Enling Nonorthogonl Multiple Access in the Sprse Code Domin istockphoto.com/vertigo3d TOWARD 5G WIRELESS INTERFACE TECHNOLOGY Fn Wei, Wen Chen, Yongpeng Wu, Jun Li, nd Yun Luo Designers of fifth-genertion (5G) wireless networks re focusing on enling highly relile low-ltency communictions tht support high dt rte nd llow mssive connectivity. Nonorthogonl multiple ccess (NOMA), n essentil enling technology tilored to ccommodte wide rnge of communiction requirements, shows potentil s tool for helping 5G networks to fulfill these promised cpilities. By coordinting connections for mssive numers of devices within the sme resource lock on power domin, frequency domin, or code domin, NOMA is superior to conventionl orthogonl multiple ccess in terms of network connectivity, system throughputs, nd other chrcteristics. Sprse code multiple ccess (SCMA) is kind of multicrrier code-domin NOMA nd hs een studied extensively. The chllenge in designing high-qulity SCMA system is crfting fesile encoding nd decoding schemes to meet the desired requirements. In this rticle, we descrie re - cent progress in designing multidimensionl codeooks, prcticl low-complexity decoder, nd grnt-free multiple ccess for SCMA systems. Our prticulr focus is on showing how the designs of the multidimensionl constelltion nd fctor grphs (FGs) hve formed the foundtion of SCMA codeooks. In ddition, we review vrious lowcomplexity SCMA decoders with specil emphsis on Digitl Oject Identifier 1.119/MVT.218.286728 Dte of puliction: 1 Octoer 218 sphere decoding. Also, we introduce SCMA grnt-free trnsmission sed on the frmework of elief propgtion (BP) nd discuss the prolem of collision resolution. Bckground New fetures for the next genertion of wireless networks hve emerged from the 3rd Genertion Prtnership Project. These fetures include enhnced moile rodnd (embb), mssive mchine-type communictions (mmtc), nd ultrrelile low-ltency communiction (URLLC). The im of embb is to permit high dt rte for wireless networks ecuse the typicl 5G trnsmission rte will e 1 G/s, with the pek rte fster thn 1 G/s, which is roughly ten or 1 times fster thn tht of the fourthgenertion networks. Besides enling these speeds, mmtc should ccommodte mssive connectivity y llowing networks to connect millions of devices within single squre kilometer, cpcity fr greter thn tht permitted y tody s conventionl networks. Menwhile, URLLC should reduce end-to-end dely to mtter of milliseconds, therey supporting such communiction cpilities s rel-time moile control nd vehicle-to-vehicle pplictions nd communictions. Conventionl orthogonl multiple ccess, such s timedivision multiple ccess, code-division multiple ccess, nd orthogonl frequency-division multiple ccess (OFDMA), ssigns the orthogonl resource to ech user exclusively. However, s mssive numers of devices re 18 1556-672/18 218ieee IEEE vehiculr technology mgzine decemer 218
connected t the sme time, ville time frequency resources quickly ecome scrce. With mssive connectivity, the inefficiency of giving every user exclusive ccess to such limited resources ecomes pprent. Moreover, chnnel codes, s they hve evolved, hve pushed conventionl point-to-point trnsmission nerly to the Shnnon limits. Thus, it is essentil to explore network communiction using next-genertion wireless interfce technologies tht tke full dvntge of the spectrl efficiency, offer more throughputs, nd ccommodte more connected users. To this end, NOMA, which llows multiple users to trnsmit simultneously within the shred resources, represents promising frontier for study. Developers hve proposed vrious NOMA techniques sed on differing principles. These include power-domin NOMA, low-density signtures (LDSs), SCMA, nd pttern-division multiple ccess. While the techniques hve different rtionles, they shre n underlying gol: tht multiple users should e le to trnsmit simultneously in ech orthogonl time frequency resource. Here, we comprehensively review recent progress on SCMA [1], code-domin NOMA. The focus is on designing codes to mke SCMA especilly relile. Also, prcticl lowcomplexity decoder for the multiuser system needs to e developed to ccommodte mssive connectivity demnds. To enle the low-ltency communiction, grntfree multiple ccess my e the preferred lterntive to conventionl request grnt multiple ccess. Thus, it is interesting to consider SCMA comined with grnt-free trnsmission. We specificlly look t the low-complexity grnt-free receiver design nd the collision resolution prolem within the contention-sed trnsmission. Function Nodes Vrile Nodes Rdio Chnnels UE 1 Chnnel Decoder 1 UE 2 Chnnel Decoder 2 Active Users Detection nd Chnnel Estimtion... UE J Chnnel Decoder J SCMA Decoder SCMA In this section, we provide rief introduction to SCMA. Figure 1 depicts the lock digrm for the uplink SCMA system. In the encoder, coded its re modulted to the multidimensionl sprse codewords consisting of the high-dimensionl lttice points. As n exmple, Figure 2 illustrtes the four-dimensionl sprse codewords with two nonzero entries. The nonzero entries cn e modulted to OFDMA sucrriers or the multiple-input, multipleoutput (MIMO) ntenns. Note tht choosing the positions of nonzero entries cn e viewed s comi ntionl prolem. Therefore, t most, ` N K j users cn e ccommodted, where K is the totl numer of sucrriers nd N denotes the numer of nonzero entries. To enle the sprse structure of codewords, the numer of nonzero entries should stisfy N % K. This reduces the likelihood tht users will experience collisions in single sucrrier nd further simplifies decoding. For the four-dimensionl codewords in Figure 2, the mximum numer of users is six, wheres, due to the sprsity of codewords, the numer of possile collisions mong users is reduced to three per sucrrier. Illustrtion of SCMA Codeword x k Codeook x k 1 1 11 * * * 1 c 1 x 1 UE 1 Chnnel Encoder 1 SCMA Encoder 1 UE 2 2 c 2 x 2 Chnnel Encoder 2 SCMA Encoder 2... J c J x UE J Chnnel Encoder J SCMA Encoder J J Figure 1 A lock digrm of SCMA systems. decemer 218 IEEE vehiculr technology mgzine 19
Codeook 1 Codeook 2 Codeook 3 Codeook 4 Codeook 5 Codeook 6 1 11 1 1 Sucrrier 1 Sucrrier 2 Sucrrier 3 Sucrrier 4 Figure 2 A four-dimensionl SCMA codeook structure. The SCMA codeook construction cn e formult - ed s suoptiml multiple-stge optimiztion prolem. Initilly, mother constelltion sed on high-dimensionl lttice points ws constructed. Therefter, lttice rottion for the mother constelltion ws further pplied to optimize the product distnce of the constelltion nd induce the dependency nd power vritions mong the lttice dimensions. The susequent design of the codeook ddresses the needs of distinct users y introducing the constelltion function opertors, including complex conjugtes, phse rottions, nd dimensionl permuttions for the lttice constelltions. Those opertors only render the distinct codewords for the users while leving the minimum Eucliden distnce of the constelltions unchnged. After receiving the superimposed codewords, the decoder performs chnnel estimtion nd dt decoding sed on pilots s well s dt signls. The ctive user identifiction is lso necessry if grnt-free trnsmission is considered. The sprse structure of SCMA codewords cn e represented y n FG s in low-density prity check (LDPC) codes. This structure enles the decoder to employ the messge-pssing lgorithm (MPA) for the itertive decoding of the dt. SCMA Encoder Design nd the Performnce Limits Anlysis As code-domin NOMA, SCMA requires, on verge, less energy for signl constelltion ecuse of the shping gin of multidimensionl codewords. Thus, the codeook design helps the SCMA system to perform etter. In this section, we review the literture out SCMA codeook design nd provide insights regrding performnce limits of the SCMA system. SCMA Codeook Design As multicrrier NOMA, the codeooks of SCMA re essentilly multidimensionl constelltion points. SCMA, s originlly plnned, presented systemtic construction method for codeook design where the high-dimensionl constelltion points were generted sed on squre-qudrture mplitude modultion (QAM). Str- QAM hs emerged s n lterntive pproch offering etter it-error-rte (BER) performnce in the fding chnnels. It lso outperforms the squre-qam in pekpower-limited systems. Consequently, reserchers rought forwrd str-qam-sed codeook design for SCMA [2]. By optimizing the coordintes of the signl points in different rings of the str-qam, the str-qam-sed SCMA enjoys lrger minimum Eucliden distnce compred with LDS nd the codeooks in [1]. To leverge the rtio of pek-to-verge power s well s the spectrum efficiency, sphericl codes hve een dpted s nother pproch for the high-dimensionl codeook design of SCMA [3]. Vrious good sphericl codes hve een constructed through inry codes, shells of lttices, permuttions of vectors or computer serching, nd y other mens. The optiml sphericl codes with low dimensions were shown to hve lrge coding gins. An SCMA codeook with good performnce cn e otined y conctenting those low-dimensionl sphericl codes. Aprt from the mother constelltion design, the FG is nother importnt feture in elevting the performnce of the SCMA system. A properly designed FG my expnd system cpcity, reduce the interference of ech sucrrier, nd reduce decoding complexity for the receiver. In [4], the cpcity of uplink SCMA is derived when the covrince mtrix of the codewords is digonl. The FG 2 IEEE vehiculr technology mgzine decemer 218
design is formulted s n integer progrming optimiztion prolem with the oject function eing the sum rte of the system. Ech link etween the vrile node nd function node in the FG is determined y mximizing the individul user rte in one sucrrier itertively. In Figure 3, the throughputs of different FG construction nd power-lloction schemes re compred. This shows tht, through the optimiztion of FGs, some users my occupy one sucrrier exclusively nd experience no interference from other users. In other words, the irregulr SCMA ws shown to hve etter system performnce. Performnce Limits of the SCMA System A system sed on multidimensionl SCMA codewords cn e viewed s equivlent to n MIMO system. In ddition, the MPA receiver my reduce or even eliminte the multiuser interference in ech sucrrier. Thus, the SCMA system cn e treted s kind of single-user MIMO system. With the known results of MIMO, the process of deriving the lower ound of symol error rte for SCMA is strightforwrd [5]. Furthermore, n inspection of the pir-wised proility of MIMO SCMA with lrge-scle fding chnnel shows tht the diversity order of SCMA is minly due to two fctors: the numer of received ntenns nd the signl-spce diversity of the SCMA multidimensionl codewords [6]. In ddition, evidence shows tht lrge-scle fding only ffects the coding gin of the system. SCMA Decoder Design The invention of turo codes hs inspired developers to pply the turo principle in the design of communiction systems. The turo principle hs lso led developers to implement soft informtion etween the SCMA decoder nd the forwrd error correction decoder. This technique lowers the coded BER of SCMA [7]. However, improved BER performnce increses decoding complexity for the receiver. This is why low-complexity decoder is especilly essentil for SCMA. As the LDPC codes, SCMA cn e represented y the FG. Thus, it is nturl to use the BP or MPA for the SCMA decoder. Due to the sprsity of the codewords, MPA hs resonle decoding complexity for the low nd middle modultion order systems. However, when the numer of users is incresing or the modultion order is high (e.g., the 32- or 64-ry SCMA), decoding ecomes prohiitively complex. As such, stisfctory low-complexity decoders for SCMA re needed. One such decoder is sed on prtil mrginliztion [8], n ide grounded in the oservtion tht the convergence rte of messge pssing for different users my e different. Prtil mrginliztion demonstrtes tht it is etter to nlyze the trnsmit symols for users with fster convergence rtes efore the lgorithm termintion. Those symols cn e sutrcted from the To enle the low-ltency communiction, grnt-free multiple ccess my e the preferred lterntive to conventionl request grnt multiple ccess. received signls. For the remining users, messge pssing will only e involved in the susequent itertions. Theoreticlly, the complexity of prtil mrginliztion is exponentil, nd the performnce is highly dependent on which portion of users re chosen to e judged first. While most work in this re focuses on simplifying decoding on the receiver side, proper constelltion design cn lso stremline computing demnds [9]. The ide is shown in Figure 4. For the multidimensionl SCMA codewords with modultion order M, one cn project tht to the constelltion with m 1 M points. Evidently, this will cuse some overlps on the point leling. Nevertheless, the decoder is le to distinguish points from one nother s long s the overlp points re sepr - ted on the other dimensions (e.g., points 1 nd 1 overlp on dimension 1 ut re seprted on dimension 2). Since m 1 M, the decoding complexity is reduced from M dc to m dc, where dc is the numer of collision users in ech sucrrier. Reserchers working on improving MPA re concentrting on updting the function nodes. In ech itertion, the MPA decoder seeks the point tht is most likely to e trnsmitted. However, the scheme requires n exhustive serch through ll possile comintions of trnsmitted signls, mking it inefficient. As n lterntive Throughput (/s/hz) 2 18 16 14 12 1 8 6 4 4 2 2 4 6 8 1 Trnsmit Power (dbm) Proposed Codeook nd Proposed Power Rndom Codeook nd Equl Power Rndom Codeook nd Proposed Power Proposed Codeook nd Equl Power Figure 3 Throughput comprisons for different codeook nd power lloction schemes. decemer 218 IEEE vehiculr technology mgzine 21
The SCMA codeook construction cn e formulted s suoptiml multiple-stge optimiztion prolem. pproch, the decoder cn lso proceed in more efficient wy y considering only the signl points ner the received signls. The ide is essentilly the sme s tht of sphere decoder. For the SCMA, the decoder seeks cndidte list first y list-sphere decoding (LSD). Next, MPA cn e operted within the cndidte list, thus simplifying decoding [1], [11]. The size of the cndidte set cn e tuned to lnce the decoding complexity nd the performnce. Essentilly, sphere decoder cn e viewed s kind of depth-first tree serch lgorithm. Figure 5 shows n exmple of serching tree with L = 5 levels. The serch process strts from the root node nd proceeds to the lef nodes. All solid lines correspond to the survivl pths during the serch, while the dotted lines correspond to the eliminted pths. The decoding complexity depends on the numer of visited nodes on the inry tree during the serch process. Thus, y voiding the unnecessry visits to nodes, simpler serch is possile if some rnches of the tree re pruned properly. SCMA is kind of multisucrrier NOMA. As such, insted of crrying out sphere decoding on different sucrriers independently, the messges re exchnged from different sucrriers so tht some rnches my e pruned in dvnce on the lower serch Y 1 1 1 Y 2 X 1 X 11 1 11 1 2 Sucrrier 1 Sucrrier 2 Figure 4 A low numer of projections for four-ry SCMA. Figure 5 A sphere decoder depth-first tree serch. Level 1 Level 2 Level 3 Level 4 Level 5 levels. More specificlly, when point is reported to e excluded in the list y one sucrrier, the other sucrriers cn circumvent the route to this point y pruning the unnecessry rnches of the serching tree. Figure 6() shows the numer of visited nodes with node pruning (NP-LSD-MPA) versus the conventionl methods (LSD-MPA). Figure 6() demonstrtes tht node pruning results in improved BER performnce. In fct, n LSD error occurs when the ctul trnsmit point is not contined within the cndidte list. Hence, if the redundncy nodes re pruned within the list, the ctul trnsmit point would likely enter the finl list nd, thus, improve the performnce. A sphere decoder for SCMA lso hs the dvntge of eing pplicle to the low numer of projection codewords proposed in [9] (see [11] for detiled discussion). SCMA with Grnt-Free Trnsmission Another chllenge for the dvnced multiple-ccess technique developers is to ddress the issue of user scheduling. In long-term evolution networks, user scheduling is relized through the request-grnt procedure, where ctive users periodiclly send scheduling requests to the se sttion (BS) nd wit for the grnts s well s resource ssignments. However, the hndshkes etween the BS nd the ctive users my result in considerle delys. Menwhile, the dynmic signling degrdes the spectrl efficiency of the network. Thus, contention-sed grnt-free trnsmission is dvocted in the future 5G network. Insted of the hndshkes, ctive users contend the shred resources nd trnsmit directly to the BS. However, two prolems rise in grnt-free multiple ccess: user identifiction nd collision resolution. Identifiction of Active Users for Grnt-Free SCMA For typicl 5G scenrios, such s those involving mmtc, the numer of users connected to the network is presumed to e huge. While millions of devices re connected to the network, only few users re communicting t the sme time. Thus, the tsk of identifying ctive users is generlly frmed s kind of compressed sensing prolem. With the understnding tht inctive users re sending no dt symols nd hve no chnnel responses, the chnnels from ll users cn e viewed s sprse vector with nonzero entries representing ctive users. Therefore, ctive users cn e recognized y detecting support of the sprse vector. In [12], three lgorithms re proposed tht use pilot signls only to estimte the sprse chnnel vectors. Generlly, chnnel estimtes sed on dt re more ccurte thn those sed only on pilot signls. Further, user ctivity informtion is contined not only in the received pilot signls ut lso the dt signls. Thus, one proposed receiver would, y exploiting oth pilot nd 22 IEEE vehiculr technology mgzine decemer 218
dt signls, perform joint user identifiction, chnnel estimtion, nd dt decoding [13]. For the prolem of estimting hyrid continuous (chnnel coefficients) nd discrete (dt symols) vriles, direct mximum likelihood detection is unrelistic ecuse it is so complex. Thus, low-complexity itertive decoder sed on the FG of SCMA is necessry. The FG representtion of SCMA with estimtion of hyrid vriles is formulted in Figure 7(). The representtion shows three loops: one for estimting chnnels, one for detecting dt, nd one for detecting user ctivity. In the dt-detection loop, the term p( xk ck ) denotes the mpping function of SCMA encoder k, which mps the coded its to the SCMA codewords. The function node ftn corresponds to the likelihood function on the tth time slot, sucrrier n. For the chnnel-estimtion loop, the tpped-dely chnnel model with length L is considered. The function z nk, corresponds to the Fourier trnsformtion of chnnel responses from the lg domin to the frequency domin. To fcilitte the detection of sprse signls, the two-lyer hierrchy chnnel model is used for modeling ech chnnel tp hkl. On the first lyer, the chnnel is ssumed to follow the Gussin distriution with vrince m kl. On the second lyer, the vrince is further modeled s gmm distriution C ( mkl, ) with noninformtive priori prmeter of, for instnce, = 1-7 nd = 1-7. Such formultion of chnnel responses leds to the Student s t distriution when integrting out the vriles m kl. The Student s t distriution exhiits hevy tils nd thus fvors sprse solutions for the prolem of identifying ctive users. Essentilly, sphere decoder cn e viewed s kind of depth-first tree serch lgorithm. With the formultion of FG, the messge pssing for dt symols my e clculted sed on BP. However, the direct BP updting is cumersome for the hyrid continuous nd discrete vrile models. The ide for rendering trctle computtion is to pproximte the virtul vriles, defined s the production of discrete dt symols nd chnnel coefficients, into some continuous distriutions for the ske of low-complexity computtion; see Figure 7() for illustrtions. To ensure the ccurcy of pproximtion, the true distriution of vriles is projected into Gussin distriution for ech user individully with the minimized Kullck Leiler (KL) divergence. This coincides with the ide of expecttion propgtion (EP) messge pssing. With Gussin distriuted messges, BP updting is now trctle y some simpler computtion. Figure 8, which demonstrtes the performnce of receiver sed on EP messge pssing, exmines mchinetype communictions where 256 coded its re contined in ech pcket. The user identifiction comprison y the joint nd pilot-ided-only detector is shown in Figure 8(). The ctivity for ech user is determined y the power of the estimted chnnels since inctive users experience the equivlent of zero chnnel coefficients. Clerly, y exploring the pilot nd dt symols concurrently, the joint detector cn chieve much lower error-detection rte. Figure 8() Averge Numer of Visited Nodes 6 5 4 3 2 1 LSD-MPA, E /N = 12 db LSD-MPA, E /N = 18 db NP-LSD-MPA, E /N = 12 db NP-LSD-MPA, E /N = 18 db LSD-LNP, E /N = 12 db LSD-LNP, E /N = 18 db BER 1 1 1 1 2 1 3 1 4 Turo SCMA (16 Points) Mx-log-MPA NP-LSD-MPA, T mx = 14 LSD-MPA, T mx = 14 LNP LSD-LNP, T mx = 35 PM-MPA, Rs = 4, m = 7 1 2 3 4 5 6 7 8 9 1 Level of the Serch Tree () 11 12 11 11.5 12 12.5 13 13.5 14 14.5 15 E /N (db) () Figure 6 An evlution of () the verge numer of nodes visited in ech level of the serching tree for the 15% overloded 16-ry SCMA system nd () the BER performnce of the 15% overloded 16-ry SCMA system. LSD-MPA corresponds to the list sphere decoder. NP-LSD-MPA denotes the LSD with node pruning, nd LNP is the low numer of projected SCMA codewords. The conventionl mx-log- MPA is used s performnce enchmrk. PM-MPA denotes the decoder sed on prtil mrginliztion [8]. decemer 218 IEEE vehiculr technology mgzine 23
compres the BER performnce for different decoding lgorithms. The pilot-ided MPA (P-MPA) lgorithm, which relies on pilots only for chnnel estimtion nd user detection, hs the worst performnce. Other joint messge-pssing receivers, such s BP-MF nd BP-GA, re less effective due to their inccurte pproximtion for the true proility. Becuse the proility estimte stems from minimized KL divergence, the performnce gp etween the BP-GA-EP receiver [13] nd receiver (Genie) with exct chnnel stte informtion nd user ctivity is only roughly 1 db. User Activity Detection Loop Chnnel Estimtion Loop p (λ 1,1 ) λ 1,1 q 1,1 h 1,1 Dt Detection Loop x t,1 p(x t,1 c t,1) p(c t,1 ) p (λ 1,l ) λ 1,l q 1,l h 1,l ϕ 1,k(1) α 1,k(1) f t,1 x t,2 p(x t,2 c t,2) p(c t,2 ) p (λ 1,L ) λ 1,L q 1,L h 1,L ϕ 1,k(dc) α 1,k(dc) f t,n x t,k p(x t,k c t,k ) p(c t,k ) p (λ K,1 ) λ K,1 q K,1 h K,1 ϕ N,k(1) α N,k(1) f t,n x t,k 1 p(x t,k 1 c t,k 1 ) p(c t,k 1 ) p (λ K,l ) λ K,l q K,l h K,l ϕ N,k(dc) α N,k(dc) x t,k p(x t,k c t,k ) p( c t,k ) p (λ K,L ) λ K,L q K,L h K,L Function Nodes Vrile Nodes () X n1 u n1 n1 I nk ftn ( nk ) f tn I xnk ftn (X nk ) X n2 f tn I ftn unk (u nk ) u nk I unk ftn (u nk ) ndc I xnk ftn (X nk ) X ndc u ndc u nk = nk X nk () (c) Figure 7 The FG representtion of () the SCMA with hyrid vriles estimtion nd () nd (c) the messge pssing within function node n. () The digrm shows the messge pssing with direct BP. (c) The digrm shows the messge pssing with EP pproximtion, i.e., the extrinsic messges for virtul vrile u, which is the production of chnnel h nd dt x, re pproximted with Gussin distriutions with the minimized KL divergence. 24 IEEE vehiculr technology mgzine decemer 218
Collision Resolution for Grnt-Free SCMA The rdio resources for grnt-free trnsmission re defined in [12]. The sic rdio resource, which is referred to s contention trnsmission unit (CTU), is defined s the comintion of time dt, frequency dt, SCMA codeook dt, nd pilot dt. The user equipment (UE) is (possily) mpped to CTUs vi the mpping rule CTUindex = UEID mod NCTU, where NCTU denotes the numer of CTUs. In mmtc, the numer of UEs would lwys exceed the numer of ville CTUs. As consequence, multiple UEs cn e mpped to the sme CTU for dt trnsmission. A collision hppens when two or more ctive UEs trnsmit concurrently within the sme CTU. To resolve the UE collision prolems, the conventionl pproch conducts retrnsmission y the rndom ckoff mechnism. However, if the sttic mpping rule is used, constnt collisions my hppen when ursty trffic occurs even when the rndom ck-off is used. Further, some CTUs my e llocted with more UEs due to the numer of UEs exceeding tht of CTUs. To circumvent the prior descried issues, n UE-to-CTU mpping rule sed on cknowledgment (ACK) feedck is proposed [14]. The ide is to use the conventionl sttic mpping rule in the first round of hndshking etween BSs nd UEs. Next, n ACK list contining the detection nd decoding results for ll UEs is fed ck from the BSs to receivers. For ech UE, two its re ssigned to indicte the sttus: (, ) for no dt received, (1, 1) for dt successfully decoded, nd (, 1) for retrnsmission needed. Figure 9 is n illustrtion of the mpping rule sed on ACK feedck. Figure 1 depicts detiled grnt-free trnsmission procedure with mpping rule sed on ACK feedck. Trnsmission dely is ssumed to e three time slots, nd MAPi denotes the mpping rule generted in the ith time slot. To strt with, MAP1 in the first time slot is set sed on conventionl sttic mpping rule. Afterwrds, with the receipt of ACK from the BS, n dptive MAP4 is determined y UEs. Specificlly, for UE j, if the code is 1, indicting tht UE j needs to retrnsmit, n exclusive CTU is immeditely ssigned gin. The BS counts the numer of CTUs ssocited with only one UE, i.e., Nsingle nd set CTUindex = j mod Nsingle. If the code is not 1, n exclusive CTU is unnecessry. The BS now counts the numer of CTUs ssocited with multiple UEs, i.e., Nmulti nd set CTUindex = j mod Nmulti + Nsingle. The susequent slots cn e hndled in similr mnner. Theoreticl nlysis of methods sed on ACK feedck shows tht the collision proility would lwys e less thn tht of conventionl sttic mpping rules. Conclusions nd Future Chllenges This rticle reviewed the stte of the rt for SCMA technologies. We specificlly considered techniques using code-domin NOMA, SCMA, s promising for wireless interfces of the future. We showed how BER Error Detection Rte 1 1 1 1 2 1 3 1 4 1 1 1 1 2 1 3 Pilot (N p = 7) Pilot (N p = 11) Joint (N p = 7) Joint (N p = 11) 1 2 3 4 5 6 7 8 9 1 E /N (db) 1 4 1 2 3 4 5 6 7 8 9 1 E /N (db) proper mother constelltion design s well s the dynmic FG construction cn led to n improved SCMA codeook design. This rticle lso descried issues relted to low-complexity decoders ccommodting multiuser decoding for SCMA. The ide is sed on sphere decoding, which voids exhustive serching during the MPA. To meet the URLLC requirement, SCMA systems dopt grnt-free trnsmission methods. We introduced receiver tht performs joint chnnel estimtion, dt decoding, nd the detection of ctive users sed on EP messge pssing. Finlly, UE-to-CTU mpping rule sed on ACK feedck, solution to the user-collision prolem. () () Genie BP-GA-EP BP-MF BP-GA P-MPA Figure 8 An evlution of () the error-detection rte y joint nd pilot-only methods nd () the BER performnce of the four-ry SCMA system. BP-GA-EP denotes the hyrid BP nd EP messge pssing with Gussin pproximtion. BP-MF represents the hyrid BP nd men-field pproximtion. BP-GA is the BP Gussin pproximtion using the centrl limit theorem. decemer 218 IEEE vehiculr technology mgzine 25
Collision CTU1 CTU2 CTU3 CTU4 CTU5 CTU8 CTU9 CTU1 1 11 UE ID : 2 3 4 5 12 13 14 15 8 18 9 19 1 2 Unsuccessfully Decoded No Trnsmission Successfully Decoded UE14 ACK: 1 11 1 1 1 Proposed Mpping Rule CTU1 CTU2 CTU3 CTU4 CTU5 CTU8 CTU9 CTU1 2 4 12 UE ID : 14 UE ID : 1 9 17 UE ID : 6 15 UE ID : 7 16 UE ID : 8 16 Figure 9 The mpping rule sed on ACK feedck. MAP1 ACK1 MAP4 ACKi 6 MAPi 3 UEs T1 T7 Ti Dt ACK Dt ACK Dt BS T4 T1 MAP1 ACK1 MAP4 MAP4 ACK7 MAP1 MAPi 3 ACKi MAPi+3 Ti+3 Figure 1 The procedure of the grnt-free trnsmission with the ACK feedcksed method. Issues relted to SCMA tht require further investigtion include the following: The decoding of SCMA relies on the loopy BP lgorithm. However, conventionl BP exhiits poor convergence ehvior on the loopy FGs. The convergence rte is slow, nd lgorithms occsionlly chieved locl optiml points. BP rules re the consequence of minimizing the constrined Bethe free energy, which is no longer convex when FG contins loops. To overcome this poor convergence, convex Bethe free energy needs to e constructed for loopy FG. Furthermore, when comined with other 5G techniques, such s mssive MIMO, the design of the SCMA decoder should lso e recst. The decoding complexity would typiclly grow exponentilly with the numer of ntenns. Thus, there is n emerging need to develop low-complexity receiver for mssive MIMO SCMA. Since multiple users shre the sme re - source element in NOMA, the user piring 26 IEEE vehiculr technology mgzine decemer 218
serves s nother interest prolem. For power-domin NOMA, with fixed power lloction, the sum rte cn e enlrged y selecting users with distinctive chnnel conditions. On the other hnd, it is etter to pir the users with similr chnnel conditions in cognitive rdio-inspired NOMA [15]. Unlike power-domin NOMA tht trnsmits on single resource element, the sitution for SCMA is rther complex when the user pring is performed on multiple crriers. Artificil intelligence (AI) comined with 5G is nother reserch trend. AI cn e used to solve prolems tht re intrctle in clssicl communiction system. For instnce, comintoril optimiztion is typiclly the NP-hrd prolem nd is frequently encountered in SCMA, such s in issues relted to codeook ssignment, user selection, nd resource lloction. Alterntive solutions to those prolems might e found y AI using mchine-lerning-sed methods. The SCMA system cn lso e formulted s n utoencoder, where the end-to-end communiction cn e joint-optimized through the construction of deep neurl networks. The utoencoder is trined through the BER or lock error rte nd cn ccommodte vrious chnnel conditions s well s system prmeters. The performnce of SCMA would likely improve with the much lower computtionl complexity. Acknowledgments This work ws supported y the Ntionl Nturl Science Foundtion of Chin under grnts 61671294 nd 617131, the Science nd Technology Commission of Shnghi Municiplity Project under grnts 16JC1429 nd 1751747, the Nturl Science Foundtion of Gungxi Province under grnt 215GXNSFDA13937, nd the Ntionl Science nd Technology Mjor Project under grnts 217ZX312-5 nd 218ZX319-2. Author Informtion Fn Wei (weifn89@sjtu.edu.cn) is currently pursuing his Ph.D. degree in informtion nd communiction engineering t the Shnghi Institute for Advnced Communiction nd Dt Science, Deprtment of Electronic Engineering, Shnghi Jio Tong University, Chin. His reserch interests include wireless communiction with focus on nonorthogonl multiple ccess. Wen Chen (wenchen@sjtu.edu.cn) is professor t the Shnghi Institute for Advnced Communiction nd Dt Science, Deprtment of Electronic Engineering, Shnghi Jio Tong University, Chin. His interests include multiple ccess, coded coopertion, nd green heterogeneous networks. Yongpeng Wu (yongpeng.wu@sjtu.edu. cn) is n ssocite professor t the Shnghi Institute for Advnced Communiction nd Dt Science, Deprtment of Electronic Engineering, Shnghi Jio Tong University, Chin. His reserch in terests include mssive multiple-input, multiple-output (MIMO) systems; mssive MIMO systems; nd physicl-lyer security. Jun Li (jun.li@njust.edu.cn) is professor t the School of Electronic nd Opticl Engineering, Nnjing University of Science nd Technology, Chin. His reserch interests include network informtion theory, ultrdense wireless networks, nd moile edge computing. Yun Luo (yunluo@sjtu.edu.cn) is professor in the Computer Science nd Engineering Deprtment, Shnghi Jio Tong Uni versity, Chin. His reserch interests include informtion theory, communiction coding theory, nd computer security. References [1] H. Nikopour nd H. Bligh, Sprse code multiple ccess, in Proc. IEEE 24th Int. Symp. Personl Indoor nd Moile Rdio Communictions (PIMRC), pp. 332 336, 213. [2] L. Yu, X. Lei, P. Fn, nd D. Chen, An optimized design of SCMA codeook sed on str-qam signling constelltions, in Proc. Int. Conf. Wireless Communictions nd Signl Processing (WCSP), pp. 1 5, Oct. 215. [3] J. Bo, Z. M, M. A. Mhmdu, Z. Zhu, nd D. Chen, Sphericl codes for SCMA codeook, in Proc. IEEE 83rd Vehiculr Technology Conf. 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