IEEE TRANSACTIONS ON WIRELESS COMMUNICATIONS, VOL. 17, NO. 1, JANUARY

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1 IEEE TAACTIO O WIELE COMMUICATIO, VOL. 7, O., JAUAY Buffer-Aided eaying For The Two-Hop Fu-Dupex eay Channe With ef-interference Mohsen Mohammadkhani azighi, tudent Member, IEEE, and ikoa Zatanov, Member, IEEE Abstract In this paper, we investigate the fading two-hop fu-dupex FD reay channe with sef-interference, which is comprised of a source, an FD reay impaired by sef-interference, and a destination, where a direct source-destination ink does not exist. For this channe, we propose three buffer-aided reaying schemes with adaptive reception-transmission at the FD reay for the cases when the source and the reay both perform continuousrate transmission with adaptive-power aocation, continuousrate transmission with fixed-power aocation, and discrete-rate transmission, respectivey. The proposed buffer-aided reaying schemes enabe the FD reay to adaptivey seect to either receive, transmit, or simutaneousy receive and transmit in a given time sot based on the quaities of the receiving, transmitting, and sefinterference channes, a degree-of-freedom unavaiabe without buffer-aided reaying. Our numerica resuts show that significant performance gains are achieved using the proposed buffer-aided reaying schemes compared with conventiona FD reaying, where the FD reay is forced to aways simutaneousy receive and transmit, and to buffer-aided haf-dupex reaying, where the haf-dupex reay cannot simutaneousy receive and transmit. The main impication of this paper is that FD reaying systems without buffer-aided reaying miss-out on significant performance gains. Index Terms Buffer-aided reaying, fu-dupex, sefinterference. I. ITODUCTIO ELAY pay an important roe in wireess communications for increasing the data rate and/or the reiabiity between a source and a destination. In genera, the reay can operate in two different modes, namey, fudupex FD mode and haf-dupex HD mode. In the FD mode, transmission and reception at the FD reay can occur simutaneousy and in the same frequency band. However, due to the in-band simutaneous reception and transmission, FD reays are impaired by sef-interference I, which occurs due to eakage of energy from the transmitter-end into the receiverend of the FD reay. Currenty, there are advanced hardware designs which can suppress the I by about 0 db in certain Manuscript received Apri 4, 207; revised August 5, 207 and October 5, 207; accepted October 22, 207. Date of pubication ovember, 207; date of current version January 8, 208. This paper was presented at the IEEE Gobecom 207. The associate editor coordinating the review of this paper and approving it for pubication was C. Lee. Corresponding author: Mohsen Mohammadkhani azighi. The authors are with the Department of Eectrica and Computer ystems Engineering, Monash University, Mebourne, VIC 800, Austraia e-mai: mohsen.mohammadkhanirazighi@monash.edu; nikoa.zatanov@monash.edu. Coor versions of one or more of the figures in this paper are avaiabe onine at Digita Object Identifier 0.09/TWC scenarios, see 2. Because of this, FD reaying with I is gaining considerabe research interest 2,. On the other hand, in the HD mode, transmission and reception take pace in the same frequency band but in different time sots, or in the same time sot but in different frequency bands. As a resut, HD reays avoid the creation of I. However, since an FD reay uses twice the resources compared to an HD reay, the achievabe data rates of an FD reaying system may be significanty higher than that of an HD reaying system. One of the first immediate appications of FD reaying is expected to be in providing support to HD base stations. In particuar, the idea is to depoy FD reays around HD base stations, which wi reay information from the HD base stations to users that are at significant distances from the base stations. The system mode resuting from such a scenario is the two-hop FD reay channe, which is comprised of a source, an FD reay, and a destination, where a direct sourcedestination ink does not exist due to the assumed arge distance between the source and the destination. In this paper, we wi investigate new achievabe rates/throughputs for this system mode, i.e, for the two-hop FD reay channe with I and inks impaired by fading. The two-hop reay channe with and without fading has been extensivey investigated in the iterature both for HD reaying as we as FD reaying with and without I. In particuar, the capacity of the two-hop HD reay channe without fading was derived in 4. On the other hand, for the twohop HD reay channe with fading, 5 proposed a conventiona decode-and-forward DF reaying scheme, where the HD reay switches between reception and transmission in a prefixed manner, and 6 proposed a buffer-aided reaying scheme where, in each time sot, the HD reay seects to either receive or transmit based on the quaities of the receiving and transmitting channes. As a resut, the rate achieved by the scheme in 6 is arger than the rate achieved by the scheme in 5, showing that buffers improve the performance of HD reays. The capacity of the two-hop FD reay channe with an ideaized FD reay without I was derived in and 5 for the cases with and without fading, respectivey. ecenty, the capacity of the Gaussian two-hop FD reay channe with I and without fading was derived in 7. However, for the two-hop FD reay channe with I and fading achievabe rates are known for ony certain specia cases, such as an I channe not impaired by fading, see 8. Motivated by the ack of advanced schemes for the genera two-hop FD reay channe with I and fading, in this paper, IEEE. Persona use is permitted, but repubication/redistribution requires IEEE permission. ee for more information.

2 478 IEEE TAACTIO O WIELE COMMUICATIO, VOL. 7, O., JAUAY 208 we investigate this channe and propose nove achievabe rates/throughputs. The nove rates/throughputs are achieved using buffer-aided reaying. Thereby, simiar to HD reays, we show that buffers aso improve the performance of FD reays with I. This means that buffer-aided reaying shoud become an integra part of FD reaying systems, i.e., that FD reaying systems without buffer-aided reaying miss-out on significant performance gains. The proposed nove buffer-aided reaying schemes for the two-hop FD reay channe with I and fading enabe the FD reay to seect adaptivey either to receive, transmit, or simutaneousy receive and transmit in a given time sot based on the quaities of the receiving, transmitting, and I channes such that the achievabe data rate/throughput is maximized. ote that such a degree of freedom is not avaiabe if a buffer is not empoyed. pecificay, we propose three bufferaided reaying schemes with adaptive reception-transmission at the FD reay, for the cases when both the source and the reay perform continuous-rate transmission with adaptivepower aocation, continuous-rate transmission with fixedpower aocation, and discrete-rate transmission, respectivey. The proposed buffer-aided schemes significanty improve the achievabe rate/throughput of the considered reay channe compared to existing schemes. In particuar, our numerica resuts show that significant performance gains are achieved using the proposed buffer-aided reaying schemes compared to conventiona FD reaying, where the FD reay is forced to aways simutaneousy receive and transmit, and to bufferaided HD reaying, where the HD reay cannot simutaneousy receive and transmit. Buffer-aided reaying schemes are widey investigated in 6, 8 29 and references therein. Most of these works investigate ony HD buffer-aided reaying systems, see 6,, From the works reated to FD buffer-aided reaying,, 2, 4 investigate reay channes with a direct ink between the source and the destination. However, the proposed FD buffer-aided reaying schemes in, 2, 4 transform to the conventiona FD reaying scheme if the direct ink between the source and the destination becomes unavaiabe. Hence, the proposed FD buffer-aided schemes in in, 2, and 4 are not optima. On the other hand, 5 proposes FD buffer-aided schemes for reaying systems with mutipe antennas. However, the proposed FD buffer-aided schemes in 5 are aso not optima. Optima FD buffer-aided reaying schemes were in 9, 0, and 29. However, the authors in 9 assumed that the I at the FD reay is negectabe, which may not be a reaistic mode in practice. imiary, the work in 0 investigates a FD reay channe where the I channe is not impaired by fading i.e., does not vary with time, which aso may not be an accurate mode of the I channe. In particuar, in practica wireess communications, due to the movement of objects/refections, the I channe is impaired by fading and thereby varies with time. As a resut, the proposed FD buffer-aided reaying schemes in 0 are not optima to the practica scenario when the I channe is impaired by fading and therefore perform very poory for that scenario. Contrary to 0, in this paper, the I channe is assumed to be Fig.. eaying system, comprised of a source,, an FD reay impaired by I,, and a destination, D, where a direct -D ink is not avaiabe. impaired by fading, and thereby the proposed FD buffer-aided reaying schemes in this paper significanty outperform the FD buffer-aided reaying schemes proposed in 0. On the other hand, the authors in 29 propose an optima FD buffer-aided reaying scheme for the case when the source and the reay transmit with a singe fixed-rate. However, in practice, wireess transmitters do not usuay transmit with a singe rate nor with a continuous-rate, but rather seect their rate adaptivey from a set of discrete-rates. To investigate this practica discrete-rate scenario, in this paper, we propose optima FD buffer-aided reaying schemes for the case when both the source and the reay seect their transmission rates from sets of discrete rates. This paper is organized as foows. In ection II, we present the system and channe modes. In ection III, we formuate a genera FD buffer-aided reaying scheme with adaptive reception-transmission at the FD reay. In ection IV, we propose optima buffer-aided reaying schemes for the cases when both the source and the reay transmit with continuous-rates, and with adaptive- and fixed-power aocation. Optima bufferaided reaying schemes for the considered reay channe with discrete-rate transmission is derived in ection V. imuation and numerica resuts are provided in ection VI, and the concusions are drawn in ection VII. II. YTEM AD CHAEL MODEL We consider the two-hop FD reay channe, which is comprised of a source,, an FD reay impaired by I,, and a destination, D, where a direct -D ink does not exist, cf. Fig.. In addition, we assume that the FD reay is a DF reay equipped with a sufficienty arge buffer in which it can store incoming data and from which it can extract data for transmission to the destination. A. Channe Mode We assume that the - and -D inks are compex-vaued additive white Gaussian noise AWG channes impaired by sow fading. Furthermore, simiar to the majority of reated papers 0,, we aso assume that the I channe is impaired by sow fading. Thereby, the I channe aso varies with time. We assume that the transmission time is divided into time sots. Furthermore, we assume that the fading is constant during one time sot and changes from one time sot to the next. Let h i and h D i denote the compex-vaued fading gains of the - and -D channes in time sot i, respectivey, and et h i denote the compex-vaued fading gain of the I channe in time sot

3 AZLIGHI et a.: BUFFE-AIDED ELAYIG FO THE TWO-HOP FD ELAY CHAEL WITH ELF-ITEFEECE 479 i. Moreover, et σn 2 and σn 2 D denote the variances of the compex-vaued AWGs at the reay and the destination, respectivey. For convenience, and without oss of generaity, we define normaized squared fading gains for the -, - D, and I channes as γ i = h i 2 /σn 2, γ D i = h D i 2 /σn 2 D,andγ i = h i 2 /σn 2, respectivey. Let P i and P i denote the transmit powers of the source and the reay in time sot i, respectivey. We assume that the I, which is received via the I channe in any symbo interva of time sot i, is independent and identicay distributed i.i.d. according to the zero-mean Gaussian distribution with variance P i h i 2, an assumption simiar to the majority of reated works 0. This assumption is reaistic due to the combined effect of various sources of imperfections in the I canceation process, and can aso be considered as the worst-case scenario of I 4. As a resut, in time sot i, the - channe is a compex-vaued AWG channe with channe gain h i and noise variance P i h i 2 σn 2. Hence, the capacity of this channe in time sot i is obtained as C i = og 2 P iγ i P iγ i. On the other hand, in time sot i, the -D channe is aso a compex-vaued AWG channe with channe gain h D i and noise variance σ 2 n D. Hence, the capacity of this channe in time sot i is obtained as C D i = og 2 P iγ D i. 2 In time sot i, we assume that the source and the reay transmit codewords encoded with a capacity achieving code, i.e., codewords comprised of n symbos that are generated independenty from compex-vaued zero-mean Gaussian distributions with variances P i and P i, respectivey. The data rates of the codewords transmitted from the source and the reay in time sot i are denoted by i and D i, respectivey. The vaues of i and D i wi be defined ater on. III. GEEAL FD BUFFE-AIDED ELYIG In this section, we formuate a genera FD buffer-aided reaying scheme with adaptive reception-transmission at the FD reay. A. Probem Formuation Depending on whether the source and/or the reay are sient, we have four different states for the considered two-hop FD reay channe with I in each time sot: tate 0: and are both sient. tate : transmits and receives without transmitting. tate 2: transmits and is sient. tate : transmits and simutaneousy receives and transmits. To mode these four states, we define three binary variabes for time sot i, q i, q 2 i, andq i, as if transmits and receives without q i = transmitting in time sot i 0 otherwise, if transmits and is sient in time q 2 i = sot i 4 0 otherwise, if transmits and simutaneousy q i = receives and transmits in time sot i 5 0 otherwise. ince the two-hop FD reay channe can be in one and ony one of the four states in time sot i, the foowing has to hod q i q 2 i q i {0, }, 6 where if q i q 2 i q i = 0 occurs, it means that the system is in tate 0, i.e., both and are sient in time sot i. To generaize the FD buffer-aided reaying scheme even further, we assume different transmit powers at the source and the reay during the different states. In particuar, et P i and P i denote the powers of the source when q i = andq i =, respectivey, and et P 2 i and P i denote the powers of the reay when q 2i = and q i =, respectivey. Obviousy, P i = 0, P2 i = 0, and P i = P i = 0whenq i = 0, q 2 i = 0, and q i = 0 hod, respectivey. In the foowing sections, we provide the optima vaues for the state seection variabes q k i, k, which maximize the achievabe rate and the throughput of the considered reay channe. To this end, we define the foowing auxiiary optima state seection scheme q i = q 2 i = Optima cheme = q i = if i > i and 2 i if 2 i > i and 2 > i if i i and 2 i, where i, 2 i, and i wi be defined ater on, cf. Theorems to. IV. BUFFE-AIDED ELAYIG WITH COTIUOU-ATE TAMIIO In this section, we provide buffer-aided reaying schemes for the case when both the source and the reay are abe to adapt their transmission rates to the underying channes in each time sot without any itation on the vaues of the transmission rates. Thereby, we provide two buffer-aided reaying schemes with continuous-rate transmission; one in which both the source and the reay aso adapt their transmit powers to the underying channes in each time sot, and the other one in which both the source and the reay transmit with fixed-powers in each time sot. 7

4 480 IEEE TAACTIO O WIELE COMMUICATIO, VOL. 7, O., JAUAY 208 A. Probem Formuation for Buffer-Aided eaying With Continuous-ate Transmission Using the state seection variabes q k i, k, and the transmit powers of the source and the reay for each possibe state, we can write the capacities of the - and -D channes in time sot i, C i and C D i, as C i = q iog 2 P iγ i q iog 2 P iγ i P iγ, 8 i C D i = q 2 iog 2 P 2 iγ Di q iog 2 P iγ Di. 9 ow, since the source is assumed to be backogged, we can set the transmission rate at the source in time sot i, i, to i = C i, wherec i is given by 8. As a resut, the achievabe rate on the - channe during time sots, denoted by, is obtained as = = i i= q iog 2 i= P iγ i q iog 2 P iγ i P iγ. 0 i On the other hand, the reay can transmit ony if it has information stored in its buffer. Let Qi, denote the amount of normaized information in bits/symbo in the buffer of the reay at the end beginning of time sot i time sot i. Then, we can set the transmission rate at the reay in time sot i, D i, to D i = min{qi, C D i}, where C D i is given by 9. As a resut, the achievabe rate on the -D channe during time sots, denoted by D, is obtained as D = = D i i= i= min {Qi, q 2 iog 2 P 2 iγ Di q iog 2 P iγ Di}, where Qi is obtained recursivey as Qi = Qi i D i. 2 Our task in this section is to maximize the achievabe rate of the considered reay channe given by. To this end, we use the foowing Lemma from 6, Th.. Lemma : The data rate extracted from the buffer of the reay and transmitted to the destination during time sots, D, is maximized when the foowing condition hods q iog 2 P iγ i i= q iog 2 P iγ i P iγ i = i= q iog 2 q 2 iog 2 P P 2 iγ Di iγ Di. Moreover, when condition hods, the rate, by, simpifies to D = q 2 iog 2 i= P 2 iγ Di D,given q iog 2 P iγ Di. 4 Proof: ee 6, Th. for the proof. Lemma is very convenient since it provides an expression for the maximum data rate, D, which is independent of the state of the buffer Qi. This is because, when condition hods, the number of time sots for which D i = min{qi, C D i} = Qi occurs is negigibe compared to the number of time sots for which D i = min{qi, C D i} = C D i occurs when, see 6. In other words, when condition hods, we can consider that the buffer at the reay has enough information amost aways. B. Buffer-Aided eaying With Continuous-ate Transmission and Adaptive-Power Aocation In this subsection, we assume that the source and the reay can aso adapt their transmit powers in each time sot such that a ong-term average power constraint P is satisfied. More precisey, P i, P i, P2 i, andp i have to satisfy the foowing constraint i= q ip i q 2iP i i= q 2 ip 2 i q ip i P. 5 ow, empoying Lemma, we devise the optimization probem for maximizing the rate, D,when, in 6, where constraint C ensures that hods, C2 constrains the vaues that q k i, k, i, can assume, C ensures no more than one state is active at a given time sot i, C4 ensures the joint source-reay power constraint in 5 hods, and constraint C5 ensure that the transmit powers are non-negative. In the foowing theorem, we provide the soution of probem 6, as shown at the top of this page, which maximizes the achievabe rate of the considered buffer-aided FD

5 AZLIGHI et a.: BUFFE-AIDED ELAYIG FO THE TWO-HOP FD ELAY CHAEL WITH ELF-ITEFEECE 48 Maximize: q k i,p k i,pk i, i,k ubject to : C: q 2 iog 2 i= P 2 q iog 2 P i= = q 2 iog 2 i= iγ Di q iog 2 P 2 iγ i q iog 2 C2 : q k i {0, }, for k =, 2, C: q i q 2 i q i {0, } C4: q ip i q 2iP i i= C5: P k i 0, Pk P iγ Di q iog 2 i= P iγ Di P P iγ i iγ i iγ Di q 2 ip 2 i q ip i P i 0, k, 6 reay channe with I for continuous-rate transmission with adaptive-power aocation. Theorem : The optima state seection variabes q k i, k, i, found as the soution of 6, are given in 7, where i, 2 i, and i are defined as i = μ og 2 P iγ i ζ P i, 7 2 i = μ og 2 P 2 iγ Di i = μ og 2 P iγ i P iγ i μ og 2 P iγ Di ζ P 2 i, 8 ζ P i ζ P i. 9 Moreover, the optima P i and P2 i, found as the soution of 6, are given by ρ P i = η γ i if γ i >η/ρ 20 0 otherwise, P 2 i = η η D i if γ D i >η 2 0 otherwise, where η ζ n2 μ μ and ρ μ. Whereas, the optima P i and P i are obtained as the soution of the foowing system of two equations μγ iγ ip i P iγ i P iγ i P iγ i μγ Di P iγ n2ζ = 0, 22 Di μγ i P iγ i P iγ i n2ζ = 0. 2 In 22-2, μ and ζ are constants found such that C and C4 in 6 are satisfied, respectivey. Proof: Pease refer to Appendix A for the proof. C. Buffer-Aided eaying With Continuous-ate Transmission and Fixed-Power Aocation In this subsection, we assume that the powers at the source and the reay cannot be adapted to the underaying channes in each time sot. As a resut P i = P, P2 i = P2, i = P,andP i = P hod i. P The maximum achievabe rate for this case can be found from 6 by setting P i = P, P2 i = P2, P i =,andp i = P, i, in 6. As a resut, we do P not need to optimize in 6 with respect to these powers. Consequenty, the constraints C4 and C5 in 6 can be removed. Thereby, we get a new optimization probem for fixed-power aocation whose soutions are provided in the foowing theorem. Theorem 2: The state seection variabes q k i, k, i, maximizing the achievabe rate of the considered buffer-aided FD reay channe with I for continuous-rate transmission with fixed-power aocation i.e., found as the soution of 6 with P i = P, P2 i = P2, P i = P,and P i = P, i, and constraints C4-C5 removed are given in 7, where i, 2 i, and i are defined as i = μ og 2 P γ i, 24 2 i = μog 2 P 2 γ Di, 25 i = μ og 2 P γ i P γ i μog 2 P γ Di. 26 In 24-26, μ is a constant found such that constraint C in 6 hods. Proof: ince the fixed-power aocation probem is a specia case of 6, when P i = P, P2 i = P2, P i = P,andP i = P, i, and when C4 and C5 are removed, we get the same soution as in 7-9, but with ζ set to ζ = 0. This competes the proof. emark : We note that in the extreme cases when γ i and γ i 0 hod, i.e., the communication

6 482 IEEE TAACTIO O WIELE COMMUICATIO, VOL. 7, O., JAUAY 208 schemes provided in Theorems and 2 converge to the corresponding schemes in 6 and 5, respectivey. In other words, in the extreme cases when we have infinite and zero I, the proposed buffer-aided schemes work as buffer-aided HD reaying and idea FD reaying, respectivey. D. Practica Estimation of the ecessary Parameters The proposed state seection scheme, given in 7, requires the computation of i, 2 i, and i in each time sot. For the two proposed buffer-aided schemes, these parameters can be computed at the FD reay with minimum possibe channe state-information CI acquisition overhead. Using i, 2 i, and i, the reay can compute the optima state seection variabes q i, q 2 i, and q i using 7, and then feedback the optima state to the source and the destination using two bits of feedback information. On the other hand, the computation of i, 2 i, and i at the reay requires fu CI of the -, -D, and I channes, as we as acquisition of the constant μ. inceμ is actuay a Lagrange mutipier, in the foowing, we describe a method for estimating this constant in rea-time using ony current instantaneous CI by empoying the gradient descent method 5. In time sot i, we can recursivey compute an estimate of the constant μ, denoted by μ e i, as μ e i = μ e i δi e D i e i, 27 where e D i and e i are rea time estimates of D and, respectivey, which can be cacuated as e i = i e i i i C i, 28 e D i = i e D i i i C Di. 29 The vaues of e 0 and e D 0 are initiaized to zero. Moreover, δi is an adaptive step size which contros the speed of convergence of μ e i to μ, which can be some propery chosen monotonicay decaying function of i with δ <. For the buffer-aided reaying scheme with adaptive-power aocation, proposed in Theorem, in addition to μ, the constant ζ found in 7-9 has to be acquired as we. This can be conducted in a simiar manner as the rea-time estimation of μ. In particuar, in time sot i, we can recursivey compute an estimate of the constant ζ, denoted by ζ e i, as where P e i = i i where P Theorem. ζ e i = ζ e i δi P e i P, 0 P e i q ip i i q 2iP 2 i q i P i P, i i, P i, P2 i, and P i are given in V. BUFFE-AIDED ELAYIG WITH DICETE-ATE TAMIIO In this section, we assume that the transmitting nodes, source and reay, do not have fu CI of their transmit inks and/or have some other constraints that it their abiity to vary their transmission rates arbitrariy. As a resut, and transmit their codewords with rates which are seected from discrete finite sets of date rates, denoted by = {, 2,...,M } and ={, 2,...,L }, respectivey, where M and L denote the tota number of non-zero data rates avaiabe for transmission at and, respectivey. Moreover, we assume P i = P, P2 i = P2, P i = P, and P i = P, i. A. Derivation of the Proposed Buffer-Aided eaying cheme With Discrete-ate Transmission In order to mode the receptions and transmissions of the FD reay for discrete data rates in time sot i, we introduce the binary variabes q mi, q 2 i, andqm, i, wherem and are chosen from m =, 2...,M and =, 2...,L, respectivey, defined as if transmits with rate m q m to i = and is sient in time sot i 2 0 otherwise, if transmits with rate q2 to D i = and is sient in time sot i 0 otherwise. if transmits with rate m to and transmits with rate i = 4 to D in time sot i 0 otherwise. ince the considered network can be in one and ony one state in time sot i, the foowing has to hod M q m i q2 i m= = m= = i {0, }, 5 where if M m= q mi L = q2 i M L= m= i = 0 hods, then and are both sient in time sot i. ince the avaiabe transmission rates at and are discrete, outages can occur. An outage occurs if the data rate of the transmitted codeword is arger than the capacity of the underying channe. To mode the outages on the - ink, we define the foowing auxiiary binary variabes { O, m i = if og 2 P γ i m 0 if og 2 P γ i < m, 6 if og 2 P γ i O, m i = P γ m i 0 if og 2 P γ 7 i P γ < m i.

7 AZLIGHI et a.: BUFFE-AIDED ELAYIG FO THE TWO-HOP FD ELAY CHAEL WITH ELF-ITEFEECE 48 imiary, to mode the outages on the -D ink, we define the foowing auxiiary binary variabes O D,2 i = if og 2 P 2 γ Di 0 if og 2 P 2 γ Di <, 8 O D, i = if og 2 P γ Di 0 if og 2 P γ Di <. 9 Hence, a codeword transmitted by the source in time sot i can be decoded correcty at the reay if and ony if iff Mm= q miom, i M L= m= io, m i > 0 hods. Using O, m i and Om, i, and the state seection variabes q m i, andqm, i, we can define the data rate of the source in time sot i, i, as i = M q m iom, im io, m im. m= m== 40 In addition, we can obtain that a codeword transmitted by the reay in time sot i can be decoded correcty at the destination iff L = q2 io D,2 i L Mm= = io D, i >0 hods. imiary, using O D,2 i and O D, i, and the state seection variabes q2 i, andqm, i, we can define the data rate of the reay in time sot i, D i, as { D i = min Qi, q2 io D,2 i where = = m= } io D, i, 4 Qi = Qi i D i. 42 The min {} in 4 is because the reay cannot transmit more information than the amount of information in its buffer Qi. Thereby, the throughputs of the - and -D channes during time sots, again denoted by and D, can be obtained as = D = M q m iom, im i= m= min i= m= = { Qi, = m= io, m im, 4 q2 io D,2 i = io D, i }. 44 Our task in this section is to maximize the throughput of the considered reay channe with discrete-rate transmission given by 4 and 44. To this end, we use the foowing Lemma from 6, Th.. Lemma 2: The throughput D, given by 44, is maximized when the foowing condition hods M q m iom, im i= m= io, m im = m= = q2 io D,2 i i= = = m= io D, i. 45 Moreover, when condition 45 hods, the throughput, D, given by 44, simpifies to D = q2 io D,2 i i= = io D, i. 46 = m= Proof: ee 6, Th. for the proof. Using Lemma 2, we devise the foowing throughput maximization probem for the considered two-hop FD reay channe with I and discrete-rate transmission Maximize: q q m 2 i,q 2 i,qm, i, i,,m io D,2 i ubject to: C: i= = = m= io D, i M q m iom, im i= m= m= = = io, m im q2 io D,2 i i= = m= = io D, i m C2 : q m i {0, }, C: q2 i {0, }, C4: i {0, }, m, C5: q m i q2 i m= m= = = i {0, }. 47 In 47, we maximize the throughput D, given by 46, with respect to the state seection variabes q mi, q 2 i, qm, i, i,, m, when conditions 5 and 45 hod, and when the

8 484 IEEE TAACTIO O WIELE COMMUICATIO, VOL. 7, O., JAUAY 208 state seection variabes are binary. The soution of probem 47 eads to the foowing theorem. Theorem : We define q i = q m i, q 2i = q2 i, and q i = q m, i, where m = arg max m {m Om, i}, = {arg max{ Om D,2 i}, and { {m, }= arg max m {m Om, i}, arg max{ Om D, }. i} Then, the optima state and rate seection variabes, q i, q 2 i, andq i maximizing the throughput of the considered two-hop FD reay channe with I and discrete-rate transmission, found as the soution of 47, are given in 7, where i, 2 i, and i are defined as i = μ m Om, i, 48 2 i = μ O D,2 i, 49 i = μ m O, m i μ O D, i, 50 In 48-50, μ is a constant found such that constraint C in 47 hods. Proof: Pease refer to Appendix B for the proof. B. Practica Estimation of the ecessary Parameters The discrete-rate transmission scheme, proposed in Theorem, requires the cacuation of the parameter μ. This parameter can be obtained theoreticay by representing constraint C in 47 as { M M } E q m iom, im io, m im m= = m= = { = E q2 io D,2 i = m= } io D, i, 5 where E {.} denotes statistica expectation. Then, using the probabiity distribution functions PDFs of the -, -D, and I channes, the parameter μ can be found as the soution of V-B. ote that soving V-B requires knowedge of the PDFs of the channes. However, the scheme proposed in Theorem can sti operate without any statistica knowedge in the foowing manner. We appy 27 to obtain an estimate of μ for time sot i, denoted by μ e i, where C i and C D i in 28 and 29 are repaced by Mm= q miom, im M L= m= io, m im and L = q2 io D,2 i L Mm= = io D, i, respectivey. We now et μ e i to take any vaue in the range 0,. Then, when two state seection variabes both assume the vaue one, according to 7, we seect one at random with equa probabiity to assume the vaue one and set the other state seection variabe to zero. For this scheme, we choose δi to vary with i ony during the first severa time sots, and then we set it to a constant for the remaining time sots. VI. IMULATIO AD UMEICAL EULT In this section, we evauate the performance of the proposed buffer-aided schemes with adaptive reception-transmission at the FD reay for the two-hop FD reay channe with I, and compare it to the performance of severa benchmark schemes. To this end, we first define the system parameters, then introduce the benchmark schemes and a deay-constrained buffer-aided reaying scheme, and finay present the numerica resuts. A. ystem Parameters For the presented numerica resuts, the mean of the channe gains of the - and -D inks are cacuated using the standard path oss mode as c 2 E{ h L i 2 }= dl α, for L {-, -D}, 52 4π f c where c is the speed of ight, f c is the carrier frequency, d L is the distance between the transmitter and the receiver of ink L, andα is the path oss exponent. In this section, we set α =, and f c = 2.4 GHz. Moreover, we assume that the transmit bandwidth is 200 khz, and the noise power per Hz is 70 dbm. Hence, the tota noise power for 200 khz is obtained as 7 dbm. On the other hand, the vaue of E{ h i 2 } is set to db. ote that E{ h i 2 } can be considered as the I suppression factor of the corresponding I suppression scheme. Finay, for the numerica exampes with discrete-rate schemes, we assume M = L and k = k = k,fork =, 2,...,M, where is defined differenty depending on the corresponding exampe. B. Benchmark chemes In the foowing, we introduce three benchmark schemes which wi be used for benchmarking the proposed bufferaided reaying schemes. For the benchmark schemes P i = P and P i = P, i, is assumed. Benchmark cheme Buffer-Aided HD eaying With Adaptive eception-transmission: The achievabe rate of empoying an HD reay and using the buffer-aided HD reaying scheme with adaptive reception-transmission proposed in 6, is given in 6, ec. III-D. Benchmark cheme 2 Conventiona FD eaying With a Buffer: In conventiona FD reaying, the reay simutaneousy transmits and receives during a time sots. Hence, there is no adaptive mode seection as in buffer-aided schemes proposed in this paper. Moreover, the power at the source and the reay are set to P = tp and P = tp, respectivey. Because there is a buffer at the FD reay, the received information at the reay can be stored and transmitted in future time sots. As a resut the achieved data rate of conventiona FD reaying with a buffer during time sots is given by { tpγ i FD,2 = min og 2, tpγ i i= i= } og 2 tpγ D i. 5 We note that the conventiona FD reaying scheme without a buffer achieves a worse performance than the conventiona FD reaying scheme with a buffer. As a resut, this scheme is not used as a benchmark.

9 AZLIGHI et a.: BUFFE-AIDED ELAYIG FO THE TWO-HOP FD ELAY CHAEL WITH ELF-ITEFEECE 485 Fig. 2. Data rate vs. average consumed power of the proposed schemes and the benchmark schemes. Left: ymmetric geometry, whith d = d D = 500 m. ight: asymmetric geometry, whith d = 700 m, and d D = 00 m. Benchmark cheme FD eaying With an Idea FD eay Without I: This is identica to the Benchmark cheme 2, except that γ i is set to zero, i.e, to h i 2 = db. by μ e i, as μ e i = μ e i δi T 0 Qi e i, 55 C. Buffer-Aided eaying chemes for Deay-Constrained Transmission The proposed scheme in 7 gives the maximum achievabe rate and the maximum throughput, however, it cannot fix the deay to a desired eve. In the foowing, simiar to 7, we propose a scheme for the state seection variabes q k i, k, which hods the deay at a desired eve. The average deay of the considered network is given by Litte s Law, as i= Qi E{T i} = i= i, 54 where i and Qi are the transmission rate of the source and the queue ength in time sot i, respectivey. The rate i is defined in 8 for continuous-rate transmission and in 40 for discrete-rate transmission. Moreover, Qi is defined in 2 for continuous-rate transmission and in 42 for discrete-rate transmission. For the proposed deay-constrained scheme, we continue to use the genera state seection scheme in 7, where i, 2 i, and i, are cacuated using 7-9 for continuous-rate transmission with adaptive-power aocation, using for continuous-rate transmission with fixedpower aocation, and using for discrete-rate transmission. ote that i, 2 i, and i in 7-9, 24-26, and are a function of the parameter μ. In contrary to the proposed buffer-aided schemes in Theorems -, where μ is found to satisfy the constant C in 6 and 47, in the buffer-aided reaying scheme for deay-constrained transmission, we use μ to ensure that the system achieves a desired average deay. To this end, μ is cacuated as foows. Let us define T 0 as the desired average deay constraint of the considered reay network. Then, in time sot i, we can recursivey compute an estimate of the constant μ, denoted where Qi is the queue ength, defined in 2 and 42 for continuous-rate transmission with fixed- and adaptive-power aocation schemes and discrete-rate transmission scheme, respectivey. Furthermore, e i is a rea time estimate of, cacuated using 28, and initiaized to zero for i = 0, i.e., e 0 = 0. Moreover, δi is an adaptive step function, which can be chosen to be a propery monotonicay decaying function of i with δ <. D. umerica esuts A of the presented resuts in this section are generated for ayeigh fading by numerica evauation of the derived resuts and are confirmed by Monte Caro simuations. In Fig. 2, we iustrate the rates achieved using the proposed FD buffer-aided schemes for continuous-rate transmission with adaptive-power aocation, continuous-rate transmission with fixed-power aocation, and discrete-rate transmissions as a function of the average consumed power P. Moreover, these rates are compared with the rate obtained by the proposed schemes in 0 and 29, as we as with the benchmark schemes outined in ection VI-B. The average gain of the I channe in this numerica exampe is set to E{ h i 2 }= db. Aso, in this exampe, the distances of the sourcereay and reay-destination inks are set to 500m for the symmetric eft figure and to 700m and 00m for the asymmetric right figure, respectivey. For the proposed scheme with continuous-rate transmission with fixed-power aocation and discrete-rate transmission, we set P i = P, P2 i = P, P i = tp and P i = tp, wheret = 0.5, i. Moreover, for the proposed scheme with discrete-rate transmission with M = andm = 2, the vaue of is optimized numericay, for a given average power P, such that the throughput is maximized. For the adaptive-power aocation scheme proposed for a fixed I channe in 0, we set the I

10 486 IEEE TAACTIO O WIELE COMMUICATIO, VOL. 7, O., JAUAY 208 Fig.. Data rate vs. the average consumed power at the source node of the proposed buffer-aided scheme for continuous-rate transmission with fixedpower aocation and the benchmark schemes when the average power at the reay is set to 25 dbm. Fig. 4. Data rate/throughput vs. the average consumed power of proposed scheme with discrete-rate transmission. channe gain to the mean of the I channe. As can be seen from Fig. 2, by increasing the power, the interference becomes dominant and therefore, our proposed schemes achieve significant performance gains compared to the scheme in 0, which is due to the fact that our schemes are deveoped for a fading I channe. eference, proposes a continuous-rate fixedpower aocation buffer-aided scheme. However, without the direct -D ink, the buffer-aided scheme in transforms to the conventiona FD reaying scheme, which we aready use as benchmark. In Fig. 2, we aso considered the fixed-rate scheme proposed in 29 and compared it with our proposed discreterate scheme for two case of M = andm = 2. For the case when we have M =, our proposed discrete-rate scheme and the scheme in 29 achieve the same throughput since both schemes are optima for a singe fixed-rate. However, for the casewhenwehavem = 2, our scheme eads to substantia gains compared to the scheme in 29. Finay, it is cear from Fig. 2, that the proposed buffer-aided schemes with and without power aocation achieve substantia gains compared to the Benchmark chemes and 2 in both symmetric and asymmetric geometries. Moreover, as can be seen from Fig. 2, the performance of the conventiona FD reaying scheme, i.e, Benchmark cheme 2, is very poor. In fact, even the proposed discrete-rate transmission scheme with M = 2 outperformsthe conventiona FD scheme for P > 0 dbm, and P > 40 dbm for symmetric and asymmetric geometries, respectivey. This numerica resut ceary shows the substantia gains that can be achieved with the proposed buffer-aided schemes compared conventiona schemes and to a previous buffer-aided schemes avaiabe in the iterature. In Fig., we compare the achievabe rates of the proposed buffer-aided scheme for continuous-rate transmission with fixed-power aocation, with the capacity of the idea two-hop FD reay channe without I, conventiona FD reaying, and the rate achieved by buffer-aided HD reaying as a function of the average transmit power at the source node, where P = P = P is adopted, for different vaues of the I. In this exampe, the power of the reay, P 2 = P = P, is set to 25 dbm. This exampe modes an HD base-station which can vary its average power P, that is heped by an FD reay with fixed average power of P = 25 dbm to transmit information to a destination. ince the transmitted power at the reay node is fixed, the maximum possibe data rate on the -D channe is around 6.2 bits per symbo. As can be observed from Fig., the performance of the proposed FD bufferaided scheme is consideraby arger than the performance of buffer-aided HD reaying when the transmit power at the source i.e., HD base-station is arger than 25 dbm. For exampe, for 5 bits/symbo, the power gains are approximatey 0 db, 25 db, 20 db, and 5 db compared to HD reaying for I vaues of 40 db, 0 db, 20 db, and 0 db, respectivey. Moreover, from Fig. we can concude that the conventiona FD reaying scheme achieves a poor performance compared to proposed FD buffer-aided reaying scheme. Overa, this exampe ceary shows that indeed it is beneficia for FD buffer-aided reays to be empoyed around HD base stations in order to increase their performance significanty. In Fig. 4, we iustrate the throughputs achieved with the proposed scheme for discrete-rate transmission with and without I, as a function of the average consumed power, P, for M =, 2, 4, 8, 6,, where is set to = bits/symb. Moreover, we set P = P, P 2 = P, P = tp and P = tp, where t = 0.5. As can be seen from Fig. 4, the I does not have a arge infuence on the throughput for ow M, i.e., M = and M = 2. As a resut, the throughputs achieved with and without I are amost identica. By increasing M, e.g.tom 4, we can see from Fig. 4 that the achieved throughput is highy infuenced by the I. The reason for this behavior is because for M = and arge transmit powers, amost a of source s codewords with rate = M bits/symb can aways be transmitted via the reay when the reay is in the fu-dupex mode, despite the generated I. However, when M 4, at arge transmit powers, source s codewords with rates cose to = M bits/symb can be transmitted via the reay, in arge percentage of the time,

11 AZLIGHI et a.: BUFFE-AIDED ELAYIG FO THE TWO-HOP FD ELAY CHAEL WITH ELF-ITEFEECE 487 Fig. 5. Participating percentage of a three states. Left: As a function of average power. ight: As a function of I. Fig. 6. Average deay unti time sot i vs. time sot i, for proposed scheme with deay-constrained transmission compared to fixed desired vaue, T 0. Fig. 7. Average deay unti time sot i vs. time sot i, for proposed scheme with deay-constrained transmission compared to fixed desired vaue, T 0. ony when the reay is in the haf-dupex mode, i.e., due to the generated I, transmitting these codeword in the fu-dupex mode is not reiabe. In Fig. 5, in the eft and right figures we show the percentage of use of the three states, as a function of the average transmit power and I, respectivey. For the eft figure, the average power of the I channe is set to db. Whereas, for the right figure, the transmit power of the nodes is set to 25 dbm. We can see from the eft figure that there are two different regions; noise dominant region and interference dominant region. In the noise dominant region, the usage of the FD mode is dominant. By increasing the power of the reay, the system fas in the interference dominant region, where the FD mode is seected ess as opposed to the HD mode which is seected more frequenty. On the other hand, we can see from the right figure that when the I is high, the system works in the HD mode, with equa percentage for modes q and q 2. As the I decreases, the FD mode becomes more dominant. Finay, in the ow I region, the proposed scheme works in the FD mode, amost excusivey. In Fig. 6, we demonstrate the achievabe rate of the proposed deay-constrained buffer-aided scheme as a function of the average desired deay, T 0, and compare it with the maximum achievabe rate obtained with the scheme in Theorem 2, which does not fix the deay. For this numerica exampe, we set P i = 24 dbm, P2 i = 24 dbm, P i = 2 dbm and P i = 2 dbm, i. We can see from Fig. 6 that by increasing the average deay, T 0, both data rates converge fast. In fact, for a deay of time sots, there is ony 7% oss compared to the maximum rate. This shows that the proposed deay-constrained buffer-aided scheme achieves rate cose to the maximum possibe rate for a very sma deay. In Fig. 7, we pot the average deay of the proposed deayconstrained scheme unti time sot i, for the case when T 0 = 5 time sots, as a function of time sot i. Fig. 7 reveas that the average deay unti time sot i converges very fast to T 0 by increasing i. Moreover, when the average deay converges to

12 488 IEEE TAACTIO O WIELE COMMUICATIO, VOL. 7, O., JAUAY 208 its desired eve, it has reativey sma fuctuations around it. This shows that the proposed deay-constrained scheme is very effective in reaching the desired eve of deay fast. VII. COCLUIO In this paper, we proposed three buffer-aided reaying schemes with adaptive reception-transmission at the FD reay for the two-hop FD reay channe with I for the cases of continuous-rate transmission with adaptive-power aocation, continuous-rate transmission with fixed-power aocation, and discrete-rate transmission, respectivey. The proposed schemes significanty improve the over-a performance by optimay seecting the FD reay to either receive, transmit, or simutaneousy receive and transmit in a given time sot based on the quaities of the receiving, transmitting, and I channes. Aso, we proposed a reativey fast and practica buffer-aided scheme that hods the deay around a desirabe vaue. Our numerica resuts have shown that significant performance gains are achieved using the proposed buffer-aided reaying schemes compared to conventiona FD reaying, where the FD reay is forced to aways simutaneousy receive and transmit, to buffer-aided HD reaying, where the HD reay cannot simutaneousy receive and transmit, and to a previous bufferaided schemes avaiabe in the iterature. This means that buffer-aided reaying shoud become an integra part of future FD reaying systems, i.e., that FD reaying systems without buffer-aided reaying miss-out on significant performance gains. APPEDIX A. Proof of Theorem We reax constraints C2 and C such that 0 q k i, k, and 0 q i q 2 i q i, and ignore constraint C5. Then, we use the Lagrangian method for soving this optimization probem. Thereby, with some simpification, we can obtain the Lagrangian function, L, as L =q 2 iog 2 P 2 iγ Di q iog 2 P iγ Di μ q 2 iog 2 P 2 iγ Di q iog 2 P iγ Di q iog 2 P iγ i q iog 2 P iγ i P iγ i ζ q ip i q ip i q 2 ip 2 i q ip i λ iq i λ 2 i q i λ iq 2 i λ 4 i q 2 i λ 5 iq i λ 6 i q i λ 7 iq i q 2 i q i λ 8 i q i q 2 i q i, 56 where μ, ζ 0, and λ k i 0 are the Lagrangian mutipiers. By differentiating L with respect to P k i and Pk i, k, and then setting the resut to zero, we obtain dl dp i = μq iγ i n2 P iγ i ζ q i = 0, 57 dl dp 2 i = μq 2 iγ Di n2 P 2 iγ Di ζ q 2i = 0, 58 dl dp i = μq iγ i n2 P iγ i P iγ i ζ q i = 0, 59 and 60, as shown at the top of the next page. ow, we cacuate P k i and Pk i, k, based on equations and the foowing three different avaiabe states. q i = : ince q i =, we set q 2 i = 0andq i = 0. As a resut 57 becomes dl dp i = μγ i n2 P iγ i ζ = 0. 6 oving 6, we can obtain P i as in 20. q 2 i = : ince q 2 i =, we set q i = 0andq i = 0. As a resut, 58 becomes dl dp 2 i = μγ Di n2 P 2 iγ Di ζ = oving 62, we can obtain P 2 i as in 2. q i = : ince q i =, we set q i = 0 and q 2 i = 0. As a resut, 59 and 60, simpify to 22 and 2, respectivey. By soving 22 and 2, we can obtain P i and P i. We note that, athough in this case there is a cosed form soution for P i and P i, since the soution is very ong, we have decided not to show it in this paper. The Lagrangian function, L, given by VII-A is bounded beow if and ony if μ og 2 P iγ i ζ P i λ i λ 2 i λ 7 i λ 8 i = 0, 6 μ og 2 P 2 iγ Di ζ P 2 i λ i λ 4 i λ 7 i λ 8 i = 0, 64 μ og 2 P iγ Di μ og 2 P iγ i P iγ i ζ P i ζ P i λ 5 i λ 6 i λ 7 i λ 8 i = We define λ 7 iλ 8 i βi, and find the system seection schemes for the three different avaiabe cases as foows. q i = : ince q i =, we set q 2 i = 0andq i = 0. As a resut, we have λ i = 0, λ 4 i = 0, and λ 6 i = 0by compementary sackness in KKT condition. Thereby, we can

13 AZLIGHI et a.: BUFFE-AIDED ELAYIG FO THE TWO-HOP FD ELAY CHAEL WITH ELF-ITEFEECE 489 dl dp i = μq iγ Di n2 P iγ Di ζ q i μq iγ iγ ip i n2 P iγ i P iγ i P iγ = i rewrite 6, 64, and 65 as μ og 2 P iγ i ζ P i βi >0, μ og 2 P 2 iγ Di ζ P 2 i βi <0, And μ og 2 P iγ Di μ og 2 P iγ i P iγ i ζ P i ζ P i βi <0, 66 respectivey. q 2 i = : ince q 2 i =, we set q i = 0andq i = 0. As a resut, we have λ 2 i = 0, λ i = 0, and λ 6 i = 0. Thereby, we can rewrite 6, 64, and 65 as μ og 2 P iγ i ζ P i βi <0, μ og 2 P 2 iγ Di And ζ P 2 i βi >0, μ og 2 P μ og 2 P iγ Di P iγ i iγ i ζ P i ζ P i βi <0, 67 respectivey. q i = : ince q i =, we set q i = 0andq 2 i = 0. As a resut, we have λ 2 i = 0, λ 4 i = 0, and λ 5 i = 0. Thereby, we can rewrite 6, 64, and 65 as μ og 2 P iγ i ζ P i βi <0, μ og 2 P 2 iγ Di And ζ P 2 i βi <0, respectivey. μ og 2 P μ og 2 P iγ Di P iγ i iγ i ζ P i ζ P i βi >0, 68 By substituting the corresponding terms in VII-A, VII-A, and VII-A by 7, 8, and 9 we can derive the optima state seection scheme in Theorem. This competes the proof. B. Proof of Theorem We use the Lagrangian method for soving 47. With some simpification, we can obtain the Lagrangian function as L = m= = = m= i= M μ m= m qm, io, m i m qm iom, i μ q 2 io D,2 i i= = qm, io D, i λ m iqm i m= λ iq 2 i = = m= λ m 2 iqm i m= λ 4 iq 2 i = λ m, 5 i i m= = = m= M λ 7 i q m i q2 i λ 8 i m= = = m= λ m, 6 i i i q m i q2 i = m= i, 69 where λ m i 0, λm 2 i 0, λ i 0, λ 4 i 0, λm, 5 i 0, λ m, 6 i 0, λ 7 i 0, and λ 8 i 0, m,, i, arethe Lagrangian mutipiers. We can rewrite VII-B equivaenty as L = μ q imax m {m Om, i} i= q imax m {m Om, i} μ i= q imax{ O D, i} q 2 imax { O D,2 i}

14 490 IEEE TAACTIO O WIELE COMMUICATIO, VOL. 7, O., JAUAY 208 λ m iqm i m= λ iq 2 i = = m= λ m, 5 i i = m= λ m 2 iqm i m= λ 4 iq 2 i = λ m, 6 i i λ 7 i q i q 2 i q i λ 8 i q i q 2 i q i. 70 To find q k i, k, which maximize 70, first, we define λ 7 i λ 8 i βi. Then, we find the optima q k i, k, as foows. q i = : ince q i =, we set q 2 i = 0andq i = 0. As a resut, the conditions which maximize 70 in this case are μmax m {m Om, i}βi >0, And, μmax{ O D,2 i}βi <0, And, μmax m {m Om, i} μmax{ O D, i}βi <0. 7 q 2 i = : ince q 2 i =, we set q i = 0andq i = 0. For maximizing 70, the foowing conditions must be hed μmax m {m Om, i}βi <0, And, μmax{ O D,2 i}βi >0, And, μmax m {m Om, i} μmax{ O D, i}βi <0. 72 q i = : ince q i =, we set q i = 0andq 2 i = 0. Thereby, the conditions which maximize 70, in this case are μmax m {m Om, i}βi <0, And, μmax{ O D,2 i}βi <0, And, μmax m {m Om, i} μmax{ O D, i}βi >0. 7 By substituting the corresponding terms in 7, 72, and 7 by 48, 49, and 50, we obtain the optima state seection scheme in Theorem. This competes the proof. EFEECE T. M. Cover and A. A. E Gama, Capacity theorems for the reay channe, IEEE Trans. Inf. Theory, vo. IT-25, no. 5, pp , ep G. Liu, F.. Yu, H. Ji, V. C. M. Leung, and X. Li, In-band fu-dupex reaying: A survey, research issues and chaenges, IEEE Commun. urveys Tuts., vo. 7, no. 2, pp , 2nd Quart., 205. E. Ahmed and A. M. Etawi, A-digita sef-interference canceation technique for fu-dupex systems, IEEE Trans. Wireess Commun., vo. 4, no. 7, pp , Ju Zatanov, V. Jamai, and. chober, On the capacity of the two-hop haf-dupex reay channe, in Proc. IEEE Goba Teecomm. Conf. GLOBECOM, an Diego, CA, UA, Dec. 205, pp A. Host-Madsen and J. Zhang, Capacity bounds and power aocation for wireess reay channes, IEEE Trans. Inf. Theory, vo. 5, no. 6, pp , Jun Zatanov,. chober, and P. Popovski, Buffer-aided reaying with adaptive ink seection, IEEE J. e. Areas Commun., vo., no. 8, pp , Aug Zatanov, E. ippe, V. Jamai, and. chober, Capacity of the Gaussian two-hop fu-dupex reay channe with residua sefinterference, IEEE Trans. Commun., vo. 65, no., pp , Mar M. Kim and M. Bengtsson, Virtua fu-dupex buffer-aided reaying in the presence of inter-reay interference, IEEE Trans. Wireess Commun., vo. 5, no. 4, pp , Apr Zatanov, D. Hraniovic, and J.. Evans, Buffer-aided reaying improves throughput of fu-dupex reay networks with fixed-rate transmissions, IEEE Commun. Lett., vo. 20, no. 2, pp , Dec K. T. Phan and T. Le-goc, Power aocation for buffer-aided fudupex reaying with imperfect sef-interference canceation and statistica deay constraint, IEEE Access, vo. 4, pp , 206. D. Qiao, Effective capacity of buffer-aided fu-dupex reay systems with seection reaying, IEEE Trans. Commun., vo. 64, no., pp. 7 29, Jan M. Khafagy, A. Ismai, M.-. Aouini, and. Aissa, On the outage performance of fu-dupex seective decode-and-forward reaying, IEEE Commun. Lett., vo. 7, no. 6, pp. 80 8, Jun omikos, T. Charaambous, I. Krikidis, D.. koutas, D. Vouyioukas, and M. Johansson, A buffer-aided successive opportunistic reay seection scheme with power adaptation and inter-reay interference canceation for cooperative diversity systems, IEEE Trans. Commun., vo. 6, no. 5, pp , May M. haqfeh, A. Zafar, H. Anuweiri, and M.-. Aouini, Maximizing expected achievabe rates for bock-fading buffer-aided reay channes, IEEE Trans. Wireess Commun., vo. 5, no. 9, pp , ep O. Taghizadeh, J. Zhang, and M. Haardt, Transmit beamforming aided ampify-and-forward MIMO fu-dupex reaying with ited dynamic range, igna Proces., vo. 27, pp , Oct P. Xu, Z. Ding, I. Krikidis, and X. Dai, Achieving optima diversity gain in buffer-aided reay networks with sma buffer size, IEEE Trans. Veh. Techno., vo. 65, no. 0, pp , Oct Z. Tian, Y. Gong, G. Chen, and J. A. Chambers, Buffer-aided reay seection with reduced packet deay in cooperative networks, IEEE Trans. Veh. Techno., vo. 66, no., pp , Mar V. Jamai,. Zatanov, H. houkry, and. chober, Achievabe rate of the haf-dupex muti-hop buffer-aided reay channe with bock fading, IEEE Trans. Wireess Commun., vo. 4, no., pp , ov J. Hajipour, A. Mohamed, and V. C. M. Leung, Efficient and fair throughput-optima scheduing in buffer-aided reay-based ceuar networks, IEEE Commun. Lett., vo. 9, no. 8, pp. 90 9, Aug T. Charaambous,. omikos, I. Krikidis, D. Vouyioukas, and M. Johansson, Modeing buffer-aided reay seection in networks with direct transmission capabiity, IEEE Commun. Lett., vo. 9, no. 4, pp , Apr M. Darabi, V. Jamai, B. Maham, and. chober, Adaptive ink seection for cognitive buffer-aided reay networks, IEEE Commun. Lett., vo. 9, no. 4, pp , Apr I. Krikidis, T. Charaambous, and J.. Thompson, Buffer-aided reay seection for cooperative diversity systems without deay constraints, IEEE Trans. Wireess Commun., vo., no. 5, pp , May W. Wicke,. Zatanov, V. Jamai, and. chober, Buffer-aided reaying with discrete transmission rates for the two-hop haf-dupex reay network, IEEE Trans. Wireess Commun., vo. 6, no. 2, pp , Feb K. T. Phan, T. Le-goc, and L. B. Le, Optima resource aocation for buffer-aided reaying with statistica Qo constraint, IEEE Trans. Commun., vo. 64, no., pp , Mar T. Isam, D.. Michaopouos,. chober, and V. K. Bhargava, Bufferaided reaying with outdated CI, IEEE Trans. Wireess Commun., vo. 5, no., pp , Mar. 206.

15 AZLIGHI et a.: BUFFE-AIDED ELAYIG FO THE TWO-HOP FD ELAY CHAEL WITH ELF-ITEFEECE Luo and K. C. Teh, Buffer state based reay seection for buffer-aided cooperative reaying systems, IEEE Trans. Wireess Commun., vo. 4, no. 0, pp , Oct C. Dong, L.-L. Yang, J. Zuo,. X. g, and L. Hanzo, Energy, deay, and outage anaysis of a buffer-aided three-node network reying on opportunistic routing, IEEE Trans. Commun., vo. 6, no., pp , Mar D. Qiao and M. C. Gursoy, tatistica deay tradeoffs in bufferaided two-hop wireess communication systems, IEEE Trans. Commun., vo. 64, no., pp , ov M. G. Khafagy, A. E hafie, A. utan, and M.-. Aouini, Throughput maximization for buffer-aided hybrid haf-/fu-dupex reaying with sefinterference, in Proc. IEEE Int. Conf. Commun. ICC, Jun. 205, pp T. iihonen,. Werner, and. Wichman, Mitigation of oopback sefinterference in fu-dupex MIMO reays, IEEE Trans. igna Process., vo. 59, no. 2, pp , Dec. 20. B. P. Day, A.. Margetts, D. W. Biss, and P. chniter, Fu-dupex MIMO reaying: Achievabe rates under ited dynamic range, IEEE J. e. Areas Commun., vo. 0, no. 8, pp , ep M. Duarte, C. Dick, and A. abharwa, Experiment-driven characterization of fu-dupex wireess systems, IEEE Trans. Wireess Commun., vo., no. 2, pp , Dec D. Bharadia, E. McMiin, and. Katti, Fu dupex radios, IGCOMM Comput. Commun. ev., vo. 4, no. 4, pp , Oct I. homorony and A.. Avestimehr, Is Gaussian noise the worstcase additive noise in wireess networks? in Proc. IEEE Int. ym. Inf. Theory IIT, Ju. 202, pp Boyd and L. Vandenberghe, Convex Optimization. Cambridge, U.K.: Cambridge Univ. Press, Zatanov and. chober, Buffer-aided reaying with adaptive ink seection Fixed and mixed rate transmission, IEEE Trans. Inf. Theory, vo. 59, no. 5, pp , May Zatanov, V. Jamai, and. chober, Achievabe rates for the fading haf-dupex singe reay seection network using bufferaided reaying, IEEE Trans. Wireess Commun., vo. 4, no. 8, pp , Aug Mohsen Mohammadkhani azighi 7 was born in Tehran, Iran, in 987. He received the B.. degree in eectrica engineering from University of Zanjan in 200, and the M.. degree in teecommunication engineering from harif University of Technoogy in 202. He is currenty pursuing the Ph.D. degree with Monash University, Mebourne, Austraia. His research interests incude information theory, wireess communications, cooperative networks, and UEP codes. ikoa Zatanov 06 M 5 was born in trumica, Macedonia. He received the Dip.Ing. and master s degrees in eectrica engineering from s. Cyri and Methodius University, kopje, Macedonia, in 2007 and 200, respectivey, and the Ph.D. degree from the University of British Coumbia UBC, Vancouver, Canada, in 205. He is currenty a Lecturer Assistant Professor with the Department of Eectrica and Computer ystems Engineering, Monash University, Mebourne, Austraia. His current research interests incude wireess communications and information theory. He received severa schoarships/awards for his research incuding UBC s Four Year Doctora Feowship in 200, UBC s Kiam Doctora choarship and Macedonia s Young cientist of the Year in 20, the Vanier Canada Graduate choarship in 202, Best Journa Paper Award from the German Information Technoogy ociety in 204, and Best Conference Paper Award at ICC in 206. He serves as an Editor of the IEEE COMMUICATIO LETTE. He has been a TPC member of various conferences, incuding Gobecom, ICC, VTC, and IWC.