Best Relay Selection Using SNR and Interference Quotient for Underlay Cognitive Networks

Transcription

1 IEEE ICC 1 - Wireess Communications Symposium Best Reay Seection Using SNR and Interference Quotient for Underay Cognitive Networks Syed Imtiaz Hussain 1, Mohamed M. Abdaah 1, Mohamed-Sim Aouini 1,, Mazen Hasna 3 and Khaid Qaraqe 1 1 Texas A&M University at Qatar, Doha, Qatar King Abduah University of Science and Technoogy, Thuwa, Saudi Arabia 3 Qatar University, Doha, Qatar E-Mais: {syed.hussain, mohamed.abdaah, khaid.qaraqe}@qatar.tamu.edu, sim.aouini@kaust.edu.sa, hasna@qu.edu.qa Abstract Cognitive networks in underay settings operate simutaneousy with the primary networks satisfying stringent interference imits. This condition forces them to operate with ow transmission powers and confines their area of coverage. In an effort to reach remote destinations, underay cognitive sources make use of reaying techniques. Seecting the best reay among those who are ready to cooperate is different in underay settings than traditiona non-cognitive networks. In this paper, we present a reay seection scheme which uses the quotient of the reay ink signa to noise ratio (SNR and the interference generated from the reay to the primary user to choose the best reay. The proposed scheme optimizes this quotient in a way to maximize the reay ink SNR above a certain vaue whereas the interference is kept beow a defined threshod. We derive cosed expressions for the outage probabiity and bit error probabiity of the system incorporating this scheme. Simuation resuts confirm the vaidity of the anaytica resuts and revea that the reay seection in cognitive environment is feasibe in ow SNR regions. I. INTRODUCTION Emerging wireess appications and consumer expectations fueed an endess desire for higher data rates. The enabing technoogies for these high data rate services have consumed amost a the avaiabe and accessibe spectrum. On the other hand, inefficient utiization of huge chunks of icensed spectrum forced reguatory authorities, industry and academia to ook for and devise methods to access this unused spectrum in cognitive manner 1,. Generay, it is suggested that if the icensed or primary user is not using the dedicated spectrum or part of it, the secondary or cognitive user can expoit this unused spectrum 1, aso referred to as spectrum hoe. Once the primary user starts its transmission, the secondary user either switches off or moves to another spectrum hoe if avaiabe. Co-existence in this fashion requires spectrum sensing and detection and generay known as interweave approach. Simutaneous in-band co-existence is possibe in overay settings where the secondary user avoids interference to the primary user by using advanced signa processing techniques. Another simper way to access the spectrum simutaneousy is the underay approach in which the secondary user stricty foows the interference imit 1. In order to obey the interference threshod, secondary users in underay mode are required to transmit at ow powers This pubication was made possibe by NPRP grants No and from the Qatar Nationa Research Fund (a member of Qatar Foundation. The statements made herein are soey the responsibiity of the authors. which imits their area of coverage. Hence, to reach distant destinations, reaying may be an attractive option. There exist various techniques and protocos for reaying a signa in cooperative networks among which ampify and forward (AF is the most popuar one due to its simpicity. As the name suggests, in this technique the received signa at the reay is just ampified and forwarded to the destination 3. Another better performing but computationay expensive approach is decode and forward (DF in which the reay decodes and reproduces the received message before forwarding it to the destination or next node 3. A genera advantage of reaying is to improve diversity order which can be further enhanced by using mutipe reays in the system 4, 5. The reays invoved in such a transmission, in most cases, must transmit on orthogona channes making this approach inefficient in terms of spectrum utiization. Seective reaying was recenty proposed as an aternative for better spectrum efficiency 6. Seective reaying has been a topic of great interest recenty in non-cognitive cooperative networks. Most commony, a reay is picked up to forward the source s message on the basis of signa to noise ratio (SNR it coud provide for the transmission. Contrariy in underay cognitive networks, a reay which coud provide the maximum SNR to the communication ink may aso be a source of strong interference to the primary user or even vioate the interference threshod. Hence, the seective reaying defines an entirey different probem in underay cognitive settings due to the stringent interference threshods. It is aso obvious that the maximum SNR can not be used as the ony criterion for the reay seection. Seective reaying has recenty been studied in a coupe of papers. A modified reay seection criterion is proposed in 7 which takes into account the interference constraint and the reays in the network are assumed to be operating in DF mode. Main contribution in this paper is the derivation of outage probabiity. Another reay seection criterion scheme is proposed in 8 which seects the best reay under the constraint of satisfying a required outage probabiity of the primary network. The outage probabiity of the secondary network is derived where the reays are operating in DF mode. In both of these papers, the secondary nodes are assumed to adapt their transmission power in order to aways satisfy the interference constraint. However, this capabiity may not aways be avaiabe. In this paper, we consider an underay secondary network with mutipe reays operating in AF mode near a primary /1/$31. 1 IEEE 4176

2 user. The secondary nodes have fixed transmission powers at their discretion. We propose a new best reay seection criterion which defines a quotient of end-to-end SNR offered by a reay to the interference it produces to the primary user. A reay which coud maximize this quotient whie maintaining the interference threshod and offering end-to-end SNR above a certain vaue is seected by the destination. We derive cosed form expressions for the cumuative distribution function (CDF of the tota SNR at the destination using moment generating function (MGF approach. We aso derive cosed form expressions for the outage probabiity and average bit error probabiity of the system. II. SYSTEM MODEL Our system mode is comprised of a secondary source S which is transmitting its signa to a secondary destination D with the hep of L secondary reays represented by R i,i = 1,,,L, in Fig. 1. This whoe network is operating in underay mode near a primary user P. A traditiona two time sot communication procedure is foowed in AF mode. The source S with transmission power E s broadcasts its signa in the first time sot. This signa is received by the destination, a the reays and the primary user with channe gains h, h 1i and h SP, respectivey. We assume that each reay is aware of the interference channe h ip form itsef to the primary user. The reays can gather this information either when the primary user is transmitting or when it is acknowedging any received signa. They aso share this information with the destination over some dedicated feedback channes. The reays are aowed to transmit at fixed power E r ; therefore, they adjust their ampification factor in order to reciprocate previous hop s channe gain. We assume that each hop in the system, either communication or interference ink, is subjected to additive white Gaussian noise (AWGN with zero mean and variance N. Hence, each reay sets its ampification factor to g i = Er E s h 1i +N. The channe gain from the i th reay to the destination is h i which we assume is known at the destination. Underay cognitive networks are required to operate under stringent interference imits which guarantees that the primary network is not affected by the secondary communication. Let λ be the interference threshod; however, for some reays the interference channe may be strong enough that they woud not satisfy this threshod. Therefore, the destination who has the channe state information (CSI avaiabe through the reays excudes such reays from the group it is going to pick the best reays, no matter what SNR they coud provide over the secondary reay ink. Let us assume that a certain number of reays out of L satisfies the interference threshod. So, we define a set U which contains the indexes of a the reays, another set A U which contains the indexes of the reays satisfying interference threshod whereas B = U Acontains the remaining indexes. Reay seection takes pace in the second time sot and the destination chooses the best one based on a criterion expained in the next section. The chosen best reay then forwards the source s message to the destination in AF mode. We assume Fig. 1. System Mode: A cognitive network operating near a primary user. that a the channes are Rayeigh distributed and therefore their squared ampitudes have exponentia distribution. The end-to-end SNR of the i th reayed ink (secondary SNR can be given as 1i i SRiD = 1i + i +1, (1 where 1i = Es h1i N is the SNR of the first hop and i = E r h i N is the SNR of the second hop. The above vaue of SRiD is tighty upper bounded by min( 1i, i which makes it a function of just one random variabe (RV and makes the ater anaysis simpe and more mathematicay tractabe 9. SRiD i = min( 1i, i. ( III. THE QUOTIENT BASED RELAY SELECTION SCHEME The best reay seection in underay cognitive networks is entirey different from the traditiona non-cognitive cooperative networks where, in most cases, the best reay is seected on the basis of maximum end-to-end SNR. Contrariy, in cognitive networks, a reay which coud maintain maximum secondary SNR may aso create more interference to the primary user in the absence of transmit power adaptation. Hence, the criterion for seecting the best reay in underay cognitive networks shoud incude the interference a reay is creating on the primary user. So, first we quantify the interference from the source to the primary in the first time sot and from the i th reay to the primary in the second time sot, respectivey, as foows I SP = E s h SP and = E r h ip. (3 The whoe transmission procedure described above coud not begin if I SP is more than λ and thus the proposed scheme coud not be anayzed. In such a case, the source woud wait unti it satisfies the interference imit and quaifies for the transmission. Hence, to anayze the proposed scheme, we assume a situation when I SP λ. Now, to pick up the best reay, we propose a quotient of the i th secondary reay ink SNR i to the interference caused by the i th reay, i.e., Z i = i. The best reay shoud maximize this quotient with two important constraints. First, as mentioned above, 4177

3 the interference eve shoud be beow the given threshod, i.e., λ. Secondy, the secondary SNR shoud be above a certain vaue, i.e., i. The second constraint avoids a situation when a reay is somehow hidden from the primary user and causing very itte interference to it, but does not provide the maximum secondary SNR. In this case, the vaue of Z i becomes extremey arge due to the very sma denominator term and that particuar reay woud aways be picked up, though it is not providing the maximum secondary SNR. Hence, the proposed best reay seection criterion can be stated as i î =maxz i =max such that i, λ, (4 i i where î is the index of the seected reay. With the secondary SNR constraint, we need to define another subset C in U, which contains the indexes of the reays satisfying the secondary SNR condition. Thus, the best reay for the above criterion ies in A C. There exists a non zero probabiity that none of the reays satisfies both constraints and the destination ony receives the direct signa from the source. As mentioned earier, both i and are independent and exponentiay distributed RVs with PDFs as foows p i ( = 1 e i and p IiP (x = 1 e x σ ip, (5 i σ ip where i and σ ip are the average vaues of the secondary SNR and interference strength through the i th reay, respectivey. If the cardinaity of A C is then the PDF of the SNR of the seected reay according the proposed criterion can be given as p s ( =p 1 (Pr p (Pr p (Pr > 1 Pr > I 1P I P I 1P I P > 1 Pr > I P I 1P I P I P 1 I P > 1 I 1P Pr > 1. I P I ( 1P To simpify the above, we can assume that the average vaues of the secondary SNRs and interference strengths are the same for a the reays. Hence, 1 = = = = and σ 1P = σ P = = σ P = σ. With this assumption, (6 can be written as i IîP p s ( =p î( Pr 1 <î, i î. (7 iiîp In the above, Pr I <î ip evauated at î.this CDF can be derived in two steps. First, (6 is simpy the CDF of ii îp we consider i,whichisz i for a the reays not seected by the destination but i A C. The conditiona CDF of Z i with secondary SNR and interference constraints can be evauated as P Zi (z; i, λ = λ xz p i (d p IiP (xdx, = P P λ 1 βe αz μz +1, (8 where P = Pr( i =e, Pλ = Pr( λ = 1 e λ σ, α = λ, β = e λ σ and μ = σ. Differentiating the above gives us the PDF of Z i μ (az + be αz p Zi (z; i, λ = (μz +1, (9 where a = αμβ and b =(α + μβ Now, we consider Y i = Z i IîP, in which IîP is the interference produced by the seected reay to the primary user and it shoud be ess than λ. TheCDFofY i with a the constraints can be evauated as P Yi (y; i,, IîP λ = λ y ˆx λ p Zi (zdz p IîP (ˆxdˆx. (1 The interference produced by the seected reay is aso exponentiay distributed with parameter σ and Z i is distributed as given in (9. Repacing these vaues in (1 and soving by using 1, Eqs , , , , we get P Yi (y; i,, IîP λ=a+ y e y Ei ( λ σ y Ei ( y (11 where A = μp λ μ+λ and Ei( is the exponentia integra. Repacing (11 with y = in (7 we get p s ( ; i,, IîP λ = e A + e 1 Δ( (1 ( ( where, for the ease of notation, Δ( Ei λ σ Ei. We notethat Δ( is infinitesimay sma quantity, speciay at higher SNR, and its higher powers coud be negected. Therefore, the above PDF coud be approximated to p s ( ; i,, IîP λ A 1 e (13 It is worthy to note that the above PDF is conditioned over, i.e., the number of reays satisfying both constraints. The vaue of mayvaryfrom to L. If =, the destination ony receives the direct signa from the source. In case =1, sti there woud be no reay seection, rather, the destination coud combine the direct and the ony reayed signa. A choice among the reays becomes avaiabe to the destination when and the destination coud seect the best reay according to the proposed scheme. Each reay in the system can satisfy these constraints with a probabiity P c = P P λ = e (1 e λ σ. Hence, the probabiity of reays avaiabe for seection out of L foows a binomia distribution ( L p (; L, P c = = L! P c (1 P c L, (14 where ( L!(L!. The unconditiona PDF of s can be found by averaging (13 using (14 for =1,,,L. Therefore ( L A 1 Pc p s (; i,, IîP λ= (1 P c L e. (15, 4178

4 Since the end-to-end SNR maintained by the seected reay shoud be above, we can evauate a truncated moment generating function (MGF of s as foows M s (s; i, λ= e s p s (; i,, IîP λd ( L A 1 Pc (1 P c L P e s = (s + 1. (16 The direct ink SNR is aso exponentiay distributed with its 1 average vaue having a we known MGF 1+s.Since the direct and the seected reay ink SNRs are competey independent, the CDF of the tota SNR at the destination, T = + s, can be given as P T ( =L 1 M (sm s (s (17 s s= where L 1 ( represents the inverse Lapace transform and again, to simpify the notation, we have dropped the constraint descriptions; however, it shoud be reminded that a the PDFs, CDFs and MGFs which foow are the truncated versions due to the posed constraints. Repacing (16 in (17 and soving by 1, Tabe , we get ( L P T ( = A 1 Pc (1 P c L P e 1 ( e 1 ( +( (18 IV. PERFORMANCE ANALYSIS A. Outage Probabiity According to the conventiona definition of outage probabiity, it represents the probabiity of having the received SNR beow a certain threshod. Hence, the outage probabiity coud be directy derived through the CDF of the tota SNR above by repacing = th,where th is the outage threshod SNR. The CDF of the tota SNR in (18 is for the situations when at east one reay satisfies the imposed constraints. However, as mentioned earier, it is possibe that none of the reays satisfies the imposed constraints and the destination receives the direct signa ony. The probabiity of this event is Pr ==(1 P c L. Furthermore, the probabiity of having the SNR ess than th with the direct signa ony is th (1 e. Hence, the outage probabiity of the system can be evauated as P out = P T ( th +(1 P c L th (1 e. (19 B. Average Bit Error Probabiity In order to find the average bit error probabiity, we first express the error probabiity conditioned over a given SNR in AWGN. This coud be written terms of standard Q function which coud then be averaged over the derived tota SNR PDF. Fig.. BER Considered Cognitive Network with L = 1,,3,4 Direct Link Ony Non Cognitive Network with L = 1,,3, SNR Per Hop (db Anaytica Simuation BER with λ =1and =1for different number of reays. We assume that the moduation scheme used in the network is inear in nature. P e =Pr = P e (ε p (d + P e (ε T p T (d, }{{}}{{} Direct ink ony Direct and best reay inks ( where P e (ε =Q( β and β is a constant depending upon the moduation scheme. InsteadofderivingthePDFof T, we can use the technique given in 11 to evauate P e using the derived CDF. P e (ε p (d = 1 π P ( t β e t dt. (1 Repacing (18 and the CDF of the direct ink SNR in ( and soving using 1, Eq , we obtain P e = (1 P c L β πp ( L 1 + A 1 (1 + Pc (1 P c L e erfc(q e ( q ( q erfc(q+ erfc(, ( where q = β+ β, q = β+ β and erfc( is the compementary error function. V. SIMULATION RESULTS Simuation resuts are obtained by varying the average per hop SNR whereas the interfering channes are generated with parameter σ =.9 and the direct ink is simuated with =.8. The noise in each hop is considered to be unit variance AWGN with zero mean. The transmission power at the source and the reay is aso assumed to be E s = E r =1. Binary phase shift keying (BPSK with β =is used as the moduation technique. System configurations with different number of reays are compared with equa power conditions. The bit error probabiity (BER of the system is presented in Fig. with λ = 1 and = 1 for different 4179

5 1 Anaytica Simuation 1 Anaytica Simuation 1 1 λ = 1, = 1 Direct Link Ony BER λ = 1, =.1 λ = 1, = 1 λ = 1, = 1 Outage Probabiity L = 1,,3,4 λ =, = SNR Per Hop (db SNR Per Hop (db Fig. 3. BER with L =4and different vaues of constraints λ and. Fig. 4. Outage probabiity with λ =1, =1and th =1for different number of reays. number of reays. BER performance of the system when it is operating on the direct ink ony i.e. none of the reays satisfies the imposed constraints is shown for comparison purposes. Simiary, the BER of the traditiona non-cognitive reay network with best reay seection is aso potted for comparative anaysis ony. In non-cognitive networks, the best reay is chosen amongst the L reays and hence the diversity order of the system remains L at any SNR. On the other hand, in the considered cognitive network, the seection takes pace out of reays, where L. Hence, on average, the diversity order of the non-cognitive network is higher than that of cognitive network where the reays are short isted based on the imposed constraints. This phenomenon resuts in better BER of non-cognitive networks at any vaue of L and SNR. If we concentrate on the performance of the considered cognitive network, we observe that from ow to medium SNR the interference to the primary is not an issue and the BER performance foows a norma trend. Increasing per hop SNR causes more and more reays to satisfy the vaue of and the BER graduay reduces. However, from medium to high SNR, the reays start vioating the interference threshod λ and get excuded from the seection poo. This causes a degradation in the performance and eventuay at high SNR none of the reays coud satisfy the interference constraint and system operates on the direct ink ony. To study the effects of interference and SNR constraints on on the proposed scheme, we simuate the system with four reays under different sets of constraint vaues, as shown in Fig. 3. The vaues of λ =1and =1serve as comparison benchmark. Increasing the SNR constraint or reducing the interference imit makes it difficut for the reays to quaify for the seection and the BER of the system increases. It is aso evident that more reays coud be avaiabe for the seection reducing the BER if the constraints are reaxed, i.e., is reduced and λ is increased. These variations aso suggest different optima operating points of the system in different settings to achieve the minimum BER. Outage probabiity of the system is depicted in Fig. 4. Simiar trends as seen in the BER are aso visibe here in outage probabiity due to the same reasons. It is cear from these resuts that the reay seection improves the system performance in ow to mid SNR range for underay cognitive networks. Whereas, in non-cognitive cooperative networks, it is feasibe at a SNR vaues. VI. CONCLUSION We proposed a reay seection scheme based on SNR and interference quotient for a cognitive network operating near a primary user. The proposed scheme maximizes the reay ink SNR whie keeping the interference to the primary beow the defined threshod. We derived the cosed form CDF of the tota SNR at the destination using MGF approach and then used it to derive BER and outage probabiity of the system in cosed forms. We showed that reay seection is ony feasibe at ow SNR in underay cognitive networks. Anaytica formuae are verified through simuations. REFERENCES 1 A. Godsmith, S. A. Jafar, I. Maric, and S. Srinivasa, Breaking spectrum gridock with cognitive radios: An information theoretic perspective, Proceedings of the IEEE, Vo. 97, No. 5, pp , May 9. S. Haykin, Cognitive radio: Brain-empowered wireess communications, IEEE J. Se. Areas Commun., Vo. 3, No., pp. 1-, 5. 3 J. N. Laneman, D. N. C. 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