This article has been accepted for publication in a future issue of this journal, but has not been fully edited Content may change prior to final publication Citation information: DOI 10.1109/TVT.2015.2504454, IEEE Transactions on Vehicular Technology IEEE TRANSACTIONS ON VEHICULAR TECHNOLOGY, VOL XX, NO X, XXX 201X Outage Analysis of Opportunistic Relay Selection in Underlay Cooperative Cognitive Networks under General Operation Conditions Khuong Ho-Van Abstract—This paper investigates the impact of practical operation conditions such as channel information imperfection (CII), independent non-identical (i.n.i) fading distributions, strict power constraints (i.e., peak transmit power constraint and primary outage constraint), and primary interference on outage performance of opportunistic relay selection (ORS) in underlay cooperative cognitive networks (UCCNs) Towards this end, the power of secondary transmitters is firstly established to meet strict power constraints and account for primary interference and CII Then, exact closed-form outage probability expressions for the secondary destination employing the maximum ratio combining (MRC) and the selection combining (SC) are proposed to promptly evaluate the effect of these conditions and provide useful insights into performance limits Numerous results illustrate significant system performance deterioration due to primary interference and CII, performance saturation phenomenon in the secondary network, performance compromise between the secondary network and the primary network, significant performance improvement with respect to the increase in the number of involved relays, a large gap between the lower outage bound (MRC’s outage performance) and the upper outage bound (SC’s outage performance), and the advantage of utilizing direct channel between the source and the destination Index Terms—Opportunistic relay selection, primary interference, channel information imperfection, cognitive radio I I NTRODUCTION N OWADAYS, the development of new wireless communication applications demands more and more radio spectrum, which conflicts with the current circumstance of available spectrum resource utilization as reported by Federal Communication Commission [1] The feasible solution to this conflict comes from the cognitive radio (CR) technology in which secondary users (SUs) can temporarily utilize the licensed spectrum allocated to primary users (PUs) without causing any significant harm to the performance of PUs [2]–[4] Therefore, the spectrum utilization efficiency can be substantially improved Conversely, the interference from SUs on PUs is a remarkable challenge to the CR technology Three modes in which SUs can operate, namely interweave, overlay and underlay, can efficiently manage this interference Manuscript received June 29, 2015; revised August 29, 2015, October 6, 2015, October 27, 2015; accepted November 6, 2015 The associate editor approving this paper for publication is Dr Edward Au K Ho-Van is with the Department of Telecommunications Engineering, HoChiMinh City University of Technology, Vietnam (e-mail: khuong.hovan@yahoo.ca) This research is funded by Vietnam National Foundation for Science and Technology Development (NAFOSTED) under grant number 102.04-2014.42 Digital Object Identifier 10.1109/TVT.2008.2007644 Among these modes, the underlay one is preferred due to its low implementation complexity According to this mode, SUs intelligently adjust their transmit power to ensure that the induced interference at PUs remains below a controllable level, which can be tolerated by PUs SUs can implement power adjustment in short-term or long-term manner According to the former, the power of secondary transmitters is constrained by either interference power constraint [2] or both interference power constraint and peak transmit power constraint [3] while according to the latter, the power of secondary transmitters is constrained by the outage probability of PUs [4] In either short-term or long-term power adjustment scheme, the transmit power of SUs is limited, ultimately shortening their radio coverage To extend the radio coverage for SUs, relaying communications technique should be exploited [5] This technique makes use of relays, which play a role as intermediate users to relay information from a transmitter to a receiver Obviously, it can improve reliability of point-to-point communications due to low path-loss effects In other words, it can increase the radio coverage without degrading system performance In relaying communications, relay selection strategy plays a very important role in improving system performance in terms of spectral efficiency, power consumption, and transmission reliability This can be attributed to the fact that selecting a single relay among a set of possible candidates requires less system resources (e.g., bandwidth and power) than multi-relay assisted transmission while maintaining the same diversity gain as the latter [3], [6] Several relay selection strategies in UCCNs were proposed (e.g., [2], [3], [7]–[11]) To be more specific, the ORS was proposed in [2], [3], [7], which adopts the relay with the maximum end-to-end signal-to-noise ratio (SNR); the authors in [7] considered the reactive relay selection (RRS) strategy, which selects the relay among all possible candidates (i.e., all relays are assumed to successfully decode source information) with the largest SNR to the destination; the N th best-relay selection strategy was proposed in [8]; the maximum secrecy capacity based relay selection strategy was investigated in [9]; the authors in [10] studied the relay selection strategy with the good compromise between the gain for SUs and the loss for PUs; the work in [11] selects the first relay whose instantaneous reward (short-term effective bit rate) is at least the same as the expected reward (long-term expected throughput) However, several assumptions have been imposed on these works for analysis tractability: i) perfect channel information; ii) no primary outage constraint; iii) independent 0018-9545 (c) 2015 IEEE Personal use is permitted, but republication/redistribution requires IEEE permission See http://www.ieee.org/publications_standards/publications/rights/index.html for more information This article has been accepted for publication in a future issue of this journal, but has not been fully edited Content may change prior to final publication Citation information: DOI 10.1109/TVT.2015.2504454, IEEE Transactions on Vehicular Technology IEEE TRANSACTIONS ON VEHICULAR TECHNOLOGY, VOL XX, NO X, XXX 201X partially-identical (i.p.i) [2], [3], [10] or independent identical (i.i) fading distributions [7]–[9], [11] Channel state information (CSI) plays an important role in system design optimization such as optimum coherent detection However, it is inevitable that this information is imperfect, inducing the study on the effect of CII on the outage behavior of relay selection strategies in UCCNs to be essential The impact of CII on the ORS and RRS strategies was studied in [12] and [13], respectively The partial relay selection strategy, which chooses the relay with the largest SNR from the source, under CII was also analyzed in [14] The common ground of works in [12]–[14] is the assumptions on i.p.i fading distributions, no primary interference, and no primary outage constraint In [15], we analyzed the outage performance of the RRS strategy under consideration of CII, i.n.i fading distributions, primary outage constraint, and the MRC at the secondary destination However, [15] did not take into account primary interference and the SC at the secondary destination Briefly, the ORS strategy is proved to be outage-optimal (e.g., [3]) Together with remarkable features that any relay selection strategy can bring such as high bandwidth utilization efficiency, wide radio range, and low transmit power, outage performance evaluation of the ORS strategy in UCCNs before practical deployment/implementation under practical operation conditions such as CII, i.n.i fading distributions, primary outage constraint, peak transmit power constraint, and primary interference is necessary and essential to expose performance limits without the need of time-consuming simulations This paper aims at such an objective1 To the best of the author’s knowledge, no analysis accounts for all these practical operation conditions Moreover, the SC and the MRC represent two extremes among signal combining techniques for space diversity in terms of implementation complexity and outage performance, where the MRC obtains the lowest outage probability (lower outage bound) but requires the most complicated implementation while the SC achieves the highest outage probability (upper outage bound) but requires the least complicated implementation [16] Therefore, when the direct channel between the source and the destination is considered in this paper, it is useful to analyze their performance to have insights into performance extremes of the ORS strategy in UCCNs as well as to expose their performance gap for appropriate choice of signal combining techniques in system design process to better trade-off with implementation complexity The contributions of the current work are summarized below: • Exactly analyze the impact of practical operation conditions such as primary interference, CII, peak transmit power constraint, primary outage constraint, and i.n.i multi-path fading channels on the outage performance of the ORS strategy in UCCNs The current paper is not a trivial extension of our previous work in [15] as follows First of all, they investigate two different relay selection strategies: the ORS strategy in the former while the RRS strategy in the latter Secondly, the former considers more general operation conditions than the latter More specifically, operation conditions in the former include all operation conditions in the latter together with primary interference and the SC at the secondary destination Primary network {gLLh} PT h=1,2 k=1,2, ,K PR interference {gLk1} Secondary network SR1 {gLDh} hop SRb gSL1 SRK {gSk1} SS transmission gbL2 hop gSD1 gbD2 SD Fig System model TABLE I N OTATIONS FOR CHANNEL COEFFICIENTS Notation gLLh ∼ CN (0, βLLh ) gLk1 ∼ CN (0, βLk1 ) gLDh ∼ CN (0, βLDh ) gSL1 ∼ CN (0, βSL1 ) gSk1 ∼ CN (0, βSk1 ) gkD2 ∼ CN (0, βkD2 ) gSD1 ∼ CN (0, βSD1) gkL2 ∼ CN (0, βkL2 ) • • • • Channel coefficient between PT and PR in the hop h, h ∈ {1, 2} PT and SRk , k ∈ K = {1, , K} PT and SD in the hop h, h ∈ {1, 2} SS and PR SS and SRk , k ∈ K = {1, , K} SRk and SD, k ∈ K = {1, , K} SS and SD SRk and PR, k ∈ K = {1, , K} Propose a power allocation condition for SUs to satisfy strict power constraints and account for primary interference and CII Derive exact closed-form outage probability expressions for the secondary destination employing the MRC and the SC to promptly assess the outage performance without exhaustive simulations Analytically prove the advantage of utilizing direct channel between the source and the destination Provide numerous results to demonstrate useful insights into the system performance II S YSTEM M ODEL A system model for the ORS in UCCNs under consideration is illustrated in Fig where the secondary source SS communicates the secondary destination SD with the assistance of the best secondary relay SRb in the group of K secondary relays, R = {SR1 , SR2 , , SRK } We assume that secondary transmitters operate in the underlay mode, and hence, there exists mutual interference between the primary network and the secondary network To be more specific, SS and SRb interfere communications between the primary transmitter PT and the primary receiver PR, and PT also causes interference to the received signals at SD and SRk , k ∈ K = {1, 2, , K} It is recalled that the primary interference caused by PUs to SUs was ignored for analysis simplicity in [3], [4], [12], [13] and references therein However, this interference cannot be omitted in a general set-up due to concurrent communication of PUs and SUs in the underlay mode It is the interference from PUs that makes the performance analysis complicated but general and practical Furthermore, it is obvious that two hops of the relay selection process in the secondary network can take place simultaneously with communication of two different 0018-9545 (c) 2015 IEEE Personal use is permitted, but republication/redistribution requires IEEE permission See http://www.ieee.org/publications_standards/publications/rights/index.html for more information This article has been accepted for publication in a future issue of this journal, but has not been fully edited Content may change prior to final publication Citation information: DOI 10.1109/TVT.2015.2504454, IEEE Transactions on Vehicular Technology IEEE TRANSACTIONS ON VEHICULAR TECHNOLOGY, VOL XX, NO X, XXX 201X primary transmitter-receiver pairs Nevertheless, in order to have a compact figure, Fig only illustrates a transmitterreceiver pair However, to reflect this general case, two different channel coefficients, gLL1 and gLL2 , corresponding to two different primary transmitter-receiver pairs are assumed in the following analysis2 We consider independent, frequency-flat, and Rayleighdistributed fading channels Consequently, the channel coefficient, gklh , between the transmitter k and the receiver l in the hop h can be modelled as a circular symmetric complex Gaussian random variable with zero mean and βklh -variance, i.e gklh ∼ CN (0, βklh ), as illustrated in Table I In contrast to existing works in relay selection where i.p.i3 or i.i4 fading distributions are assumed for simplicity of performance analysis, the current paper investigates i.n.i fading distributions, and hence, all βklh ’s, ∀{k, l, h} are not necessarily equal Therefore, our work is more general and practical It is inevitable that channel estimation algorithms cannot obtain perfect CSI Hence, channel estimation error (CEE) should be modeled in order to support performance analysis In this paper, we resort to the well-known CEE model used in [12], [13] To this effect, the real channel coefficient, gklh , is related to the estimated one, gˆklh , as follows gˆklh = µklh gklh + − µ2klh ξklh , (1) where ξklh is the CEE and µklh is the correlation coefficient, ≤ µklh ≤ 1, characterizing the average quality of channel estimation As elaborately addressed in [12], all random variables {ˆ gklh , gklh , ξklh } are modelled as CN (0, βklh ) As illustrated in Fig 1, the ORS takes place in two hops In the first hop, SS broadcasts the signal uS with transmit power PS (i.e., PS = EuS {|uS | } where EX {x} denotes statistical expectation over random variable X) while PT is concurrently transmitting the signal uL1 with transmit power PL The signals from SS and PT cause the mutual interference between the primary network and the secondary network To this effect, the received signals at the primary receiver PR and the secondary receivers (i.e., SRk , and SD), correspondingly, can be expressed as vLL1 = gLL1 uL1 + gSL1 uS + nL1 (2) vSl1 = gSl1 uS + gLl1 uL1 + nl1 , l ∈ {D, K} (3) where nlh ∼ CN (0, N0 ) is the additive white Gaussian noise (AWGN) at the corresponding receivers Using (1) to rewrite (2) and (3) as vLL1 = The gˆLL1 uL1 − µLL1 1−µ2LL1 ξLL1 uL1 +gSL1 uS +nL1 (4) µLL1 case that multiple primary transmitter-receiver pairs co-exist in single orthogonal channel may make the system model more general However, for tractable analysis, the current paper considers only one primary transmitterreceiver pair This is suitable to several practical and popular multiple access techniques such as time division multiple access (TDMA), frequency division multiple access (FDMA), orthogonal frequency division multiple access (OFDMA), code division multiple access (CDMA) This means that β klh ’s are partitioned into groups of equal value For example, βLkh = α1 , βkDh = α2 , βkLh = α3 , βSkh = α4 with ∀SRk ∈ R and α1 = α2 = α3 = α4 are assumed (e.g., [2], [3], [10], [12], [13]) This means that β klh ’s, ∀{k, l, h} are equal (e.g., [7]–[9], [11]) − µ2Sl1 gˆSl1 uS − ξSl1 uS + gLl1 uL1 + nl1 (5) µSl1 µSl1 From (4) and (5), one can express the signal-to-interference plus noise ratio (SINR) at the primary receiver and the secondary receivers in the first hop as vSl1 = γLL1 = |ˆ gLL1 | PL (1−µ2LL1) βLL1 PL +|gSL1 | µ2LL1 PS +µ2LL1 N0 (6) γSl1 = |ˆ gSl1 | PS (1 − µ2Sl1 ) βSl1 PS + µ2Sl1 |gLl1 | PL + µ2Sl1 N0 (7) This paper applies the ORS strategy (e.g., [3]) to remedy the effect of CII and primary interference in UCCNs This strategy selects the relay SRb that obtains the largest end-toend SINR5 , i.e b = arg max (γSk1 , γkD2 ) , k∈K (8) where γkD2 is the SINR of the signal received at SD from SRk in the second hop This signal can be represented in the same form as (5), i.e vkD2 = gˆkD2 uk − µkD2 1−µ2kD2 ξkD2 uk +gLD2 uL2 +nD2 , (9) µkD2 where k ∈ K, uL2 is the signal transmitted by PT with the power PL , and uk is the signal transmitted by SRk with the power Pk Therefore, γkD2 can be computed in the same manner as (7), i.e γkD2 = |ˆ gkD2 | Pk (1−µ2kD2 )βkD2Pk +µ2kD2 |gLD2 | PL +µ2kD2N0 (10) In the second hop, PR also receives the desired signal from PT and the interference signal from SRb By exchanging notations, the SINR at PR in the second hop can be expressed in the same form as (6), i.e γLL2 = |ˆ gLL2 | PL (1−µ2LL2)βLL2 PL +|gbL2 | µ2LL2 Pb +µ2LL2 N0 (11) This paper takes advantage of the direct channel between SS and SD for further performance improvement Therefore, at SD, both signals received from SS and SRb should be combined in a wise manner to restore the source information The MRC and the SC are two popular combining techniques where the MRC is better but more complicated than the SC [16] Therefore, their outage performance should be analyzed to expose the performance extremes of the ORS in UCCNs To this effect, the total SINRs at SD for the MRC and the SC, respectively, are represented as γSC = max γSD1 , max (γSk1 , γkD2 ) , (12) γMRC = γSD1 + max (γSk1 , γkD2 ) , (13) k∈K k∈K where max (γSk1 , γkD2 ) is the SINR of the SS−SRb −SD k∈K relaying channel The ORS can be implemented in a distributed manner using the timer method in [6] where each relay SRk sets its timer with the value that is inversely proportional to (γSk1 , γkD2 ) and the relay with the timer that runs out first is selected 0018-9545 (c) 2015 IEEE Personal use is permitted, but republication/redistribution requires IEEE permission See http://www.ieee.org/publications_standards/publications/rights/index.html for more information This article has been accepted for publication in a future issue of this journal, but has not been fully edited Content may change prior to final publication Citation information: DOI 10.1109/TVT.2015.2504454, IEEE Transactions on Vehicular Technology IEEE TRANSACTIONS ON VEHICULAR TECHNOLOGY, VOL XX, NO X, XXX 201X It is noted that for the compact figure, the system model in Fig only shows one primary transmitter-receiver pair Generally, it is possible that communication of two different primary transmitter-receiver pairs takes place in two different hops In such a case, we assume all primary transmitters have the same transmit power of PL The case of different transmit powers designed for different primary transmitters can be straightforwardly extended III P OWER C ONSTRAINTS FOR S ECONDARY U SERS In the underlay mode, the transmit power of SUs must be properly allocated to satisfy the primary outage constraint for guaranteeing reliable communication for PUs (e.g [4]) This constraint forces the outage probability of PUs to be below a pre-defined threshold θ Therefore, the smaller θ, the more reliable communication of PUs Towards this end, the transmit powers of SS and SRb must be controlled to meet the following two primary outage constraints, correspondingly: Pr {γLL1 < ηL } = FγLL1 (ηL ) ≤ θ (14) Pr {γLL2 < ηL } = FγLL2 (ηL ) ≤ θ, (15) where Pr{W } denotes the probability of the event W , ηL = 2TL − with TL being the required spectral efficiency in the primary network, and FX (x) denotes the cumulative distribution function (cdf) of X In addition, secondary transmitters (i.e., SS and SRb ) are constrained by their designed peak transmit powers (i.e., PSm and Pbm ) As such, the transmit powers of SS and SRb are also upper-bounded by PSm and Pbm , respectively, i.e PS Pb ≤ ≤ PSm Pbm (16) (17) Lemma For maximizing the radio coverage and meeting both primary outage constraint in (14) and peak transmit power constraint in (16), the transmit power of SS must be established as e−ηL κLL1 PL βLL1 max −1,0 , PSm , (18) PS = ηL µLL1 βSL1 1−θ where κLLh = − µ2LLh + µ2LLh N0 , h ∈ {1, 2} PL βLLh (19) Proof Please see Appendix A By following Lemma 1, one immediately infers that the transmit power of SRb that meets both primary outage constraint in (15) and peak transmit power constraint in (17) as well as maximizes the radio coverage can be expressed as Pb = e−ηL κLL2 PL βLL2 max −1,0 , Pbm ηL µLL2 βbL2 1−θ Generality: To meet both peak transmit power constraint and primary outage constraint, the powers of secondary transmitters in (18) and (20) can be uniquely represented as µ N LLh −ηL 1−µLLh + P β L LLh e PL βLLh ,Pum −1,0 max Pu = ηL µ2LLh βuLh 1−θ D Y (21) where the first hop corresponds to (u, h) = (S, 1) while the second hop corresponds to (u, h) = (b, 2) The following are comments on how the degree of reliable communication (DoRC) in the primary network (i.e., θ) affects the performance trend of the secondary network: • For high DoRC requirement in the primary network (i.e., small θ), no power is allocated to SUs (i.e., Pu = 0) This can be attributed to the fact that D is proportional to θ Therefore, the small θ can cause D < 1, resulting in Pu = In such a scenario, the secondary network is always in outage • For moderate DoRC requirement in the primary network (i.e., moderate θ), Pu is completely controlled by Y Since Y is proportional to θ, the power of secondary transmitter increases with respect to θ, enhancing the performance of the secondary network • For low DoRC requirement in the primary network (i.e., large θ), Pu is totally determined by Pum , independent of θ Consequently, the secondary network suffers performance saturation The above comments show that there exists a performance compromise between the primary network and the secondary network: higher DoRC in the primary network results in lower performance in the secondary network and vice versa These comments will be excellently supported by simulation results in Section V IV P ERFORMANCE A NALYSIS The outage probability is an important metric for system performance evaluation In this section, we derive two exact closed-form outage probability expressions at SD for the MRC and the SC, which are then applied to investigate the outage performance of the ORS in UCCNs without time-consuming simulations in the next section The outage probability is defined as the probability that the total SINR is below a predefined threshold ηS Due to the two-hop nature of the ORS, ηS is related to the required spectral efficiency, TS , in the secondary network as ηS = 22TS − (20) It is noted that even though the power allocation for SUs to satisfy the primary outage constraint was carried out (e.g [4]), CII has not been accounted yet Consequently, (18) and (20) include the existing works (e.g [4]) as special cases when µklh = 1, ∀{k, l, h}; for example, when µLLh = 1, (18) reduces to [4, eq (8)] A Selection Combining For the SC, the outage probability can be expressed as OPSC = Pr {γSC ≤ ηS } = Pr{γSD1 ≤ ηS } Pr max min(γSk1 , γkD2 ) ≤ ηS k∈K W1 (22) W2 0018-9545 (c) 2015 IEEE Personal use is permitted, but republication/redistribution requires IEEE permission See http://www.ieee.org/publications_standards/publications/rights/index.html for more information This article has been accepted for publication in a future issue of this journal, but has not been fully edited Content may change prior to final publication Citation information: DOI 10.1109/TVT.2015.2504454, IEEE Transactions on Vehicular Technology IEEE TRANSACTIONS ON VEHICULAR TECHNOLOGY, VOL XX, NO X, XXX 201X Before computing W1 and W2 for completing the analytic evaluation of (22), we introduce the cdf of γSl1 where l = {D, K} By following the same derivation procedure as (58) in the appendix A, one immediately obtains the cdf of γSl1 as HSl1 e−κSl1 x , x ≥ 0, x + HSl1 FγSl1 (x) = − (23) after analytically evaluating (33) Towards this end, we firstly substitute (29) into (33): φB = E|gLD2 |2 e −|gLD2 |2 ηSPL k∈B µ2 kD2 βkD2 Pk Ik e−ηS κkD2 (35) k∈B Then using the fact that the pdf of |gLD2 |2 is f|gLD2 |2 (x) = e /βLD2 , x ≥ since gLD2 ∼ CN (0, βLD2 ), in (35), one obtains −x/βLD2 where PS βSl1 , µ2Sl1 PL βLl1 µ2 N = − µ2Sl1 + Sl1 PS βSl1 HSl1 = κSl1 ∞ (24) φB = e µ2 kD2 β P k∈B kD2 k −xηSPL k∈B It is apparent that W1 is the cdf of γSD1 evaluated at ηS : W1 = FγSD1 (ηS ) = (25) To analytically evaluate W2 in (22), it is recalled that γkD2 ’s in (10) are correlated since they contain a common term gLD2 Thus, (γSk1 , γkD2 )’s are also correlated Consequently, we must resort to the conditional probability to compute W2 In other words, W2 in (22) should be rewritten as Ik e−ηS κkD2 f|gLD2 |2 (x)dx −ηS κkD2 k∈B Ik e + ηS βLD2 PL µ2kD2 k∈B βkD2 Pk (36) B Maximum Ratio Combining For the MRC, the outage probability is expressed as OPMRC = Pr {γMRC ≤ ηS } = Pr max (γSk1 , γkD2 ) ≤ ηS − γSD1 (37) k∈K W2=E|gLD2 |2 Pr max min(γSk1,γkD2) ≤ ηS |gLD2 |2 k∈K = E|gLD2 |2 k∈K (26) (1 − Ik Jk ) , Since (γSk1 , γkD2 )’s are correlated, (37) should be rewritten in terms of the conditional probability as (38) where Pk = Pr { γSk1 ≥ ηS − γSD1 | γSD1 } , where Ik = Pr {γSk1 ≥ ηS } = − FγSk1 (ηS ) , (27) Jk = Pr γkD2 ≥ ηS | |gLD2 |2 (28) Qk = Pr γkD2 ≥ ηS − γSD1 | γSD1 , |gLD2 | µ2kD2 N0 βkD2 Pk (30) k∈K K K−i+1 K−i+2 i tk , w1 =1 w2 =w1 +1 K−i+1 K−i+2 K ··· w1 =1 w2 =w1 +1 φG , k∈B B = {∅, G, K} (32) is the value of the element in the K set (43) wi =wi−1 +1 k∈B (33) Pk Qk (44) Theorem ΦB is represented in the exact closed form as ΦB = e−ηS GB MB k∈B (−HSk1 ), (45) where GB = k∈B (κSk1 + κkD2 ), (46) (34) In (34), ∅ denotes the empty set Obviously, the derivation of the exact closed-form representation of W2 is completed j th ΦG , Obviously, the derivation of the exact closed-form representation of OPMRC is completed after analytically evaluating (44), which is given in the following theorem wi =wi−1 +1 Ik Jk w1 =1 w2 =w1 +1 ΦB = EγSD1 ,|gLD2 |2 where φB = E|gLD2 |2 K ··· where W2 = φ∅ + (−1)K φK + i i=1 (31) wi =wi−1 +1 k∈G (−1) K−i+1 K−i+2 (−1)i where G = {K [w1 ] , K [w2 ] , , K [wi ]}6 , to expand the product in (26), one obtains K [j] (41) K−1 tk + ··· (−1) i=1 Pk = − FγSk1 ( ηS − γSD1 | γSD1 ) HSk1 = e−κSk1 (ηS −γSD1 ) ηS − γSD1 + HSk1 K K K−1 (40) OPMRC = Φ∅ + (−1) ΦK + (1 − tk ) = + (−1) i=1 Using (10) to evaluate Qk in (40) as (42) Then applying (31) to expand the product in (38), one obtains Applying the fact that k∈K K−1 Using (23), one can represent Pk in (39) as Using (10) to evaluate Jk in (28) as (29) where Pk has the same form as (20) with changing b to k and κkD2 = − µ2kD2 + (39) MB = CB AΥ(GB ,ηS −CB )+ BkΥ(GB ,ηS +HSk1 ) , (47) k∈B CB = − βLD2 PL k∈B µ2kD2 βkD2 Pk −1 , (48) 0018-9545 (c) 2015 IEEE Personal use is permitted, but republication/redistribution requires IEEE permission See http://www.ieee.org/publications_standards/publications/rights/index.html for more information This article has been accepted for publication in a future issue of this journal, but has not been fully edited Content may change prior to final publication Citation information: DOI 10.1109/TVT.2015.2504454, IEEE Transactions on Vehicular Technology IEEE TRANSACTIONS ON VEHICULAR TECHNOLOGY, VOL XX, NO X, XXX 201X ηS 1−µ2kD2 βkD2 Pk +µ2kD2 |gLD2 | PL +µ2kD2 N0 −ηS 2 Jk = Pr |ˆ gkD2 | ≥ |gLD2 | = e Pk = EγSD1 ,|gLD2 |2 Qk = Pr =e |ˆ gkD2 |2 ≥ −(ηS −γSD1 ) A= (−CB − HSk1 ) j∈B\k , (49) (HSk1 − HSj1 ) , −1 , Notation {βkD2 }5k=1 {βLDh }2h=1 {βLLh }2h=1 {βkL2 }5k=1 βSD1 βSL1 {βLk1 }5k=1 {βSk1 }5k=1 (50) (52) T (a, b, c) = [Ei(ab + ac) − Ei(ab)] e−ab , (53) V (a, b, c) = 1/b − eac /(b + c) + aT (a, b, c) (54) (42) TABLE II FADING POWERS Υ(a, b) = HSD1 [(κSD1 +C)C{T (a−κSD1 ,−b, ηS ) (51) −T(a−κSD1 , HSD1 , ηS )}−CV(a−κSD1 , HSD1 , ηS )] C = (b + HSD1 ) γSD1 , |gLD2 |2 −1 Bk = (HSk1 + CB ) (38) − µ2kD2 βkD2 Pk + µ2kD2 |gLD2 | PL + µ2kD2 N0 |gLD2 | (29) (1 − Pk Qk ) , γSD1 ≤ ηS Pk −1 k∈B , k∈K k∈K (ηS − γSD1 ) µ2 P κkD2 + βkD2 PL kD2 k P kD2 k max (γSk1 , γkD2 ) ≤ ηS − γSD1 γSD1 , |gLD2 | Pr OPMRC = EγSD1 ,|gLD2 |2 µ2 κkD2 + βkD2 PL |gLD2 |2 Value {4.1869, 3.9739, 6.1132, 6.1170, 3.1688} 0.5727 11.1803 {3.8879, 1.7570, 2.7599, 3.8838, 4.5439} 1.0000 1.2761 {1.8055, 0.9608, 1.2328, 1.5706, 2.3124} {15.5592, 17.0076, 10.7495, 9.8886, 19.4494} V R ESULTS AND D ISCUSSIONS with Ei(x) being the exponential integral function defined in [17, eq (8.211.1)], which is a built-in function in most computation software (e.g., Matlab) Proof Please see Appendix B It is worth emphasizing that although the ORS was investigated in open literature (e.g., [3], [12]), the derivation of its exact closed-form outage probability expressions in (22) and (43) are more complicated and general than existing works7 for the following reasons: i) i.n.i fading distributions are considered; ii) primary interference from PUs exists; iii) CII, primary outage constraint, and direct channel are taken into account To the best of the author’s knowledge, (22) and (43) are completely novel and represented in a very convenient and compact form for the analytical evaluation as demonstrated in the next section Moreover, it is straightforwardly seen from (22) that the outage probability of the ORS in underlay dual-hop cognitive networks (i.e., without accounting for the direct channel) is just OPDH = W2 Since W1 < and OPMRC < OPSC , the utilization of the direct channel is always beneficial in terms of low outage probability (i.e., OPMRC < OPSC < OPDH ) for both MRC and SC This section presents numerous results to validate the proposed analytical expressions as well as to demonstrate the outage performance of the ORS in UCCNs with respect to key system parameters such as peak transmit powers of primary and secondary transmitters, severe degree of CII, the number of relays, and the DoRC requirement of PUs For illustration purpose, we only investigate a primary transmitter-receiver pair and select arbitrary fading powers which generate i.n.i fading distributions as shown in Table II To limit casestudies, we assume: i) peak transmit powers of all SUs are equal, i.e., Pum = Pm , ∀u ∈ {S, K}; ii) the required spectral efficiencies in the primary network and the secondary network are TL = 0.7 bits/s/Hz and TS = 0.4 bits/s/Hz, correspondingly; iii) all correlation coefficients for different channels are identical, i.e., µklh = µ, ∀{k, l, h} In the sequel, three different relay sets ({SR1 }, {SRk }3k=1 , {SRk }5k=1 ) are illustrated for K = 1, 3, 5, respectively Common remarks are withdrawn from all results in Figures 2–5 as follows: • The analysis perfectly matches the simulation, verifying the accuracy of the proposed expressions For example, [12] studied the ORS under assumptions: i.p.i fading distributions, no primary interference from PUs, no primary outage constraint, and no direct channel 0018-9545 (c) 2015 IEEE Personal use is permitted, but republication/redistribution requires IEEE permission See http://www.ieee.org/publications_standards/publications/rights/index.html for more information This article has been accepted for publication in a future issue of this journal, but has not been fully edited Content may change prior to final publication Citation information: DOI 10.1109/TVT.2015.2504454, IEEE Transactions on Vehicular Technology IEEE TRANSACTIONS ON VEHICULAR TECHNOLOGY, VOL XX, NO X, XXX 201X 10 10 −1 −2 10 −3 10 −4 10 0.7 Sim.: K=1 & SC Ana.: K=1 & SC Sim.: K=3 & SC Ana.: K=3 & SC Sim.: K=5 & SC Ana.: K=5 & SC Sim.: K=1 & MRC Ana.: K=1 & MRC Sim.: K=3 & MRC Ana.: K=3 & MRC Sim.: K=5 & MRC Ana.: K=5 & MRC 0.75 0.8 −1 10 Outage probability Outage probability 10 −2 10 0.85 µ 0.9 0.95 −3 Fig Outage probability versus µ ‘Sim.’ and ‘Ana.’ denote ‘Simulation’ and ‘Analysis’, respectively • • The outage performance is significantly enhanced with respect to the increase in the number of relays This is attributed to the fact that the larger K, the higher probability to choose the best relay, and so, the smaller the outage probability As a result, the relay selection plays a key role in UCCNs, not only because of the reduced requirement of the total transmit power and the transmission bandwidth, but also because of the dramatically improved performance The MRC is significantly better than the SC, as expected in Section II Notably, the outage performance gap between the MRC and the SC substantially increases with respect to the increase in K This result again emphasizes the importance of the relay selection in improving the performance extremes (i.e., the lower and upper outage bounds) of UCCNs Moreover, the exposure of this large gap can provide a flexible choice of signal combining techniques in system design process to better trade-off with implementation complexity It is recalled that µ characterizes the quality of the channel estimator Therefore, in order to evaluate the impact of CII on the outage performance of the ORS in UCCNs, we should investigate the outage probability with respect to µ Fig shows the outage probability as a function of µ for Pm /N0 = 15 dB, PL /N0 = 17 dB, θ = 0.2 It is seen that the secondary network stops working for a wide range of µ To be more specific, the secondary network is always in outage for µ < 0.8 (i.e., only small estimation error is enough to cease the secondary network) When the channel estimation is better (e.g., µ ≥ 0.8), the outage performance of the secondary network is considerably improved In other words, the channel estimation becomes a decisive factor for the performance of the ORS in UCCNs, and any inefficient channel estimation can lead to a unfavorable consequence to the system performance We can interpret this performance trend as follows Conditioned on parameters (PL , βLLh , ηL , βuLh , N0 , Pum , θ), Y in (21) is proportional to µLLh = µ 10 0.02 Sim.: K=1 & SC Ana.: K=1 & SC Asym.: K=1 & SC Sim.: K=3 & SC Ana.: K=3 & SC Asym.: K=3 & SC Sim.: K=5 & SC Ana.: K=5 & SC Asym.: K=5 & SC Sim.: K=1 & MRC Ana.: K=1 & MRC Asym.: K=1 & MRC Sim.: K=3 & MRC Ana.: K=3 & MRC Asym.: K=3 & MRC Sim.: K=5 & MRC Ana.: K=5 & MRC Asym.: K=5 & MRC 0.04 0.06 0.08 0.1 θ 0.12 0.14 0.16 0.18 Fig Outage probability versus DoRC of PUs (i.e., θ) ‘Asym.’ denotes ‘Asymptotic analysis’ for large values of µ (e.g., µ ≥ 0.8 in Fig 2) Therefore, the powers of secondary transmitters are also increased with the better channel estimation (i.e., larger values of µLLh = µ), eventually improving the outage performance However, small values of µ (e.g., µ < 0.8 in Fig 2) causes D in (21) to be less than 1, resulting in Y = Therefore, no power is allocated to SUs and hence, the secondary network is complete in outage Fig illustrates the effect of the DoRC requirement of PUs on the outage performance of SUs for Pm /N0 = 15 dB, PL /N0 = 17 dB, µ = 0.96 This DoRC is managed by θ, which represents how many percentage the primary network is in outage Results show some interesting comments as follows: • • • The high DoRC (e.g., θ ≤ 0.05 in Fig 3) requirement in the primary network causes the secondary network to be always in outage Consequently, the secondary network cannot operate concurrently with the primary network In other words, conditioned on the operation parameters, SUs cannot adjust their transmit powers to meet the primary outage constraint, i.e (18) and (20) results in PS = Pb = When the primary network requires the moderate DoRC (e.g., 0.05 < θ ≤ 0.16 in Fig 3), the outage performance of the secondary network is drastically enhanced with the increase in θ This is attributed to the fact that the larger θ enables the primary network to tolerate the more interference from the secondary network, and thus, the secondary network can utilize more power for transmission, ultimately improving its outage performance When the primary network is not stringent in the DoRC (i.e., low DoRC requirement), the secondary network experiences the performance saturation phenomenon for large values of θ (e.g., θ > 0.16 in Fig 3) This 0018-9545 (c) 2015 IEEE Personal use is permitted, but republication/redistribution requires IEEE permission See http://www.ieee.org/publications_standards/publications/rights/index.html for more information This article has been accepted for publication in a future issue of this journal, but has not been fully edited Content may change prior to final publication Citation information: DOI 10.1109/TVT.2015.2504454, IEEE Transactions on Vehicular Technology IEEE TRANSACTIONS ON VEHICULAR TECHNOLOGY, VOL XX, NO X, XXX 201X 10 10 Sim.: K=1 & SC Ana.: K=1 & SC Sim.: K=3 & SC Ana.: K=3 & SC Sim.: K=5 & SC Ana.: K=5 & SC Sim.: K=1 & MRC Ana.: K=1 & MRC Sim.: K=3 & MRC Ana.: K=3 & MRC Sim.: K=5 & MRC Ana.: K=5 & MRC −2 10 −3 10 10 15 20 P /N (dB) L 25 30 35 Sim.: K=1 & SC Ana.: K=1 & SC Asym.: K=1 & SC Sim.: K=3 & SC Ana.: K=3 & SC Asym.: K=3 & SC Sim.: K=5 & SC Ana.: K=5 & SC Asym.: K=5 & SC Sim.: K=1 & MRC Ana.: K=1 & MRC Asym.: K=1 & MRC Sim.: K=3 & MRC Ana.: K=3 & MRC Asym.: K=3 & MRC Sim.: K=5 & MRC Ana.: K=5 & MRC Asym.: K=5 & MRC −1 10 Outage probability Outage probability −1 10 −2 10 40 Fig Outage probability versus PL /N0 comes from the fact that8 since the power of secondary transmitters is completely controlled by Pm , irrespective of the increase in θ, according to (21), fixing Pm (e.g Pm /N0 = 15 dB) makes the outage probability unchanged The performance saturation implicitly means that the ORS in UCCNs gets zero diversity gain in the presence of imperfect channel information All above comments can be mathematically interpreted and mentioned in Section III Also, the results show that better performance of the primary network (i.e., lower θ) induces worse performance of the secondary network (i.e., larger outage probability) and vice versa As such, the performance compromise between the secondary network and the primary network should be accounted when designing UCCNs Fig demonstrates the outage performance of the ORS in UCCNs with respect to the variation of PL /N0 for Pm /N0 = 15 dB, θ = 0.1, and µ = 0.96 Some interesting comments are exposed as follows: −3 10 10 P /N (dB) m 15 20 Fig Outage probability versus Pm /N0 is large and increases, the interference that the primary network imposes on the secondary network considerably increases, ultimately degrading the outage performance of the secondary network (i.e., increasing the outage probability) At the very large values of PL (e.g., PL /N0 ≥ 35 dB in Fig 4), the secondary network is complete in outage For small values of PL (e.g., PL /N0 ≤ 15 dB in Fig 4), the increase in PL drastically improves the outage performance This is attributed to the fact that according to (21), PL is proportional to Y while the power of secondary transmitters is controlled by the minimum of Y and Pm , and thus at small values of PL and the fixed value of Pm , the power of secondary transmitters is proportional to PL , ultimately enhancing the performance of the secondary network as PL increases and the interference caused by the primary network to the secondary network is not significant (due to small PL ) For large values of PL (e.g., PL /N0 > 15 dB in Fig 4), the Y term in (21) is larger than Pm and thus, the power of secondary transmitters is fixed at the value of Pm (e.g., Pm /N0 = 15 dB in Fig 4) Meanwhile, as PL Fig illustrates the outage performance of the ORS in UCCNs with respect to the variation of Pm /N0 for θ = 0.1, PL /N0 = 17 dB, and µ = 0.96 It is observed that the system performance is drastically enhanced with the increase in Pm This makes sense since Pm upper bounds the power of secondary transmitters (e.g., (21)) and thus, the larger Pm , the larger the transmit power, ultimately mitigating the corresponding outage probability However, the secondary network experiences the performance saturation at large values of Pm /N0 (e.g., Pm /N0 ≥ 16.5 dB in Fig 5) We can interpret this phenomenon as follows9 The power of secondary transmitters in (21) is controlled by the minimum of Pm and PL Consequently, as Pm is larger than a certain level (e.g., Pm /N0 ≥ 16.5 dB in Fig 5), the power of secondary transmitters is totally determined by PL , making the outage performance unchanged irrespective of any increase in Pm Nevertheless, the performance saturation level is significantly reduced with respect to the increase in K; for example, the performance saturation level reduces more than fifteen times when K increases from to for the secondary destination It is recalled from (21) that Y → ∞ as θ → Consequently, for low DoRC requirement (i.e., θ → 1), the power of secondary transmitters Pu in (21) becomes Pm = Pum By plugging this result of Pu = Pm into (22) and (43), the performance saturation levels (or asymptotic performance) in Fig for the SC and the MRC are straightforwardly computed It is recalled from (21) that for large values of P m = Pum (i.e., Pm → ∞), the power of secondary transmitters Pu in (21) becomes Y By plugging this result of Pu = Y into (22) and (43), the performance saturation levels (or asymptotic performance) in Fig for the SC and the MRC, respectively are immediately computed • • 0018-9545 (c) 2015 IEEE Personal use is permitted, but republication/redistribution requires IEEE permission See http://www.ieee.org/publications_standards/publications/rights/index.html for more information This article has been accepted for publication in a future issue of this journal, but has not been fully edited Content may change prior to final publication Citation information: DOI 10.1109/TVT.2015.2504454, IEEE Transactions on Vehicular Technology IEEE TRANSACTIONS ON VEHICULAR TECHNOLOGY, VOL XX, NO X, XXX 201X with the MRC The performance saturation again shows no diversity gain achievable in the presence of imperfect channel information VI C ONCLUSIONS This paper proposes an outage analysis framework for the ORS in UCCNs under general practical operation conditions: CII, i.n.i fading channels, primary interference, and both peak transmit power constraint and primary outage constraint Firstly, the power allocation for SUs was proposed to satisfy these power constraints and account for primary interference and CII Then, exact closed-form outage probability expressions for the secondary destination with the MRC and the SC were derived to analytically evaluate the system performance in key operation parameters without time-consuming simulations Numerous results illustrate that i) the secondary network experiences performance saturation, vanishing diversity gain; ii) CII significantly deteriorates system performance; iii) the underlay mode causes mutual interference between the primary network and the secondary network, which represents the performance compromise between them; iv) the relay selection is essential in UCCNs for outage performance improvement, and transmission bandwidth and total transmit power reduction; v) two performance extremes (the outage performance of the MRC and the SC) of the ORS in UCCNs are far away from each other, especially at large number of relays; vi) the utilization of the direct channel is always beneficial Let X = |ˆ gLL1 | PL and Y = − µ2LL1 βLL1 PL + 2 |gSL1 | µLL1 PS + µ2LL1 N0 Since gˆLL1 ∼ CN (0, βLL1 ) and gSL1 ∼ CN (0, βSL1 ), it is straightforward to infer that the probability density function (pdf) of X and the pdf of Y , respectively are expressed as fY (x) = x L βLL1 −P , x≥0 x−r −1 − µ2 P β e LL1 S SL1 , µ2LL1 PS βSL1 x≥r (55) (56) where r = − µ2LL1 βLL1 PL + µ2LL1 N0 Given γLL1 = X/Y in (6), one can express FγLL1 (ηL ) as ∞ ηL y FγLL1 (ηL ) = r fX (x) dxfY (y) dy (57) Substituting (55) and (56) into (57) and after some algebraic manipulations, one obtains the closed-form expression of FγLL1 (ηL ) as FγLL1 (ηL ) = − PL βLL1 e−ηL κLL1 , PL βLL1 + ηL µ2LL1 PS βSL1 PL βLL1 ηL µ2LL1 βSL1 e (60) e−ηL κLL1 PL βLL1 max −1, , PSm (61) ηL µ2LL1 βSL1 1−θ To maximize the radio coverage, the equality in (61) must hold, and thus, PS is reduced to (18), completing the proof PS ≤ A PPENDIX B P ROOF OF T HEOREM Inserting (41) and (42) into (44), one obtains (62) where GB and CB are defined in (46) and (48), respectively Apparently, (62) coincides with (45) Therefore, in order to complete the proof, we must prove that MB in (62) coincides with (47) Towards this end, we firstly evaluate the LB term in (62) as ∞ LB = e ηS −γSD1 βLD2 CB x ηS −γSD1 βLD2 CB x ∞ e = f|gLD2 |2 (x) dx βLD2 e −β x LD2 (63) dx = CB / (γSD1 − ηS + CB ) eGB γSD1 A + γSD1 −ηS +CB eGB γSD1 Bk γSD1 −ηS −HSk1 k∈B (64) where A and Bk are defined in (49) and (50), respectively By denoting MB = CB EγSD1 Υ (a, b) = EγSD1 {eaγSD1 / (γSD1 − b)} , fγSD1(x) = HSD1 κSD1 e−κSD1 x (66) + x+HSD1 (x+HSD1)2 Inserting (66) into (65) and then applying the partial fraction expansion, one obtains ηS Υ(a, b) = eax fγ (x) dx x − b SD1 ηS (κSD1 + C) C e(a−κSD1 )x x−b (67) (a−κSD1 )x −1 (65) we can infer that (64) coincides with (47) As such, the last step in this proof is to prove that (65) matches (51) To this end, we should firstly compute the pdf of γSD1 Given FγSD1 (x) in (23), the pdf of γSD1 is immediately deduced as the derivative of FγSD1 (x): = HSD1 −ηL κLL1 1−θ e−ηL κLL1 PL βLL1 max − 1, ηL µ2LL1 βSL1 1−θ Finally, combining (60) with (16) results in PS ≤ (58) where κLL1 is defined in (19) Using (58), one deduces PS that meets (14) as PS ≤ The right-hand side of (59) becomes negative when e−ηL κLL1 + θ < In such a case, no power is allocated to SS (i.e., PS = 0), implying the primary channel unavailable for the secondary transmission Because the power is nonnegative, the constraint in (14) is equivalently rewritten as Substituting the above into (62) and then performing the partial fraction expansion, one obtains A PPENDIX A P ROOF OF L EMMA fX (x) = (PL βLL1 )−1 e (59) − e x + HSD1 −C e(a−κSD1 )x (x + HSD1 ) dx, 0018-9545 (c) 2015 IEEE Personal use is permitted, but republication/redistribution requires IEEE permission See http://www.ieee.org/publications_standards/publications/rights/index.html for more information This article has been accepted for publication in a future issue of this journal, but has not been fully edited Content may change prior to final publication Citation information: DOI 10.1109/TVT.2015.2504454, IEEE Transactions on Vehicular Technology IEEE TRANSACTIONS ON VEHICULAR TECHNOLOGY, VOL XX, NO X, XXX 201X 10 ηS −γSD1 −ηS GB GB γSD1 βLD2 CB |gLD2 | ΦB = e EγSD1 E|gLD2 |2 e (−HSk1 ) e γSD1 − ηS − HSk1 k∈B k∈B (62) LB MB where C is defined ax in (52) By defining two specialax functions, c e c e dx and V (a, b, c) = (x+b) T (a, b, c) = x+b dx, one can infer that (67) exactly agrees with (51) Consequently, in order to complete the proof, it is imperative to derive their exact closed-form expressions T (a, b, c) is represented in closed-form as (53) by firstly changing variables and then using [17, eq (2.325.1)] while V (a, b, c) is expressed in closed-form as (54) by applying the integral by part Therefore, the proof is completed Khuong Ho-Van received the B.E (with the firstrank honor) and the M.S degrees in Telecommunications Engineering from HoChiMinh City University of Technology (HCMUT), Vietnam, in 2001 and 2003, respectively, and the Ph.D degree in Electrical Engineering from University of Ulsan, Korea in 2006 During 2007-2011, he joined McGill University, Canada as a postdoctoral fellow Currently, he is an associate professor at HCMUT His major research interests are modulation and coding techniques, diversity techniques, and cognitive radio R EFERENCES [1] FCC, Spectrum policy task force report, ET Docket 02−135, Nov 2002 [2] J Si, Z Li, H Huang, J Chen, and R Gao, “Capacity analysis of cognitive relay networks with the PU’s interference,” IEEE Commun Lett., vol 16, no 12, pp 2020−2023, Dec 2012 [3] J Lee, H Wang, J G Andrews, and D Hong, “Outage probability of cognitive relay networks with interference constraints,” IEEE Trans Wireless Commun., vol 10, no 2, pp 390−395, Feb 2011 [4] L Sibomana, H Tran, H J Zepernick, and C Kabiri, “On non-zero secrecy capacity and outage probability of cognitive radio networks,” in Proc WPMC, New Jersey, USA, Jun 2013, pp 1−6 [5] A Nosratinia, T E Hunter, and A Hedayat, “Cooperative 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However, it is inevitable that this information is imperfect, inducing the study on the effect of CII on the outage behavior of relay selection strategies in UCCNs to be essential The impact of CII on... ORS strategy in the former while the RRS strategy in the latter Secondly, the former considers more general operation conditions than the latter More specifically, operation conditions in the... in underlay cognitive radio,” in Proc IEEE CROWNCOM, Osaka, Japan, Jun 2011, pp 306−310 [11] T Jing, S Zhu, H Li, X Xing, X Cheng, Y Huo, R Bie, and T Znati, Cooperative relay selection in cognitive