Performance Analysis of Low Latency Multiple Full-Duplex Selective Decode and Forward Relays

Performance Analysis of Lo w Latenc y Multiple Full-Duple x Selecti v e Decode and F orward Rel ays Fatima Ezzahra Airod Communica tio n Systems INPT Rabat, M orocco Email: airod@inpt.ac.ma Houda Cha fna ji Communica tio n Systems INPT Rabat, Morocco Email: chafnaji@inpt.ac.ma Halim Y anikomeroglu Systems an d Co m puter Engineering Cartelon Uni versity Ottawa, Canada Email: halim@sce.carleton.ca Abstract —In order to f ollow up with mission-critical appli- cations, new f eatures need to b e carried to satisfy a reliable communication with r educed latency . W ith this r egard, this paper p roposes a low latency cooperativ e transmission scheme, where multiple ful l -duplex relays, simultaneously , assist th e communication b etween a source node and a d estination node. First, we present th e communication model of th e proposed transmission scheme. Th en, we derive the outage p robability closed-fo rm for two cases: asynchronous transmission (where all relays ha ve different processing delay) and synchronous transmissions (where all r elays ha ve the same processing delay ). Finally , using simulations, we confirm the theoretical results and compare the proposed multi-relays transmission scheme with relay selection schemes. Index T erms —Mul t i-relay system, Selective decode and for - ward, Ful l-duplex, Low latency applications, Ou tage probability . I . I N T RO D U C T I O N Future wireless networks, i.e. , 5G, op en n ew p erspectives and a llow the existence of div ersified services with th e aim of bringin g a wide variety of novel application s, among wh ich we distinc t mission-critical app lications. T o e n sure the radio commun ication for such application s, very low latency as well as extreme reliab ility are re q uired, whence came, the definition of u ltr a-reliable and low latency commun ications (URLLC). As on e o f flexible defin ed 5G service categories, URLLC need s to be car r ied in cellular networks in order to enable and sup p ort se vera l applications, and targets important sectors nam ely , health, industry and transpor tatio n. Ho wever , the reque sted char acteristics or f unctionalities will not be the same, as each application inq uires v arious perf ormance requirem ents which m a kes their setting mo r e conflictin g and challengin g [1], [2]. In this co ntext, th e use of coo peration concept provides spatial and temporal diversity , and constitutes a goo d alternative to support advanced communicatio ns with increased channel cap acity [ 3], [4]. In general, there are various w ays of relay processing in cooper a tive networks, among which we distinct mainly two fa- miliar techniques: am plify-an d-forward (AF) and deco de-and- forward (DF) [5]. I n AF sche m e, th e relay simp ly amplifies the received sign al and for wards it towards the destination. How- ev er , this relaying scheme su ffers f rom n oise amplification. I n the DF scheme, the r e lay first decodes the sign al rece ived fr om the so u rce, re-encod es and re-tr ansmits it to the destination. This app roach suf fers from er r or prop agation when the relay transmits an erroneo u sly d ecoded data block. Selecti ve DF , where th e relay only tra n smits when it can reliably decode the data packet, h as been introduced as an efficient method to reduce er ror propagatio n [6]. Overall, all prop osed coop erative schemes aim to incr ease the diversity order of the system, hence, improving the network perfo rmance. Even if th e full-dup lex (FD) relaying mode generates loop interferen ce from th e r e lay input to th e relay output, it still practical to use o n coo perative relaying systems du e to its spectral efficiency [7], [8]. The FD r elay requ ires th e du pli- cation of radio frequ ency cir cuits to transmits and receives simultaneou sly in the same time slot and in the same frequ ency band. I t has been shown that the FD m ode still fea sib le ev en with the p resence of significan t loop in terference [7], especially with recen t advances n oted in antenna technolo g y and signal p r ocessing techn iques. In [9], a novel techn ique for self-interfer e nce cancellatio n u sing antenna cancellation was depicted for FD transm ission s. In the same con text, thr ough passiv e suppression and activ e self-interfer ence cancellation mechanisms, an experiment stud y was pro posed in [1 0]. Hence, these prac tical growths incite au thors to a dopt FD commun ications in their researc h, thus, get rid of spectral inefficiency c a used by h alf-dup lex (HD) relaying mode. In cooperative systems, one o r multiple r elays may b e used to assist tra n smission between a sour ce and a destination nodes. Th e application of the relay selection principle on FD system permits the mergin g o f space diversity as we ll as the spectral efficiency [11]. Th e refore, several works in the literature have conside r ed the relay selection concept applied to their studied multiple r elays systems [11]–[13]. The b est proved r elay selection p olicy for FD coo perative networks is the optimal relay selection (OS) [1 1], [13]. This scheme takes into consider ation the glob al channel state inf ormation (CSI) of the source to rela y channels as well as that o f the relay to d estination ch annels. So, despite its proved pe rforman ce, the OS induces more system overhead [11], [14], [ 15], hence, more system latency . W ith the aim of r e ducing the system latency and the imple m entation comp lexity , partial relay selec- tion (PS) schem e tha t require s just the CSI knowledge of one hop, were intr o duced in [11]. T o the best of our knowledge, only few works c a r ried the multiple relays model without relay selection. In [16], the per forman ce of HD multiple decode- and-fo rward system, were inv estigated for non iden ti- cal distributed chan nels. Recently , FD-AF coo p erative system were studied [3]. The au thors prop osed a forced d elayed FD relaying schem e, wh ere an iterativ e successive interf e r ence cancellation mode l was used to withdr aw th e ac c umulation effect between signals at the d estination. In this paper, we propo se a m ultiple FD relaying sch e me, wh e r e no n -contro lled selecti ve decod e and forward (SDF) r elays, simultan eously , assist the com m unication between a source an d destination nodes. First, we d eriv e the outage probab ility closed-for m o f the proposed system. Then, as a benchmark, we inves tigate the perfor mances compar ison with the OS and th e PS r e lay selection schemes. The re st of the pa p er is o rganized as follows: Section II presents the commu nication m odel of th e pr oposed tr ans- mission scheme. The o utage pro bability of multiple FD-SDF relays is derived in Section III. In Section IV, Numerical results are shown and discussed. The paper is conclud ed in Section V . Notations • x , x , and X d enote, respectively , a scalar q u antity , a column vector , an d a matrix. • C N ( µ, σ ) represents a circularly symmetric complex Gaussian distrib u tion with mean µ an d v aria n ce σ . • δ m,n is the Kronecker sym b ol, i.e., δ m,n = 1 for m = n and δ m,n = 0 for m 6 = n . • ( . ) ⋆ , ( . ) ⊤ , and ( . ) H are con jugate, the tran spose, and the Hermitian transpose, respec ti vely . • C is set of comp lex numbe r . • For x ∈ C N × 1 , x f denotes the d iscrete Fourier transform (DFT) of x , i.e. , x f = U N x , with U N is a unitary N × N matrix wh o se ( m, n ) th element is ( U N ) m,n = 1 √ N e − j (2 π mn/ N ) , j = √ − 1 . • | . | deno tes the absolute v alu e. • E { . } is used to denote the statistical expectation. • P r ( X ) is the probab ility of occurrence of the e vent X . I I . C O M M U N I C A T I O N M O D E L W e con sider a m ulti-relay co operative system, where a set R of N FD-relays (R k ) , ( k = 1 , ..., N ) assists the commun ication between a sourc e (S) and a destination (D) , as d epicted in Fig. 1. Since all rela y s oper ate in FD mod e , we take into account the residual self-interference (RSI) generated from r elay’ s in put to r e lay’ s outpu t, as we ll as inter-relay interferen ce (IRI). The source- destination S → D , source- relay S → R k , the relay interfer ence R k ′ → R k , i.e., RSI ( k = k ′ ) and IRI ( k 6 = k ′ ) , and r elay-destination R k → D chan n els, ar e represen ted by h ab , with a b ǫ { SD , SR k , R k ′ R k , R k D } . In th is p aper, all ch annels are assumed indepen dent iden tically distributed (i.i.d.) zero mean circularly symmetric complex Gaussian ∼ C N (0 , σ 2 ab ) . W e assume a perfect CSI at th e receiv er nodes and limited CSI at the tra n smitter no des, i.e., the tran smitter is only aware of the processing d elay at the relay nodes. In th is work, we consider all relay s a r e operating using SDF relaying mode, where the relay transmits only when it ca n correctly dec ode the sou rce message. The received sign als, at time instan ce i , at relay R k and destina tio n D are, re sp ectiv ely , giv en by y R k ( i ) = p P S h SR k x s ( i ) + X R k ′ ∈R L p P R h R k ′ R k x s ( i − τ k ′ ) + n R k ( i ) , = p P S h SR k x s ( i ) + V R k ( i ) | {z } RSI+IRI + n R k ( i ) , (1) y D ( i ) = p P S h SD x s ( i ) + X R k ∈R L p P R h R k D x s ( i − τ k ) | {z } Direct + Rela y ed signal + n D ( i ) | {z } Noise , (2) where P S and P R denote, respectiv ely , the tran smit po wer of S an d R k , x s ( i ) is the source tr ansmitted signal at channel use i with E [ x s ( i ) x ⋆ s ( i ′ )] = δ i,i ′ , and R L ⊂ R den otes the set of L relays th a t correctly decode the sou rce message. n R k ∼ C N (0 , N R ) a n d n D ∼ C N (0 , N D ) respectively den o te, a ze r o-mean co mplex additive white Gaussian noise at the relay R k and the destination D . W ithout loss of ge n erality and for the sake of presen ta tio n, we ass ume N D = N R = 1 . The processing d elay at relay R k is de noted τ k , V R k ( i ) covers the RSI + IRI at a relay R k after und ergoing all known can cellation technique s and pr actical isolation [8], [17]. V R k ( i ) is assumed to b e eq uiv alen t to a zer o mean complex Gaussian r andom variable ∼ C N (0 , σ 2 RSI , R k + σ 2 IRI , R k ) , with σ 2 RSI , k = σ 2 R k R k and σ 2 IRI , k = X R k ′ ∈R L k ′ 6 = k σ 2 R k ′ R k . From (2), we can see that the destination no de will re c ei ve the sou rce n ode transmitted sign al x s at dif ferent time instance due to the proce ssing d e la y τ k at the relay R k . In or der to alle viate the inter-symbol interfer e nce (ISI) caused by the delayed signal, equalization is need ed at th e destination side . For that purp o se, we propose a cyclic-prefix (CP) tran smission at th e sour ce side in order to perf orm fre q uency-do main equalization (FDE) at the destination no de. In this pap er , we a ssum e that all channel gains chan ge indepen d ently fro m one block to anothe r and rem ain constant during one block of T + τ CP channel uses, where T r epresents the number of transmitted code-words a n d τ CP the CP length ( τ CP ≥ max k ( τ k ) ). Hence, (2) can b e rewritten in vector fo rm to jointly take into a c count the T + τ CP received signal as [18] y D = H x s + n , (3) where y D = [ y D (0) , ..., y D ( T − 1)] ⊤ ∈ C T × 1 , x s = [ x s (0) , ..., x s ( T − 1)] ⊤ ∈ C T × 1 , with R k R k ’ R N S D h S R k h S R 1 h R 1 D h R k D h R k ’ D h R N D h R 1 R 1 h R k R k h R k ’ R k ’ h R N R N h R 1 R 2 h R k ’ R N R 1 h S R k’ h S D h R 2 R 1 h R N R k ’ h R k R k ’ h S R N h R k ’ R k Fig. 1. The FD SDF m ulti-relay system. n = [ n D (0) , ..., n D ( T − 1)] ⊤ ∈ C T × 1 and H ∈ C T × T is a circulant matrix that can be d ecomposed as H = U H T ΛU T , (4) where Λ is a diagonal matr ix whose ( i, i ) -th element is λ i = p P S h SD + X R k ∈R L p P R h R k D e − j ( 2 π i τ k T ) . (5 ) The sign al y D can be therefo re represented in the freq uency domain as y D f = Λx s f + n f . (6) At the destination , the instantaneous end-to- end eq uiv alen t signal-to-in terference and noise ratio (SINR), at frequen cy bin i , is expre ssed as γ i = λ i λ H i = P S | h SD | 2 + α L + A, (7) where α L = P R | X R k ∈R L h R k D e − j ( 2 π i τ k T ) | 2 , A = 2 √ P S √ P R X R k ∈R L  | h SD h * R k D | co s  2 π i τ k T + θ k  and θ k = angle  h SD h * R k D  . I I I . O U TAG E P RO B A B I L I T Y In this section, we d eriv e the proposed transmission scheme outage proba bility . For that purpo se, let’ s first intro duce the instantaneou s SINRs for each link. The received instantaneou s SINR of S → D , S → R k and R k → D links are, respectively , denoted γ SD = P S | h SD | 2 , γ R k D = P R | h R k D | 2 and γ SR k = P S | h SR k | 2 P R  σ 2 RSI , R k + σ 2 IRI , R k  +1 . Note that all SINRs are exponentially distributed ran dom variables. The multiple SDF FD relay system outag e probability can be e xpressed as P out = P S → D out Y R ′ ∈R P S → R ′ out + N X L =1 X R L P S R L D out Y R ∈R L  1 − P S → R out  Y R ′ ∈ R L P S → R ′ out , (8) where R L denotes the set of L relays not in o utage an d R L , R \ R L . P S → D out and P S → R out denote respecti vely , the outage pr obability of S → D link and S → R link, and can be expressed as P S → D out = Pr( γ SD < η ) = 1 − e − η P S σ 2 SD P S → R k out = Pr( γ SR k < η ) = 1 − e − η ( P R ( σ 2 RSI , R k + σ 2 IRI , R k ) +1 ) P S σ 2 SR , (9) where η = 2 r  T + τ C P T  − 1 , with r is the bit rate per channel use. Note that the factor T + τ C P T means that the tran sm ission of T useful code-words oc c u pies T + τ C P channel uses. P S R L D out denotes, the ou tage probability o f a c o operative system whe re a set R L of L relays assist the co mmunicatio n between nod e S and no de D , and it can be derived as follows: P S R L D out = Pr 1 T + τ C P T − 1 X i =0 log 2 (1 + γ i ) < r ! . (10) T o der iv e the closed f orm expression of (10), we con- sider two cases, i.e., the asynch r onous transmission ( τ k 6 = τ k ′ , ∀ k 6 = k ′ ) and the syn chrono us transmission ( τ k = τ k ′ = τ , ∀ k 6 = k ′ ) . • Asy nchronous transmission In the asynchr onous transmission , all relays forward signals to the destina tio n with different delay pro cessing, i.e., ( τ k 6 = τ k ′ , ∀ k 6 = k ′ ) . Inspired from [1 9], we ha ve T − 1 X i =0 log 2 (1 + γ i ) = P T − 1 i =0 log 2 n  1 + P S | h SD | 2 + α L  ×  1 + A 1+ P S | h SD | 2 + α L o , and thereby , we get, T − 1 X i =0 log 2 (1 + γ i ) = T − 1 X i =0 log 2  1 + P S | h SD | 2 + α L  + T − 1 X i =0 log 2  1 + A 1 + P S | h SD | 2 + α L  . (11) Thanks to arithmetic-g eometric mean ine q uality f or com- plex n umber, we get P S | h SD | 2 + α L > A . Th u s, us- ing the first T aylor expa nsion, log 2  1 + A 1+ P S | h SD | 2 + α L  ≈ 1 ln(2) A 1+ P S | h SD | 2 + α L . Noting that T − 1 X i =0 cos  2 π i τ k T + θ k  = 0 . Therefo re, the second term in (11) vanishes . Thus, (1 1) can be approximated as T − 1 X i =0 log 2 (1 + γ i ) ≈ T − 1 X i =0 log 2  1 + P S | h SD | 2 + α L  = T − 1 X i =0 log 2  1 + P S | h SD | 2 + P R | h R L D | 2 + α L − 1 + β L ) = T − 1 X i =0 log 2  1 + P S | h SD | 2 + P R | h R L D | 2 + α L − 1  + T − 1 X i =0 log 2 1 + β L 1 + P S | h SD | 2 + P R | h R L D | 2 + α L − 1 ! , (12) with β L = 2 P R X R k ∈R L  | h R L D h * R k D | co s  2 π i τ L − τ k T + ϕ L,k  and ϕ L,k = angle  h R L D h * R k D  . No ting tha t 1 + P S | h SD | 2 + P R | h R L D | 2 + α L − 1 > P R | h R L D | 2 + α L − 1 ≥ β L and using the same mathematical manipulatio ns as befo re, we can easily proof that the secon d term in (12) vanishes. Repeating the same mathematical manipulations, we foun d that (12) can be approx imated as T − 1 X i =0 log 2 (1+ γ i ) ≈ T log 2 1 + P S | h SD | 2 + P R X R k ∈R L | h R k D | 2 ! . (13) From (13), we can see that using equalization at the desti- nation side, for asynchrono us transmission, allows to virtually separate different spatial p aths and the r eby achieve a full spatial di versity . Therefo re, P S R L D out can be d e r iv ed as P S R L D out =Pr T T + τ C P log 2 1 + γ SD + X R k ∈R L γ R k D ! < r ! =Pr γ SD + X R k ∈R L γ R k D < η ! = η Z 0 Pr ( γ SD < η − y ) × f X R k ∈R L γ R k D ( y ) d y . (14) For simplicity , we co n sider all relays experie n ce the same R k → D lin k q uality , i.e., σ 2 RD = σ 2 R k D , ∀ k . Therefo re, X R k ∈R L γ γ R k D follows gamma distrib ution with para m eters L and γ RD = P R σ 2 RD , and with probab ility distribution fu nction (pdf) f X R k ∈R L γ γ R k D ( x ) = 1 γ RD e − x γ RD  x γ RD  L − 1 ( L − 1)! . So ac c ord- ing ly , after som e man ipulations, we get the expression of P S R L D out as depicted b elow: P S R L D out = γ  L, η γ RD  Γ( L ) − e − η γ SD Γ( L ) ×  γ SD γ SD − γ RD  L × γ  L, η γ SD − γ RD γ RD γ SD  , (15 ) where γ SD = P S σ 2 SD , Γ( L ) = ( L − 1)! is the factorial of L − 1 , and γ ( n, x ) presents the lower incom plete Gamma fun ction which is given by R x 0 t n − 1 e − t d t [20, 8. 3 50.1] . Thereby , b y substituting (9) and (1 5) into (8 ), we get the closed form expression of the outage p robab ility for the asyn chrono us case. • Sy nchronous transmission In the syn chrono us tra n smission, all relays forward signals to the destina tio n with the same delay p rocessing. T h ere- fore, λ i in (5) can be exp r essed as λ i = √ P S h SD + √ P R X R k ∈R L h R k D ! e − j ( 2 π i τ k T ) . W e see clearly that the syn- chrono us transmission is equ i valent to one relay system with R → D channel h syn = X R k ∈R L h R k D ∼ C N (0 , X R k ∈R L σ 2 R k D ) and r eceiv ed instantaneo us SINR γ syn = P R | h syn | 2 . T hus, synchro n ous transmission r epresents th e worst scenario whe r e adding more relays d oes not ad d any diversity to the system [3]. By referr ing to the proof in [19], P S R L D out can be derived as P S R L D out ≈ Pr  T T + τ CP log 2 (1 + γ SD + γ syn ) < r  =Pr ( γ SD + γ syn < η ) = η Z 0 Pr ( γ SD < η − y ) × f γ syn ( y ) d y (16) where f γ syn ( y ) = 1 γ syn e − y γ syn represents the pdf of γ syn , with γ syn = P R X R k ∈R L σ 2 RD . Hence, the (16) can be expressed as P S R L D out =  1 − e − η γ syn  −  γ SD γ SD − γ syn  e − ¯ γ S D η ×  1 − e − η  γ SD − γ syn γ syn γ SD   . (17) Finally , by su bstituting (9) an d (17) into ( 8), we ge t the closed form expression of synchron ous case outage probabil- ity . I V . N U M E R I C A L R E S U L T S In this section, u sing Monte-Carlo simulations, we ev aluate the p erform a nce of the studied FD Multi-re lay system, with non controlled SDF relay s. For compariso n , we consider two relay selection sch emes, i.e., the OS as the high latency relay selection scheme and the PS as the low latency scheme. Note that both con sidered re la y selection sche mes requir e more system overhead than the proposed schem e, an d hence, mo re system latency . For simplicity , we assume all relays experien ce the same chan nel qu ality , i.e ., σ 2 SR = σ 2 SR k , σ 2 RD = σ 2 R k D , σ 2 RSI = σ 2 RSI , k , and σ 2 IRI = σ 2 IRI , k , ∀ k = 1 , ..., N . Besides, fo r all simulations, we assume that σ 2 SD = 0 dB , r = 2bps / Hz , T = 50 0 , and τ CP = 10 . For a fair compa rison, we set the relay transmit p ower of th e prop osed multi-relay scheme to P R = E R L and the r elay selec tio n sch emes to E R . Fig. 2 and Fig. 3 illu stra te the p erform ances of the inves- tigated system mod el in section II. They r epresent, r espec- ti vely , asynchro nous and synch ronou s cases, where th e outage probab ility of the three relaying schemes, cited a b ove, are plotted versus σ 2 IRI . Moreover , to point out the impact of the number of re lay s on the system pe rforman ces, the evaluation is perfor med for two different num ber o f relay s, i.e . , N = 5 and N = 10 , for a fixed v alue of RSI, i.e., σ 2 RSI = 0dB . First, we notice that the simulation r e sults match perfectly with the the- oretical analysis, obtain ed in section II I, for both syn chrono us and asyn chrono us cases. From Fig. 2, that represents the b est scenario where all relays are asynchr onous, w e c an see clearly that the system perform ances become better as N increases, mainly due to the addition a l spatial div ersity . Furthermor e, depend ing on the inter-relay-interfer ence level at the relay s, i.e., σ 2 IRI , the three consider ed relayin g schemes ou tp erform each other . In term of outage p robability , when the system suffers from high IRI, OS schem e offers the best performan ce gain but at the price o f h ig h system overhead. For low I RI, i.e., σ 2 IRI < σ 2 RSI , th e pr oposed multi-relay scheme becom es the be st choice in term of both o utage pro bability and latency . Note that, du e to the distance betwee n the transmit and recei ve antennas th at redu ces naturally th e IRI, we should co nside r σ 2 IRI < σ 2 RSI for practical scen arios. Now , we tu r n to the worst scenario w h ere all r elays ar e synchr onous. From Fig. 3, we no tice that the curves of syn c hrono u s case h av e a very bad slope and saturate a t low σ 2 IRI . In fact, in the synchron ous case adding mo re relays does n o t ad d any spatial diversity to the system. E ven for a such bad scenario, we c a n see, fro m Fig. 3, that for N = 5 , th e mu lti-relay transmission scheme outperf orms the moderate latency relay selection PS at low σ 2 IRI . Now , we focu s on the asyn chrono us scenario an d ev alu ate the ou tag e p robability of th e studied system versus σ 2 SR . In Fig. 4, we consider the scenario of a stro ng R k → D link, i.e., σ 2 RD = 10 dB , and we can see clear ly that the propo sed mu lti- relay system and the OS scheme of fer the same per forman ces, while outperf orming the PS schem e with the increase of σ 2 SR . In Fig. 5, as the R k → D link q uality decreases, i.e., σ 2 RD = 0 dB , we start to n otice that the OS sch eme, provides better perfor mances than the multi-relay system when σ 2 SR ≥ 4 dB . This is du e to the fact that, in OS sch e me, the relaying tra n smit power E R is fully used b y the best R k → D link while, in multi-relay scheme, the relay ing transmit power E R is shared equally between L r elay links, i.e., P R = E R L . E ven thoug h, the pr oposed scheme still p erform s better tha n the PS scheme . V . C O N C L U S I O N In this p aper, we pro posed a low latency cooperative trans- mission scheme, wher e mu ltiple FD- SDF relays, simu ltane- ously , assist the communica tio n between a sou rce node and a destination node. First, the an alytical expr e ssion of the outag e probab ility were deriv ed fo r two cases, i.e., asyn chron o us and synchro n ous tran smissions. Then, using Monte-carlo simula- tions, we compa red the propo sed multi-r elays transmission scheme with two d ifferent relay selectio n schemes, i.e., the -4 -2 0 2 4 6 8 10 σ I RI 2 (dB) 10 -5 10 -4 10 -3 10 -2 10 -1 10 0 Outage probability Async multi-relay N=10 sim Async multi-relay N=10 anal OS Relay selection N=10 PS Relay selection N=10 Async multi-relay N=5 sim Async multi-relay N=5 anal OS Relay selection N=5 PS Relay selection N=5 Fig. 2. Outage probabili ty versus the IRI of async hronous case for σ 2 SR = 8 dB , σ 2 RD = 10 dB , σ 2 RSI = 0 dB , and P S = E R = 5 dB . -4 -2 0 2 4 6 8 10 σ I RI 2 (dB) 10 -4 10 -3 10 -2 10 -1 10 0 Outage probability Sync multi-relay N=10 sim Sync multi-relay N=10 anal OS Relay selection N=10 PS Relay selection N=10 Sync multi-relay N=5 sim Sync multi-relay N=5 anal OS Relay selection N=5 PS Relay selection N=5 Fig. 3. Outage probabilit y versus the IRI of synch ronous case for σ 2 SR = 8 dB , σ 2 RD = 10 dB , σ 2 RSI = 0 dB , and P S = E R = 5 dB . OS sch e me req uiring the knowledge of glob al CSI an d the PS scheme requirin g the knowledge o f partial CSI. Simulation re- sults reveal that the proposed multi-r e lay transmission schem e and relay selection schemes outperf orm e a ch other in term of outage pro bability , dep e nding on IRI, nu mber of relays, and channel links quality . As the pro posed m u ltiple FD c ooperative relaying scheme d oes not req uire any c e n tral compo nent, thus, getting r id of r elay selection signaling messages an d thereby , reducing the system latency while incre a sin g the system diversity , we can say th at it can be co nsidered as a good candidate for very low laten cy application s. R E F E R E N C E S [1] R. Abreu, P . Mogensen, and K. I. 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