Energy-Efficient Cooperative Cognitive Relaying Schemes for Cognitive Radio Networks

Transcription

1 Energy-Efficient Cooerative Cognitive Relaying Schemes for Cognitive Radio Networks Ahmed El Shafie, Student Memer, IEEE, Tamer Khatta, Memer, IEEE, Amr El-Keyi, Memer, IEEE arxiv:46.55v3 [cs.ni] 6 Oct 7 Astract We investigate a cognitive radio network in which a rimary user PU may cooerate with a cognitive radio user i.e., a secondary user SU for transmissions of its data ackets. The PU is assumed to e a uffered node oerating in a time-slotted fashion where the time is artitioned into equallength slots. We develo two schemes which involve cooeration etween rimary and secondary users. To satisfy certain quality of service QoS requirements, users share time slot duration and channel frequency andwidth. Moreover, the SU may leverage the rimary feedack message to further increase oth its data rate and satisfy the PU QoS requirements. The roosed cooerative schemes are designed such that the SU data rate is maximized under the constraint that the PU average queueing delay is maintained less than the average queueing delay in case of noncooerative PU. In addition, the roosed schemes guarantee the staility of the PU queue and maintain the average energy emitted y the SU elow a certain value. The roosed schemes also rovide more roust and otentially continuous service for SUs comared to the conventional ractice in cognitive networks where SUs transmit in the sectrum holes and silence sessions of the PUs. We include rimary source urstiness, sensing errors, and feedack decoding errors to the analysis of our roosed cooerative schemes. The otimization rolems are solved offline and require a simle -dimensional grid-ased search over the otimization variales. Numerical results show the eneficial gains of the cooerative schemes in terms of SU data rate and PU throughut, average PU queueing delay, and average PU energy savings. Index Terms Cognitive radio, rate, queue staility, otimization rolems. I. INTRODUCTION Secondary utilization of the licensed frequency ands can efficiently imrove the sectral density of the under-utilized licensed sectrum. Cognitive radio secondary users are intelligent devices that use cognitive technologies to adat with variations, and exloit methodologies of learning and reasoning to dynamically reconfigure their communication arameters [] [4]. This allows the secondary users SUs to utilize the sectrum whenever it is free to use and with the maximum ossile data rates. Cooerative diversity is a recently emerging technique for wireless communications that has gained wide interest [5] [8] Part of this aer was ulished in the IEEE International Conference on Comuting, Networking and Communications ICNC, 5 []. A. El Shafie is with the University of Texas at Dallas, USA ahmed.elshafie@utdallas.edu. T. Khatta is with Electrical Engineering, Qatar University, Doha, Qatar tkhatta@ieee.org. A. El-Keyi is with Wireless Intelligent Networks Center WINC, Nile University, Giza, Egyt aelkeyi@nileuniversity.edu.eg. The work of T. Khatta is suorted y Qatar National Research Fund QNRF under grant numer NPRP The statements made herein are solely the resonsiility of the authors. where multile channels are used to communicate the same information symol. Recently, cooeration in cognitive radio networks, referred to as the cooerative cognitive relaying, where the SU hels in relaying some of the undelivered rimary user PU ackets, has got extensive attention [9] [6]. In articular, the SU functions as a relay node for the PU whenever the PU acket cannot e decoded at its destination. The authors of [9] showed that the maximum achievale rate can e achieved y simultaneous transmissions of PU and SU data signals over the same frequency and. The SU data signals are jointly encoded with PU data signals via dirty-aer coding techniques. Hence, the SUs know erfectly the PU s data. In [], the authors assumed that the SU decodes-andforwards the undelivered PU ackets during the idle eriods of the PU. The SU maximizes its throughut y adjusting its transmit ower level. A. Related Work In [], the authors investigated the scenario of deloying a dum relay node in cognitive radio networks to increase network sectrum efficiency. The relay node aids oth the PU and the SU. The roosed scheme is investigated for a network consisting of a air of PUs and a air of SUs. In [3], the authors considered a network with one uffered PU and one uffered SU where the SU is allowed to access the channel when the PU s queue is emty. The SU has a relaying queue to store a fraction of the undelivered PU ackets controlled through an adjustale admittance factor. A riority of transmission is given to the relayed PU ackets over the SU own ackets. The SU aims at minimizing its average queueing delay suject to a ower udget for the relayed rimary ackets. In [5], the authors characterized some fundamental issues for a wireless shared channel comosed of one PU and one SU. The authors considered a general multi-acket recetion model, where concurrent acket transmission could e correctly decoded at receivers with a certain roaility that is characterized y the system s arameters e.g., acket length, data rates, time slot duration, andwidth, etc.. The PU has unconditional channel access, whereas the SU accesses the channel ased on the activity state of the PU, i.e., active or inactive, during a time slot. The sectrum sensing rocess is imractically assumed to e erfect. The SU is assumed to e caale of relaying the undelivered PU ackets as in [3]. If the PU is sensed to e inactive during a time slot, the SU accesses the channel with roaility one, and if the PU is active, the SU randomly accesses the channel simultaneously with the PU or attemts to decode the rimary acket with

2 the comlement roaility. The maximum stale throughut region of the network is otained via otimizing over the access roaility assigned y the SU during the active eriods of the PU. Releasing ortions of rimary systems time slot duration and andwidth for the SUs has een considered in several works, e.g., [], [4], [7]. In [], the authors roosed a sectrum leasing scheme in which PUs may lease their owned andwidth for a fraction of time to SUs ased on decode-andforward DF relaying scheme and distriuted sace-time coding. In [4], the authors roosed a new cooerative cognitive scheme, where the PU releases ortion of its andwidth to the SU. The SU utilizes an amlify-and-forward relaying scheme. It receives the rimary data during the first half of the time slot, then forwards the amlified data during the second half of the time slot. In [7], the authors considered an SU equied with multile antennas sharing the sectrum with a single-antenna energy-aware PU, where the PU aims at maximizing its mean transmitted ackets er joule. The users SU and PU slit the time slot duration and the total andwidth to satisfy certain quality of service QoS for the PU that cannot e attained without cooeration. Both users maintain data uffers and are assumed to send one data acket er time slot. B. Contriutions Given the need for shorter transmission times and low latency communications [8] [], we develo two cooerative cognitive schemes which allow the SU to transmit its data its simultaneously with the PU under the constraint of short communication times and the resence of ractical sensing and feedack cost considerations. Under our roosed schemes, the PU may cooerate with the SU to enhance its QoS, i.e., to enhance its average queueing delay and maintain its queue staility. Hence, cooeration is otional for the PUs. If cooeration is eneficial for the PU, it releases ortion of its andwidth and time slot duration for the SU. In turn, the SU incurs ortion of its transmit energy to relay the rimary ackets. The SU emloys a DF relaying scheme. The time slot is divided into several intervals or time hases that change according to the adoted cooerative scheme, as will e exlained later. In our first roosed cooerative scheme, the SU lindly forwards what it receives from the PU even if the rimary destination can decode the data acket correctly at the end of the PU transmission hase. On the other hand, in our second roosed scheme, the SU forwards what it receives from the PU if and only if the rimary destination could not decode the PU transmission of the rimary acket; or if the SU considers the feedack message as a negativeacknowledgement from the rimary destination. However, as will e exlained later, there is a cost for using the second cooerative scheme which is a reduction in the time availale for transmission data of users due to the resence of an additional feedack duration. These ractical issues are quantified analytically in this work. In this aer, the rimary feedack channel is assumed to e modeled as an erasure channel model and can e undecodale at the secondary terminal. This will e justified in Section VI. The contriutions of this aer are summarized as follows We design two cooerative cognitive schemes which involve cooeration etween the PUs and the SUs. The two schemes differ in terms of time slot structure and rimary feedack mechanism. Both schemes achieve a significant PU energy savings. We consider ractical assumtions for the cognitive radio network. Precisely, unlike most exiting literature, we consider sectrum sensing errors and rimary feedack recetion errors at the SU. Moreover, we consider the imact of the time durations sent on sectrum sensing and feedack message transmission on the achievale data rates. In addition, the PU data urstiness is taken into consideration. We roose two QoS measures for the PU and include them in the roosed otimization rolems as constraints. Secifically, we assume a constraint on the PU average queueing delay and a constraint on the staility of the PU queue. Moreover, we consider a ractical energy constraint on the SU average transmit energy. The otimization rolems are stated under such constraints. This aer is organized as follows. In the next section, we introduce the system model adoted in this aer. In Section III, we analyze the PU queue and derive the PU average queueing delay and PU queue staility condition. Our first roosed cooerative scheme is exlained in Section V. In Section VI, we descrie our second roosed cooerative scheme. The numerical results are shown in Section VIII. We finally conclude the aer in Section IX. II. SYSTEM MODEL We consider a wireless network comosed of orthogonal rimary channels, where each channel is used y one PU. Each rimary transmitter-receiver air coexists with one secondary transmitter-receiver air. For simlicity, we focus on one of those orthogonal channels. Each orthogonal channel is comosed of one secondary transmitter s, one rimary transmitter, one secondary destination sd and one rimary destination d. The SU is equied with two antennas: one antenna for transmission data and the other for data recetion and sectrum sensing. The PU is equied with a single antenna. Moreover, the PU has an infinite-length uffer for storing a fixed-length ackets. The arrivals at the PU queue are indeendent and identically distriuted i.i.d. Bernoulli random variales from one time slot to another with mean λ [, ] ackets er time slot. Thus, the roaility of a data acket arrival at the PU queue in an aritrary time slot is λ. A list of the key variales is given in Tale I. A. Channel Model We assume an interference wireless channel model, where concurrent transmissions are assumed to e lost data if the received signal-to-noise-lus-interference-ratio SINR is less As argued in the cognitive radio literature, e.g., [9] [7] and the references therein, the roosed cooerative cognitive scheme and theoretical develoment resented in this aer can e generalized to cognitive radio networks with more PUs and more SUs.

3 3 TABLE I: List of Key Variales. Symol Descrition Symol Descrition τ s Sectrum sensing time duration T and W Time slot coherence time duration and channel total andwidth, resectively R Average SU data rate P Average transmit information ower Q Queue at the PU τ f Feedack message duration R l e and R l SU transmission data rate under scheme P l µ l,c when the PU queue is emty and nonemty, resectively Average service rate of the PU queue under scheme P l α j,k Channel gain of the j k link with mean σ j,k P FA False alarm roaility at the SU P MD Misdetection roaility at the SU λ Average arrival rate at the PU s queue D l,c Average queueing delay at the PU queue under scheme P l f Proaility that SU decodes the PU s feedack message D,nc Average queueing delay at the PU queue with no cooeration µ,nc Average service rate of the PU queue with no cooeration E l Secondary mean transmit energy under scheme P l E Maximum transmit energy y the SU PU acket size in its T i and W i Time and andwidth assigned to user i {, s} under cooeration than a redefined threshold, or equivalently, if the instantaneous channel gain is lower than a redefined value. 3 We roose a DF relaying technique, where the SU decodes and then forwards the PU acket. The SU is assumed to e a fulldulex terminal which means that it can receive and transmit at the same time. To avoid the looack self-interference imairments which can significantly reduce the achievale rates, we assume that the SU cannot transmit and receive over the same frequency and. However, the SU can transmit data over a frequency and and receive over the other. Both SU and PU transmit with a fixed ower sectral density of P Watts/Hz. The total transmit ower changes ased on the used andwidth er transmission. When a node transmit over a andwidth of W j Hz, the average transmit ower is P W j Watts. Time is slotted and a slot has a duration of T seconds. Channel coefficient etween node j and node k, denoted y ζ j,k, is distriuted according to a circularly symmetric Gaussian random variale, which is constant over one slot, ut changes indeendently from one time slot to another. The exected value of the channel gain α j,k = ζ j,k is σj,k, where denotes the magnitude of a comlex argument. Each receiving signal is ertured y a zero-mean additive white Gaussian noise AWGN with ower sectral density N Watts/Hz. The outage of a channel link occurs when the transmission rate exceeds the channel rate. The outage roaility etween two nodes j and k without and with the resence of interference from other nodes are denoted y P j,k and P I j,k, resectively. These outage roailities are 3 This will e discussed later in Aendix B. functions of the numer of its in a data acket, the slot duration, the transmission andwidth, the transmit owers, and the average channel gains as detailed in Aendices A and B. B. Primary Access and Secondary Access Permission The PU transmits its data whenever it has a acket to send. That is, it does not have any restrictions on using the sectrum. Without cooeration, the PU uses the entire time slot duration and total andwidth for its own data signal transmissions, while the SU does not gain any sectrum/channel access even if the PU s queue is emty. This is ecause, in ractice, the SU may erroneously misdetect the rimary activity and hence it may cause harmful interrution on the rimary system oeration, e.g., collisions and ackets loss, that can cause sever acket losses and data delays. In case of cooeration, and ased on the roosed cooerative cognitive schemes that will e exlained shortly, the PU will release a ortion of its time slot duration and total andwidth to the SU. The SU will then e allowed to use the sectrum. In ractice, the SU may get ermission to access the sectrum if it either rovides economic incentives for the PU or erformance enhancement incentives. Similar to [5], [4], [7] and the references therein, we consider erformance enhancement incentives. III. QUEUE STABILITY, PU QUEUE MODEL, AND PU QUEUEING DELAY A. Staility A queueing system is said to e stale if its size is ounded all the time. More secifically, let Q T denote the length of

4 4 queue Q at the eginning of time slot T {,, 3,... }. Queue Q is said to e stale if lim lim x T Pr{QT < x} = For the PU queue, we adot a late-arrival model where a newly arrived acket to the queue is not served in the arriving time slot even if the queue is emty. 4 Let A T denote the numer of arrivals to queue Q in time slot T, and H T denote the numer of deartures from queue Q in time slot T. The queue length evolves according to the following form: Q T+ = Q T HT + + A T where z + denotes maxz,. We assume that deartures occur efore arrivals, and the queue size is measured at the early eginning of the time slot []. B. PU Queueing Delay Let µ = H, where Ṽ denotes the exected value of V, e a general notation for the mean service rate of the PU queue. Solving the state alance equations of the Markov chain modeling the PU queue Fig., it is straightforward to show that the roaility that the PU queue has m ackets, denoted y ν m, is given y m ν m = ν λ µ = ν η m, m =,,..., 3 µ λ µ µ where η = λµ. Since the sum over all states roailities λ µ is equal to one, i.e., m= ν m =, the roaility of the PU queue eing emty is otained y solving the following equation ν + ν m = ν + ν m= m= µ η m = 4 After some mathematical maniulations and simlifications, ν is given y ν = λ µ 5 The PU queue is stale if µ > λ. Alying Little s law, the PU average queueing delay, denoted y D, is then given y D = λ Using 3, D is rewritten as m= mν m 6 D = ν mη m 7 λ µ m= Sustituting with ν into D, the PU average queueing delay is then given y D = λ µ λ 8 Following are some imortant remarks. Firstly, the PU average queueing delay cannot e less than one time slot, which is attained when the denominator of 8 equals to the numerator. This condition imlies that µ = ackets/time slot, i.e., the minimum of D is attained if the service rate of the PU queue is equal to unity. 4 This queueing model is considered in many aers, see for examle, [], [5], [] and the references therein. l 3 u u l u u 3 m l m l m l m l m Fig. : Markov chain of the PU s queue. State self-transitions are omitted for visual clarity. D [slots] =.3 [ackets/slot]: analyt. =.3 [ackets/slot]: sim. =. [ackets/slot]: analyt. =. [ackets/slot]: sim. =. [ackets/slot]: analyt. =. [ackets/slot]: sim [ackets/slot] Fig. : PU average queueing delay versus µ for different values of λ. To verify the average queueing delay exression and show the imact of oth λ and µ, we lotted the curves in Fig.. As shown in the figure, increasing µ decreases the average queueing delays. Moreover, the average queueing delay is increasing with the increase of the data arrival rate λ. As shown analytically, the minimum average queueing delay is time slot when µ = ackets/slot. Secondly, the rimary ackets average queueing delay, D, decreases with increasing of the mean service rate of the PU queue, µ. On the other hand, µ deends on the channels outage roailities which, in turn, are functions of the links arameters, acket size, transmission time durations, occuied andwidth, and many other arameters as shown in Aendices A and B. Hereinafter, when necessary, we aend a second suscrit to the used notations to distinguish etween the cases of cooeration c and no cooeration nc. We also aend a new suerscrit to distinguish etween the roosed schemes. IV. NON-COOPERATIVE AND COOPERATIVE USERS A. Non-Cooerative Users Let T denote the time slot duration that a PU is allowed to transmit data over a total andwidth of W Hz. Without cooeration, the time slot is divided into two non-overlaed hases: a transmission data hase, which takes lace over the time interval [, T τ f ]; and a feedack hase whose length is τ f seconds, which takes lace over the time interval [T τ f, T ]. The feedack hase is used y the rimary destination to notify the rimary transmitter aout the decodaility status of its acket. If the PU queue is nonemty, the PU transmits exactly one acket of size its to its resective

5 5 destination. The PU and rimary destination imlement an Automatic Reeat-reQuest ARQ error control scheme. The rimary destination uses the cyclic redundancy code CRC its attached to each acket to ascertain the decodaility status of the received acket. The retransmission rocess is ased on an acknowledgment/negative-acknowledgement ACK/NACK mechanism, in which short-length ackets are roadcasted y the rimary destination to inform the rimary transmitter aout its acket recetion status. If the PU receives an ACK over the time interval [T τ f, T ], it removes the data acket stored at the head of its queue; otherwise, a retransmission of the acket is generated at the following time slots. The ARQ scheme is untruncated which means that there is no maximum on the numer of retransmissions and an erroneously received acket is retransmitted until it is decoded correctly at the rimary destination [], [3], [5], []. Without cooeration, a data acket at the head of the PU queue is served if the d link is not in outage. Using the derived results in Aendix A for the channel outage roaility, the mean service rate of the PU queue, denoted y µ,nc, is given y W T τ f µ,nc =ex N P σ,d 9 It is noteworthy from 9 that increasing the feedack duration, τ f, decreases the service rate of the PU queue. This is ecause the time availale for transmission data decreases with increasing τ f ; hence, the outage roaility increases which reduces the service rate. Since the PU transmits with a fixed W T τ f rate of R = its er channel use, increasing W or T decreases the channel outage roaility as seen in 9. However, increasing R decreases the throughut since the numer of decoded its er seconds is decreased. Hence, one should comute the numer of decoded its er second er Hz which is given y µ,nc =ex N Letting R = W T, we have µ,nc =ex W T τ f P σ,d T W T R τ f T N P σ,d R Using the first derivative of µ,nc in with resect to, the otimal acket size is P σ,d N = W T τ W f T ln where W is Lamert-W omega function. From this interesting result, increasing the feedack duration τ f will decrease the acket size. This is exected since the allowed time to send a data acket will decrease. On the other hand, we can see that increasing the time slot duration T or the average receive SNR P σ,d N at the rimary destination increases the otimal acket size. This imlies that more acket size can e suorted y the communication system. However, increasing T and W linearly increase the otimal acket size. When T PU throughut [its/sec/hz] Fig. 3: PU throughut [its/sec/hz] versus R [its/sec/hz]. is sufficiently longer than τ f, this leads to P σ W,d N = W T 3 ln Thus, the numer of its er channel use R that maximizes the throughut in its/sec/hz is P σ R = W,d W T = N 4 ln To verify our analytical finding and show the imact of R on the PU throughut [its/sec/hz], we lot Fig. 3. As can e seen from Fig. 3, the PU throughut increases with R until a eak is reached, then the throughut decreases until it reaches zero. Hence, there is an otimal value for the acket size or R for a given T W that maximizes the PU throughut. This value is given y 4. Increasing the average receive SNR P σ,d N increases the PU throughut and also increases the otimal R. This matches our discussion elow. According to 8, and using 9, the PU average queueing delay in case of non-cooerative PU is given y D,nc = λ λ = µ,nc λ W T τ f ex N P σ λ,d 5 with λ <µ,nc which reresents the staility condition of the PU queue when there is no cooeration. B. Cooerative Users When the SU is ale to assist the PU with relaying a ortion of the rimary ackets, the PU, in return, may release a ortion of its sectrum to the SU for its own transmission data if cooeration is eneficial for the PU. In addition to releasing some andwidth for the SU, the PU releases a ortion of its time slot duration to the SU to retransmit the rimary acket. If the cooeration is eneficial for the PU, it cooerates with the SU. If the PU queue is nonemty, the PU releases W s W Hz to the SU for its own data transmission, and releases T s seconds of the time slot to the SU for relaying the rimary ackets. The used andwidth for oth transmission and retransmission of the rimary acket is W = W W s Hz

6 6 with transmission times T and T s, resectively. Throughout the aer, we use the analogy of suands to distinguish etween the rimary oerational frequency suand, W, and the secondary oerational frequency suand, W s. Sectrum Sensing: The SU senses the rimary suand, W, for τ s seconds from the eginning of the time slot to detect the ossile activities of the PU. If this suand is sensed to e idle unutilized y the PU, the SU exloits its availaility y sending some of its data its. We assume that the SU emloys an energy-detection sectrum-sensing algorithm. Secifically, the SU collects a numer of samles over a time duration τ s T, measures their energy, and then comares the measured energy to a redefined threshold to make a decision on the PU activity [3]. Detection reliaility and quality deend on the sensing duration, τ s, and can e enhanced y increasing τ s. Secifically, as τ s increases, the rimary detection ecomes more reliale at the exense of reducing the time availale for secondary transmission over the rimary suand if the PU is actually inactive. This is the essence of the sensing-throughut tradeoff in cognitive radio systems [3]. Since the sensing outcome is imerfect and suject to errors due to AWGN, the SU may interfere with the PU and cause some acket loss and collisions. To cature the imact of sensing errors, we define P MD as the roaility of misdetecting the rimary activity y the secondary terminal, which reresents the roaility of considering the PU inactive while it is actually active; and P FA as the roaility that the sensor of the secondary terminal generates a false alarm, which reresents the roaility of considering the PU active while it is actually inactive. The values of sensing errors roailities are derived in Aendix C. Imortant Notes and Remarks: In the following, we state some imortant notes regarding our roosed cooerative schemes. A communication link is assumed to e ON in a given time slot if it is not in outage. In articular, a link is ON if the instantaneous data rate of that link is higher than the used transmission data rate at the transmitter. In this case, the roaility of it-error rate is very low and can e neglected. Otherwise, the communication link is said to e OFF i.e., unale to suort the transmission rate. In other words, the it-error rate is unounded average symol error rate is almost and data retransmission should take lace in the following transmission times. The CSI of the s d, s and s sd links are assumed to e known accurately at the SU a similar assumtion of knowing the CSI at the transmitters is found in many aers, for examle, [4] and the references therein. 5 This allows the SU to etter utilize the sectrum and hels the PU whenever necessary and ossile. We assume that the SU always has data its to transmit and it transmits its data with the instantaneous channel rate of its link, i.e., s sd link. This is realized through the imlementation of adative modulation 5 Note that the channel coefficient etween the SU and the rimary destination can e estimated y the rimary destination and fed ack to the SU. The rimary destination only needs to send the state of the channel, i.e., ON or OFF, which can e realized through a one-it inary feedack ilot signal. schemes which is one of the main advantage of the cognitive radio devices [4]. Since the SU has the CSI of all the communication links as exlained in the revious ullet, in each time slot, the SU ascertains the state of the s d link, i.e., ON or OFF link, y comaring α s,d to the decoding threshold α th,s,d. Further details on a link state is rovided in Aendix A. After that, the SU can take decisions ased on the other links to etter hel the PU. Since the SU oeration is ased on the sectrum sensing outcomes, the time assigned to channel sensing, denoted y τ s, should e less than the PU transmission time T i.e., τ s < T. In articular, the SU cannot set τ s to e longer than the time assigned to PU transmission. If the s link is in outage i.e., OFF, this means that the SU will not e ale to decode the PU acket since the noise signal dominates the data signal and the transmission data rate is higher than the channel rate. Each PU acket comes with a CRC so that receivers rimary destination and SU check the checksum to indicate the status of the decoded acket. Hence, if the SU cannot decode the rimary acket in a time slot, i.e., the s link is in outage, or if the PU s queue is emty, the SU will not waste energy in forwarding what it receives from the wireless channel ecause it knows with certainty that the received acket is a noisy acket i.e., has no data when the PU queue is emty. Consequently, the SU saves its energy from eing wasted in a useless rimary data retransmission, and it instead exloits that amount of energy for the transmission of its own data. This is critical since the SU energy is constrained and needs to e otimized. The data signals transmitted over suand W s are indeendent of the data signals transmitted over suand W. Hence, when there is an interference over suand W due to simultaneous transmissions from the SU and the PU, the data signals over suand W s do not get affected. If the PU is active in a given time slot and the SU misdetects its activity, a concurrent transmission takes lace over the rimary suand, W. Hence, the SU data its transmitted over W are lost since the transmission data rate is higher than the link rate, and the rimary acket could survive if the received SINR is higher than the decoding threshold. This event occurs with roaility P I,d.6 See Aendix B for further details. We assume that the rimary ARQ feedack is unencryted and is availale to the SU. A similar assumtion is found in many references, e.g., [] and the references therein. If the SU transmits concurrently with the rimary destination during the feedack hase, the feedack message acket may e undecodale at the PU. For this reason, the SU remains silent/idle during the rimary feedack duration to avoid disturing the rimary system oeration. 6 Throughout this aer, X = X.

7 7 Feedack duration Sensing duration Hence, the SU transmits its own data over W s and remains silent over W to avoid causing any interference or disturance for the feedack message transmission. If the PU was inactive during [, T ], there is no feedack message in the current time slot. However, since the SU does not know the exact state of the PU during a time slot, it remains idle. To summarize, the SU does not access the sectrum allocated to the PU, W, during the feedack duration to avoid disturing the feedack message transmission. Fig. 4: Time slot structure under roosed scheme P. In the figure, τ s is the sectrum sensing time duration, T is the PU transmission time of the rimary data acket, T s is the time duration assigned to the secondary transmission of the rimary acket, and τ f is the feedack duration. Note that T + T s + τ f = T. V. FIRST PROPOSED SCHEME In this section, we exlain our first roosed cooerative scheme, denoted y P, and derive the achievale data rates and the energy emitted y the SU. The time slot structure under P is shown in Fig. 4. In our first roosed cooerative scheme, the oeration of the SU during any aritrary time slot changes over four hases: [, τ s ], [τ s, T ], [T, T + T s ], and [T + T s, T + T s + τ f ] or simly [T τ f, T ]. A. Scheme Descrition Before roceeding to the scheme descrition, we note that if the PU is active during a time slot, its transmission takes lace over [, T ], whereas the secondary retransmission of the rimary acket takes lace over [T, T + T s ]. The oeration of the SU during each hase is descried as follows. Time interval [, τ s ]: The SU simultaneously senses the rimary suand, W, and transmits its own data over W s. The sensing outcome is then used for the secondary oeration over [τ s, T ]. Time interval [τ s, T ]: If the SU detects the PU to e active, it simultaneously transmits its own data over W s, and attemts to decode the PU transmission over W. If the SU detects the PU to e inactive, it transmits its own data over oth suands, W and W s. If the PU is active and the SU finds the rimary suand to e free of the PU transmission, there will e interference etween the PU and the SU over W. 3 Time interval [T, T + T s ]: If the PU s queue is emty, the SU transmits its own data over oth suands. If the links s and s d are simultaneously ON and the PU queue is nonemty, the SU simultaneously transmits its own data over W s and retransmits the rimary acket over W. If either the s link or the s d link is OFF, the SU transmits its own data over oth suands. 4 Time interval [T τ f, T ]: If the PU was active during [, T ], then its resective receiver roadcasts a feedack message to indicate the status of the acket decodaility. B. PU and SU Data Rates and SU Emitted Energy A acket at the head of the PU queue Q,c is served if the SU detects the rimary activity correctly and either the direct ath or the relaying ath 7 is not in outage; or if the SU misdetects the rimary activity and the d link is not in outage. Let µ l,c denote the mean service rate of the PU under scheme P l, l {, }. The mean service rate of the PU queue under scheme P is then given y µ,c = P MD P,d P,s P s,d +P MD P I,d 6 where P MD P I,d denotes the roaility of correct rimary acket decoding at the rimary destination when the SU misdetects the rimary activity over W. Let R l e and R l denote the SU transmission data rate under scheme P l when the PU queue is emty and nonemty, resectively, and R = log + α s,sdp N denote the instantaneous data rate of the s sd link in its/sec/hz. Based on the descrition of scheme P, the SU transmission data rate when the PU queue is emty is given y R e = τ s δ s +T τ s P FA δ s +P FA + T s W R 7 where δ s = W s /W. When the PU queue is nonemty, the SU transmission data rate is given y R T = δ s + P MD +P MD P,s Ts +P MD P,s T s P s,d δ s +P s,d W R 8 The term P,s aears in R ecause the SU, when the s link is in outage, uses the entire andwidth for its own data transmission. Furthermore, the term P s,d aears in the exression of R ecause the SU, in each time slot, knows the channel state etween itself and the rimary destination and uses the allocated andwidth to the PU for its own transmission data when that channel is in outage. Let I[L] denote the indicator function, where I[L] = if the argument is true. The SU transmission data rate when it oerates under scheme P l is then given y R l s = I[Q l,c = ]R l e + I[Q l,c ]R l 9 7 The relaying ath is defined as the ath connecting the PU to rimary destination through the SU; namely, links s and s d. Since the channels are indeendent, the roaility of the relaying ath eing not in outage is P,s P s,d.

8 8 The exected value of I[L] is equal to the roaility of the argument event. That is, Ĩ[L] = Pr{L} The mean SU transmission data rate is then given y R l s = Pr{Q l l,c = } R e + Pr{Q l l,c } R Recalling that Pr{Q l,c = } = ν l and Pr{Ql,c } = ν l, the mean SU transmission data rate under scheme P is then given y R s = ν +ν τ s δ s +T τ s P FA δ s +P FA +T s W G s T δ s + P MD +P MD P,s Ts +P MD P,s T s P s,d δ s +P s,d W G s P where G s is the exected value of log + α s,sd N, which is given y see Aendix D for details G s = ln ex Γ, 3 P N σ s,sd P N σ s,sd where Γ m, s = /s ex zzm dz is the uer incomlete Gamma function. According to the descried scheme, the mean SU transmit energy, denoted y E, is given y E = ν +ν τ s δ s +T τ s P FA δ s +P FA +T s W P 4 τ s δ s +T τ s P MD δ s +P MD +T s W P Note that we assume that the maximum average emitted secondary energy is E; hence, E must e at most E. VI. SECOND PROPOSED SCHEME In our second scheme, denoted y P, we assume a variation in the rimary feedack mechanism to further imrove the achievale erformance for oth PU and SU. More secifically, we assume the existence of two rimary feedack hases within each time slot. Each transmission of the rimary acket y either the PU or the SU is followed y a feedack hase to inform the transmitter PU or SU aout the decodaility of the transmitted acket. In other words, a feedack message is sent y the rimary destination when it receives a coy of the exected rimary acket. 8 The first feedack hase is receded y the PU transmission of the rimary acket, whereas the second feedack hase is receded y the SU transmission of the rimary acket. The PU queue dros the acket if it receives at least one ACK in any time slot. Otherwise, the acket will e retransmitted y the PU in the following time slots until its correct decoding at the rimary destination. On the one hand, the gain of this cooerative scheme over the first roosed scheme lies in its aility to revent unnecessary retransmissions of a successfully decoded rimary 8 Each acket comes with an identifier ID and a certain laeled numer that is generated y the transmitter. In addition, the destination sends the exected numer of the next acket as art of the feedack message. acket at the rimary destination. More secifically, if the rimary destination can decode the PU transmission correctly, then the SU does not need to retransmit the same rimary acket over the rimary suand and over the time assigned for relaying; hence, the SU can instead use the time assigned for relaying and the rimary suand to transmit its own data its to its destination. 9 Consequently, using scheme P enales the SU to increase its average transmission rate via using the allocated andwidth and time duration for PU transmissions and its transmit energy to send its own data. On the other hand, there is a considerale cost due to aending an extra feedack duration to the time slot. This cost is converted to an increase in the outage roailities of the links and the reduction in the users rates. This is ecause the total time allocated for data its and ackets transmissions is reduced y τ f seconds relative to the total transmission time in case of scheme P. Under cooerative scheme P, the secondary oeration in any aritrary time slot changes over five hases as shown in Fig. 5: [, τ s ], [τ s, T ], [T, T + τ f ], [T +τ f, T +τ f +T s ] and [T τ f, T ]. A. Decoding of Primary Feedack Message at the SU The correctness of the feedack message decoding at the SU is ascertained using the checksum aended to the feedack message acket. The decoding of a rimary feedack message at the SU can e modeled as an erasure channel model. In articular, the rimary feedack message is assumed to e decoded correctly at the SU with roaility f. If the SU cannot decode the rimary feedack message in a given time slot, it considers this feedack message as a NACK feedack message. Another ossiility is to assume that the SU considers the nothing as a NACK message with roaility ω and considers it as an ACK message with roaility ω. Using such arameter allows the SU to use a fraction of the nothing events that would e an ACK, which means that the SU does not need to retransmit the rimary acket, for its own data its transmission. The SU can otimize over ω to alleviate wasting the channel resources without further contriution to the rimary service rate when the rimary acket is already decoded successfully at the rimary destination. The rimary mean service rate in this case is given y µ,c =P MD P,d βp,s P s,d +P MD P I,d 5 where β = f + f ω is the roaility of considering the overheard feedack message as a NACK when the rimary destination sends a NACK feedack which occurs if the d link is in outage. From 5, the rimary mean service rate is arameterized y ω. The maximum rimary 9 This is ecause the retransmission of the rimary acket y the secondary transmitter does not rovide further contriution to the rimary throughut. In addition, the retransmission of the rimary acket causes oth energy and andwidth losses that can e used otherwise for the SU data transmission. This event is referred to as nothing event. The nothing event is considered when the SU fails in decoding the feedack message, or when the PU is idle at this time slot, i.e., Q =.

9 9 service rate is attained when ω = since the SU will relay more PU ackets. For simlicity, we consider the case of ω = which guarantees the highest QoS for the PU. B. Scheme Descrition The PU transmission occurs over [, T ] and the secondary retransmission of a rimary acket occurs over [T +τ f, T + τ f +T s ]. Note that the feedack message is considered y the SU as a NACK feedack message if the d link is in outage and the feedack message is decoded correctly at the SU terminal; or if the feedack message is undecodale at the SU. The roaility that the SU considers the overheard rimary feedack message as a NACK is then given y Γ f =P,d f +f 6 In the sequel of this susection, we descrie the ehavior of the SU during each hase. Time interval [, τ s ] and [τ s, T ]: The oeration of the system over the time intervals [, τ s ] and [τ s, T ] is similar to the first cooerative scheme during the same time intervals. Time interval [T, T +τ f ]: If the PU queue is nonemty during the ongoing time slot, at the end of the PU dedicated transmission time, the SU transmits its own data over W s, and remains silent over W to avoid causing a concurrent transmission with the feedack message transmitted from the rimary destination to the PU. If the PU queue is emty during the ongoing time slot, the SU transmits its own data over oth suands. 3 Time interval [T + τ f, T τ f ]: Uon decoding the entire rimary acket, the SU discerns the actual true state of the PU, i.e., active or inactive. The SU transmits its own data over oth suands if the PU was active during the time interval [, T ], the rimary destination correctly decoded the PU acket, and the SU successfully decoded the rimary feedack message, i.e., considered it as an ACK feedack; or if the s d link is in outage; or 3 if the PU was inactive during the time interval [, T ]. If the PU was active during the time interval [, T ], the secondary terminal considered the feedack message sent over [T, T +τ f ] as a NACK feedack, and the s d link is not in outage; the SU simultaneously transmits its own data over W s and retransmits the rimary acket over W. 4 Time interval [T τ f, T ]: If the SU retransmitted the acket over [T + τ f, T τ f ], another feedack message will e sent over this hase y the rimary destination. Hence, the SU simultaneously transmits its own data over W s and remains silent over W. If the SU decides not to retransmit the rimary acket, there will e no rimary feedack message. Therefore, the SU transmits its own data over oth suands. If the PU queue is emty during the ongoing time slot, the SU transmits its own data over oth suands over this feedack duration i.e., [T τ f, T ]. C. PU and SU Data Rates and the SU Emitted Energy A data acket stored at the head of the PU queue Q,c is served in a given time slot if the SU detects the rimary activity correctly, and the direct link is not in outage; or if Feedack duration Sensing duration Fig. 5: Time slot structure under roosed scheme P. In this scheme, there are two feedack message durations. Hence, T + T s + τ f = T. the SU detects the rimary activity correctly, and the direct link is in outage, the SU considers the rimary feedack message as a NACK signal, and the relaying link is not in outage; or 3 if the SU misdetects the rimary activity, and the direct link is not in outage. The mean service rate of the PU queue is similar to the first scheme and is given y µ =P MD P,d P,s P s,d +P MD P I,d 7 We note that the exression 7 is similar to 6. However, the maximum assigned transmission data times for users under P are lower than P as P has two feedack durations. When the PU is inactive, the SU instantaneous transmission rate is given y R τ s δ s +T τ s P FA +P FA δ s +Ts W R 8 e = When the PU is active, the SU instantaneous transmission rate is given y R = T δ s +P MD T s P,s Γf Ps,d δ s +P s,d +Γf +P,s +P MD T s W R The mean SU transmission data rate is then given y τ s δ s +T τ s P FA +P FA δ s +Ts R s =ν +ν T δ s +P MD T s W G s 9 P,s Γf Ps,d δ s +P s,d +Γf +P,s +P MD T s W G s 3 According to the descrition of scheme P, the mean SU transmit energy is given y E = ν τ s δ s +T τ s P FA +P FA δ s +Ts W P + ν τ s δ s +T τ s P MD δ s +P MD +T s W P 3

10 VII. PROBLEM FORMULATION AND PRIMARY MEAN A. Prolem Formulation ENERGY SAVINGS We assume that users otimize over T = T τ f T s and W = W W s. It is noteworthy that there is a ossiility to otimize over the sectrum sensing time τ s, however, for simlicity, we assume that the sectrum sensing time is fixed and redetermined. Sensing time otimization is out of scoe of this aer. The otimization rolem is formulated such that the secondary average data rate is maximized under a certain PU average queueing delay, the PU queue staility condition, and an energy constraint on the secondary average transmit energy, given y E l E where E denotes the maximum average SU transmit energy. The otimization rolem under roosed scheme P l {P, P } is stated as follows max. T,W s.t. Rl s D,c l < D,nc, µ l,c > λ, E l E 3 τ s T T l, W W, T +T s =T l where T l is the oerational constraint on T +T s when users oerate under scheme P l, and D,c l = λ /µ l,c λ is the average queueing delay of the PU queue under cooeration. Under our first cooerative scheme, the maximum allowale transmission time is T τ f ; hence, T = T τ f. On the other hand, under our second cooerative scheme, the maximum allowale transmission time is T τ f ; hence, T = T τ f. It should e ointed out here that if the rimary feedack message is always undecodale at the SU, i.e., f = or if the d link is always in outage, scheme P always outerforms scheme P. This is reasonale since the SU will always retransmit the rimary acket with a lower transmission time for each user due to the existence of two feedack durations in P. In addition, when τ f increases, P may outerform P for some system arameters ecause it may e the case that the reduction in the maximum allowale transmission time due to the resence of an additional feedack duration is higher than the gain of knowing the status of the rimary acket decodaility at the SU efore the secondary retransmission of the rimary acket. The otimization rolem 3 is solved numerically using a two-dimensional grid-ased search over T and W. The otimal arameters otained via solving the otimization rolem 3 are announced to oth users so that W and T are known at the PU and the SU efore actual oeration of the communications system. If the otimization rolem is infeasile due to the dissatisfaction of one or more of the constraints in 3, the SU will not e allowed to use the sectrum and its achievale rate is zero. A simle method to solve the otimization rolem 3 is to divide the domains of T and W into K oints. Then, solve the otimization rolem 3 for K times and select the solution that satisfies the constraints and has the highest ojective function. Our roosed solution to the otimization rolem in 3 is stated in Algorithm. It is worth noting that the PU average queueing delay constraint can e relaced y a constraint on the mean service Algorithm Otimization Procedure : Select a large numer K : Set i = 3: loo: 4: Generate δ where δ = W /W 5: loo: 6: Set j = 7: Generate τs T T l T where = T /T 8: Comute W s = W T and T s = T l T τ s l 9: Comute Zi, j = R s in 3 : Set j = j + : If j K, goto loo : Set i = i + 3: If i K, goto loo 4: Select W = δ W and T = T that maximize R l s i and j corresonding to highest Zi, j and satisfy the constraints in 3 rate of the PU queue. Since the delay constraint is given y D,c l = λ /µ l,c λ <D,nc = λ /µ,nc λ, the mean service rate of the PU queue under cooeration must e greater than the mean service rate of the PU queue without cooeration. In articular, µ l,c > µ,nc 33 Comining the delay constraint with the staility constraint, the PU queue mean service rate should e at least µ l,c > max B. Mean Primary Energy Savings {µ,nc, λ } 34 In the asence of cooeration, the PU transmission takes lace over T τ f seconds and occuies W Hz. Hence, the PU energy consumtion er time slot is P W T τ f joules/slot. However, when the SU hels the PU in relaying its ackets, the PU transmits only in a fraction T /T of the time slot with transmission andwidth W Hz. Hence, its energy consumtion er time slot is only P W T P W T τ f joules/slot. In this case, the average rate of the PU energy savings, defined as the ratio of the energy savings over the original energy consumtion, is given y φ= P W T τ f Pr{Q,nc } P W T Pr{Q l,c } P W T τ f Pr{Q,nc } 35 Using the fact that Pr{Q,nc } = λ /µ,nc if λ < µ,nc, and otherwise, Pr{Q l,c } = λ /µ l,c, and noting that there is no cooeration if the PU queue is unstale, we get φ= W T max{µ,nc, λ } W T τ f µ l 36,c From the aove ratio, we can see that the less the andwidth and the transmission time that the PU occuies, the more energy savings for the PU. We note that the PU queue under cooeration should e stale, otherwise, the otimization rolem is infeasile and there will e no cooeration. We also note that using less andwidth and shorter transmission time

11 imroves the low roaility of intercet/low roaility of detection LPD/LPI characteristics of the communication link that aears to e esecially critical in military alications. Hence, it is always useful to use shorter transmission times and lower andwidth. VIII. NUMERICAL RESULTS In this section, we resent some simulations of the roosed cooerative schemes. We define a set of common arameters: the targeted false alarm roaility is P FA =., W = MHz, T = 5 msec, = 5 its, E = 5 6 joule, τ s =.5T, σs,d =σ s,sd =., σ,s =, P = Watts/Hz, and N = Watts/Hz. Fig. 6 shows the maximum average SU data rate of our roosed cooerative schemes. The second roosed scheme is lotted with three different values of f. The figure reveals the advantage of our second roosed scheme over our first roosed scheme for f =.5 and f =. However, for f =, the first roosed scheme outerforms the second one. This is reasonale since when f = there is no gain from having a feedack message after the PU transmission; hence, using the second roosed scheme wastes τ f seconds of the time slot that can e used otherwise in increasing users data rates. The figure also demonstrates the imact of arameter f on the erformance of the second roosed scheme, i.e., scheme P. As shown in the figure, increasing f enhances the erformance of scheme P. In addition to the common arameters, the figure is generated using σ,d =.5, τ f =.5T and the values of f in the figure s legend. Fig. 7 shows the imact of the feedack message duration, τ f, on the erformance of our roosed cooerative schemes. The mean SU transmission data rate and the PU data arrival rate feasile range decrease with increasing τ f. When the value of τ f is considerale, i.e., τ f =.T, the first scheme outerforms the second scheme. This is ecause the maximum allowale transmission data time of nodes under scheme P in this case is T τ f =.6T, whereas the maximum allowale transmission time under scheme P is T τ f =.8T. For small values of τ f, the second roosed scheme outerforms the first scheme since the SU can use the time duration assigned for relaying and the rimary suand to transmit its data in case of correct acket decoding after the PU transmission. The arameters used to generate the figure are the common arameters, σ,d =.5, f = and the values of τ f in the lot. Figs. 8, 9 and resent the rimary mean service rate, the PU average queueing delay, and the average PU ower savings, resectively, under our roosed cooerative schemes. The case of non-cooerative users is also lotted in Figs. 8 and 9 for comarison uroses. The figures demonstrate the gains of the roosed schemes for the PU over the non-cooeration case. Note that without cooeration etween the two users, the PU queue is unstale when λ >. ackets/slot and, hence, the queueing delay is unounded. On the other hand, with cooeration, the PU queue remains stale over the range from λ = to λ =.95 ackets/slot. The second scheme achieves etter erformance than the first scheme in terms of rimary QoS. Fig. reveals that more that 95% of the average rimary energy will e saved for λ =. ackets/slot. When λ =.8 ackets/slot, the rimary energy savings is almost 78%. For λ.95, the PU queue ecomes unstale even with cooeration; hence, the cooeration ecomes noneneficial for the PU and the PU ceases cooeration with the SU. Hence, the SU doest gain any access to the sectrum, and the rimary energy savings ecomes zero since the PU will send its data over the entire time slot duration and channel andwidth. The arameters used to generate the figures are the common arameters, σ,d =.5, σ s,d =, τ f =.5T and f =. Note that the erformance of our two roosed schemes are close to each other ecause the outage roaility of the rimary channel is high and the direct link i.e., the d link is in outage most of the time. Hence, under scheme P, the SU retransmits the rimary ackets almost every time slot instead of transmitting its own data signals. Accordingly, oth roosed schemes almost achieve the same erformance. Mean secondary rate [its/slot] 4.5 x P, f = P, f =.5 P, f = P..4.6 λ [ackets/slot].8 Fig. 6: The maximum SU data rate in its er slot for the roosed schemes. Scheme P is lotted with three different values of rimary feedack correct decoding, f. Mean secondary rate [its/slot] 4.5 x τ f =.T τ f =.5T P P λ [ackets/slot] Fig. 7: The maximum mean SU data rate in its er time slot. The schemes are lotted for two values of the feedack duration τ f. IX. CONCLUSIONS In this aer, we develoed two cooerative cognitive schemes which allow the SU to access the rimary sectrum