Int J Electron Commun (AEÜ) 69 (2015) 1700–1708 Contents lists available at ScienceDirect International Journal of Electronics and Communications (AEÜ) journal homepage: www.elsevier.com/locate/aeue Outage analysis in cooperative cognitive networks with opportunistic relay selection under imperfect channel information Khuong Ho-Van ∗ Telecommunications Engineering Department, Ho Chi Minh City University of Technology, 268 Ly Thuong Kiet Str., District 10, Ho Chi Minh City, Viet Nam a r t i c l e i n f o Article history: Received February 2015 Accepted August 2015 Keywords: Opportunistic relay selection Imperfect channel information Cognitive radio Performance saturation a b s t r a c t This paper proposes exact and limit outage probability expressions for thoroughly evaluating the performance of cooperative cognitive networks with opportunistic relay selection under imperfect channel information, independent and non-identical (i.n.i.) Rayleigh fading channels, maximum transmit power constraint, and interference power constraint The proposed derivations can be straightforwardly extended to corresponding analysis in dual-hop cognitive networks with opportunistic relay selection to investigate how much performance gain can be achieved from using the direct channel between the source and the destination in relaying communications Numerous results illustrate significant outage performance degradation and performance saturation due to channel information imperfection but the degradation and saturation level can be remedied by increasing the number of relays Also, the channel direct brings a considerable performance improvement without any additional expense of system resources such as power and bandwidth Moreover, channel information imperfection can cause interference power at primary users to exceed a pre-defined level, deteriorating the quality of service of primary users © 2015 Elsevier GmbH All rights reserved Introduction Traditional static spectrum allocation is not flexible and induces low spectrum utilization efficiency [1] This issue turned with high radio spectrum demand of emerging wireless services requires appropriate solutions to mitigate current spectrum under-utilization Cognitive radio technology, which allows secondary/unlicensed users (SUs) to opportunistically access the spectrum inherently allotted to primary/licensed users (PUs), is a right solution to these critical issues [2] Nevertheless, in order to assure transparent communication of PUs, SUs must limit their transmit power for acceptable interference at PUs, and thus, reducing the communication coverage of secondary transmitters With the advantage of wide radio coverage, relaying techniques have recently been incorporated into SUs to complement the drawback of the short radio range of SUs [3] The relaying process can be assisted by multiple relays for high performance but low bandwidth efficiency due to the requirement of orthogonal channels for different relays in order to prevent mutual interference As such, selecting a single relay among all possible candidates according ∗ Corresponding author Tel.: +84 1229900719 E-mail address: khuong.hovan@yahoo.ca http://dx.doi.org/10.1016/j.aeue.2015.08.004 1434-8411/© 2015 Elsevier GmbH All rights reserved to a certain criterion is preferred to optimize system resource utilization (e.g., power and bandwidth), in comparison with multirelay assisted transmission while remaining the same diversity order [4] Furthermore, channel state information is very important in the process of system design optimization (e.g., optimal signal detection) However, it is inevitable that this information cannot be collected without any error Therefore, the impact of imperfect channel information (ICI) on the outage performance of relay selection criteria in cognitive relaying networks should be thoroughly investigated before practical implementation The impact of ICI1 on the opportunistic relay selection in dual-hop cognitive networks (i.e., without considering the direct channel), which selects the relay with the maximum end-to-end The impact of ICI on cognitive radio networks was studied in different aspects; for example, dual-hop relaying with relay selection (e.g., [7,6,5]), direct transmission (i.e., no relay) [8], the amplify-and-forward relay selection (e.g., [10,9]), relay non-selection (e.g., [11,13,15,12,14]) Moreover, several relay selection criteria in cognitive radio networks are suggested without investigating the impact of ICI in [16–18,27,28,26,29,23,30,24,31,38,32,35,36,34,25,33,37,39,44,43,42,40,41] The current paper concentrates on the opportunistic relay selection in decode-and-forward cooperative cognitive networks, and thus, the literature related to the aspects studied in [11,16–18,27,28,26,29,23,30,24,31,38,32,35, 36,34,25,33,37,44,43,42,40,7,6,8,10,9,13,15,12,14,39,41,5] should not be further surveyed K Ho-Van / Int J Electron Commun (AEÜ) 69 (2015) 1700–1708 signal-to-noise ratio (SNR), is investigated in [45] Nevertheless, this work does not investigate ICI on all fading channels simultaneously, that is, ICI on interference channels (i.e., channels from SUs to PUs) while perfect channel information (PCI) on transmission channels (i.e., between SUs); or ICI on transmission channels but PCI on interference channels Also, [45] only considers independent partially-identical (i.p.i.) fading distributions (i.e., relays are assumed to be closely located) The effect of ICI on the reactive relay selection, which selects the relay among all possible candidates (i.e., all relays are assumed to correctly decode source information) with the largest SNR to the destination, and the Lth-worst relay selection, which selects the Lth-worst relay, is investigated in [46,47] However, both [46,47] are limited to the case of ICI on interference channels while PCI on transmission channels, and the i.p.i fading distribution assumption The effect of ICI on the partial relay selection, which simply selects the relay with the largest SNR from the source, is studied in [42,48–50] Nevertheless, for analysis simplicity, the works in [42,48–50] impose several assumptions such as only ICI on interference channels while PCI on transmission channels, i.p.i fading distributions, and dual-hop relaying The opportunistic relay selection is proved to be capacityoptimal [16], and hence, it is interesting to predict its informationtheoretic performance limit (i.e., outage probability) Motivated by the above, this paper thoroughly analyzes its outage performance The contributions of this paper are summarized below: • Propose an exact closed-form outage probability expression for cooperative cognitive networks with opportunistic relay selection, neglecting all assumptions of [45] More specifically, this expression is applicable to a general scenario: ICI on all channels concurrently, i.n.i fading distributions, maximum transmit power constraint, interference power constraint, the usage of the direct channel • Derive the performance limit of cooperative cognitive networks with opportunistic relay selection, which proves no diversity gain achievable in the presence of ICI • Perform numerous comparisons between dual-hop and cooperative cognitive networks with opportunistic relay selection, which demonstrate a significant gain of utilizing the direct channel in relaying communications at almost no expense of system resources (e.g., power and bandwidth) • Provide numerous results to have useful insights into system performance such as performance saturation phenomenon and considerable performance deterioration due to ICI, significant performance improvement with respect to the increase in the number of relays • Outline an interference probability2 expression to reflect the effect of channel information imperfection on the quality of service of primary users Illustrative results are also provided to show that the interference probability is proportional to the number of relays, which conflicts with outage performance improvement of secondary users when the number of relays increases, establishing the performance trade-off between the primary network and the secondary network with respect to the number of relays 1701 and limit outage analysis framework for the opportunistic relay selection in cooperative cognitive networks as well as in dual-hop cognitive networks is elaborately described in Section The interference probability expression is outlined in Section Results and discussions on the outage performance of these networks as well as the interference probability are provided in Section Finally, the paper is closed with useful conclusions in Section System model A cooperative cognitive network with opportunistic relay selection is demonstrated in Fig Cooperative relaying is implemented in the secondary network in which information transmission from the source Ss to the destination Sd is helped by the selected relay Sb in the group of K relays, S = {S1 , S2 , , SK } We assume cognitive radios to operate in the underlay mechanism (e.g., [16,19–22]), and hence, Ss and Sb interfere the PU, namely Pp , but the interference level at Pp must be lower than the maximum interference power, I, that can be tolerated by Pp We investigate frequency-flat and i.n.i Rayleigh fading channels Therefore, the channel coefficient, htr , between a transmitter and a receiver, where t and r denote the indices of the transmitter and the receiver, respectively (the specific values of t and r will be specified later), can be modelled as a circular symmetric complex Gaussian random variable with zero mean and 1/ tr -variance, i.e htr ∼CN(0, 1/ tr ) Since our work investigates i.n.i fading distributions, all tr ’s, ∀{t, r}, are not necessarily equal Therefore, it is more general and practical than most existing works on relay selection where i.p.i (i.e., tr ’s are partitioned into groups of identical value For example, sr ’s, rd ’s, rp ’s with r ∈ {1, , K} are assumed to be identical in [7,16,23,24,26,29,42,45–48]) or independent and identical (i.e., tr ’s, ∀{t, r}, are equal in [25,27,28,31]) fading distributions are assumed for simplicity of performance analysis It is inevitable that PCI is impossibly available owing to the limitations of channel estimation algorithms As such, in order to support performance analysis, we should model channel information imperfection appropriately In this work, we apply the well-known channel information imperfection model used in [8,10,13,39,42,45,46,48,49,51] According to this model, the real channel coefficient, htr , is related to the estimated one, hˆ tr as hˆ tr = tr htr + 1− tr εtr , (1) Primary receiver Pp Phase S1 Sb Phase The rest of the current paper is structured as follows The system model under consideration is presented in Section Exact SK Interference probability is defined as the probability that the interference power constraint is invalidated Some works proposed the interference probability expression for the partial relay selection (e.g., [42,48,50]) and the reactive relay selection (e.g., [46]) To the best of the author’s knowledge, the interference probability expression for the opportunistic relay selection have not been presented in open literature Sd Ss Secondary network Fig System model 1702 K Ho-Van / Int J Electron Commun (AEÜ) 69 (2015) 1700–1708 where εtr is the channel estimation error, t ∈ s, 1, , K , r ∈ p, 1, , K, d As elaborately discussed in [8], all random variables {hˆ tr , htr , εtr } are modelled as CN(0, 1/ tr ) Moreover, the correlation coefficient ≤ tr ≤ is a constant, characterizing the average quality of channel estimation As exposed in Fig 1, cooperative relaying with opportunistic relay selection takes place in two phases In the first phase, Ss transmits the signal vs with transmit power Ps (i.e., Ps = Evs {|vs |2 } where EX { · } denotes the expectation over the random variable X) A certain secondary transmitter St , t ∈ s, 1, , K must obey the underlay mechanism on one hand (i.e., Pt |htp |2 ≤ I), and the maximum transmit power P designed for it (i.e., Pt ≤ P) on the other hand For maximum transmission coverage, the upper-bound of the transmit power is chosen, i.e Pt = min(I/|htp | , P) Due to the unavailability of channel information, the transmit power must be set with the estimated channel information (e.g., [8]) as Pt = min(I/|hˆ | , P) The received signal at Sr , r ∈ 1, , K, d , can be expressed as usr = hsr vs + nsr in which nsr ∼CN(0, N0 ) is the additive white Gaussian noise (AWGN) at the secondary receiver Sr Plugging (1) into usr , one obtains usr = hˆ sr sr sr 1− vs − sr εsr vs + nsr , (2) which generates the signal-to-noise ratio (SNR) at Sr in the first phase as sr Evs {|hˆ sr vs / = Evs ,nsr {|nsr − 1− sr | } sr εsr vs / sr | = ˇsr |hˆ sr |2 (3) } By denoting I = I/N0 , P = P/N0 , = I/P, x = |hˆ sp |2 , the ˇsr term in (3) can be represented in a compact form as ˇsr = sr Ps (1 − sr )Ps + sr sr N0 = ⎧ ⎪ ⎨ ⎪ ⎩ sr I sr sr x (1 − sr )I + (1 − sr P sr )P + sr sr ,x > = max(min( k∈R sk , kd )), where R = 1, 2, , K and kd is the SNR of the Sk − Sd channel The expression of kd can be inferred in the same manner as sr , i.e kd ˇkd = ⎪ ⎩ (1 − The outage probability is defined as the probability that e2e is below a threshold , i.e PoCC = Pr{ e2e ≤ } where = 22R − with R being the required transmission rate and Pr X denotes the probability of the event X Since e2e contains two correlated quantities, sd and sbd , PoCC must be evaluated in terms of conditional probabilities, i.e PoCC = Pr max ( = Ex sd , ⎧ ⎪ ⎨ sbd ) ≤ + (1 − kd P )P + kd )I kd kd kd = Ex Pr max ( Pr sd ≤ x Pr sbd ≤ x ⎪ ⎭ Á Since hˆ tr ∼CN 0, 1/ tr sd , ⎫ ⎪ ⎬ Ä ⎪ ⎩ (7) x (8) , the probability density function (pdf) hˆ tr hˆ tr z ≥ Therefore, it immediately follows that Á = Pr ˇsd hˆ sd sd ˇsd ≤ =F x hˆ sd ˇsd x = − Qsd , (9) where Qsd = e− has a common form as Qtr = e− further simplified after using (4) and (7) as ⎧ ⎪ ⎪ ⎨ A e− tr = ⎪ ⎪ ⎩ , yk < with yk = |hˆ kp |2 It is noted that opportunistic relay selection can be implemented in a distributed manner using the timer method in [4] where each relay Sk sets its timer with the value that is inversely proportional to min( sk , kd ) and the relay with the timer that runs out first is selected In the second phase, the selected relay Sb decodes the source signal and re-encodes the decoded information before forwarding to Sd Then, Sd can decode the source information by selectioncombining the received signals in both phases Therefore, the total SNR at Sd can be represented as e2e = max( sd , sbd ) It is recalled ≤ sd ˇsd , yk > sbd ) and the cumulative distribution function (cdf) of hˆ tr are − tr z and F − tr z for expressed as f (z) = tr e (z) = − e = − e− kd I kd kd yk 3.1 Exact analysis (6) where ⎧ ⎪ ⎨ This section firstly presents an exact outage analysis in cooperative cognitive networks with opportunistic relay selection, which is then used to infer system performance limits The proposed analysis framework is relatively general, and hence, based on it, a similar analysis in dual-hop cognitive networks with opportunistic relay selection (e.g [45]) can be performed to expose the advantage of utilizing the direct channel in relaying communications without time-consuming simulations (4) (5) = ˇkd |hˆ kd |2 , Outage performance analysis ,x < Opportunistic relay selection opts for a relay, namely Sb , with the maximum end-to-end SNR Therefore, the SNR at Sd through the relaying channel is expressed as sbd that the implementation of the selection combining in this paper is simpler than the maximum ratio combining without significant performance degradation [52] Therefore, the selection combining is preferable in practical applications Moreover, since both sd and ˆ sbd contain a common term x = |hsp | , they are correlated Furthermore, the quantities min( sk , kd ) for different k inside the maximum operator in (5) are correlated since they also contain x These SNR correlations (i.e., between sd and sbd , and between min( sk , kd ) and min( si , id ), ∀(k, i)) make the performance analysis in next sections complicated but accurate It is also noted that for analysis simplicity, [45] assumed that min( sk , kd ) is uncorrelated with min( si , id ), ∀(k, i) while this does not hold tr Qtr = e− ˇtr tr tr I Btr z , z = hˆ , z = hˆ > tr ˇtr , which is (10) < with Atr = e( − Btr =e −1 tr ) 2+ 1− tr tr P tr (11) K Ho-Van / Int J Electron Commun (AEÜ) 69 (2015) 1700–1708 where A = obtains The Ä term in (8) can be decomposed as Ä = Pr max (min ( sk , k∈R ≤ kd )) x Ä = + (−1)K Qkd k∈R Pr ( sk , kd ) ≤ x = − Pr ( ≥ sk , kd ) x Pr x ··· s1 =1 s2 =s1 +1 K − Pr sk ≥ ≥ kd Qkd su =su−1 +1 k∈A Qsk (19) k∈A Plugging (9) and (19) into (8) results in the simplified form of PoCC as k=1 = K (−1)u u=1 K Qsk k∈R K−u+1 K−u+2 K−1 + k=1 , to expand the product in (15), one R [s1 ] , , R [su ] K = 1703 x (12) PoCC = T∅ + (−1)K TR Qkd k∈R k=1 K−u+1 K−u+2 K−1 Since kd is independent of x, the conditional probability Pr becomes the unconditional one Pr kd ≥ x kd ≥ Therefore, (12) can be further rewritten as + (−1) u K ··· s1 =1 s2 =s1 +1 u=1 TA su =su−1 +1 Qkd , (20) k∈A where W = {∅, A, R} and K Ä= − Pr sk ≥ x Pr ≥ kd (13) TW = Ex k=1 (1 − Qsd ) Inserting (3) and (6) into (13) and after some basic manipulations, one obtains K Ä= ˇsk hˆ sk − Pr ≥ x ˇkd hˆ kd Pr ≥ Qsk ⎧ ⎨ − Ex ⎫ ⎬ Qsk ⎩ = Ex Qsk k∈W k∈{W,d} ⎭ k∈W = Tˆ W − Tˆ {W,d} (21) k=1 K = hˆ sk − Pr ≥ k=1 ˇsk x hˆ kd Pr ≥ It is apparent that the derivation of the exact closed-form expression of PoCC is completed after analytically evaluating Tˆ G in (21) where G is either W or {W, d} Towards this end, we use (10) and then evaluate the resulting integrals as ˇkd K = 1− 1−F k=1 hˆ sk x ˇsk Eyk 1−F hˆ kd ˇkd ∞ yk Tˆ G = Ex Qsk + Using the general notation in (10) for both Qsk and Qkd , one can simplify (14) as − Qsk Eyk = Qkd k=1 (1 − Qkd Qsk ) sp e − sp x x dx Bsk dx k∈G (15) = Qkd = Akd e − − kp yk dyk kp e Bkd kp e− kp yk dyk + kp −D kd e Dkd + Bkd Ck , (16) where Akd and Bkd are given in (11) with appropriate subscript substitutions, and = − e− = kp kd kd I (17) + kp Using the fact that K (1 − ak ) = + (−1)K k=1 ak k∈R K−u+1 K−u+2 K−1 (−1)u + u=1 e ak , su =su−1 +1 k∈A x dx Bsk sp e − sp x dx k∈G = sp −EG EG Ask + Cs e k∈G Bsk , (22) k∈G where {Ask , Bsk } and Cs are given in (11) and (17) with appropriate subscript substitutions, respectively, and EG = sp + I sk sk (23) k∈G It is worth emphasizing that although the opportunistic relay selection in this paper is elaborately discussed (e.g., [45]), the derivation of its exact closed-form outage probability expression in (20) has not been reported in any open literature for the general case of i.n.i fading distributions, cooperative relaying, and ICI on all channels concurrently On contrary, [45] considers dual-hop relaying, i.p.i fading distributions, and ICI either on interference channels or transmission channels To the best of the author’s knowledge, (20) is totally novel and represented in a very convenient and compact form for the analytical evaluation Furthermore, K ··· s1 =1 s2 =s1 +1 k∈G k∈G + kd kd yk I Akd Ask sp sk sk sp + I − ∞ k=1 ∞ Dkd sk sk I k∈G In (15), Qkd = Eyk Qkd Its exact closed-form representation is obtained by using the compact form of Qkd in (10) as Ck Ask e− − sp x K Ä= = sp e k∈G (14) K = (18) R[j] stands for the jth element of the set R 1704 K Ho-Van / Int J Electron Commun (AEÜ) 69 (2015) 1700–1708 this section provides a relatively general analysis framework, which is easily extended to the corresponding analysis in dual-hop cognitive networks with opportunistic relay selection Indeed, the outage probability of dual-hop cognitive networks with opportunistic relay selection is given by PoDH = Pr sbd ≤ = Ex {Ä} (24) By following the same procedure of deriving PoCC in (20), one obtains PoDH = Tˆ ∅ + (−1)K Tˆ R K−u+1 K−u+2 K−1 K (−1)u s1 =1 s2 =s1 +1 u=1 Tˆ A ··· su =su−1 +1 Qkd , (25) k∈A It is interesting to discover from (20), (21), (25) that TW < Tˆ W and PoCC < PoDH In other words, cooperative relaying under consideration in this paper is always better than dual-hop relaying in [45] at no significant cost of system resources (e.g., power and bandwidth), and hence, the former should be used in practice It is also noted that (25) accounts for the correlation among the quantities min( sk , kd ) in sbd for different k and has not been reported in any open literature while [45] ignores this correlation in performance limit analysis 3.2 Performance limit analysis To have insights into system performance limits, we should investigate the outage performance in the high SNR regime, i.e P → ∞ Since I = P, this regime also implies I → ∞ Therefore, based on (4) and (7), one can approximate the quantity Qtr in (10) as P,I→∞ Qtr → Atr (26) Using (26), we can also approximate the quantities in (9), (15), (16) as K P,I→∞ {Qkd , Á, Ä} → {Akd , − Asd , (1 − Ask Akd )} (27) k=1 Substituting (27) into (20), we obtain the outage performance limit (i.e., in the high SNR regime) of cooperative cognitive networks with opportunistic relay selection as (28) It = Pt |htp | = K = (1 − Ask Akd ) (29) k=1 It is observed from (28) and (29) that the performance limits of both dual-hop and cooperative cognitive networks with opportunistic relay selection depend only on constants Atr , which are functions of correlation coefficients tr As such, these networks experience performance saturation phenomenon at high SNRs P,I→∞ {x, y, } → P,I→∞ P,I→∞ X, Y, x → X, y → Y, I |hˆ | ,P |htp | (30) / hˆ ), It Due to channel information imperfection (i.e., htp = can exceed the maximum interference power I, violating the interference power constraint which is a critical requirement for guaranteeing the quality of service of PUs The probability that the interference power at the PU exceeds I is defined as the interference probability, J For the opportunistic relay selection under consideration, there are two cases which cause the interference power at the PU to exceed I: • Case 1: This case corresponds the first phase of cooperative relaying process as shown in Fig The source modifies its transmit power Ps inaccurately and causes an interference power Is in (30) to be larger than I • Case 2: This case happens when the source does not interfere with the PU in the first phase However, when the selected relay Sb is active in the second phase, it adjusts its transmit power Pb incorrectly and causes an interference power Ib in (30) to be larger than I Based on the total probability law, the interference probability is given by J = Pr Is > I + Pr Is ≤ I, Ib > I + Pr = Pr Is > I Is ≤ I, Ib > I Sb is selected Pr Sb is selected , b=1 Following the same procedure of deriving (28), one can achieve the outage performance limit of dual-hop cognitive networks with opportunistic relay selection (i.e., in the high SNR regime) as The interference power It at the PU caused by the secondary transmitter St can be expressed as K (1 − Ask Akd ) k=1 DH CC Interference probability K CC P o = (1 − Asd ) Po DH again from (28) and (29) that P o /P o = 1/(1 − Asd ), and hence, the saturation level of cooperative relaying is 1/(1 − Asd ) times smaller than that of dual-hop relaying These results encourage utilizing the direct channel in relaying communications Qkd k∈R + (equivalently, no diversity gain can be achievable) and their saturation levels only depend on the quality of channel estimators (i.e., tr ) In other words, ICI completely destroys the advantage of the relay selection in terms of diversity gain (i.e., zero diversity order) This is contrast to the case of PCI (i.e., tr = 1), where the diversity order is always non-zero Indeed, inserting tr = into (28) and (29) results in zero outage probability and hence, the non-zero diversity order is achievable However, the saturation level of cooperative relaying is smaller than that of dual-hop relaying This can be seen is the short-hand representation which denotes (31) where the event {Sb is selected} is min( sb , bd ) > min( sk , kd ), ∀k ∈ R\b Substituting {Is , Ib } in (30), { sb , sk } in (3), and { bd , kd } in (6) into (31) results in an expression with many correlated random variables Therefore, it is impossible to obtain an approximate/exact closed-form expression of J Consequently, we borrow simulations in the next section to investigate the effect of imperfect channel information on the primary network Results and discussion This section provides numerous results to corroborate the validity of the proposed analytical expressions, investigate the impact of ICI on the outage behavior of cooperative cognitive networks with opportunistic relay selection and on the interference probability, and highlight the advantage of the direct channel in relaying K Ho-Van / Int J Electron Commun (AEÜ) 69 (2015) 1700–1708 1705 10 −1 10 −2 10 −3 Outage probability 10 −4 10 −5 Sim.: K=1 & DH Exact Ana.: K=1 & DH Sim.: K=1 & CC Exact Ana.: K=1 & CC Sim.: K=3 & DH Exact Ana.: K=3 & DH Sim.: K=3 & CC Exact Ana.: K=3 & CC Sim.: K=5 & DH Exact Ana.: K=5 & DH Sim.: K=5 & CC Exact Ana.: K=5 & CC 10 −6 10 −7 10 −8 10 Fig Outage probability versus P 10 communications The fading power of the t − r channel is assumed −˛ as 1/ tr = dtr where dtr is the distance between the transmitter t and the receiver r while ˛ is the path-loss exponent Without loss of generality, we choose ˛ = and fixed user coordinates: Ss at (0, 0), 10 −9 −10 10 15 20 P (dB) 25 30 35 40 Fig Outage probability versus P for perfect channel information Sd at (1, 0), Pp at (0.6, 0.7), Sk at {(0.4612, − 0.1765), (0.4867, k=1 − 0.1373), (0.5182, 0.0621), (0.5282, 0.1780), (0.4686, − 0.0431)} In the sequel, ‘Ana.’, ‘Sim.’, ‘CC’, and ‘DH’ stand for ‘Analysis’, ‘Simulation’, ‘Cooperative Relaying’, and ‘Dual-hop Relaying’, respectively; three groups of relays are considered: K = for {S1 }, K = for Sk , K = for Sk k=1 k=1 Fig demonstrates the outage behavior of the opportunistic relay selection in both dual-hop and cooperative cognitive networks with respect to the variation of P = P/N0 for = 0.2 and R = bit/s/Hz Two availability levels of channel information are illustrated: PCI (i.e., tr = 1, ∀ {t, r}) and ICI with randomly selected and mutually different correlation coefficients ( sd = 0.9144, sp = 0.9231, kd k=1 = {0.9037, 0.9107, 0.9681, 0.9007, 0.9749}, kp k=1 = 0.9438, 0.9040, 0.9556, 0.9345}, {0.9095, sk k=1 = {0.9168, 0.9627, 0.9094, 0.9662, 0.9528}) It is observed that the exact analysis (i.e., (20) and (25)) perfectly agrees with the simulation for the whole range of P while the performance limit analysis (i.e., (28) and (29)) is in a perfect agreement with the simulation at large values of P (e.g., P ≥ 30 dB), verifying the validity of the proposed expressions5 In addition, in the case of ICI, both cooperative and dual-hop cognitive networks with opportunistic relay selection suffer the error floor phenomenon in the high SNR regime, which is already discussed and analytically proved in Section 3.2 In other words, opportunistic relay selection does not contribute any diversity gain in the case of ICI, which is contrast to the case of PCI where the diversity order is always non-zero6 To be more specific, in the case of PCI, both networks obtain a non-zero As discussed in Section 3.2, PCI makes zero outage probability in the high SNR regime and hence, no performance limit for this case is shown in Fig To see no error floor even at very low outage probabilities, we extend the plot of Fig for the case of PCI at high SNRs The results are illustrated in Fig It is seen that both cooperative and dual-hop cognitive networks with opportunistic relay selection not experience performance saturation phenomenon and the former is superior to the latter, especially at high SNRs This comes from the fact that the former has a higher diversity order than the latter It is also noted that for PCI, [16] proposed the exact and asymptotic outage analysis in dual-hop cognitive networks with opportunistic relay selection but assumed the statistical independence of terms in sbd More specifically, [16] assumed that min( sk , kd ) is uncorrelated with diversity order and the achievable diversity order of cooperative relaying is larger than that of dual-hop relaying (i.e., the outage probability curve of the former has a larger slope than that of the latter) Also, the saturation level of the former is considerably lower than that of the latter Briefly, the former is significantly better than the latter for any system parameters under consideration This observation shows the importance of utilizing the direct channel in relaying communications without any additional cost of system resources (e.g., bandwidth and power) Moreover, both networks are drastically degraded by ICI, especially at high SNRs Nevertheless, their performance can be considerably improved with the increase in the number of relays since the more relays are available, the higher chance of selecting the best relay is In the almost same context as Fig except P = 20 dB, Fig investigates the impact of the outage threshold (or the required transmission rate R) on the outage performance of the opportunistic relay selection in both dual-hop and cooperative cognitive networks It is seen that the simulation perfectly matches the analysis, verifying the accuracy of the proposed expressions Additionally, the outage performance of both networks is significantly deteriorated with respect to the increase in the outage threshold 2R − This makes sense because given operation conditions, =2 the more stringent the system performance requirement (i.e., the larger outage threshold), the higher outage probability the system suffers Also, the performance of the opportunistic relay selection is considerably enhanced with better quality of channel estimation (i.e., from ICI to PCI), which exposes the importance of channel estimation in cognitive radio networks Moreover, similar to Fig 2, increasing the number of involved relays can further improve system performance For all operation parameters under consideration, cooperative relaying is always better than dual-hop relaying, which is already proved in Section In the almost same context as Fig except P = 20 dB, Fig on the outage investigates the effect of the proportional factor performance of both dual-hop and cooperative cognitive networks min( si , x = hˆ sp id ), ∀(k, i) while this does not hold since both contain a common term , as discussed in Section 1706 K Ho-Van / Int J Electron Commun (AEÜ) 69 (2015) 1700–1708 0 10 10 −1 10 −1 Outage probability Outage probability Sim.: K=1 & DH Exact Ana.: K=1 & DH Sim.: K=1 & CC Exact Ana.: K=1 & CC Sim.: K=3 & DH Exact Ana.: K=3 & DH Sim.: K=3 & CC Exact Ana.: K=3 & CC Sim.: K=5 & DH Exact Ana.: K=5 & DH Sim.: K=5 & CC Exact Ana.: K=5 & CC −2 10 −2 10 Color codes blue: K=1 & DH magenta: K=1 & CC green: K=3 & DH red: K=3 & CC cyan: K=5 & DH black: K=5 & CC −3 10 10 −3 10 −4 10 −5 10 −6 10 0.5 Sim.: PCI Ana.: PCI Sim.: ICI Ana.: ICI 0.6 0.7 ρ 0.8 0.9 Fig Outage probability versus −4 10 0.5 1.5 R (bits/s/Hz) Fig Outage probability versus R with opportunistic relay selection It is seen that the simulation and the analysis are in an excellent agreement, again confirming the validity of the proposed expressions Additionally, the outage performance of both networks is significantly improved with respect to the increase in This is reasonable because the increase in = I/P is equivalent to the increase in I and thus, inducing the PU more tolerable with the interference from SUs Therefore, SUs can operate with high transmit powers, eventually mitigating their outage probability Moreover, the outage performance of the opportunistic relay selection is considerably enhanced with better quality of channel estimation and the higher number of involved relays, especially at high SNRs Furthermore, taking the advantage of the direct 10 channel always improves the system performance for all operation parameters under consideration It is recalled that the correlation coefficient tr controls the quality of the channel estimator and the larger tr , the more accurate the estimated channel information Consequently, in order to investigate the effect of ICI on the outage performance of cooperative cognitive networks with opportunistic relay selection, we should investigate the outage probability with respect to tr Without loss of generality, we assume all tr ’s to be equal, i.e tr = , ∀{t, r} in Fig 6, which demonstrates the outage probability as a function of for P = 20 dB, = 0.2, R = bit/s/Hz It is observed that the simulation excellently matches the analysis, again validating the accuracy of the proposed expressions In addition, ICI significantly degrades the performance of cognitive radio networks More specifically, the system is always in outage as < 0.5, and a slight improvement of estimated channel information accuracy (e.g., = 0.9 → 1.0) significantly reduces the outage probability (e.g., PoCC is reduced more than 104 times for K = 5) However, the performance degradation due to ICI can be complemented by increasing the number of involved relays Moreover, cooperative cognitive networks are more robust to ICI and drastically outperforms dual-hop counterpart for any system parameters 10 −1 Interference probability Outage probability 10 −2 10 Sim.: PCI Ana.: PCI Sim.: ICI Ana.: ICI Color codes blue: K=1 & DH magenta: K=1 & CC green: K=3 & DH red: K=3 & CC cyan: K=5 & DH black: K=5 & CC −3 10 K=1 K=3 K=5 −2 10 −3 −4 10 −1 10 10 0.2 0.4 μ 0.6 Fig Outage probability versus 0.8 10 I (dB) 15 Fig Interference probability versus I 20 K Ho-Van / Int J Electron Commun (AEÜ) 69 (2015) 1700–1708 Fig illustrates the interference probability with respect to the variation of I = I/N0 for P = 10 dB, R = bit/s/Hz, and ICI with randomly selected and mutually different correlation coefficients ( kd k=1 = {0.9037, 0.9107, 0.9681, 0.9007, 0.9749}, kp k=1 = {0.9095, 0.9438, 0.9040, 0.9556, 0.9345}, sk k=1 = {0.9168, 0.9627, 0.9094, 0.9662, 0.9528}, = 0.9144, sp = sd 0.9231) It is recalled from (31) that both dual-hop and cooperative relaying schemes results in the same interference probability since (31) is independent of the direct channel Therefore, the interference probability in this figure represents for both schemes It is seen that the increase of I reduces the interference probability This is reasonable in the sense that the larger I, the more interference power the PU can tolerate Therefore, given other system parameters, the probability that the interference power exceeds I decreases However, the interference probability is proportional to the number of the relays In other words, the quality of service in the primary network is degraded with respect to the increase in the number of the relays This conflicts with the outage performance trend in the secondary network where the outage performance is improved with respect to the increase in the number of the relays As a result, there is a performance trade-off between the primary network and the secondary network with respect to the number of relays under the condition of imperfect channel information on all channels concurrently Conclusions This paper proposes an exact and limit outage analysis framework for cooperative cognitive networks with opportunistic relay selection under a general scenario: imperfect channel information for all channels concurrently, i.n.i Rayleigh fading channels, and both maximum transmit power constraint and interference power constraint This framework is straightforwardly extended to the corresponding analysis in dual-hop cognitive networks with opportunistic relay selection for comparison convenience and emphasis of the importance of the direct channel without time-consuming simulations Numerous results demonstrate that (i) channel information imperfection significantly impacts the outage performance, especially for high SNRs and small number of relays; (ii) relaying cognitive networks experience performance saturation at high SNRs and the saturation level only depends on the quality of channel estimator; (iii) the opportunistic relay selection in the case of imperfect channel information does not bring any diversity gain for both cooperative and dual-hop cognitive networks; (iv) increasing the number of relays can dramatically improve the outage performance irrespective of channel information imperfection degree but also degrade the quality of service of primary users; (v) the outage performance of relaying cognitive networks is considerably enhanced with taking advantage of the direct channel without any significant cost of system resources (e.g., power and bandwidth) Acknowledgement This research 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