 correctly decoded the primary message; the third termrepresents the case where a retransmission is requested but 𝐷𝑠

has failed to decode the primary message. We can see from(14) that the secondary network only causes interference on𝐷𝑝 when a retransmission occurs, and if the primary messagewas correctly decoded by 𝐷𝑠

3.Let 𝒫{𝑂𝑠𝑠} and 𝒫{𝑂𝑠𝑟} be the outage probabilities of the

𝑇𝑠 → 𝐷𝑠 and 𝑇𝑠 → 𝑅𝑠 links, respectively, then:

𝒫{𝑂𝑠𝑠} = 𝒫{log2(1 + ∣ℎ𝑠𝑠∣2𝑃𝑠) < ℛ𝑠}, (15)

𝒫{𝑂𝑠𝑟} = 𝒫{log2(1 + ∣ℎ𝑠𝑟∣2𝑃𝑠) < ℛ𝑠}. (16)

In order for the relay 𝑅𝑠 to cooperate, the occurrence ofthree events is necessary: 1) 𝐷𝑠 needs to decode the messagefrom 𝑇𝑝; 2) 𝑅𝑠 also needs to correctly receive the message

3In order to simplify the derivation, we consider that 𝑑𝑠𝑝 ≈ 𝑑𝑟𝑝.

773

from 𝑇𝑝; 3) 𝑅𝑠 has to receive the message transmitted by𝑇𝑠. Defining as 𝒫{𝑂𝑝𝑟} the probability that the relay has notdecoded the primary message and as 𝒫{𝑈𝑟} the probabilitythat the secondary link is active and that the relay has decodedboth the primary and the secondary messages, then:

𝒫{𝑂𝑝𝑟} = 𝒫{log2(1 + ∣ℎ𝑝𝑟∣2𝑃𝑝) < ℛ𝑝}, (17)

𝒫{𝑈𝑟} = 𝒫{𝑈𝑑} ⋅ [(1− 𝒫{𝑂𝑝𝑟}) ⋅ (1− 𝒫{𝑂𝑠𝑟})]. (18)

The outage probability in the link from 𝐷𝑠 to 𝑅𝑠 is:

𝒫{𝑂𝑟𝑠} = 𝒫{log2(1 + ∣ℎ𝑟𝑠∣2𝑃𝑠) < ℛ𝑠}. (19)

Considering a SDF-based cooperative scheme, the through-put of the secondary becomes4:

𝒯 𝑆𝐷𝐹𝑐𝑜𝑜𝑝 =

ℛ𝑠

2⋅ 𝒫{𝑈𝑑} ⋅ (1− 𝒫{𝑂𝑠𝑠})

+ℛ𝑠

2⋅ 𝒫{𝑈𝑟} ⋅ (1− 𝒫{𝑂𝑟𝑠}) ⋅ 𝒫{𝑂𝑠𝑠}, (20)

For a IDF-based cooperative scheme, the throughput is

𝒯 𝐼𝐷𝐹𝑐𝑜𝑜𝑝 = ℛ𝑠 ⋅ 𝒫{𝑈𝑑} ⋅ (1− 𝒫{𝑂𝑠𝑠})

+ℛ𝑠

2⋅ 𝒫{𝑈𝑟} ⋅ (1− 𝒫{𝑂𝑟𝑠}) ⋅ 𝒫{𝑂𝑠𝑠}. (21)

In both (20) and (21), the first term refers to the case where𝐷𝑠 decodes the message from 𝑇𝑠, while the second term refersto the case where 𝐷𝑠 does not decode the message from 𝑇𝑠

but does decode the message from the relay 𝑅𝑠. In the firstterm of (21), the expected rate is ℛ𝑠 instead of ℛ𝑠

2 due tothe fact that, in the IDF scheme, if 𝐷𝑠 is able to decode themessage transmitted by 𝑇𝑠 (situation informed via an ACKsignal to both the 𝑇𝑠 and the relay 𝑅𝑠), then 𝑇𝑠 is allowedto send a new message in the next slot, remaining the relaysilent. In this way, the IDF-based protocol can achieve twicethe throughput of the SDF-based scheme [7].

C. Non-cooperative Secondary Network

When the secondary network is non-cooperative, as pro-posed in [5], the outage probability of the secondary link𝒫{𝑂𝑠} becomes

𝒫{𝑂𝑠} = 1− (𝒫{𝑈𝑑} ⋅ 𝒫{log2(1+ ∣ℎ𝑠𝑠∣2𝑃𝑠) ≥ ℛ𝑠}), (22)

leading to a throughput given by

𝒯𝑠 = ℛ𝑠(1− 𝒫{𝑂𝑠}). (23)

4𝐷𝑠 applies selection combining with the messages received from 𝑇𝑠 and𝑅𝑠, so that an outage occurs only if the 𝑇𝑠 → 𝐷𝑠 and 𝑅𝑠 → 𝐷𝑠 links arein outage simultaneously.

−15 −10 −5 0 50

0.5

1

1.5

2

2.5

Ps (dB)

Thr

ough

put (

bpcu

)

Primary with secondary NLOS − blue

Coop.secondaryNLOS

Non−coop. secondaryNLOS

Primary withoutsecondary

SDF protocol − greenIDF protocol − blue

Fig. 2. Throughput versus 𝑃𝑠, for ℛ𝑝 = 4 bpcu, ℛ𝑠 = 4 bpcu, 𝑃𝑝 = 10dB, 𝜆𝑝𝑝 = 𝜆𝑠𝑝 = 𝜆𝑟𝑝 = 1, 𝜆𝑝𝑠 = 𝜆𝑝𝑟 = 𝜆𝑠𝑠 = 24, 𝜆𝑠𝑟 = 𝜆𝑟𝑠 = 44,considering the NLOS scenario.

IV. NUMERICAL RESULTS

This section presents some numerical results in order to in-vestigate the performance of the proposed cooperative scheme.It is considered a path-loss coefficient 𝛼=4. We also considerthat 𝑑𝑠𝑝≈𝑑𝑟𝑝, 𝑑𝑝𝑠≈𝑑𝑝𝑟 and 𝑑𝑠𝑟=𝑑𝑠𝑠/2 (relay is positionedexactly halfway between 𝑇𝑠 and 𝐷𝑠). The distances in thenetwork are considered normalized with respect to 𝑑𝑝𝑝 = 1.Finally, we assume that 𝑇𝑠 and 𝑅𝑠 transmit with the samepower 𝑃𝑠.

Fig. 2 shows the system throughput versus the secondarytransmit power. The non-cooperative scheme proposed in [5]is compared to the cooperative scheme proposed in this paper.We consider a non line-of-sight (NLOS) scenario, so that 𝑚=1 for all channels. Moreover, ℛ𝑝 = 4 bits per channel use(bpcu), ℛ𝑠=4 bpcu, 𝑃𝑝=10 dB, 𝜆𝑝𝑝=𝜆𝑠𝑝=𝜆𝑟𝑝=1, 𝜆𝑝𝑠=𝜆𝑝𝑟 =𝜆𝑠𝑠 =24, 𝜆𝑠𝑟 =𝜆𝑟𝑠 =44. These parameters correspondto a topology where the secondary network is closer to 𝑇𝑝

than to 𝐷𝑝.We can see from Fig. 2 that the IDF-based proposed scheme

outperforms the scheme proposed in [5] for all values of 𝑃𝑠.We can also observe that the SDF-based proposed schemeperforms similarly to the IDF-based proposed scheme when𝑃𝑠 is relatively small, that is, in the range of secondarytransmit power that causes minimum harm to the primarycommunication. For instance, with the proposed scheme, it ispossible to achieve a secondary throughput between 0.5 and1.0 bpcu (with either IDF or SDF protocol) without impactingsignificantly on the primary performance, while the secondarynetwork achieves almost zero throughput at this range oftransmission power according to the scheme proposed in [5].

Fig. 3 evaluates the existence of some line-of-sight (LOS)in the links 𝑇𝑝 → 𝑅𝑠 and 𝑇𝑝 → 𝐷𝑠, by setting 𝑚𝑠𝑠 =𝑚𝑠𝑟 = 𝑚𝑟𝑠 = 𝑚𝑝𝑟 = 𝑚𝑝𝑠 = 2 (𝑚𝑝𝑝 = 𝑚𝑠𝑝 = 𝑚𝑟𝑝 = 1 iskept unchanged). The idea is to better reflect the fact that

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−15 −10 −5 0 50

0.5

1

1.5

2

2.5

3

Ps (dB)

Thr

ough

put (

bpcu

)

Primary withoutsecondary

Primary with secondary LOS − black

Non−coop. secondaryLOS

Coop. secondaryLOS

SDF protocol − greenIDF protocol − blue

Fig. 3. Throughput versus 𝑃𝑠, for ℛ𝑝 = 4 bpcu, ℛ𝑠 = 4 bpcu, 𝑃𝑝 = 10dB, 𝜆𝑝𝑝 = 𝜆𝑠𝑝 = 𝜆𝑟𝑝 = 1, 𝜆𝑝𝑠 = 𝜆𝑝𝑟 = 𝜆𝑠𝑠 = 24, 𝜆𝑠𝑟 = 𝜆𝑟𝑠 = 44,considering the LOS scenario.

−20 −15 −10 −5 0 50

0.5

1

1.5

2

2.5

3

3.5

4

4.5

5

Ps (dB)

Thr

ough

put (

bpcu

)

SDF protocol − greenIDF protocol − blue

Primary without secondary

Coop. secondary LOS

Coop.secondaryNLOS

Non−coop. secondary NLOS

Non−coop. secondaryLOS

Primary with secondary NLOS − blue Primary with secondary LOS − black

Fig. 4. Throughput versus 𝑃𝑠, for ℛ𝑝 = 4 bpcu, ℛ𝑠 = 6 bpcu, 𝑃𝑝 = 10dB, 𝜆𝑝𝑝 = 𝜆𝑠𝑝 = 𝜆𝑟𝑝 = 1, 𝜆𝑝𝑠 = 𝜆𝑝𝑟 = 24, 𝜆𝑠𝑠 = 44, 𝜆𝑠𝑟 = 𝜆𝑟𝑠 = 84.Both LOS and NLOS cases are considered.

the secondary network is closer to 𝑇𝑝 than to 𝐷𝑝. As wecan see, the performance of the proposed scheme increasesconsiderably specially in the 𝑃𝑠 range where the impact onthe primary performance is negligible.

In Fig. 4 it is considered that the nodes of the secondarynetwork are even closer to each other, by assuming that𝜆𝑝𝑝 = 𝜆𝑠𝑝 = 𝜆𝑟𝑝 = 1, 𝜆𝑝𝑠 = 𝜆𝑝𝑟 = 24, 𝜆𝑠𝑠 = 44,𝜆𝑠𝑟 =𝜆𝑟𝑠 =84. We also consider that 𝑚𝑝𝑝 =𝑚𝑠𝑝 =𝑚𝑟𝑝 =1,𝑚𝑠𝑠 = 𝑚𝑠𝑟 = 𝑚𝑟𝑠 = 𝑚𝑝𝑟 = 𝑚𝑝𝑠 = 4, ℛ𝑝 = 4 bpcu,ℛ𝑠 = 6 bpcu, and 𝑃𝑝 = 10 dB. We can see that havingthe secondary nodes closer to each other is more favorableto the proposed scheme, increasing the secondary throughputthat can be achieved without significantly harming the primary

performance.Finally, it is important to point out that if the secondary

network is much closer to the 𝐷𝑝 than to 𝑇𝑝, both theproposed scheme and the scheme in [5] do not perform well,achieving very low secondary throughput or, on the otherhand, significantly degrading the performance of the primarynetwork.

V. CONCLUSION

This paper presented a new cooperative protocol for overlaycognitive radio, in which the secondary network exploits theprimary retransmissions. Through the use of cooperation, thethroughput of the secondary network can be significantlyincreased, with a very small performance loss imposed tothe primary network. The best configuration for the proposedscheme is when the secondary nodes are close to each otherand nearby the primary transmitter.

ACKNOWLEDGMENT

This work was supported by CAPES and CNPq (Brazil).

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