Decoding Delay and Outage Performance Analysis of Full-Duplex Decode-Forward Relaying: Backward or Sliding Window Decoding

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1 Decoing Delay an Outage Performance Analysis of Full-Duplex Decoe-Forwar Relaying: Backwar or Sliing Winow Decoing Ahma Abu Al Haija Member IEEE an Chintha Tellambura Fellow IEEE Abstract High reliability an low latency are critical performance targets in fifth generation cellular networks. How oes a full-uplex ecoe-forwar relay fare in this context? To answer this question we analyze the outage an average ecoingelay for both joint an sequential sliing winow ecoing. For comparison we also analyze ecoing elay of backwar ecoing an consier its existing outage analysis. In our analysis We consier a block faing channel with full channel state information CSI availability at receivers an with limite CSI at transmitters; outage events at both relay an estination an channel variation over ifferent blocks in sliing winow ecoing. Moreover by analyzing the asymptotic performance at high SNR we prove that both joint an sequential ecoing achieve a full iversity orer of two an erive the coing gain gaps between backwar ecoing joint an sequential sliing winow ecoing. To see the benefits of full-uplex relaying we also inclue the performance of half-uplex schemes an conclue that the preferre scheme epens on the rate outage an elay requirements for a specific service. Inex terms Decoe-forwar relaying backwar an sliing winow ecoing ecoing elay outage an iversity analysis. I. INTRODUCTION Because wireless relays improve the throughput reliability an coverage area of moern an fifth generation 5G cellular networks they are utilize in LTE-A release [ wireless backhaul an evice-to-evice DD communication [ [3. As in Fig. a relay noe can be a small-cell base station connecting a user equipment UE to a macro-cell base station. The performance of a relaying scheme is measure by ecoing elay achievable rate an outage which have been analyze extensively for half-uplex HD relays [4 [9. However full-uplex FD wireless relays may potentially ouble the spectral efficiency [ an hence are receiving significant research interest. They are inclue in 5G wireless applications such as machine-to-machine communications that require high reliability an low latency [3. Because FD raio noes can simultaneously transmit an receive on the same frequency the funamental performance limit is the signal leakage from the output of the transceiver to the input the self-interference which can cause significant performance egraation. This may be mitigate by millimeter waves [ passive suppression analog an igital cancellations [ [4. Nevertheless resiual self-interference which Manuscript receive January 6 6; revise June 7 6; accepte August 8 6. This work was supporte in part by grants from the Natural Science an Engineering Research Council of Canaa NSERC. This work was presente at the IEEE Global Communications Conference 6. The associate eitor coorinating the review of this paper an approving it for publication was M. Direnzo. The authors are with the Department of Electrical an Computer Engineering University of Alberta Emonton AB T6G H9 Canaa abualhai@ualberta.eu; ct4@ualberta.eu. Color versions of one or more of the figures in this paper are available online at Digital Object Ientifier.9/TCOMM Macrocell Relay Small cell UE DeNB Source Fig.. Relay channel Applications in 5G networks. Destination DD Relay is seen as aitive noise by the receiver [5 may be moele by increasing the noise power receive at the relay [6. Thus these harware an signal processing evelopments strongly suggest the feasibility an viability of FD raio which is currently being triale for cellular networks. Therefore characterizing the performance of FD relays is beneficial for both acaemic an inustrial researchers. The main performance measures we consier are the outage probability an ecoing elay. In this paper we efine the ecoing elay as the average number of transmissions blocks the estination waits before ecoing the information. Hence from now on ecoing elay refers to block ecoing elay. We focus on FD relays with a ecoe-forwar DF strategy. Thus the relay ecoes using sliing winow ecoing SWD or backwar ecoing BD. In each transmission block epening on links faing conitions the transmission scheme switches between the irect transmission DT moe i.e. relay is not transmitting an the DF relaying moe. A. Backgroun an Motivation The outage of the BD case has been analyze for coherent [7 [6 an inepenent an coherent DF relaying [6. In BD the estination e.g. base station in Fig. initializes ecoing from the last transmission block which leas to a long ecoing elay. However low latency ms is critical for elay-sensitive machine-type communications such as traffic safety an inustry processes in 5G networks [3. SWD has lower elay since the estination only waits one extra block to ecoe the source information. SWD can be joint or sequential [7 [8. In joint ecoing the estination D ecoes the source S information by simultaneously utilizing two receive blocks. In sequential ecoing however D first ecoes a bin inex about source information in one block an then the source information in an earlier block. Since both BD an joint SWD achieve the same rate [8 the same outage analysis is assume [6. However in a block faing channel their outage probability values iffer. Moreover in sequential ecoing there are outage events for S information an the bin inex as well [6.

2 B. Relate Work In FD DF relaying over B transmission blocks BD has a ecoing elay of B blocks whereas that of SWD is one for a single relay channel [7 [8 an n < B for an n-relay channel [9. This elay stems from the superposition block Markov encoing at S that requires BD or SWD at D [7 [8. Hence the elay can be further reuce by switching between DT an DF relaying [5 [7 [ or by the relay R forwaring S information only when ecoing at D fails as in hybri-automatic retransmission request systems [. Most existing works assume HD relays incluing ual-hop transmission [4 DF relaying [5 [ [4 an partial DF relaying [7 [9 [ [5 [9. The system in Fig. can achieve a full iversity orer of two if it switches from DF relaying to DT when R goes to outage [5 or when the gain of S-D link excees that of S-R link [7 [. This switching requires S an R to have limite channel state information CSI via feeback from D [3. References [3 [3 stuy the achievability an outage of DF relaying for multiple-antennas systems. For multiple relays outage has been analyze for DF relaying of a multi-hop relay network [33 single an multi-relay selection over Rayleigh [34 [35 an Nakagami-m [36 faing channels. Outage of FD DF relaying has not been extensively analyze except for BD consiering partial DF relaying [7 coherent full DF relaying over network wie scenario [6 an inepenent an coherent full DF relaying [6 [37. Full iversity orer of two can be achieve when the system swithces between DT an DF relaying moes [7. By further switching the DF moe into inepenent an coherent relaying R can save part of its power up to 9% which egraes the outage performance unless S an R have full CSI [6 [37. C. Main Results an Contributions We investigate the FD DF relaying with BD an SWD schemes [7 [8 [38. The link switches between DT an DF moes as in [7. We erive the ecoing elay for BD an SWD an the outage for joint an sequential SWD. Our analysis may help characterize DF relaying in network wie scenarios or in other cooperative multi-user channels such as two-way relay channel [39 cognitive raio [4 an interference channel with source cooperation [4. As is customary [7 we assume the block faing channel moel an the availability of full CSI at receivers an limite CSI at transmitters. More specifically for any transmission block each of R an D knows the phases an amplitues of the channel gains. Both S an R further know the phases of their respective links to D which helps them perform coherent transmission. They also know the relative amplitue orer between S R an S D links which helps them perform DF relaying when the S R link is stronger or DT when the S D link is stronger. D performs either BD joint or sequential SWD [7 [8. Average block ecoing elay of BD an SWD are erive in close form. The ecoing elay epens on statistics of S-R an S-D links that etermine the ratio of DT an DF moe usage. While the DT moe is elay free the DF moe is not. Hence the total elay epens on the average number of times for the DF moe. Results show that the ecoing elay of BD increases with the number of transmission blocks while that of SWD approaches one. Outage performances for joint an sequential SWD are erive consiering the outage events at both R an D an the channel variation over two transmission blocks. Moreover in sequential ecoing outage events for both the bin inex an S information are consiere. 3 Diversity orers for joint an sequential SWD are erive consiering the high SNR outage. We show that they both achieve a full iversity orer of two provie that S allocates no more than target rate portion of its power to the new information in each transmission block. 4 Coing gain gaps are also erive at high SNR between sequential an joint SWD BD scheme in [6 an HD DF scheme in [7. Results show that FD DF relaying with BD [6 [6 [4 outperforms SWD while joint ecoing outperforms sequential ecoing an they both outperform HD DF relaying [7 for a wie range of SNR. However at high SNR HD DF relaying scheme in [7 outperforms the FD relaying with SWD. Analysis an results illustrate the elay-outage traeoffs between BD SWD an HD transmission. Since 5G network supports multiple raio access technologies [ [ the optimal scheme for a specific service may be chosen base on its outage throughput an elay requirements. D. Paper Organization The reminer of this paper is organize as follows. Section II presents the relay channel moel. Section III escribes the DF relaying with BD joint an sequential SWD an erives their achievable rates. Section IV erives the average block ecoing elay for BD an SWD techniques. Section V erives the DF relaying outage with joint an sequential SWD while Section VI erives their iversity orers an coing gains. Section VII presents numerical results an Section VIII conclues the paper. II. CHANNEL MODEL The basic relay channel has one S communicating with D via R Fig.. For FD transmission over B blocks B N an B the receive signals at block k {... B} are given by Y rk h rsk X sk + Z rk Y k h sk X sk + h rk X rk + Z k where Y rk Y k is the k th receive signal block at R D an Z rk an Z k are inepenent an ientically istribute i.i.. complex Gaussian noise terms CN. X sk an X rk are the k th signal blocks transmitte by S an R respectively. We consier block faing channel where the links remain constant in each transmission block an change inepenently in the next block. Hence in block k each link gain is moele by Rayleigh faing an pathloss as follows: h ijk h ijk / αij/ ij g ijk e θ ij i {r } j {s r} where h ijk CN represents small scale faing. The large scale faing is capture by pathloss where ij is the

3 3 h rs Y r X r h r Although such switching is somewhat complicate we emphasize that only one bit feeback is neee from D to S an R. This small non-user ata feeback information satisfy the ultra lean esign requirement for 5G networks [3 which will also support multiple raio access technologies that enable switching among ifferent moes base on channel qualities an service requirements. X s h s Y Fig.. Basic Relay channel moel. istance between noes i an j an α ij is the attenuation factor. Let g ijk an θ ijk be the amplitue an the phase of a link coefficient in block k respectively. Then g ijk h ijk / αij/ ij is Rayleigh istribute while θ ijk is uniform in [ π. We assume full CSI at receivers an partial CSI at transmitters. This assumption implies the following. In receiving R knows h rsk an D knows h sk an h rk. In transmitting S knows statistical not exact instantaneous knowlege of the links which is use by S to optimize its transmit power to minimize the outage. Moreover S an R each knows the phase of its respective link to D an they both know the orer between grsk an g sk. The phase knowlege at transmitters is important for coherent transmission while the amplitue orer knowlege etermines the optimal transmission scheme as specifie in Section III. The CSI at transmitters can be obtaine via feeback from D [3. We assume that the relay signal Y rk oes not have a selfinterference noise term. This assumption may be justifie ue to the following reasons. First efficient self-interference cancellation of up to B has been emonstrate for WiFi raios [4. Secon since goo statistical moels for the resiual self-interference are unerevelope [ it may be moele as another source of noise. Thus to incorporate the resiual self-interference we may increase the noise power or ecrease the transmit power in. We consier no external interference in this moel as we focus on the funamental outage an elay performance. In a larger setting such as in an a hoc or cellular network the system will be interference limite rather than noise limite. Moreover although our elay an outage analyses may be generalize to inclue interference this topic is beyon the scope of this paper. III. DF RELAYING SCHEME We consier the FD DF scheme in [7 [8 [38 where the transmission is carrie over B blocks B >> B N an S aims to sen B messages through B blocks. However DF relaying may not occur for all k {... B}. Instea DT replaces DF relaying epening on the relative channel gains of S R g rsk an S D g sk links as in [7. This is because when g rsk < g sk ecoing at R may constrain the achievable rate. In orer to etermine the operating moe for block k {... B} S must know the relative orer of g rsk an g sk. In the last transmission block S sens only the ol information no new information. This may reuce the average achievable rate. However this rate reuction becomes negligible as the number of blocks B [8. A. Direct Transmission Moe: g rsk g sk This moe for block k occurs when S R link is weaker than S D link g rsk g sk. Clearly we have a classical point-to-point communication without R where S sens its information irectly to D at rate R log + gsk as is the transmit power of S. B. DF Relaying Moe: g rsk > g sk This moe for block k occurs when S R link is stronger than S D link g rsk > g sk. This scheme uses superposition block Markov encoing [ [8 Chapter 6 where R ecoes S information in block k w k an then forwars it coherently with S to D in block m > k in which the S R link is also stronger than S D link g rsm > g sm. D then utilizes the signals receive from S an R an performs either BD or SWD for w k. Transmission Scheme: Assume that S R link is stronger than S D link in blocks v k an m where v < k < m an v k m {... B}. In block k S uses superposition coing to encoe its new information w k with the ol information w v sent in block v. S then transmits the signal that conveys this superpose coewor for w k an w v. Next in block k R ecoes w k an transmits the signal of its coewor for w k in block m. Transmit Signals: S an R respectively construct their Gaussian transmit signals as follows: X sk ρ U w k + ρ U w v X rk P r U w v 3 where U j N for j { }. Coewor U conveys new information w k while U conveys ol information w v. Here R allocates its power P r for the signal U while S allocates the transmission powers ρ an ρ for signals U an U respectively. The power allocation parameters ρ ρ satisfy the power constraint ρ + ρ. 3 Decoing: The ecoing at R is straightforwar where in block k R alreay knows w v from the ecoing in block v an it can reliably ecoe w k at the following rate: R log + g rskρ C. 4 D ecoes S information using BD joint or sequential SWD as follows: Backwar Decoing BD: In this ecoing D ecoes w v in block k given that it knows w k from the ecoing in block m. D then can reliably ecoe w v at the following rate [8: R log + gskp s + grkp r + g sk g rk ρ P r C. 5 From 4 an 5 the achievable rate with BD is given as follows: R min{c C } 6

4 4 Joint Sliing Winow Decoing SWD: Here D ecoes w k from the receive signals in blocks k an m Y k Y m given that it alreay knows w v from the previous ecoing step from signals Y v an Y k. The reliable rate for w k at D is given as follows [7 [38: R log + gskρ + log + g sm ρ + g rm P r + g sm g rm ρ P r + g sm ρ C 3. 7 From 4 an 7 the achievable rate with joint ecoing is given as follows: R min{c C 3 } 8 Remark. Formulas 6 an 8 show that SWD achieves the same rate for each source message as BD in AWGN channels but with much shorter ecoing elay since C C 3 as g sk g sm. However the two ecoing schemes are not equivalent in faing channels since C C 3 as g sk g sm which can lea to ifferent outages. Moreover although both BD an SWD in faing achieve the same average sum rate for all B messages sent in all B blocks each message experiences ifferent outage because of channel variation over ifferent blocks. Sequential Sliing Winow Decoing: Another scheme calle DF via binning was propose in [8. In this scheme S messages are sorte into equal size groups an a bin inex l is given for each group. Then in each block S sens the new message an the bin inex of the previous message l v. R ecoes the new message in one block an forwars the bin inex of that message in the next block. The transmit signals for this scheme are similar to 3 but replacing each w v by l v. D performs sequential ecoing where it first utilizes its receive signal in block m to ecoe l k at the following rate: R b log + g sm ρ + grm P r + g sm g rm ρ P r + gsm ρ C 4 9 where R b is the transmission rate for the bin inex l k which is less than the transmission rate R R b R. D next goes back to block k an ecoes the transmit information w k given that it knows l v an l k where w k l k at the following rate: R R b log + g skρ C 5. Then from 4 9 an the achievable rate with sequential ecoing is given as in 8. Remark. Unlike joint ecoing sequential ecoing simplifies the ecoing at D but complicates the encoing at S an R since they nee to group the information into bins an etermine the optimal binning inex rate. Remark 3. Although achieving the same rate the outage probabilities of joint an sequential SWD are ifferent. In joint ecoing D ecoes S information w k using the receive blocks k an m simultaneously. However in sequential ecoing D first ecoes the bin inex l k in block m an then w k in block k. The outages for these schemes are erive in Section V. IV. AVERAGE BLOCK DECODING DELAY Throughput an low latency are specifie for applications in 5G networks [3. For instance traffic safety requires an ento-en latency of ms or less [3 but vehicular telematics can tolerate a latency of s [43. Hence the optimal transmission scheme epens on the application requirements. Although FD relaying achieves significantly better rates than HD relaying [ the latter has no ecoing elay since the ecoing is performe at the en of each transmission block [7. In contrast FD relaying has at least one block ecoing elay when using SWD. Hence a rate-elay trae-off exists between FD an HD DF relaying schemes. In this section we erive the average ecoing elay for both BD an SWD. For these schemes the elay occurs only in DF moe since in DT moe D ecoes S information at the en of a transmission block. Hence the average ecoing elay epens on the ecoing technique an channel statistics that etermine the ratio between DT an DF moes. A. Backwar Decoing BD Here the ecoing elay for block k {... B} is either uring DT moe or B k uring DF relaying moe. Therefore the ecoing elay Tk BD for any transmission block k is given as follows: T BD k P[g rsk g sk + P[g rsk > g sk B k a B k + µ s where a is obtaine by using the Rayleigh istribution of g sk an g rsk as shown in [ [7 Proof of Lemma. µ i E[gi is the mean of g i for i {s r rs}. The following theorem yiels the average ecoing elay T BD. Theorem. The average ecoing elay for FD DF relaying with BD T BD is given by: T BD.5B / + µ s. Proof. Obtaine by summing Tk BD in over all k {... B } iviing the summation over B an then using the summation ientity n k k.5nn+ as shown in Appenix A.. Theorem shows that the elay increases as the number of blocks B increases thus limiting the usefulness of BD for elay sensitive applications although it has better outage than SWD as shown in Sections VI an VII. B. Sliing Winow Decoing The average ecoing elays of SWD for both joint an sequential methos are ientical as D utilizes two receive blocks to ecoe S information. The elay for the k th block is for DT moe an varies from to B k uring DF moe epening on subsequent channel realizations after block k that etermine the DT an DF moes. For example the ecoing elay for S information in block 4 w 4 is if g rs4 > g s4 g rs5 < g s5 an g rs6 > g s6 since D will wait till block 6 to ecoe w 4. However if g rsk > g sk an g rsn g sn for all k < n < B k the ecoing

5 5 elay then is B k as R will forwar w k in the last block B regarless of the link orer in block B. Generally the ecoing elay Tk SW D for any transmission block k is given as follows: T SW D k P[g rsk g sk + P[g rsk > g sk P P B k+ i ip[g rsk+i > g sk+i i n P[g rsk+n < g sk+n B k + B k P[g rsk+n < g sk+n. 3 T SW D k n By using Rayleigh istributions Tk SW D becomes as follows: [ B k+ + µ s + B k i µs µ s + µi s i µ s + i B k. 4 The average ecoing elay T SW D is then given as follows: Theorem. The average ecoing elay for FD DF relaying with joint or sequential SWD T SW D is given as follows: [ B T SW D µ s µs. 5 B µ s + Proof. Sum Tk SW D in 3 over all k {... B } ivie over B an then use the ientity n k xk xx n x as shown in Appenix A.. Theorem shows two reasons for preferring SWD over BD for elay sensitive applications. First the SWD ecoing elay approaches one as the number of blocks approaches infinity B. This is because if the message in block k is through DF relaying moe an D ecoes it in block m the ecoing elay for this message is m k while the ecoing elays for other messages sent in blocks k + k +... m are zero which makes the average equal to one. Secon for a message sent in block k formula 3 implies that the probability of ecoing this message in block m > k ecreases as m increases since the event of this probability occurs when g rsk > g sk g rsm > g sm an g rsi < g si for all i {k+ k+... m }. In contrast in BD the message sent in block k will be ecoe after B k blocks when g rsk > g sk that occurs with / + µ s probability. V. OUTAGE FOR SLIDING WINDOW DECODING Many wireless applications tolerate a maximum outage percentage e.g. % for VoIervice in LTE release 8 [44. Since the outage of BD is erive in [7 [6 [4 we erive here the outage of FD DF relaying with joint an sequential SWD by consiering both DT an DF moes over two blocks. A. Joint Sliing Winow Decoing The outage is relate to the achievable rate for DT moe in Section III-A an DF moes given in 4 an 7. We analyze the outage as follows. Define P an P as outage for DT an DF moes respectively. The average outage probability P JSW D o can then be obtaine as follows: Theorem 3. For a given target rate R with specific power allocation ρ ρ the average outage probability P JSW o D of the FD DF scheme with joint SWD is given as follows: P JSW D o P + P P + P r + P 6 with P P[R > log + g skρ grsk g sk P JSW D P r P [R > C g rsk > g sk P [ R > C 3 R C g rsk > g sk where P is the outage uring DT moe P r an P JSW D are the outages uring DF moe P r is the outage at R; P JSW D is the outage at D when there is no outage at R. Proof. From the outage events in DT an DF moes when R is higher than the achievable rate in 4 an 7. P P r an P JSW D can be analytically expresse as follows: Lemma. The probabilities P P r an P JSW D in Theorem 3 can be expresse as follows: P e η µ s e η µrs+µ s µrsµ s + µ s P r e η µ s µrs e η µrs+µ s µrsµ s + µ s P JSW D e η µrs η ζ η where η + η η fγ β ζ β γ ζ fγ β ζ β γ if fγ β ζ β γ if R η R η ρ ζ Pr.5 δ β ρ ζ δ + βρ R fγ β ζ 4γ β µ s + γ ρ e γ +β µ s ρ > R 7 ρ R R ρ R + γ ρ + γ ρ R ρ e ζ µ r 8 Proof. P P r are erive in [ [6 Theorem 4 while P JSW D is obtaine using the Rayleigh statistics of g sk g sm g rsk g rk an g rm as shown in Appenix B. Remark 4. We obtain numerically the optimal resource allocation ρ ρ that minimizes P o since Theorem 3 specifies JSW D the outage for a fixe resource allocation. B. Sequential Sliing Winow Decoing The outage here is similar to that of joint ecoing except for the outage at D uring the DF moe. In sequential SWD an outage at D can occur not only for S information w but also for the bin inex l. An outage for l leas to an outage for w since each l represents a group of w w l. The average outage probability P SSW o D can be obtaine as follows:

6 6 Theorem 4. For a given target rate R with specific resource allocation power ρ ρ an binning rate R b the average outage probability P SSW o D of the FD DF scheme with sequential SWD is given as in Theorem 3 except replacing P JSW D by P SSW D which is given as follows: P SSW D P + P where 9 P [ R b > C 4 R C g rsk > g sk P [ R R b > C 5 R b C 4 R C g rsk > g sk. P is the outage probability of the bin inex l at D when there is no outage at R P is the outage probability of S information w at D when there is no outage at R for w or at D for l. P an P can be analytically expresse as follows: P e η µ s µrs e η µ s +µrs µ s µrs µ s + µ { rs ζ4 f P β ζ 3 β if s ρ > R b P f β ζ 3 β if s ρ R b P e η µrs e η 3 µ s e ζ 4 µ s + ζ 4 f P β ζ 3 β if s ρ > R b P f β ζ 3 β if s ρ R b where η 3 R R b ζ 4 R b ρ R b ρ ζ 3 Pr.5 R b + β ρ β ρ f β ζ 3 β e µ s f β ζ 3 β µ s e β µ s Proof. See Appenix C. e ζ 3 β µ + ζ 3 s µ r µ r Remark 5. As in Theorem 3 we numerically optimize resource SSW D allocation ρ ρ R b that minimizes P o. As per Remark compare with joint ecoing sequential ecoing simplifies the ecoing at D but has another variable R b to be optimize. Moreover joint ecoing outperforms sequential ecoing as shown in the following Lemma: Lemma. For a given target rate R with specific resource allocation ρ ρ an R b The outage gap between joint an sequential SWD ecoing is given as follows: P SSW D o JSW D P o P [ R b > C 4 R C 3 ξ + P [ R b C 4 R > C 5 + R b R C 3 ξ where ξ is the event that R C g rsk > g sk an C C 4 an C 5 are given in Section III.B. Proof. Obtaine by comparing P JSW D an P SSW D P + P since P an P r are the same for both techniques. Since C 3 C 4 + C 5 as shown in 79 an P JSW D in 6 an P an P in 9 can be expresse as follows: P JSW D P [ R b > C 4 R > C 3 ξ + P [ R b C 4 R > C 3 ξ P P [ R b > C 4 R > C 3 R C 3 ξ P P [ R R b > C 5 R b C 4 R > C 3 R C 3 ξ Then from P JSW D P SSW D we obtain. VI. ASYMPTOTIC PERFORMANCE AT HIGH SNR While the analysis in Section V etermines the outage at any SNR analyzing the asymptotic performance at high SNR simplifies the iversity orer analysis of SWD an allows easier comparison with BD [7 [6 [4. A. Diversity Orer Before formal erivation we intuitively see from 6 an 9 that the iversity orer is two for joint an sequential SWD since both DT an DF relaying moes require at least two ifferent links to fae for an outage at R or D. More specifically for both joint an sequential SWD an outage occurs at D in DT moe when both g sk an g rsk are fae as euce from P JSW D in 6. The same hols for the outage at R in DF relaying moe consiering P JSW r D in 6. For joint SWD an outage at D in DF relaying moe occurs when g sk g sm an g rm are fae as euce from P JSW D in 6. For sequential SWD on the one han P in 9 can be reuce to zero by setting R b R since at high SNR R has enough power to transmit the ecoe information an there is no nee to bin S messages into groups. On the other han from 9 C 4 in P is maximize when ρ. Hence an outage occurs when both g sm an g rm are fae. Without loss of generality assume equal transmit powers from S an R P r P an efine a nominal SNR µ s P as the receive power at D in DT moe. Note that this SNR is always proportional to P. Hence to prove that the iversity orer is two we show that the ominant term of outage is proportional to P [45 [46. Theorem 5. For full-uplex DF relaying with joint or sequential SWD the iversity orer is two since the outage probabilities for joint P JSW o D an sequential P SSW o D SWD at high-snr respectively approach the following values: P JSW o D J P P SSW o D J P 3 J R + R µ s J R µ rs + a µ + κ s µ s + a R κ a R a for a < R. Sketch of the Proof:. From [ [6 Corollary we obtain P an P r as follows: P R P P r R µ s µ s a P. 4 Then for joint SWD using the first orer Taylor series expansion e x x in 7 Appenix D shows that P JSW D is given as follows: { P P JSW D µ s µ ra P K 3 if s ρ > R R µ s P K P if s ρ 5 R

7 7 where a an a are the power ratios efine as a ρ /P a ρ /P a {a a } an K an K are constants that epen on the power ratios a a target rate R an the average channel gains. They are expresse as follows: K a R K a R x a a R x a x a R x + x µ r x + a µ r + µ s x a x 6 Hence P JSW D P 3 only when a < R otherwise P JSW D P. However eceasing a will increase the outage at R P r. Therefore to minimize the outage we set a R. Then we obtain P JSW o D as in 3. Similarly for sequential SWD using the first orer Taylor series expansion e x x in Appenix E shows that is given as follows: P SSW D P SSW P SSW µ s + R a R a if Ps µ s a R P ρ > R b µ r µs if µ r + R b a a ρ R b R R b µ s a P if µ r if µs µ r + R b a a ρ > R b 7a ρ R b 7b Then by setting a < R an R b R P SSW /P in 7a while P SSW in 7b respectively. Theorem 5 implies that the full-iversity orer of two is achieve by SWD provie that S allocates no more than R portion of its power to the new information sent in DF moe for both joint an sequential ecoing. Moreover R allocates a ifferent bin inex for each message R b R in sequential ecoing scheme which is equivalent to no binning. The first constraint a < R consiering C 3 in 7 an C 4 in 9 reuces the interference at D cause by the new information when ecoing the ol information bin inex in joint sequential SWD. However while this constraint ecreases the outage at D it increases the outage at R. Hence the outage at R becomes ominant in DF moe. The other conition R b R for sequential SWD implies that at high SNR R sens S information no binning an D ecoes it through one block instea of two blocks. More specifically it is sufficient for D to irectly ecoe the ol information w k in block m instea of the bin inex l k in block m an then w k in block k. B. Coing gains gaps The coing gain gap is the SNR gap between two schemes that is require to achieve the same outage performance. Having the outage expressions at high SNR in Theorem 5 for joint an sequential SWD in [ [6 Corollary for BD an in [ [7 Theorem 3 for HD transmission we can erive some coing gain gaps as follows. SNR gap between BD [6 an joint SWD: To achieve the same performance of BD the SNR in joint SWD shoul be increase by the following gap: Lemma 3. For the same outage at high SNR the SNR gap Γ in B between BD an joint SWD is given as follows: Γ SNR JSWD SNR BD 5 log + R 5 logϑ 8 where ϑ + a + µ r a / a sinh a + an a is the solution for f a given as.5 f a µ r a a a sinh a.5 µ r a a 3. Proof. Obtaine by comparing the outage of joint SWD in Lemma 5 with that of BD given in [ [6 Corollary as: P BD o R P + R µ s µ s a P 9 + R P a /a sinh a +. µ s µ r Then by setting PBD o a f a we obtain a that minimizes P BD o. Last by setting logp SW o D logp BD o we obtain the SNR gap in 8. SNR gap between joint an sequential SWD: To achieve the same performance of joint SWD the SNR in sequential SWD shoul be increase by the following gap: Lemma 4. For the same outage at high SNR the SNR gap Γ in B between joint an sequential SWD is given as follows: Γ SNR SSWD SNR JSWD 5 logϑ 5 log + R 3 where ϑ + a + µ rs κ µ s + a R an a R is the solution for f a given as f a a 3 µ s + µ rs κ a R R + a R a + R κ a R 3 where κ is given in 3 Proof. Following similar analysis in Lemma 3 but replacing P BD o with P SSW o D in 3. As a simpler expression Γ is upper boune as follows: Proposition. The SNR gap Γ in Lemma 4 is upper boune as follows: µ rs Γ < 5 log + R + R R 3

8 8 Proof. Obtaine from limits of J in 3 when a R lim a R J an since µ rs/µ s + <. Remark 6. The SNR gap Γ 3 between BD an sequential SWD is the sum of Γ an Γ. 3 SNR gap between joint SWD an HD DF scheme [7: Similar to Lemmas 3 an 4 the SNR gap between joint SWD an HD DF relaying in [7 is given as follows: Lemma 5. For the same outage at high SNR the SNR gap Γ in B between FD DF relaying with joint SWD an HD scheme [7 is given as follows: Γ 4 SNR JSWD SNR HD 5 log + R 5 log +.5 R + 3 Proof. Obtaine by comparing the high SNR outage of joint SWD in Lemma 5 with that of HD DF scheme in [ [6 Theorem 3 which can be optimize to become as follows: P HD o R µ s P + R 8µ s P 33 Then by setting logp JSW o D logp HD o we obtain the SNR gap in 3. Remark 7. Accoring to 3 Γ 4 > for any R >. Hence at high SNR HD DF outperforms FD DF with SWD. More iscussions are given in Section VII-C. Moreover Γ 4 epens on the target rate R only but not on channel gains. Remark 8. Similar to remark 6 the SNR gap Γ 5 between FD DF with BD an HD DF is the sum of Γ an Γ 4. Remark 9. From the elay outage an coing gain analyses in Sections IV an VI-B respectively there is a clear traeoff between elay an outage performance as BD has longer elay than SWD but better outage performance. Average ecoing elay s r 5 Backwar ecoing rs 7 rs rs 5 Simulate results Sliing winow ecoing 3 Number of blocks B Fig. 3. Decoing elay of BD an SWD versus the number of block B with s r 5 an ifferent rs. Fig. 4. Decoing elay of FD DF relaying with BD for any R location in D plan where B. VII. NUMERICAL RESULTS We now provie numerical results for ecoing elay an outage using our erive expressions. In our Monte Carlo simulations S an R have ientical transmit powers P r P an all links experience Rayleigh faing an the average channel gain for each link from noe j to i is given as µ ij ij with a pathloss factor α.4. The average α receive SNR in B at D for the signal from S is efine as SNR log P/ α s. 34 To optimize minimize the outage the simulations vary the power parameters ρ ρ for joint an sequential SWD an the binning rate R b for sequential SWD. A. Average Decoing Delay Fig. 3 shows the ecoing elays of BD an SWD versus B for several noe istances. Analytical results an Monte Carlo simulations 6 realizations match perfectly. The elay for SWD is always one while for BD it increases as B increases an rs ecreases. This is because for any block k with S R link stronger than S D the elay for BD is B k. However the elay for SWD is n { B k} an the probability of ecoing in block m m k +n ecreases as n increases. Figures 4 an 5 stuy the impact of R location by showing Fig. 5. Decoing elay of FD DF relaying with SWD for any R location in D plan where B. the average ecoing elay as a function of the coorinates of R x r y r. The locations of S an D are fixe at 5 an 5. These inter-noe istances are vali for 5G small cells of m raii [. The channel gains an µ s vary for each R location which affect the elay consiering an 5 formulas. Similar to Fig. 3 BD is highly sensitive to R location an B varying between 5 an 48 whereas that of SWD is virtually static e.g. between.99 an.

9 9 s rs 7 r 5 s rs 7 r 5 R5 bps/hz Outage Probability R 3 bps/hz BD [6 Joint SWD Sequential SWD Simulate results Asymptotic joint SWD Asymptotic sequential SWD R 5 bps/hz SNR B Fig. 6. Outage probabilities of FD DF relaying with BD joint an sequential SWD at ifferent target rates R. As shown in Theorems an the elay of SWD is less than while it can reach B/ in BD. Besies in both schemes the elay increases as R gets closer to S since the DF moe occurs more often than DT moe as the probability of having S R link stronger than S D link increases Section IV. B. Outage Behavior an Diversity Orer Fig. 6 shows the outage probabilities versus SNR for BD [4 joint an sequential SWD of the FD DF relaying scheme along with the noe istances. Monte Carlo simulations 6 realizations match perfectly with our analytical results. All ecoing techniques achieve a iversity orer of two. However BD has the best outage performance while sequential ecoing has the worst. For elay-sensitive applications joint SWD appears best ue to its shorter ecoing elay than BD an better outage performance than sequential ecoing. The asymptotic outage curves in Theorem 5 coincie with exact curves of SWD at high SNR. For joint an sequential SWD the asymptotic curves are almost ientical which is expecte from Proposition as the coing gain gap Γ for R 3 an 5 bps/hz. In contrast between BD an joint SWD the coing gain gap Γ at outage 6 is B for R 3 5 bps/hz. Lemma 3 leas to quite close values where Γ B for R 3 5 bps/hz. Fig. 7 illustrates the optimal power ratio a ρ /P from S to its new information versus SNR with ifferent ecoing techniques. For joint an sequential SWD a ecreases as SNR increases. These results match the conclusions from Theorem 5 about the require constraint on a < R to achieve a full iversity orer of two. For BD the optimal a is less sensitive to SNR slightly increases with SNR. This implies that at high SNR R experiences higher outages than D. Hence consiering the rate constraints C an C in 6 S allocates more power to the new information in each transmission block in orer to reuce the outage at R. C. Comparison with Existing Schemes Fig. 8 compares the outage probabilities of DT ual-hop transmission [4 full an HD DF relaying schemes. For the HD scheme we consier the coherent full DF relaying an joint ecoing at D since [7 shows that it outperforms all Optimal power ratio a ρ /P BD [6 Joint SWD Sequential SWD Simulate results SNR B Fig. 7. Optimal power allocation portion a ρ /P to minimize outages of FD DF relaying with BD joint an sequential SWD. Outage Probability R5 bps/hz s rs 7 r Full-uplex BD [6 7 Full-uplex joint SWD Full-uplex sequential SWD Half-uplex DF scheme [7 Direct transmission Dual-hop [ SNR B Fig. 8. Outage probabilities of FD DF relaying with BD an SWD SWD HD DF relaying [7 ual-hop [4 an irect transmissions at R 5 bps/hz. other existing HD schemes [5 [8 [9. While FD DF relaying with BD outperforms HD DF relaying FD DF relaying with SWD unerperforms HD DF relaying [7 at high SNR which is expecte from Lemma 5. Accoring to this Lemma the coing gain gap Γ 4 is.87 B which matches the gap Γ 4.93 B at outage 6 in Fig. 8. In HD [7 each block is ivie into phases: broacast an coherent relaying phases which reuces the achievable rate an the outage performance. However in SWD D treats the new information of block m as noise which creates the interference shown in 7 an 9. Therefore results imply that at low SNR FD with SWD outperforms HD DF because of the rate loss that stems from iviing each transmission block into two phases. However at high SNR HD outperforms FD since the interference in SWD becomes significant. While S can reuce this interference by allocating R or less portion of its power to the new information this power allocation increases the outage at R as shown in Theorem 5. Fig. 9 consiers the channel settings in Fig. 8 an illustrates the threshol SNR below which FD DF scheme with joint an/or sequential SWD outperforms HD DF scheme in [7 for Partial DF relaying outperforms full DF relaying in HD transmission at low SNR [7. However it has more parameters to optimize like rate an power allocation for public an private message parts [7.

10 SNRB Analytical Simulations Region C: Half-uplex DF [7 Region B: Full-uplex DF with joint SWD s rs 7 r 5 Region A: Full-uplex DF with joint or sequential SWD Target rate R bps/hz Fig. 9. Threshol SNR below which joint an/or sequential SWD outperforms HD scheme in [7. ifferent target rates. In region A both joint an sequential SWD outperform the HD scheme in [7; in region B only joint SWD outperforms HD scheme while in region C neither joint or sequential SWD outperforms the HD scheme. Hence HD scheme is preferre at high SNR an high target rate. It is also observe that for R > 3.5 bps/hz the threshol SNR is almost a linear function of the target rate R with a slope of for sequential joint SWD. This simple relation can be appealing to the practical esigners since by knowing only the SNR they can ecie between FD joint or sequential SWD or HD DF relaying for the best performance. Figures 8 an 9 imply that epening on the require rate outage an latency switching among HD an FD relaying with BD or SWD is an optimal strategy. 5G networks envisage such switching among multiple raio access technologies [ [. VIII. CONCLUSION Full-uplex ecoe-forwar relaying is an extremely important technology enabler for 5G wireless. We have erive the ecoing elay an outage for joint an sequential sliing winow ecoing techniques. Both large scale pathloss an small-scale Rayleigh faing were consiere. Diversity orers SNR gaps an coing gains were erive in etail. Our analysis an numerical results imply that ifferent schemes are optimal for ifferent applications epening on the throughput reliability an elay requirements. However generally joint sliing winow ecoing has the avantages of shorter ecoing elay than backwar ecoing better outage performance an fewer parameters to optimize than sequential ecoing. APPENDIX A: PROOF OF THEOREMS AND The average ecoing elay for BD an SWD is erive. A.: Proof of Theorem First we sum the ecoing elay at each block k Tk BD in over all k {... B } an ivie over B to obtain T BD as follows: B k T BD µ rs+µ s B k B B k B B k k 35 + µ s B Then applying he summation ientity n k k.5nn + to B k k we obtain T BD in. A.: Proof of Theorem First let υ µrs +µ s an υ υ µ s +µ s. Then we simplify Tk SW D in 4 as follows: T SW D k υ [ µ s B k+ i iυ i + B kυ B k υ Now we simplify the first term as follows: B k+ µ s i a υ µ s υ µ s υ iυ i 36 υ B kυ B k + B k + υ B k+ υ B kυ B k υ υ B k+ + υ B k B kυ υb k 37 where a is obtaine from the ientity n i ixi. By substituting 37 into 36 we obtain x n+x n+ +nx n+ x T SW D k + υ B k. 38 Secon we sum the ecoing elay at each block k Tk SW D in 38 over all k {... B } an ivie over B to obtain T SW D as follows: B T SW D k + υb k B + B υb k υ k. 39 B B Last by applying he summation ientity n k xk xxn x to 39 we obtain T SW D in. APPENDIX B: PROOF OF LEMMA Let γ g sk γ g rk an γ 3 g rsk be the channel amplitues in block i while β g sm an β g rm be the channel amplitues in block m. The Rayleigh ensity for any γ l l { 3} or β l for l { } may be given as follows: P[x l x l /µ l e x l µ l x <. 4 We may now express outage at D P JSW D in 6 as follows: P JSW P [ R > C 3 R C g rsk > g sk 4a P [ R > C 3 γ 3 > η γ γ 3 P [ η < γ η γ 3 > η β ζ β ζ η ζ ζ η η f γ γ 3 β β γ γ 3 β β where η η ζ an ζ are given in 8 while f γ γ 3 β β 6γ γ 3 β β µ s µ r e γ µ + γ 3 s µrs + β µ + β s µ r 4b 4 After integrating 4b we obtain 7 in Lemma. The lower boun on γ 3 is obtaine from the secon constraint in 4a as follows: R log + γ 3ρ γ3 > η.

11 From the first constraint in 4a we obtain the upper bouns on β an β are obtaine from 4a as follows: + γ β ρ + β Pr ρ + + β ρ R β ζ. Similar to β β [. Hence ζ shoul also be nonnegative ζ > which as more constraints on γ : ζ fβ 43 fβ β Ps + γρ R ρ R + γρ Now let a + γ ρ R ρ an b R + γ ρ. Then it is easy to show that a > if γ > η an b < if γ < η. After that formula 43 is non-negative in the following cases: Case a < an b > : this case happens when γ > η an γ < η. However this case cannot occur since > ρ. More specifically if γ > η then γ > η for sure. Case a < an b < : this case happens when γ < η an γ < η. In this case fβ for all β [. Case 3 a > an b < : this case happens when γ < η an γ > η. In this case fβ for all β [ ζ. Now Since γ [ in cases an 3 we obtain the following subcases by checking whether R ρ > or < : If /ρ < R then β < when < γ < η while β < ζ when η < γ < η. If /ρ > R then β < ζ when < γ < η. From the above cases we obtain formula 7 in Lemma. APPENDIX C: PROOF OF THEOREM 4 C.: Outage Probability for the Bin Inex In 9 P is given as follows: P P [ R b > C 4 R C g rsk > g sk P [ [ R b > C 4 P γ3 > η γ γ 3 P [ γ 3 > η γ γ 3 { [ P P β ζ 3 β ζ 4 if s ρ > R b P [ P β ζ 3 β if s R b γ3 ρ 44a 4γ γ 3 e γ µ + γ 3 s µrs γ γ 3 η µ s { ζ4 ζ3 fβ P β β β if s ρ > R b ζ3 fβ P β β β if s 44b ρ R b where η is given in 8 ζ 3 an ζ 4 are given in an fβ β is given as fβ β 4β β e β µ + β s µ r 45 µ s µ r After integrating 44b we obtain in Theorem 4. The bouns on γ an γ 3 are straightforwar. The upper boun on β is obtaine from the first constraint in 44a. It is straightforwar to show that R b > C 4 β ζ 3. We then obtain another boun on β since β is non-negative i.e. ζ 3 > β ζ 4. By checking whether ζ 4 is positive or negative we obtain the following two cases: If /ρ > R b then ζ 4 > β < ζ 4 an β ζ 3. If /ρ < R b then ζ 3 > for all β [. From these two cases we obtain formula in Theorem 4. C.: Outage Probability for S information In 9 P is given as follows: P P [ R b C 4 R R b > C 5 R C g rsi > g si P [ R b C 4 P [ γ η 3 γ 3 > η γ γ 3 P [ [ R b C 4 P γ η 3 γ 3 > η P [ [ γ 3 > η P γ η 3 P [ β > ζ 3 β ζ 4 +P [ P β > β > ζ 4 if s ρ > R b P [ P β > ζ 3 β > if s ρ R b e η µrs e R R b ρ µ s ζ4 ζ 3 fβ β β β + e ζ 4 µ s if ζ 3 fβ β β β if ρ ρ 46 > R b R b where η 3 ζ 3 an ζ 4 are given in an fβ β is given in 45. After integrating 46 we obtain in Theorem 4. The analysis for P is quite similar to that for P except aing a new constraint R R b > C 5 an inverting the constraint R b C 4. From R R b > C 5 we get another boun on γ which is γ η 3. We further get the following two cases from the constraint R b C 4 : If /ρ > R b then ζ 4 >. Hence we have β > ζ 3 for < β < ζ 4 since ζ 3 > uring this interval of β. However we have β > for β > ζ 4 since ζ 3 < uring this interval of β. If /ρ < R b then ζ 3 > for all β [. From these two cases we obtain in Theorem 4. APPENDIX D: DERIVATION OF P JSW D Starting from the outage expressions in Lemma we can show that at high SNR ζ an ζ in 8 are given as follows: R /γ ρ ρ R /γ P a a ζ β P β ζ R γ ρ /P + P γ ρ R ρ R γ P a 47 a P a R + γ P Then consiering 7 we analyze the integrals when /ρ > R an /ρ > R. D.: When /ρ > R First consiering ζ in 47 we approximate fγ β ζ in 8 as follows: fγ β ζ 4γ β e γ +β µ s e ζ µ r µ s a 4γ β µ γ + β s µ s b 4γ β µ s β µ r ζ µ r R /γ P a a 48

12 where a is obtaine by the first-orer Taylor series expansion e x x an b is obtaine by smallest orer of γ an β since their integral limits are proportional to /P. Next we approximate the first integration in 7 as follows: P JSW η ζ a η 4γ β 3 µ s µ r γ ζ 4 µ s µ r R /γ P a a β γ R /γ P a a γ 49 where a is obtaine by evaluating the integral over β an ζ is given in 47. Then by substituting x γ P we obtain the first integral in Lemma 5 for P/ρ > R. D.: When /ρ < R At high SNR P JSW P JSW a e η µrs e η µrs R / b η R / c e R µ s Ps can be expresse as follows: R / fγ β ζ β γ e η µrs γ µ s e γ µ s µ r µ r + µ s R γ Pr a a γ R η µ s R R / µ s γ µ s γ µ s µr µ r + µ R s γ a Pr γ a γ µ s µ r µ r + µ s R γ Pr a a γ R K 5 µ s where K is given in 6. In 5 a is obtaine by evaluating the integral over β ; b is obtaine from the first orer Taylor series expansion e x x; c is obtaine by consiering the factors that lea to the lowest orer of as the higher orers will be reunant at high SNR; an is obtaine by using integration by substitution where we set x R γ a Ps an perform some mathematical manipulations. APPENDIX E: DERIVATION OF P SSW D Starting from the outage expressions in Theorem 4 it is easy to show that at high SNR ζ 3 in is given as follows: ζ 3 β R b a a. 5 Then f β ζ 3 in can be expresse as follows: f β ζ 3 β e µ s a β3 µ s β µ s e β R b a a R b a a µ r µ r. 5 where a is obtaine from the first orer Taylor series expansion for e x x. Similarly we approximate f β ζ 3 in as follows: f β ζ 3 β /µ s. 53 Then we can easily approximate the outages for the bin inex an S information as follows. E.: Outage Probability for the Bin Inex Using 5 an 5 we approximate P SSW follows: P SSW e η µ s µrs e η µ s +µrs µ s µrs µ s + µ { rs ζ4 f P β ζ 3 β if s ρ > R b P f β ζ 3 β if s ρ R b { ζ4 a f β ζ 3 β if µ s + f β ζ 3 β if in as ρ ρ 54 > R b R b where a is obtaine by using the Taylor series expansion e x x. Evaluating the integral over β leas to 7a. E.: Outage Probability for S information Following similar steps to P SSW an Using 5 an 53 we can approximate P SSW as follows: P SSW µrs e η e η e ζ 4 µ s + ζ 4 3 µ s f β ζ 3 β if f β ζ 3 β if ρ ρ > R b R b 55 We obtain 7b by evaluating the integral over β consiering the first-orer Taylor series expansion e x x. REFERENCES [ J. Korhonen Introuction to 4G mobile communications. Artech House 4. [ Y. Niu Y. Li D. Jin L. Su an A. V. Vasilakos A survey of millimeter wave mmwave communications for 5G: opportunities an challenges available online: Feb. 5. [3 Ericsson 5G raio access: capabilities an technologies Ericsson White Paper Uen Rev C Stockholm Sween Apr. 6. [4 M. O. Hasna an M. S. Alouini Optimal power allocation for relaye transmissions over Rayleigh faing channels in IEEE VTC Apr. 3. [5 J. Laneman D. Tse an G. Wornell Cooperative iversity in wireless networks: Efficient protocols an outage behavior IEEE Trans. Inf. Theory vol. 5 no. pp Dec. 4. [6 L. Pinals A. Abu Al Haija an M. Vu Link regime an power savings of ecoe-forwar relaying in faing channels IEEE Trans. Commun. vol. 64 no. 3 pp Mar. 6. [7 A. Abu Al Haija an M. Vu Outage analysis for coherent ecoeforwar relaying over Rayleigh faing channels IEEE Trans. Commu. vol. 63 no. 4 pp Apr. 5. [8 R. U. Nabar H. Bolcskei an F. W. Kneubuhler Faing relay channels: performance limits an space-time signal esign IEEE J. Sel. Areas Commun. vol. no. 6 pp Aug. 4. [9 M. Yuksel an E. Erkip Broacast strategies for the faing relay channel in IEEE Milcom. vol. 4. [ M. Mohammai H. A. Suraweera Y. Cao I. Krikiis an C. Tellambura Full-uplex raio for uplink/ownlink wireless access with spatially ranom noes IEEE Trans. Commun. vol. 63 no. pp Dec. 5. [ Z. Zhang K. Long A. V. Vasilakos an L. Hanzo Full-uplex wireless communications: challenges solutions an future research irections Proceeings of the IEEE vol. 4 no. 7 pp July 6.

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[43 Huawei 5G: A technology vision Huawei Technologies Co. Lt. 3. [44 3GPP Lte physical layer framework for performance verification TS R r Generatin Partnership Project 3GPP St. Louis USA Feb. 7. [45 Z. Wang an G. B. Giannakis A simple an general parameterization quantifying performance in faing channels IEEE Trans. Comm. vol. 5 no. 8 pp Aug. 3. [46 Y. Dhungana an C. Tellambura Uniform approximations for wireless performance in faing channels IEEE Trans. Commun. vol. 6 no. pp Nov. 3. Ahma Abu Al Haija S -M 5 receive the B.Sc. an M.Sc. egrees in electrical engineering from Joran University of Science an Technology JUST Irbi Joran an the Ph.D. egree in electrical engineering from McGill University Montreal QC Canaa in 6 9 an 5 respectively. He is currently a Postoctoral Fellow with the Electrical an Computer Engineering Department University of Alberta Emonton AB Canaa. Between February 3 an August 4 he was a Visiting Stuent at Tufts University Mefor MA USA. His research interest inclues cooperation in multiuser channels resource allocation for cooperative communication systems wireless communications an performance analysis an evaluation over faing channels. Chintha Tellambura F receive the B.Sc. egree with first-class honor from the University of Moratuwa Sri Lanka in 986 the M.Sc. egree in Electronics from the University of Lonon Unite Kingom in 988 an the Ph.D. egree in Electrical Engineering from the University of Victoria Canaa in 993. He was a Postoctoral Research Fellow with the University of Victoria an the University of Brafor He was with Monash University Australia from 997 to. Presently he is a Professor with the Department of Electrical an Computer Engineering University of Alberta. His current research interests inclue the esign moelling an analysis of cognitive raio networks heterogeneous cellular networks an multiple-antenna wireless networks. Prof. Tellambura serve as an eitor for both IEEE Transactions on Communications an IEEE Transactions on Wireless Communications an was the Area Eitor for Wireless Communications Systems an Theory in the IEEE Transactions on Wireless Communications uring 7-. Prof. Tellambura an co-authors receive the Communication Theory Symposium best paper awar in the IEEE International Conference on Communications Ottawa Canaa. He is the winner of the prestigious McCalla Professorship an the Killam Annual Professorship from the University of Alberta. Prof. Tellambura has authore or coauthore over 49 journal an conference publications with total citations more than an an h-inex of 55 Google Scholar.