Power Control and Relay Selection in Full-Duplex Cognitive Relay Networks: Coherent versus Non-coherent Scenarios
aa r X i v : . [ c s . I T ] M a r Power Control and Relay Selection in Full-DuplexCognitive Relay Networks: Coherent versusNon-coherent Scenarios
Le Thanh Tan,
Member, IEEE,
Lei Ying,
Member, IEEE, and Daniel W. Bliss,
Fellow, IEEE
Abstract —This paper investigates power control and relayselection in Full Duplex Cognitive Relay Networks (FDCRNs),where the secondary-user (SU) relays can simultaneously receiveand forward the signal from the SU source. We study bothnon-coherent and coherent scenarios. In the non-coherent case,the SU relay forwards the signal from the SU source withoutregulating the phase; while in the coherent scenario, the SU relayregulates the phase when forwarding the signal to minimize theinterference at the primary-user (PU) receiver. We consider theproblem of maximizing the transmission rate from the SU sourceto the SU destination subject to the interference constraint atthe PU receiver and power constraints at both the SU sourceand SU relay. We develop low-complexity and high-performancejoint power control and relay selection algorithms. The superiorperformance of the proposed algorithms are confirmed usingextensive numerical evaluation. In particular, we demonstrate thesignificant gain of phase regulation at the SU relay (i.e., the gainof the coherent mechanism over the noncoherent mechanism).
Index Terms —Full-duplex cooperative communications, opti-mal transmit power levels, rate maximization, self-interferencecontrol, full-duplex cognitive radios, relay selection scheme,coherent, non-coherent.
I. I
NTRODUCTION
Cognitive radio is one of the most promising technologiesfor addressing today’s spectrum shortage [1], [2]. This paperconsiders underlay cognitive radio networks where primaryand secondary networks transmit simultaneously over the samespectrum under the constraint that the interference caused bythe secondary network to the primary network is below a pre-specified threshold [3]. In particular, we consider a cognitiverelay network where the use of SU relay can significantlyincrease the transmission rate because of path loss reduction.Most existing research on underlay CRNs has focused on thedesign and analysis of cognitive relay networks with half-duplex (HD) relays [2].Different from these existing work, this paper considers full-duplex relays, which can transmit and receive simultaneouslyon the same frequency band [4], [5]. Comparing with HDrelays, FD relays can achieve both higher throughput and lowerlatency with the same amount of spectrum. Design and analy-sis of FDCRNs, however, are very different from HDCRNs dueto the presence of self-interference , resulted from the powerleakage from the transmitter to the receiver of a FD transceiver.The FD technology can improve spectrum access efficiency in
The authors are with the School of Electrical, Computer and EnergyEngineering, Arizona State University, Tempe, AZ 85287, USA. Emails: { tlethanh,lei.ying.2,d.w.bliss } @asu.edu. cognitive radio networks [6]–[8] where SUs can sense andtransmit simultaneously. However these results assume theinterweave spectrum sharing paradigm under which SUs onlytransmit when PUs are not transmitting. Moreover, engineeringof a cognitive FD relaying network has been considered in [9],[10], where various resource allocation algorithms to improvethe outage probability have been proposed. These existingresults focus on either minimizing the outage probability oranalyzing performance for existing algorithms.This paper focuses on power control and relay selection inFDCRNs with explicit consideration of self-interference. Weassume SU relays use the amplify-and-forward (AF) protocol,and further assume full channel state information in both thenon-coherent and coherent scenarios and the transmit phaseinformation in the coherent scenario. We first consider thepower control problem in the non-coherent scenario. We for-mulate the rate maximization problem where the objective isthe transmission rate from the SU source to the SU destination,and the constraints include the power constraints at the SUsource and SU relay and the interference constraint at thePU receiver. The rate maximization problem is a non-convexoptimization problem. However, it becomes convex if we fixone of two optimization variables. Therefore, we propose analternative optimization algorithm to solve the power controlproblem. After calculating the achievable rate for each FDrelay, the algorithm selects the one with the maximum rate.We then consider the coherent scenario, where in additionto control the transmit power, a SU relay further regulates thephase of the transmitted signal to minimize the interferenceat the PU receiver. We also formulate a rate maximizationproblem, which again is nonconvex. For this coherent scenario,we first calculate the phase to minimize the interference at thePU receiver. Then we prove that the power-control problembecomes convex when we fix either the transmit power of theSU source then optimize the transmit power of the SU relayor vice versa. We then propose an alternative optimizationmethod for power control. Extensive numerical results arepresented to investigate the impacts of different parameters onthe SU network rate performance and the performance of theproposed power control and relay selection algorithms. Fromthe numerical study, we observe significant rate improvementof FDCRNs compared with HDCRNs. Furthermore, the co-herent mechanism yields significantly higher throughput thanthat under the non-coherent mechanism. SR h ! K SR h SP h R D h K R D h R R h K K
R R h SD h k R P h k R D h k SR h k k R R h Fig. 1. System model of power allocation with relay selection for the cognitivefull-duplex relay network.
II. S
YSTEM M ODEL
We consider a cognitive relay network which consists ofone SU source S , K SU relays R k ( k = 1 , . . . , K ), one SUdestination D , and one PU receiver P as shown in Fig. 1.The SU relays are equipped with FD transceivers to work inthe FD mode. Therefore the receiver performance of each SUrelay is affected by the self-interference from its transmittersince the transmit power is leaked into the received signal.Each SU relay R k uses the AF protocol, and amplifies thereceived signal from S with a variable gain G k and forwardsthe resulting signal to SU destination, D . We denote h SR k , h R k D , h SD , h R k P and h R k R k by the corresponding channelcoefficients of links S → R k , R k → D , S → D , R k → P and R k → R k . Let P S denote the transmit power of SU source S . We also denote by x S ( t ) , y R k ( t ) and y D ( t ) the generatedsignal by the SU source, the transmitted signals at the SU relayand the received signals at the SU destination, respectively.Let us consider a specific SU relay (say relay R k ). Fig. 2illustrates the signal processing at the relay. At time t , thereceived signals at SU relay R k and SU destination D are y ( t ) = h SR k p P S x S ( t )+ h R k R k ( y ( t )+∆ y ( t ))+ z R k ( t ) (1) y D ( t ) = h R k D y R k ( t ) + h SD p P S x S ( t ) + z D ( t ) , (2)where z R k ( t ) and z D ( t ) are the additive white Gaussiannoises (AWGN) with zero mean and variances σ R k and σ D ,respectively; y D ( t ) and y ( t ) are the received signals at SUrelay R k and SU destination D ; and y ( t ) is the receivedsignal after the amplification. In the following, we ignore thedirect signal from the SU source to the SU destination (i.e., thesecond part in equation (2)). Note that this assumption is has !" !" $ % k SR h SP h k R D h !" K R P h k k R R h k R z ! k k R R h y y y ! f y y y k R y Fig. 2. The process at FD relay R k . been used in the literature [4], [10] when there is attenuationon the direct transmission channel.The transmitted signals at SU relay R k is y R k ( t ) = y ( t ) + ∆ y ( t ) , where y ( t ) = f (ˆ y ) = G k ˆ y ( t − ∆) . We should note thatthe SU relay amplifies the signal by a factor of G k and delayswith duration of ∆ . In the noncoherent scenario, ∆ is fixed.In the coherence scenario, the delay ∆ will be optimized tominimize the interference at the PU receiver. Furthermore, ∆ y ( t ) is the noise and follows the i.i.d. Gaussian distributionwith zero mean and variance of P ∆ = ζP R k [4], [5]. G k canbe expressed as G k = h P S | h SR k | + ζP R k | h R k R k | + σ R k i − / . We assume that the channel h R k R k is perfectly estimated andhence the received signal after self-interference cancellation is ˆ y ( t ) = p P R k ( y ( t ) − h R k R k y ( t ))= p P R k h h SR k p P S x S ( t )+ h R k R k ∆ y ( t )+ z R k ( t ) i . (3)In the equation above, y ( t ) is known at SU relay R k andtherefore is used to cancel the interference. However, theremaining h R k R k ∆ y ( t ) is still present at the received signalsand is called the residual interference. So we can write thetransmitted signals at SU relay R k as follows: y R k ( t ) = G k h SR k p P R k p P S x S ( t − ∆) + ∆ y ( t )+ G k h R k R k p P R k ∆ y ( t − ∆)+ G k p P R k z R k ( t − ∆) . (4)III. P OWER C ONTROL AND R ELAY S ELECTION
In this section, we study the problem of maximizing therate between SU source and SU destination while protectingthe PU via power control and relay selection.
A. Problem Formulation
Let C k ( P S , P R k ) denote the achieved rate of the FDCRNwith relay R k , which is the function of transmit power of SUsource S and transmit power of SU relay R k . Assume the interference caused by the SU source and relay, I k is requiredto be at most I P to protect the PU.Now, the rate maximization problem for the selected relay R k can be stated as follows: Problem 1: max P S ,P Rk C k ( P S , P R k ) s.t. I k ( P S , P R k ) ≤ I P , ≤ P S ≤ P max S , ≤ P R k ≤ P max R k , (5)where P max S and P max R k are the maximum power levels forthe SU source and SU relay, respectively. The first constrainton I k ( P S , P R k ) requires that the interference caused by theSU transmission is limited. Moreover, the SU relay’s transmitpower P R k must be appropriately set to achieve good tradeoffbetween the rate of the SU network and self-interferencemitigation.Then the relay selection is determined by k ∗ = arg max k ∈{ ,...,K } C ∗ k (6)where C ∗ k is the solution of (5). In the following, we showhow to calculate the achieved rate, C k ( P S , P R k ) and theinterference imposed by SU transmissions, I k ( P S , P R k ) . B. The Achievable Rate
When SU relay R k is selected, the achievable rate of thelink S → R k → D based on (1) and (2) is as follows: C k = log P Rk | h RkD | σ D P S | h SRk | ˆ ζP Rk + σ Rk A (7)where A = 1 + P R k | h R k D | σ D + P S | h SR k | ˆ ζP R k + σ R k (8) ˆ ζ = | h R k R k | ζ (9)Recall that we assume the direct signal from the SU sourceto the SU destination is negligible. C. The Imposed Interference at PU
We now determine the interference at the PU caused by theCRN. The interference is the signals from the SU source S and the selected relay R k : y PU I ( t ) = h SP p P S x S ( t )+ h R k P y R k ( t )+ z P ( t ) (10)where z P ( t ) is the AWGN with zero mean and variance σ P , and y R k ( t ) is defined in (4).We next derive and analyze the interference in twocases: coherent and non-coherent. In particular, we focus oncoherent/non-coherent transmissions from the SU source andthe SU relay to the PU receiver. All other transmissionsare assumed to be non-coherent. In the coherent scenario,the phase information is needed in the coherent mechanism.This information can be obtained by using methods such as the implicit feedback (using reciprocity between forwardand reverse channels in a time-division-duplex system), andexplicit feedback (using feedback in a frequency-division-duplex system) [11] or the channel estimation [12].
1) Non-coherent Scenario:
From (10) and (4), the receivedinterference at the PU caused by the SU source and theselected relay can be written as follows: I non k ( P S , P R k ) = | h SP | P S + | h R k P | ζP R k + G k | h R k P | P R k h | h SR k | P S + | h R k R k | ζP R k + σ R k i (11)After simple calculation, we obtain I non k ( P S , P R k ) = | h SP | P S + | h R k P | P R k (1 + ζ ) (12)
2) Coherent Scenario:
Combining (10) with (4), the re-ceived interference at the PU is ¯ I coh k ( P S , P R k , φ ) = (cid:12)(cid:12) A + Be − jφ (cid:12)(cid:12) (13)where A = h SP p P S + h R k P p ζP R k = | A | ∠ φ A (14) B = (cid:18) h SR k p P S + h R k R k p ζP R k + σ R k √ j ) (cid:19) × G k h R k P p P R k = | B | ∠ φ B (15)and φ = 2 πf s ∆ , f s is the sampling frequency.Before using ¯ I coh k ( P S , P R k , φ ) in the constraint of the op-timization problem, we can minimize ¯ I coh k ( P S , P R k , φ ) overthe variable φ at given ( P S , P R k ) , i.e., min φ ¯ I coh k ( P S , P R k , φ ) . (16) Theorem 1.
The optimal solution to (16) is φ opt = π + φ B − φ A I coh k ( P S , P R k ) = ¯ I coh k ( P S , P R k , φ opt ) = ( | A | − | B | ) . (17)The proof can be found in the technical report [13].IV. P OWER C ONTROL AND R ELAY S ECTION IN THE N ON - COHERENT S CENARIO
At the SU relay, we assume the self-interference is muchhigher than the noise, i.e., ˆ ζP R k >> σ R k . Therefore, we omitthe term σ R k in the object function. Moreover log (1 + x ) isa strictly increase function in x , so we rewrite Problem 1 as Problem 2: max P S ,P Rk ¯ C k ( P S , P R k ) s.t. I non k ( P S , P R k ) ≤ I P , ≤ P S ≤ P max S , ≤ P R k ≤ P max R k , (18)where ¯ C k ( P S , P R k ) = P Rk | h RkD | σ D P S | h SRk | ˆ ζP Rk ¯ A , (19) ¯ A is given as ¯ A = 1 + P R k | h R k D | σ D + P S | h SR k | ˆ ζP R k (20)and ˆ ζ is calculated in (9). Lemma 1.
Problem 2 is a nonconvex optimization problemfor variables ( P S , P R k ) . Lemma 2.
Given P S ∈ [0 , P max S ] , Problem 2 is a convexoptimization problem in terms of P R k . Similarly, given P R k ∈ (cid:2) , P max R k (cid:3) , Problem 2 is also a convex optimization problemin terms of P S . The proofs for these lemmas are omitted and can be found inthe technical report [13]. Since
Problem 2 is non-convex, weexploit alternating-optimization problem (according to Lemma2, the problem is convex when we fix one variable andoptimize the other) to solve
Problem 2 , where each stepis a convex optimization problem and can be solved usingstandard approaches [14]. Finally, we determine the best relayby solving (6).We now consider the special case of ideal self-interferencecancellation, i.e., ˆ ζ = 0 . We characterize the optimal solutionsfor Problem 1 in the special case by the following lemma.
Lemma 3.
Problem 1 is a convex optimization problem forvariables ( P S , P R k ) when ˆ ζ = 0 . The proof of Lemma 3 is in our technical report [13]. Basedon Lemma 3, we can solve
Problem 1 when ˆ ζ = 0 by usingfundamental methods [14].V. P OWER C ONTROL AND R ELAY S ELECTION IN THE C OHERENT S CENARIO
Again, we assume that the self-interference is much higherthan the noise at the selected relay, i.e., ˆ ζP R k >> σ R k . Problem 1 can thus be reformulated as
Problem 3: max P S ,P Rk ¯ C coh k ( P S , P R k ) s.t. I coh k ( P S , P R k ) ≤ I P , ≤ P S ≤ P max S , ≤ P R k ≤ P max R k , (21)where ¯ C coh k ( P S , P R k ) = P Rk | h RkD | σ D P S | h SRk | ˆ ζP Rk P Rk | h RkD | σ D + P S | h SRk | ˆ ζP Rk (22)and ˆ ζ is calculated in (9).To solve Problem 3 , the new variables are introduced as p S = √ P S and p R k = p P R k . Hence Problem 3 can beequivalently formulated as
Problem 4: max p S ,p Rk ˘ C coh k ( p S , p R k ) s.t. I coh k ( P S , P R k ) ≤ I P , ≤ p S ≤ p P max S , ≤ p R k ≤ p P max R k , (23) where the objective function is written as ˘ C non k ( p S , p R k ) = p Rk | h RkD | σ D p S | h SRk | ˆ ζp Rk p Rk | h RkD | σ D + p S | h SRk | ˆ ζp Rk (24)We give a characterization of optimal solutions for Problem4 by the following lemmas.
Lemma 4.
Problem 4 is not a convex optimization problemfor variable ( p S , p R k ) . Lemma 5.
Given p S ∈ (cid:2) , p P max S (cid:3) , Problem 4 is a convexoptimization problem for variable p R k . Similarly, given p R k ∈ (cid:2) , p P max R k (cid:3) , Problem 4 is also a convex optimization problemfor variable p S . The proofs of these lemmas can be found in our techni-cal report [13]. Based on Lemma 5, we again develop thealternating-optimization strategy to solve
Problem 4 , whereeach step is a convex optimization problem and can besolved using basic approaches [14]. The relay selection is thendetermined by solving (6).We now investigate the special case of ideal self-interferencecancellation, i.e., ˆ ζ = 0 . We then characterize the optimalsolutions for Problem 4 in the special case by the followinglemma.
Lemma 6.
Problem 4 is a convex optimization problem forvariables ( P S , P R k ) when ˆ ζ = 0 . The proof of Lemma 6 is in our technical report [13].According to Lemma 6, we can solve
Problem 4 in thisspecial case by using standard approaches [14].VI. N
UMERICAL R ESULTS
In the numerical evaluation, we chose the key parameters ofthe FDCRN as follows. Each link is a Rayleigh fading channelwith variance one (i.e., σ SR k = σ R k D = 1), except σ SD = 0.1.The noise power at every node is also set to be one. Thechannel gains for the links of the SU relay-PU receiver andSU source-PU receiver are assumed to be Rayleigh-distributedwith variances { σ SP , σ R k P } ∈ [0 . , . We also assume thatthe impact of imperfect channel estimation is included in onlythe parameter ζ .We first demonstrate the efficacy of the proposed algo-rithms by comparing their achievable rate performances withthose obtained by the optimal brute-force search algorithms.Numerical results are presented for both coherent and non-coherent scenarios. In Table I, we consider the scenario with ζ = 0.001, 8 SU relays and P max = 20 dB. We comparethe achievable rate of the proposed and optimal algorithmsfor ¯ I P = { , , , , , } dB. These results confirm that ourproposed algorithms achieve rate very close to that attainedby the optimal solution (i.e., the errors are lower than 1%).We then consider a FDCRN SU relays with ζ = 0, 0.001,0.01, and 0.4, which represent ideal, high, medium and lowQuality of Self-Interference Cancellation (QSIC), respectively. TABLE IA
CHIEVABLE RATE VS ¯ I P ( P max = 20 dB ) ¯ I P (dB) 0 2 4 6 8 10 ζ = 0 . , Optimal 4.3646 5.1933 5.5533 5.6944 5.8162 5.9155Coherent Greedy 4.3513 5.1807 5.5496 5.6811 5.8131 5.8826scenario ∆ C (%) ζ = 0 . , Optimal 1.2390 1.6946 2.2118 2.7753 3.3718 3.9902Non-coherent Greedy 1.2309 1.6856 2.2018 2.7650 3.3610 3.9791scenario ∆ C (%) Achievable Rate vs P max and ¯ I P ¯ I P (dB) A c h i e v a b l e R a t e ( b i t s / s / H z ) Gap
Coherent P max = 10, 15, 20, 25 dB Noncoherent P max = 10, 15, 20, 25 dB Fig. 3. Achievable rate versus the interference constraint ¯ I P for K = 8 , ζ = 0 , P max = { , , , } dB, and both coherent and non-coherentscenarios. Achievable Rate vs P max and ¯ I P ¯ I P (dB) A c h i e v a b l e R a t e ( b i t s / s / H z ) NoncoherentCoherent
Gap P max = 10, 15, 20, 25 dB P max = 10, 15, 20, 25 dB Fig. 4. Achievable rate versus the interference constraint ¯ I P for K = 8 , ζ = 0 . , P max = { , , , } dB, and both coherent and non-coherentscenarios. The tradeoffs between the achievable rate of the FDCRN andthe interference constraint are shown in Figs. 3, 4, 5 and 6under different values of ζ. In these numerical results, wechose P max S = P max R k = P max for simplicity.We have the following observations from these numericalresults. Firstly, the achievable rates of the coherent mechanismare always significantly higher than those of the non-coherentmechanism. This is because the phase is carefully regulatedto reduce the interference at the PU receiver imposed by theSU transmissions, which allows higher transmit power both atthe SU source and the SU relay. Furthermore, the achievablerate decreases as expected when the QSIC increases due tothe increase of self-interference at the FD relay.We now show the achievable rates of the FDCRN underdifferent values of P R k when fixing P S = 5 dB in Fig. 7. The Achievable Rate vs P max and ¯ I P ¯ I P (dB) A c h i e v a b l e R a t e ( b i t s / s / H z ) NoncoherentCoherent
Gap P max = 10, 15, 20, 25 dB P max = 10, 15, 20, 25 dB Fig. 5. Achievable rate versus the interference constraint ¯ I P for K = 8 , ζ = 0 . , P max = { , , , } dB, and both coherent and non-coherentscenarios. Achievable Rate vs P max and ¯ I P ¯ I P (dB) A c h i e v a b l e R a t e ( b i t s / s / H z ) Gap
NoncoherentCoherent P max = 10, 15, 20, 25 dB P max = 10, 15, 20, 25 dB Fig. 6. Achievable rate versus the interference constraint ¯ I P for K = 8 , ζ = 0 . , P max = { , , , } dB, and both coherent and non-coherentscenarios. channel gains of the links of the SU relay-PU receiver and SUsource-PU receiver were assumed to be Rayleigh-distributedwith variances { σ R k P , σ SP } ∈ [0 . , . Fig. 7 evaluates thenon-coherent scenario, K = 10 SU relays and ¯ I P = 8 dB. Allfour cases (low, medium, high and ideal QSIC) have similarbehaviors and achieve higher rate than the half-duplex case.For low QSIC (i.e., ζ = 0 . ), the rate first increases thendecreases as P R k increases where the rate decrease is due tothe strong self-interference.Fig. 8 illustrates the achievable rates of the FDCRN against P S for fixed P R k = 5 dB in the non-coherent scenario. Weconsidered K = 10 SU relays and ¯ I P = 8 dB. The resultsfrom both Figs. 7 and 8 confirm that the proposed powerallocation for the FDCRN outperforms the HDCRN.We finally present the coherent scenario, K = 10 SU relays −10 −5 0 500.20.40.60.811.21.41.6 P R k (dB) A c h i e v a b l e r a t e ( b i t s / s / H z ) Achievable Rate vs P R k Full−duplexHalf−duplex ζ = 0.4, 0.01, 0.001, 0 Fig. 7. Achievable rate versus the transmitted powers of SU relay P R k forfixed P S = 5 dB, K = 10 , ¯ I P = 8 dB, P max = 25 dB, and the non-coherentscenario. P S (dB) A c h i e v a b l e r a t e ( b i t s / s / H z ) Achievable Rate vs P S Full−duplexHalf−duplex ζ = 0.4, 0.01, 0.001, 0 Fig. 8. Achievable rate versus the transmitted powers of SU source P S forfixed P R k = 5 dB, K = 10 , ¯ I P = 8 dB, P max = 25 dB, and the non-coherent scenario. −5 0 5 10 15 20 2500.511.52 P R k (dB) A c h i e v a b l e r a t e ( b i t s / s / H z ) Achievable Rate vs P R k Full−duplexHalf−duplex ζ = 0.4, 0.01, 0.001, 0 Fig. 9. Achievable rate versus the transmitted powers of SU relay P R k forfixed P S = 5 dB, K = 10 , ¯ I P = 8 dB, P max = 25 dB, and the coherentscenario. and ¯ I P = 8 dB. Fig. 9 demonstrates the achievable rates of theFDCRN under different values of P R k when fixing P S = 5 dB;while Fig. 10 demonstrates the achievable rates of the FDCRNunder different values of P S when fixing P R k = 5 dB. In thecoherent scenario, we also have the same observations as thosein the non-coherent scenario. P S (dB) A c h i e v a b l e r a t e ( b i t s / s / H z ) Achievable Rate vs P S Full−duplexHalf−duplex ζ = 0.4, 0.01, 0.001, 0 Fig. 10. Achievable rate versus the transmitted powers of SU source P S forfixed P R k = 5 dB, K = 10 , ¯ I P = 8 dB, P max = 25 dB, and the coherentscenario. VII. C
ONCLUSION
This paper studied power control and relay selection inFDCRNs. We formulated the rate maximization problem,analyzed the achievable rate under the interference constraint,and proposed joint power control and relay selection algo-rithms based on alternative optimization. The design andanalysis have taken into account the self-interference of theFD transceiver, and included the both coherent and non-coherent scenarios. Numerical results have been presented todemonstrate the impacts of the levels of self-interference andthe significant gains of the coherent mechanism.A
CKNOWLEDGMENT
This work was supported in part by the NSF under GrantCNS-1262329, ECCS-1547294, ECCS-1609202, and the U.S.Office of Naval Research (ONR) under Grant N00014-15-1-2169. R
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