An Improved Detection Scheme for Distributed IDM-STCs in Relay-Systems

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1 An Improved etetion Sheme for istriuted IM-STCs in Relay-Systems F Lenkeit, Wüen, A ekorsy epartment of Communiations Engineering University of Bremen, Germany {lenkeit, wueen, dekorsy}@antuni-remende Astrat This paper is onerned with the appliation of distriuted Interleave-ivision-Multiplexing Spae-Time Codes (dim-stcs) in relaying systems with error-prone relays applying eode-and-forward (F) In ase of erroneous deoding at the relays, error propagation ours whih is not onsidered y the original detetion sheme for IM-STCs Hene, a new Reliaility Aware Iterative etetion Sheme (RAI) is proposed whih takes the deoding suess of the relays as well as their deoding reliaility into aount By optimally inorporating this knowledge in the detetion proess at the destination, sustantial performane gains ompared to the original detetion sheme are ahieved The proposed RAI sheme even outperforms adaptive relaying as it expliitly exploits also erroneous relays, whih is not the ase for the adaptive sheme I INTROUCTION Spae-Time Coding is one of the prominent tehniques whih evolved in the ontext of Multiple Input Multiple Output (MIMO) systems as it has shown to e a very effiient transmit diversity exploiting strategy if no Channel State Information (CSI) is availale at the transmitter [], [2] Nowadays, Spae- Time Codes (STCs) are also applied in distriuted form in relaying systems, sine multiple relays an e grouped into soalled virtual antenna arrays (VAAs) whih allow the adoption of MIMO tehniques [3], [4] However, due to the distriuted fashion of VAAs, some restritions apply Partiularly, the exhange of information among the relays is limited and, thus, a perfet ooperation among the relays of one VAA is not possile Moreover, imperfet synhronisations among the nodes of a VAA may lead to severe drawaks for transmission shemes whih require orthogonality among the relay signals These restritions have to e taken into aount when applying MIMO tehniques to relay systems as they an severely influene the overall system performane In [5] and [6] a STCs approah has een presented ased on the non-orthogonal multiple aess sheme Interleave- ivision Multiple Aess (IMA) [7] This Interleave- ivision-multiplexing Spae-Time Code (IM-STC) does not require any synhronisation among the transmitting nodes, making it a promising andidate also for relay systems Hene, the IM-STC has first een applied to unoded eodeand-forward (F) relay systems in a distriuted fashion in [8] and has later on een extended for oded systems and additional relay protools in [9] It has een shown, that This work was supported in part y the German Researh Foundation (FG) under grant KA the distriuted IM-STC (dim-stc), due to its flexiility regarding ode rate and numer of transmitting nodes and due to its roustness against asynhronisms, is in fat a good hoie for relay systems But it also has een pointed out, that imperfet deoding at the relays has to e taken into aount as it leads to error propagation whih severely degrades the overall performane Consequently, in [0] a modifiation of the ommon iterative detetion strategie for IM-STCs [5] has een presented whih expliitly takes the deoding reliaility of the relays into aount Speifially, the relay signals have een weighted aording to the reliaility of the orresponding relays, efore they have een omined The resulting Fq- INST sheme has shown a signifiant performane improvement ompared to the ommon detetion sheme from [9] However, the ahieved performane was still poor ompared to adaptive relay shemes in whih only orret relays forward to the destination, while all erroneous relays stay silent [4] In this paper, a Reliaility Aware Iterative etetion sheme (RAI) for dim-stcs in two-hop relay systems is proposed, whih leads to an even etter performane than adaptive relay shemes This is ahieved y optimally exploiting all availale information at the destination from the orret as well as from the erroneous relays The idea ehind this sheme is, that depending on the numer of erroneous its, the relay information of the erroneous relays is still highly orrelated to the soure information and, hene, may still ontriute to the overall detetion Speifially, a grouping of the relays is introdued and the relays are split into those, whih ould deode suessfully and those whih ould not While the suessful relays are omined and jointly deoded as y the ommon detetor, the erroneous relays are all proessed separately After the final iteration, the signals of the orret relays and of the erroneous relays are omined using a weighting similar to [0] A Overview II SYSTEM MOEL A two-hop relay-system as depited in Fig is onsidered, where a single soure S ommuniates with one destination via N parallel relays R n, n N No diret link from soure to destination is assumed and the hannel impulse responses from S to R n and from R n to are given y h n and g n, respetively Frequeny-seletive lok Rayleigh fading hannels h n and g n with L h and L g iid hannel taps

2 S Fig R h g h N R N (N ) d R g N d S d S Topology of the onsidered two-hop relay system are assumed and the hannel impulse responses are normalized suh, that the total reeived power does not depend on L h and L g, ie, E{ h n 2 } = E{ g n 2 } = The path loss on eah hop is given y d ǫ suh that h n = d ǫ hn and g n = d ǫ g n, where d denotes the distane etween the orresponding nodes and ǫ is the path loss exponent Moreover, eah reeiving node, ie, R n and experienes additive white gaussian noise (AWGN) of power σn 2 ue to the half-duplex onstraint, the transmission time an e divided into a Broadast Phase in whih the soure roadasts its information to the relays and a Multiple Aess Phase in whih the relays simultaneously forward the proessed information to the destination B Broadast Phase C x C onv C rep Π M Fig 2 Blok diagram of Soure S In the first phase, the soure roadasts its information to the relays applying IMA [7] Fig 2 shows the transmitter struture of the soure, where the inary information sequene F L 2 of length L is enoded y a hannel ode C of rate R onsisting of a serial onatenation of a onvolutional ode C onv of rate R,onv and a repetition ode C rep of rate R,rep Furthermore, a Cyli Redundany Chek (CRC) ode is applied whih allows the relays and the destination to determine their deoding suess The oded sequene F L 2 of lengthl is then interleaved y an interleaverπ resulting in the interleaved ode sequene Finally, the interleaved ode its are mapped onto symols from the normalized QPSK alphaet A resulting in the transmit sequene x A Lx of length L x with σx 2 = The symols x are then roadasted to all relays The reeived signal y n at relay R n is given as the onvolution of the soure signal x with the orresponding hannel impulse response h n plus additive white gaussian noise n n C Lx+Lh of power σn 2 as y n = h n x+n n () In Fig 3 the struture of the relay R n is shown First, in order to resolve inter-symol interferene (ISI) introdued y the first hop, IMA multi-user detetion (MU) is performed using the iterative soft-rake algorithm [7] The MU at relay R n delivers Log-Likelihood-Ratios (LLRs) Λ Rn of the user information( sequene ) After hard deision, these estimates ˆ Rn = Q Λ Rn form the relay information sequene n y n Λ Rn ˆRn n n n x n MU C Π n M Fig 3 Blok diagramm of Relay R n as ˆ Rn n where n denotes the information sequene at relay R n ontaining the hard estimates of the user sequene Note, that due to deoding errors at the relay, the information sequenes and n an e different from eah other Hene, a CRC hek is applied in order to determine the deoding suess The outome of this CRC hek is signaled to the destination where it is later on used y the new proposed detetion sheme However, independent of this outome, the relay information sequenes are enoded using the same hannel ode C as the soure, interleaved y a relay speifi interleaver Π n and mapped onto symols from the same symol alphaet A C Multiple Aess Phase In the seond phase, the transmit signals x n A Lx of all relays are roadasted simultaneously to the destination Under the assumption of perfet deoding at all relays, the user signal is transmitted from all N relays and, hene, a distriuted IM-STC is formed aross the N relays, omparale to [6] The reeive signal y at the destination onsists of the superposition of the relay signals x n onvolved with the orresponding hannel impulse responses g n plus additive white gaussian noise n C Lx+Lg as y Fig 4 IC y = N g n x n +n (2) n= III COMMON ETECTION SCHEME N N Π Π N N + Λ Struture of the ommon detetion sheme for dim-stcs In order to separate all N relay signalsx n at the destination, an iterative turo detetion as depited in Fig 4 is applied [5] After soft-rake ased Interferene Canelation (IC) with respet to all N layers, relay speifi interleaving is reversed Π n ( ), and the LLRs ΛIC n desriing are summed up = N n= ( n n ˆ ) (3) Eq (3) an e interpreted as deoding of the IM-STC Using, soft-input soft-output hannel deoding is performed After deoding of the repetition ode C rep whih is a summation of the orresponding LLRs, the onvolutional ode C onv is deoded using the well-known BCJR algorithm

3 [] The BCJR delivers LLRs Λ for the information its as well as LLRs Λ for the ode its In order to otain the extrinsi information generated y the overall deoder, the input LLRs are sustrated from the output LLRs, = Λ The extrinsi information is then re-interleaved y the relay speifi interleavers Π n and fed ak to the IC where it is used as a-priori information for the next iteration This iterative detetion proess is repeated until the maximum numer of iterationsn it is reahed Finally, a hard quantization of the LLRs Λ of the information its leads to the hard estimates ˆ The desried detetion sheme is optimal if all relays transmitted the same odeword, ie, n =, n N In pratial relaying systems, however, perfet deoding at the relays annot e ahieved In this ase, the ommon detetion sheme is no longer optimal, as it does not take any reliaility information regarding the first hop transmission and the deoding at the relays into aount One possiility to overome these drawaks is to apply an adpative relay sheme, ie, allowing only orret relays to forward to the destination [4] However, sine erroneous relays may still ontriute to the overall transmission it does not seem reasonale to disale them ut to let them transmit anyway It should then e the task of the destination to handle the orret als well as the erroneous relays properly, and to optimally exploit all availale information IV IMPROVE ETECTION SCHEME In order for the detetor at the destination to e ale to ope with deoding errors at the relays, a suitale model desriing the overall transmission inluding the deoding reliailities of the relays is required On the one hand, this model should e aurate enough to atually improve the detetion at the destination, on the other hand it should e simple enough to avoid an exessive inrease in the omplexity of the detetor or in the signaling overhead A Equivalent transmission model In [2], [3] the orrelation etween a soure information word and its hard estimate at the relay was modeled ased on a inary symmetri hannel (BSC) with a ertain rossover proaility Adopting this desription, the relay information word n is modeled here as n = BSC n {,q n } (4) where q n is the it error proaility of the estimate regarding the soure information word, ie, ˆ Rn q n = d H(,ˆ Rn ) L, (5) with d H ( ) denoting the Hamming distane and L the length of the information sequene For perfet deoding at the relay this rossover proaility is zero and it inreases as the deoding reliaility of the relay dereases Based on this desription, an equivalent joint transmission model onsisting of soure proessing, transmission over the first hop to the n n n x n BSC n C Π n M Fig 5 Equivalent transmission model for transmission of via R n to The shaded BSC lok represents the shaded loks from Fig 2 and Fig 3 relay and proessing at the relay, as depited in Fig 5 an e formulated Oviously, the alulation (5) requires perfet knowledge of at R n whih is not availale in pratial systems However, an estimation of q n using the LLRs Λ Rn of the information its generated y the MU at the relay is possile [4] enoting this estimate ˆq n, it holds { ˆq n = E +e ΛRn } L L i= +e ΛRn,i (6) In this paper, it is assumed that in ase of suessful deoding at the relay, ACK is signaled to the destination, while unsuessful deoding leads to the signaling of a NAK in form of ˆq n For a detailed disussion of this signaling refer to [0] B Reliaility Aware Iterative etetion (RAI) Using the presented equivalent joint transmission model, the new Reliaility Aware Iterative etetion sheme (RAI) for detetion at the destination is proposed In order to improve the detetion quality signifiantly ompared to the ommon detetion sheme disussed in setion III, this detetion sheme takes the deoding suess (ACK/NAK) of the relays as well as the error proailitities ˆq n into aount ) Relay grouping: One prolem of the ommon detetion sheme as well as the improved sheme from [0] is the summation (3) of the LLRs n of all relays, regardless of their deoding suess Sine all layers are deoded jointly, only extrinsi information for the sum signal is availale By using this ommon extrinsi information as a-priori information for the next iteration for all relay signals, it is impliitly assumed that all relays transmitted the exat same signal This is, however, learly not the ase if one or more relays were erroneous and, hene, transmitted a different ode word than the orret relays Proessing all signals separately and omining them after the final iteration, on the other hand, is also suoptimal, as all orret relays in fat have transmitted the same signal and should, hene, e omined in order exploit this knowledge during the iterative detetion Therefore, a grouping of the orret relays on the one hand and all erroneous relays on the other hand is introdued Sine all orret relays have transmitted the same ode word n =, their LLRs are omined after relay speifi de-interleaving All erroneous relays, however, may have transmitted pairwise different ode words and, hene, are all proessed separately For the sake of notational simpliity, the set of indies of the orret relays R and the set of indies of erroneous relays R with R = {n ˆq n = 0, n N} R = {n ˆq n 0, n N}, (7a) (7)

4 erroneous Π ρ() ρ() ρ() ρ() ρ(k) Π ρ(k) Λ ρ() ρ(k) ρ(k) Λ ρ(k) y IC soft omining Λ ˆ ρ Π ρ() (weighting) Π ρ(i) ρ ρ() ρ(i) ρ() ρ(i) ρ() ρ(i) ρ + Λ ρ orret Fig 6 Struture of the proposed RAI sheme for dim-stcs and the orresponding indexing funtions ρ(i), i I = R and ρ(k), k K = R are introdued Thus, the indies of the orret relays are given y ρ() up to ρ(i) and the indies of the erroneous relays y ρ() up to ρ(k), ie, ρ(i) =, i I ρ(k), k K (8a) (8) Applying this grouping results in the detetion struture given in Fig 6 The LLRs delivered from the IC are grouped ased on the deoding suess (ACK/NAK) at the relays Sine the orret relays have transmitted the same ode words, their LLRs are summed ( up) after relay speifi deinterleaving and are then jointly deoded, similar to the ommon detetion sheme (ottom part) The erroneous relays, however, have transmitted different ode words and are, therefore, proessed and deoded separately (top part) The expliit deoding, hard deision and susequent re-enoding at the relays ensures, that all relays atually transmitted a valid ode word whih is fundamental for the validity of the presented equivalent transmission model The goal of this first stage of the detetion is the est possile estimation of the relay information words n and not of the soure information word After the last iteration, the estimates for the relay information words are given as LLRs at the output of the K + deoders 2) Weighted Comining: Having estimated the relay information words n, now an overall estimate for the soure information word should e determined This estimate should not only inlude the information from the orret relays, ut also the information from the erroneous relays as, depending on the error proailities ˆq ρ(k), the relay information of the erroneous relays is still orrelated to the soure information Taking the BSC model (4) into aount, an estimate Λ ρ(k) ρ = I i= Π- ρ(i) ρ(i) for ased on the deoder output Λ ρ(k) an e formulated [3] ( ) Λ e ρ(k) Λ ρ(k) ( ˆq ρ(k) )+e Λ ρ(k) ˆq ρ(k) = log (9) e Λ ρ(k) ( ˆq ρ(k) )+e Λ ρ(k) ˆq ρ(k) The error proaility ˆq ρ(k) of the BSC herey leads to a weighting of the estimate of the relay information word given y the LLRs Λ ρ(k) For ompletely unorrelated ρ(k) and, ie ˆq ρ(k) = 05, the relay transmitted no information regarding and, hene,λ ρ(k) = 0 But as ˆq ρ(k) dereases,λ ρ(k) tends to Λ ρ(k) giving an estimate of with respet to the information from relay R ρ(k) Sine all hannels are statistially independent, the oservations from all relays an e summed up resulting in the estimate K Λ = Λ ρ + Λ ρ(k) (0) k= Finally, hard quantization leads to the overall estimate ˆ V NUMERICAL RESULTS A two-hop relay system with one soure, N = 4 parallel relays R n and one destination as depited in Fig is onsidered The distane etween the soure and the destination is normalized to d S = and the inter-relay distane is set to d R = 02 Frequeny-seletive lok Rayleigh fading with L = L h = L g iid hannel taps is assumed on oth hops and the path loss exponent is set to ǫ = 3 For hannel oding, a omination of the non-reursive half-rate (5,7) 8 onvolutional ode and a repetition ode of rate R,rep = /4 is applied and the odeword length is set to L = 024 odeits The QPSK alphaet A with σx 2 = is hosen For detetion at the relays and at the destination, respetively, N it = 0 iterations are performed

5 avg no of orret relays L = L = /σ n 2 in db Fig 7 Average numer of orret relays for flat (L =, solid) and frequeny seletive hannels (L = 4, dashed) First, the average numer of orret relays is given in Fig 7 As an e seen, in the low SNR region, ie, up to approx /σ 2 n = 3 db, on average more relays are orret for the flat hannel (L = ) as for the frequeny seletive hannel (L = 4) This is due to the soft-rake detetion at the relays, whih resolves every multi-path propagation seperately Sine the hannel impulse responses are normalized to unit power, the SNR per hannel tap is lower for the frequeny seletive hannel than for the flat hannel and, hene, a worse performane is ahieved However, aove /σ 2 n = 3 db the influene of the offered frequeny diversity for the frequeny seletive hannel dominates the drawak of a lower SNR per hannel tap, resulting in a etter performane for the frequeny seletive hannel In Fig 8 the ahieved Frame Error Rates (FERs) at the destination for the ommon detetion sheme (F) as well as for the proposed RAI sheme are given As enhmark, also the sheme from [0] (Fq-INST) and the adaptive sheme are shown The proposed RAI learly outperforms F as well as Fq-INST for flat (solid) as well as for frequeny seletive hannels (dashed) It even ahieves a etter performane than the adaptive sheme due to the exploitation of erroneous relays Interestingly, y omparing the slopes of the FER urves, the RAI sheme ahieves the same diversity degree for flat hannels as the ommon sheme for frequeny seletive hannels This is due to the hoie of the simulation parameters, ie, N = 4 relays and L = 4 hannel taps for the frequeny seletive hannels The ommon sheme oviously only exploits frequeny-diversity ut almost no spatial diversity while the RAI sheme also fully exploits the availale spatial diversity VI CONCLUSION In this paper, distriuted Interleave-ivision Multiplexing Spae-Time Codes (dim-stc) have een applied for twohop eode-and-forward relay systems After introduing an equivalent transmission model for the soure-relay transmission, the novel Reliaility Aware Iterative etetion Sheme (RAI) was proposed whih expliitly takes the deoding suess as well as the deoding reliailities of the relays into aount for detetion at the destination ue to the optimal omining of the information from the orret as well as from the erroneous relays, the proposed RAI sheme outperforms even adaptive relaying shemes, as these do not exploit erroneous relays Morever, the presented sheme is very flexile and an easily e extended to multi-user senarios FER F Fq-INST [0] adaptive RAI /σ n 2 in db Fig 8 FERs at the destination for ommon detetion (F), modified detetion with weighting from [0] (Fq-INST), the adaptive relay sheme and the proposed RAI sheme for L = (solid) and L = 4 (dashed) hannel taps REFERENCES [] S Alamouti, A Simple Transmit iversity Tehnique for Wireless Communiations, IEEE Journal on Seleted Areas in Communiations, vol 6, no 8, pp , Ot 998 [2] V Tarokh, N 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