IEEE WIRELESS COMMUNICATIONS LETTERS, VOL. 8, NO. 1, FEBRUARY 2019 245 Sequential Relay Selection in D2D-Enabled Cellular Networks With Outdated CSI Over Mixed Fading Channels Jules M. Moualeu , Senior Member, IEEE, Telex M. N. Ngatched , Senior Member, IEEE, and Daniel B. da Costa , Senior Member, IEEE Abstract—The impact of outdated channel state information on two sequential relay selection schemes for device-to-device underlaid cellular networks over mixed fading channels is inves- tigated. To this end, the mutual outage probability (MOP) is analyzed in which an easy-to-evaluate analytical expression for the MOP is derived. Moreover, an asymptotic analysis of the MOP at high signal-to-noise ratio is provided, and the diversity order is evaluated. Index Terms—Cellular network, D2D communication, mixed fading, mutual outage probability, outdated CSI. I. INTRODUCTION RELAY-AIDED underlay inband device-to-device (D2D) communication in cellular networks [1] has recently attracted a great deal of attention. From a physical-layer (PHY) security perspective, the interference issue inherent to such networks can be advantageous and exploited as a friendly jamming signal to prevent wiretapping [2]. Unlike a conventional jammer which consumes its power merely on interfering with the eavesdropper, D2D communication is able to achieve its own transmission at the same time yielding a win-win situation for the cellular network and D2D links in terms of security provisioning and high spectral efficiency, respectively. In [1], a full-duplex (FD) orthogonal frequency-division multiplexing (OFDM) D2D dual-hop system where multiple FD relays assist the device transmitter was investigated assum- ing non-security requirements. The impact of interference and outdated CSI on the performance of a vehicle-to-vehicle (V2V) cooperative relaying system was studied in [3]. Despite the popularity of relay-aided D2D-enabled cellular networks, pro- viding wireless secure transmissions for the cellular network and throughput improvement for D2D communication concur- rently has not yet been investigated in the open literature. In Manuscript received August 8, 2018; revised September 1, 2018; accepted September 2, 2018. Date of publication September 4, 2018; date of cur- rent version February 19, 2019. The work of J. M. Moualeu was supported by the Centre for Telecommunications Access Services, University of the Witwatersrand under Project COEF013. The work of T. M. N. Ngatched was supported by the Natural Sciences and Engineering Research Council of Canada. The work of D. B. da Costa was supported in part by CNPq under Grant 302863/2017-6, and in part by FUNCAP. The associate editor coordinating the review of this paper and approving it for publication was G. Yu. (Corresponding author: Jules M. Moualeu.) J. M. Moualeu is with the School of Electrical and Information Engineering, University of the Witwatersrand, Johannesburg 2000, South Africa (e-mail: jules.moualeu@wits.ac.za). T. M. N. Ngatched is with the Faculty of Engineering and Applied Science, Memorial University, St. John’s, NL A1B 3X5, Canada (e-mail: tngatched@grenfell.mun.ca). D. B. da Costa is with the Department of Computer Engineering, Federal University of Ceará, Sobral 62010-560, Brazil (e-mail: danielbcosta@ieee.org). Digital Object Identifier 10.1109/LWC.2018.2868645 this letter, we propose two sequential relay selection strategies in D2D-assisted cellular network with the aim of providing wireless security for the cellular network as well as through- put enhancement for the D2D communication. In particular, we investigate the impact of outdated channel state information (CSI) on the performance of the underlying system assuming that both networks experience different fading models. To this end, an analytical expression for the mutual outage probabil- ity (MOP) which assesses the cooperation between the two networks is presented. Furthermore, an asymptotic analysis of the MOP at high signal-to-noise (SNR) is derived, which gives some insights into the effect of the key system parameters on the proposed scheme. II. SYSTEM AND CHANNEL MODELS We consider a scenario with multiple uplink transmissions among L cellular users (CUs) and one base station (BS), in which each CU transmits on a dedicated channel in the pres- ence of a passive eavesdropper (PE). Both the BS and the PE optimally combine the received signals from the L CUs using a maximal-ratio combiner in an effort to maximize the probability of secure transmission and eavesdropping, respec- tively. Meanwhile, a D2D system which consists of one device transmitter (DT), one device receiver (DR) and N D2D relays is allowed to reuse the CU channels for its own commu- nication.1 It is assumed that all nodes are equipped with a single antenna, and there is no direct communication between DT and DR due to shadowing.2 Moreover, the BS has full knowledge of all the channel statistics and the channels in the cellular network experience η–μ fading, while the D2D links are subject to Rayleigh fading.3 Such mixed fading scenario is suitable to model real urban microcell and indoor wireless environments [6]. The D2D transmissions occur in two time slots while the cellular transmissions take place in only one time slot. Both the D2D and cellular transmissions are assumed to be well synchronized. In the first time slot, DT transmits to all the relays by reusing channels allocated to the CUs, while all the CUs remain silent with the aim of acquiring in return a higher security for their transmissions by the D2D commu- nication in the next time slot. The above-mentioned scenario 1It is worthwhile to note that the PE is part of the cellular network and can be distinguishable from the D2D pairs (i.e., DT or DR) or the relay devices. 2In practice, a strong direct link might not be feasible due to shadow- ing stemming from the presence of physical obstacles. Recently, relay-based D2D communications systems (see [4] and the references therein) have been proposed as a means to overcome the shadowing issues and to extend coverage. 3The assumption of Rayleigh faded D2D links has been widely adopted in numerous previous works (see, for instance, [2], [5] and references therein), while the choice of the η-μ distribution to model the cellular link propagation is motivated by the fact it can accurately model small-scale variations of the fading signal under non-line-of-sight (NLOS) conditions. 2162-2345 c© 2018 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. https://orcid.org/0000-0003-0307-1931 https://orcid.org/0000-0001-7646-9452 https://orcid.org/0000-0002-5439-7475 246 IEEE WIRELESS COMMUNICATIONS LETTERS, VOL. 8, NO. 1, FEBRUARY 2019 provides mutual benefits for both the CU network and the D2D system. The received signals at the nth relay is given by yRn = √ Pt fns + zRn , where Pt is the transmit power at DT, fn is the channel gain of the DT–Rn link, s is the transmitted signal, and zRn is the additive white Gaussian noise (AWGN) with zero mean and variance σ2. All the relays attempt to decode the received signal, and only the ones that successfully estimate the transmitted signal form a decoding set. A single relay, denoted by Rθ, is chosen from the decoding set to forward the signal to DR in the second time slot. The received signal at DR is given by yDR = √ PRθgRθ ŝ + ∑L k=1 √ Pcuk dkxk + zDR, where Pcuk and PRθ are the transmit powers at CUk and Rθ, respectively, gRθ and dk are the channel gains of the Rθ–DR link and the CUk–DR link, respectively, ŝ is the estimated source signal, zDR is the zero-mean AWGN with variance σ2, and Rθ rep- resents the best relay which is selected based on the following criterion Rθ = arg max j∈Ds { γ̂j ,DR } , (1) with Ds denoting the decoding set, γ̂j ,DR = PRj σ2 |ĝj |2 and ĝj is the outdated channel gain of the Rj –DT link. In (1), γ̂j ,DR denotes the SNR at the time of selection and may dif- fer from the actual SNR, denoted by γj ,DR, at the transmission instant due to mobility and feedback delay. The relationship between the actual channel gain gj and the outdated one ĝj can be expressed as gj = √ ρ1ĝj + √ 1 − ρ1uj , where ρ1 denotes the correlation coefficient between gj and ĝj with 0 ≤ ρ1 ≤ 1, and uj is a circularly complex Gaussian random variable (RV) having the same variance as ĝj . In the meantime, the L CUs transmit to the BS while the PE attempts to intercept the trans- missions. The received signals at the BS and the PE can be written as yBS = ∑L k=1 √ Pcuk hkxk + √ PRψbRψ ŝ + zBS and yPE = ∑L k=1 √ Pcuk ekxk + √ PRψcRψ ŝ + zPE, where PRψ represents the transmitted power at the relay Rψ , xk is the transmitted signal from the k th CU, hk , ek , bRψ and cRψ stand for the channel gains of the CUk–BS, CUk–PE, Rψ–BS and Rψ–PE links, respectively, zBS and zPE are the zero-mean AWGN with variance σ2 at BS and PE, respectively. In the sequel, it is assumed that all the CUs transmit with the same power Pcu, and for the sake of easy notation, the subscripts b and c will be used in place of bRψ and cRψ , respectively. Given that the cellular transmissions to the BS experience η–μ fading [7] and are optimally combined, the probability density function (PDF) of the SNR at the receiver’s combiner output can be obtained with the help of [7] and [8, eq. (8.445.1)], and is given by fγh (x ) = 2 √ π� Lμi h Γ(Lμh) exp ( −2μh�hx γ̄h ) × ∞∑ k=0 H 2k h μ2Lμh+2k h k !Γ(Lμh + k + 0.5) x2Lμh+2k−1 γ̄ 2Lμh+2k h , (2) where γh = ∑L k=1 γhk = Pcu σ2 ∑L k=1 |hk |2, Γ(·) is the Gamma function, γ̄h = E{γh} denotes the average SNR, with E{·} denoting expectation, and μh represents the num- ber of multipath clusters. From (2), the cumulative distribution function (CDF) can be expressed as Fγh (x ) = √ π Γ(Lμh) ∞∑ k=0 H 2k h 2−2Lμh−2k+1 k !Γ(Lμh + k + 0.5)�Lμh+2k h × Υ ( 2Lμh + 2k , 2μh�hx γ̄h ) , (3) where Υ(·, ·) denotes the lower incomplete Gamma function [8, eq. (8.350.1)]. Both �h and Hh are dependent of ηh and can be given in two formats (please, see [7] for details). III. MUTUAL OUTAGE PROBABILITY ANALYSIS The MOP can describe the mutual cooperation between the D2D communication and cellular network and is defined as the probability that either of the rate associated with any of the two systems falls below its corresponding predefined rate [9]. It can be expressed mathematically as MOP = P{γBS < γS or γe2e < γT}, where γS = 2RS − 1 is the secrecy threshold, RS is the secrecy rate, γT = 2RT − 1 is the specified sec- ondary threshold with RT denoting the secondary threshold rate and RT not necessarily equal to RS , γe2e is the end-to- end secondary signal-plus-interference-to-noise ratio (SINR), and P{·} denotes probability. Since the RVs γBS and γe2e are independent, the above-mentioned MOP expression can further be expressed as MOP = FγBS(γS ) + Fγe2e(γT), (4) where FX (x ) means the CDF of the RV X. A. Exact MOP From the yBS expression, note that in the cellular network there is interference affecting the cellular transmissions, which can be beneficial from the information-theoretic viewpoint, and can be used to mainly confound the eavesdropper.4 The selection criterion adopted from [10] can be defined as Rψ = arg max j∈R { 1 + ∑L k=1 γhk 1 + γ̂bj } = arg min j∈R γ̂bj , (5) where R = N −{Rθ} represents the set of relays that have not been selected for the transmission to DR in the second time slot, and γ̂bj = PRj σ2 |b̂j |2 is the SNR at the time of selection, which may differ from the actual SNR at the transmission instant, denoted by γbj . The relationship between the actual channel gain bj and the outdated one b̂j is given by bj =√ ρ2b̂j + √ 1 − ρ2wj , where ρ2 is the correlation coefficient between bj and b̂j , with 0 ≤ ρ2 ≤ 1, and wj is a circularly complex Gaussian RV having the same variance as bj . From yBS, the SINR can be expressed as γBS = γh 1+γb , and based on probability theory, the CDF of γBS can be evaluated as FγBS(x ) = ∫ ∞ 0 Fγh (x (1 + y))fγb (y)dy , (6) which requires the determination of the PDF fγb (·). In (6), the PDF of the actual γb at the transmission instant is given by fγb (x ) = ∫ ∞ 0 fγb |γ̂b (x |y)fγ̂b (y)dy , (7) 4It is worth mentioning that ideally, such an interference should only affect the eavesdropper. However, in practical setups, the BS and PE can be in close range and therefore both will be affected by the same interfering source. MOUALEU et al.: SEQUENTIAL RELAY SELECTION IN D2D-ENABLED CELLULAR NETWORKS WITH OUTDATED CSI OVER MIXED FADING CHANNELS 247 FγBS (γS ) = M √ π Γ(Lμh)γ̄b(ρ2 + M (1 − ρ2)) ∞∑ k=0 ( Γ(2Lμh + 2k)H 2k h 2−2Lμh−2k+1 k !Γ(Lμh + k + 0.5)�Lμh+2k h ) ⎧ ⎪⎪⎪⎪⎨ ⎪⎪⎪⎪⎩ γ̄b(ρ2 + M (1 − ρ2)) M − 2Lμh+2k−1∑ m=0 γm S m! ( 2μh�h γ̄h )m ⎛ ⎜ ⎜ ⎜ ⎝ M γ̄b(ρ2 + M (1 − ρ2)) + 2μh�hγS γ̄h︸ ︷︷ ︸ Δ ⎞ ⎟ ⎟ ⎟ ⎠ −(m+1) exp ( M γ̄b(ρ2 + M (1 − ρ2)) ) Γ(m + 1,Δ) ⎫ ⎪⎪⎪⎪⎬ ⎪⎪⎪⎪⎭ (11) Fγeff RD (x ) = l l−1∑ m=0 ( l − 1 m ) (−1)m m + 1 { 1 − 2 √ π� Lμd d Γ(Lμd ) exp ( − (m + 1)x γ̄RD (1 + m(1 − ρ1)) ) ∞∑ k=0 H 2h d μ2Lμd+2k d Γ(2Lμd + 2k) k !Γ(Lμd + k + 0.5)γ̄2Lμd+2k d × ( 2μd�d γ̄d + (m + 1)x γ̄RD (1 + m(1 − ρ1)) )−(2Lμd+2k) } . (15) where the conditional PDF fγb |γ̂b (x |y) can be expressed as fγb |γ̂b (x |y) = λ exp (−(ρ2y + x ) (1 − ρ2)γ̄b ) I0 ( 2 √ ρ2xy (1 − ρ2)γ̄b ) , (8) with λ = 1 (1−ρ2)γ̄b , I0(·) denoting the modified Bessel func- tion of the first kind and zeroth order. Also, in (5), the selection is equivalent to the worst relay selection so that the PDF of γ̂b can be given by fγ̂b (x ) = M γ̄b exp ( −Mx γ̄b ) , (9) where M = N−1. By substituting (8) and (9) in (7) and with the help of [8, eqs. (6.614.3), (9.220.2), and (9.215)], and after some algebraic manipulations, we get fγb (x ) = 1 γ̄b(ρ2 + M (1 − ρ2)) exp ( −Mx γ̄b(ρ2 + M (1 − ρ2)) ) . (10) Now, by plugging (3) and (10) into (6), and with the help of [8, eqs. (8.352.1) and (3.382.4)] and many algebraic manip- ulations, an analytical expression for the CDF of γBS can be obtained as in (11), shown at the top of this page, with Γ(·, ·) denoting the upper incomplete Gamma function [8, eq. (8.350.2)]. Next, we evaluate the CDF of γe2e which in its general form can be written as Fγe2e(γT) = ( FγSR(γT) )N + N∑ l=1 ( N l ) ( FγSR(γT) )N−l × ( 1 − FγSR(γT) )lFγeff RD (γT). (12) In order to evaluate (12), the CDFs of γSR and γeff RD are required. The expression of the former can easily be obtained as FγSR(γT) = 1 − exp(− γT γ̄SR ), where γ̄SR is the average SNR of the channel between DT and a D2D relay. However, the derivation of the CDF of γeff RD is a bit more involving. Knowing that γeff RD = γ Rθ DR 1+γd , where γd = ∑L k=1 γdk , from probability theory, Fγeff RD (γT) can be evaluated as Fγeff RD (γT) = ∫ ∞ 0 F γ Rθ RD (γT(1 + y))fγd (y)dy . (13) To obtain the CDF of γRθ RD , which corresponds to the best relay in the D2D communication, we use a similar approach to that used to derive (10), which yields F γ Rθ RD (y) = l l−1∑ m=0 ( l − 1 m ) (−1)m m + 1 × { 1 − exp ( − (m + 1)y γ̄RD (1 + m(1 − ρ1)) )} . (14) Upon substituting (2) (with the subscript h and d interchanged) and (14) into (13), and with the help of [8, eq. (3.382.4)], and after some algebraic manipulations, Fγeff RD (x ) can be obtained as shown in (15), at the top of this page. Finally, plugging (15) and the aforementioned expression of FγSR(γT) into (12), and together with (11) into (4), the MOP is attained. Although such an expression is not given in closed-form, the derived series is steadily convergent and requires around 20 terms to achieve precise results. In addition, the derived exact MOP can be easily implemented in most popular computer softwares, such as MATHEMATICA. B. Asymptotic MOP Now, the asymptotic behavior of the MOP is investigated. Firstly, we start with the asymptotic expression of FγBS(γS ). As γ̄h = γ̄ → ∞, (3) is dominated by the term corre- sponding to k = 0. With the approximation Υ(s, x ) ≈ x s s (x → 0), (3) can be reduced to F∞ γh (x ) ≈ G1x2Lμh γ̄2Lμh , where G1 = √ π� Lμh h μ 2Lμh−1 h LΓ(Lμh )Γ(Lμh+0.5) . Substituting (10) and the above- mentioned expression F∞ γh (x ) in (6) and after performing some algebraic manipulations, (11) can be approximated by F∞ γBS (γS ) ≈ (G1β −1γ 2Lμh S eβEi(−2Lμh , β))γ̄−2Lμh , where β = γ̄b(ρ2 +M (1− ρ2)) and Ei(·) is the exponential integral defined in [8, eq. (8.211.1)]. Next, we focus on the high-SNR approximation of (15). Since the relay selection in the D2D communications is based on the nature of the CSI, the analysis consider two scenarios: outdated CSI (0 ≤ ρ1 < 1) and perfect CSI (ρ1 = 1), and it is assumed that γ̄SR = γ̄RD = γ̄ → ∞ for the above- cited scenarios. Under the latter assumption, (12) reduces 248 IEEE WIRELESS COMMUNICATIONS LETTERS, VOL. 8, NO. 1, FEBRUARY 2019 to F∞ γe2e (γT) ≈ ∑N l=1 (N l ) Fγeff RD (γT). Considering perfect CSI, with the help of Iv (z ) = π(z/2)vG1,0 1,3 ( z2 4 | 1 2 0,−v , 1 2 ), the binomial expansion (1 + a)b = ∑b j=0 (b j ) aj , and [11, eq. (2.24.3.1)], and after tedious manipulations, (12) can be approximated by F∞ γe2e (γT) ≈ ΘγN T γ̄N ( μd γ̄d )Lμd− 1 2 N∑ j=0 ( N j )( γ̄d μd�d )2Lμd+j × G1,2 2,3 (( Hd �d )2 ∣ ∣ ∣ ∣ ∣ 1−(2Lμd+j ) 2 , 2−(2Lμd+j ) 2 0,−Lμd + 1 2 , 1 2 ) , (16) where Θ = πμ Lμd+1 2 d � Lμd d Γ(Lμd )γ̄ Lμd+1 2 d and Gm,n p,q (·| ·· ) is the Meijer G-function defined in [8, eq. (9.301)]. Similarly, assuming outdated CSI, (12) is approximated by F∞ γe2e(γT) ≈ NΘγT γ̄ ( N∑ m=0 ( N − 1 m ) (−1)m 1 + m(1 − ρ1) ) × ( μd γ̄d )Lμd− 1 2 1∑ j=0 ( 1 j )( γ̄d μd�d )2Lμd+j × G1,2 2,3 (( Hd �d )2 ∣∣∣∣ ∣ 1−(2Lμd+j ) 2 , 2−(2Lμd+j ) 2 0,−Lμd + 1 2 , 1 2 ) . (17) Remark 1: The asymptotic MOP for any arbitrary value of ρ2 and ρ1 = 1 is given by using the derived F∞ γBS (γS ) and (16) in (4), and the diversity order is given by Gd1 = min(2Lμh ,N ). Remark 2: The asymptotic MOP for any arbitrary value of ρ2 and 0 ≤ ρ1 < 1 is given by using the derived F∞ γBS (γS ) and (17) in (4), and the diversity order is given by Gd2 = min(2Lμh , 1). IV. NUMERICAL RESULTS AND DISCUSSIONS Without loss of any generality, in this section we assume the following parameters: ηh = 1.5, μh = 0.5, ηd = 0.5, μd = 8, γ̄SR = γ̄RD = γ̄h = γ̄, γ̄d = γ̄b = 10 dB, and RS = RT = 1 bit/s/Hz. Fig. 1 shows the MOP performance for various values of the correlation coefficients ρ1 and ρ2. It can be observed that as ρ2 approaches unity, there is no substantial performance gain as opposed to when ρ1 tends to unity. Hence, it can be implied that for relay selection with perfect CSI in the D2D communication, the mutual cooper- ation between the D2D and cellular networks become more beneficial to both systems regardless of the nature of the CSI used for the second relay selection strategy. Fig. 2 illustrates the analytical MOP performance as a function of the num- ber of relays N with varied L and ρ1. As can be seen, for a fixed ρ1, i.e., ρ1 ∈ {0.1, 0.9, 1}, the MOP improves as L decreases. This implies that a large number of CUs can have a detrimental effect on the mutual cooperation between the D2D communication and cellular network. This is due to the fact that all the CUs interfere with the D2D communication at the DR and therefore, the impact of interference is substantial. Moreover, we note that the performance gap between L = 4 and L = 10 greatly increases as ρ1 improves. Furthermore, there is an error floor in all cases as N becomes fairly large. It can be inferred that a very populated D2D communication in terms of relays, does not further benefit the two networks. Fig. 1. MOP versus γ̄ for L = N = 4 and different ρ1 and ρ2. Fig. 2. MOP versus N for γ̄ = 25 dB, ρ2 = 0.1, and various ρ1. REFERENCES [1] S. Dang, G. Chen, and J. P. Coon, “Multicarrier relay selection for full- duplex relay-assisted OFDM D2D systems,” IEEE Trans. Veh. Technol., vol. 67, no. 8, pp. 7204–7218, Aug. 2018. [2] C. Ma et al., “Interference exploitation in D2D-enabled cellular networks: A secrecy perspective,” IEEE Trans. Commun., vol. 63, no. 1, pp. 229–242, Jan. 2015. [3] P. S. Bithas, G. P. Efthymoglou, and A. G. Kanatas, “V2V cooperative relaying communications under interference and outdated CSI,” IEEE Trans. Veh. Technol., vol. 67, no. 4, pp. 3466–3480, Apr. 2018. [4] J. 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I documenti PDF creati possono essere aperti con Acrobat e Adobe Reader 5.0 e versioni successive.) /JPN /KOR /NLD (Gebruik deze instellingen om Adobe PDF-documenten te maken waarmee zakelijke documenten betrouwbaar kunnen worden weergegeven en afgedrukt. De gemaakte PDF-documenten kunnen worden geopend met Acrobat en Adobe Reader 5.0 en hoger.) /NOR /PTB /SUO /SVE /ENU (Use these settings to create PDFs that match the "Recommended" settings for PDF Specification 4.01) >> >> setdistillerparams << /HWResolution [600 600] /PageSize [612.000 792.000] >> setpagedevice