SCMA with Low Complexity Symmetric Codebook Design for Visible Light Communication
Sparse code multiple access (SCMA) is attracting significant research interests currently, which is considered as a promising multiple access technique for 5G systems. It serves as a good candidate for the future communication network with massive no…
Authors: Shun Lou, Chen Gong, Qian Gao
1 SCMA with Lo w Comple xity Symmetric Codebook Design for V isible Light Communication Shun Lou, Chen Go ng, Qian Gao, an d Zhengy uan Xu Abstract —Sparse code multiple access (SCMA) is attra cting significant resear ch interests curr en tly , which is considered as a promising multiple access technique f or 5G systems. It serves as a good candidate for the future communication netw ork with massiv e nodes due to its capability of h andling user ov erloadin g. Introducing SCMA to visib le light communication (VLC) can prov ide another opp ortu n ity on d esign of transmission protocols fo r the communication network with massi ve nodes due to the limited communication range of VLC, which reduces the interference intensi t y . Howev er , when applyin g SCM A in VLC systems, we need to modify th e SCMA codebook to accommodate the re al and positiv e signal r equirement fo r V L C. W e appl y multi- dimensional constellation design methods to SCMA codebook. T o reduce th e design complexity , we also propose a symmet- ric codebook design. For all the proposed design approaches, the minimum Eucli d ean distance aims to be maximized. Our symmetric codebook design can reduce design and detection complexity simultaneously . Simulation r esults show that our design implies fast con ver gence with respect to th e number of iterations, and outp erf orms the design th at si mp ly modifi es the existing approaches to VLC signal requirements. I . I N T RO D U C T I O N In recent ye ars, the 5th gen eration communicatio n (5G) is attracting more and more attentio n due to the rapid develop- ment of mo bile communicatio n [1]. The main pu rpose for 5G commun ication is to supp ort three typical scen arios inclu d ing enhanced mob ile br o adband (eMBB), massi ve machine type commun ications (mMTC) and ultra- reliable and low latency commun ications (uRLL C). The co n ventional orth ogona l multi- ple access (OMA) schemes such as orth o gonal frequency divi- sion multiplexing (OFDM) exhibit certain bo ttleneck in coping with massive machin e connectivity . Then , n on-or thogon al mul- tiple access such as low-density signatu re ( L DS) is p roposed [2] [3], which can support massi ve connectivity for massi ve number of users. Sparse cod e multiple access (SCMA) with optimized co de- book design can outperfo r m L D S due to the shaping gain. SCMA is first p roposed as an improvement of LDS in [4], both having low density ch aracteristic. It is shown in [5] that SCMA can sup port massi ve connectivity , lo w latency and This work wa s supported by Nationa l Key Ba sic Research Program of China (Grant No. 2013CB3 29201), K ey Program of Nati onal Nat ural Sci ence Foun- dation of China (Grant No. 61631018), Ke y Research Program of Frontier Sci- ences of CAS (Grant No. QYZD Y -SSW -JSC003), Ke y Projec t in Science and T echnolog y of Guangdong Pro vince (Grant No. 2014B010119001), Shen zhen Peacoc k Plan (No. 110817003 6003286), and the F undamental Research Funds for the Central Univ ersities. The authors are with Key Laboratory of Wirel ess- Optical Communication s, Chinese Academy of Science s, Univ ersity of Sci- ence and T echnolog y of China, Hefei, Anhui 230027, China. Z. Xu is also with Shenzhen Graduate School , Tsinghua Uni ve rsity , Shenzhen 518055, China. Email: loushun@mail.ustc .edu.cn; { cgong821, qgao,xuzy } @ustc.edu.cn. reduced overhead for grant-fr ee uplink. SCMA provides the oppor tunity of transmitting the amo u nt of data mo re than that of resource block called ov erload. An SCMA encod e r maps the inform ation bits to a m ulti-dimen sional codeword, wh ich is different f r om the con ventional mo d ulation. Note that the transmitted co deword is spa r se fo r m itigating th e interference of d ifferent u sers. At the recei ver, message pass algo rithm (MP A) can be a pplied to detect the sign al of each user [6] [7], which can u tilize the sparse property of the tran smitter , and thus sharply reduce the complexity of mu lti-user d etection. Therefo re, it is crucial to de sign good codeb ook o f each user f or a large shap ing gain and low comp lexity detection algorithm . A mu lti-stage design ap proach of SCMA codeb ooks is propo sed in [8]. Th e mother constellation with a goo d Eu- clidean d istance pro file is created primarily based on th e design prin ciples of lattice constellations [9], and th en different constellation operators such as phase rotations can be app lied on the m other constellation to build multiple codebo oks for different users. Finally , all cod e books are mapped into a higher dimension through Latin matrix for sparsity . Multi- dimensiona l SCMA codebo ok d esign based on con stellation rotation an d interleaving is in vestigated in [10], as an extension of [8]. In [11], an improved method based on star-QAM signaling constellation s is propo sed for designing SCMA codebo oks. The aforem entioned metho ds are b ased on a mu lti- stage heu ristic optimization ap p roach, which may lead to a suboptimal solution . T o fur th er im prove the perfor mance, a joint op tim ization of th e constellation with mapping m atrix is propo sed in [12]. It solves the optimization pro blem th rough semi-definite relax ation (SDR), wh ich outp e rforms th e mu lti- stage optimizatio n . On the o th er hand , visible ligh t comm u nication (VLC) based on light-emitting diode (LED) is attrac tin g more and more attention [13] [14] du e to its long lifetime, low power con- sumption, an d the capab ility for high-rate on -off switch in g that enables the mod ulation for communicatio n. Besides the h igh data r ate commu nication, it is a goo d cand idate for mMT C or uRLLC, with massive comm unication nod es and low data rate, due to the limited co mmunicatio n rang e and th us lo wer interferen ce. Th e n designing SCMA fo r a VLC system [15] is o f significant interest. H owever , since the signals for LED- based VLC must b e real and positive, certain m odifications on the conv entional SCMA a re needed. Note that SCMA is a special type of non-orthogo nal multip le access (NOMA), where power-domain NOMA has been studied in [1 6]. W e ad- dress the codebook design for SCMA and propose a sy m metric codebo ok structure to red uce th e design c omplexity . Mor eover , 2 we for m ulate the c o deboo k design prob lem to max imize the minimum E uclidean distance in the codebo ok, and transform it into a co n vex second -orde r cone pr ogramm ing (SOCP) problem . Our sym m etric code book design can significantly reduce the design an d detection complexity simultan e o usly . Simulation results show that ou r scheme can outperf orm the design tha t simply m o difies the co n ventional sch eme for non- negativ e signals. I I . S Y S T E M M O D E L A. S parse Cod e Multip le Access N-dimensional modulation Mapping vector N-dimensional modulation Mapping vector + AWGN MPA Detection å 1 b J b 1 C J C 1 X J X 1 V J V h y Fig. 1: SCMA system mod el. SCMA is a novel codebo ok-ba sed non -ortho g onal multiple access techn iq ue that can improve th e spectral efficiency . W e consider an SCMA system with J users and K physical resources, where the overload factor is defined as λ = J /K . An SCMA tra nsmitter consists of a n SCMA en coder and an SCMA multiplexer , as shown in Figur e 1. The SCMA enco der is de fin ed as a mapping from in put bits to a multi-d imensional codeword. In other words, l og 2 ( M ) bits are en coded to a K - dimensiona l codeword from the predefin ed u ser codebook with size M . The K -dimensional co deword can be o b tained from an N - dimension cod ew ord thro ugh inserting K − N zero s, which can be regarded as being sparse since N < K . T he transform pro cess can be regard ed as a map ping matrix V with K − N zeros in each row . Th e structure o f SCMA can be repre sen ted as a f actor g raph, a s shown by Figure 2, where RNs an d VNs deno te resource no des and variable nodes, respectively . VNs RNs 1 u 2 u 3 u 4 u 5 u 6 u 1 r 2 r 3 r 4 r Fig. 2: A factor graph for SCMA with J = 6 and K = 4. The corr e sponding factor grap h matrix F for SCMA can be expressed a s follows, F = 1 1 1 0 0 0 1 0 0 1 1 0 0 1 0 1 0 1 0 0 1 0 1 1 , (1) where user j and resour c e k ar e connected if and o n ly if F j,k = 1 . Let F i denote i -th column of F . Then, the mappin g matrix for user i can be obtained via setting V i = diag ( F i ) and eliminating all 0 column vectors, such as V 1 = 1 0 0 1 0 0 0 0 , V 2 = 1 0 0 0 0 1 0 0 , V 3 = 1 0 0 0 0 0 0 1 (2) Since six co lumns ca n suppo rt six users in the four slots, the above matrix F can achieve the overloading factor λ = 150% . Note that the num ber o f users superp osed o n a resource expressed by d f remains the same, and all users hav e the same number of dimension of n on-zer o entries N . In this case, we hav e d f = 3 a n d N = 2 . Then SCMA cod ew ords of J users can be multip lexed in a synchr o nous man ner, defined as SCMA multiplexer, a s shown Figure. 3. + + + + + = 1 u 2 u 3 u 4 u 5 u 6 u Fig. 3: SCMA multiplexer with J = 6 and K = 4. The r e ceiv ed sign a l for the SCMA system ca n be expressed as follows, y = J X j =1 diag ( h j ) x j + n = J X j =1 diag ( h j ) V j c j + n , (3) where h j denotes the chann e l vector of user j ; n denotes the additive white Gau ssian noise ( A WGN); c j denotes the N - dimensiona l codeword; and x j denotes the correspo n ding K - dimensiona l codeword. At th e r eceiv er , based on the received signal y and chann el state inform ation (CSI), th e detectio n of J user s can b e realized by apply in g MP A, wh ich is an iterativ e detection appro ach based on factor graph. The spar sity of codeboo k ma y limit the numb er o f connectivity , im plying the redu ced complexity decodin g via message passing even if for a large overloaded factor λ . B. S parse Cod e Multiple Access for VLC Since VLC systems are based o n inten sity mo dulation and direct detectio n (IM- D D ) , the mo dulated signals need to be real and positive. Fu ndamen tal problems for SCMA ar e the codebo ok design and low complexity dete c tion algorithm . Note that the SCMA enc o der directly maps the inpu t bits of each user to a m ulti-dimen sional com plex cod ew ord encoded accordin g to th e predefin ed codeboo ks. Howe ver, SCMA for RF communicatio n ca nnot be app lied to VLC systems directly , since the complex signal cannot be 3 transmitted an d received in a VL C system, via constructin g the spar sity in the freq uent dom ain. An alter n ativ e method is to divide the co m plex signal to r eal and imag inary parts, an d the two parts are transmitted in d ifferent resource blocks. The positive sign al can be achieved b y adding a DC bias. Then we can combine the real and imagin a ry parts at th e receiver to de tect the in formatio n bits. W e can also ado pt A CO- OFDM [17] and DCO-OFDM [ 1 8] to transmit real sign a l by Hermitian sym metry in a VL C system. The SCMA codeb ook design based on OFDM can be modified to satisfy the non- negativ e constraint for the VLC. Howe ver , the a f oremen tioned methods are b o th b a sed on structured cod ebook design for RF technolog y . Furth er perfo rmance im provement can be achieved if we can design the multi- d imension r eal codeboo k fo r VLC, while ma in taining th e spar sity . I I I . C O N S T E L L A T I O N D E S I G N A. Multi- dimension Constellation Design for SCMA For two matrices with the same nu m ber of rows U ∈ C p × n and W ∈ C p × l , the set of the a r bitrary column sum of U and W can be defined as fo llows, U ⊕ W = U ⊗ e T l + e T n ⊗ W , (4) where e T l and e T n are all-one row vectors with length l and n , respectively , and oper ator ⊗ de n otes the Kron ecker pr oduct. The set of the arb itr ary c o lumn difference o f U and W can be defined as follows, U ⊖ W = U ⊗ e T l − e T n ⊗ W . (5) Let C i denote the pr e d efined co deboo k for user i . The su- perimpo sed co dew ord matrix S for all u sers can be represented as follows, S = C 1 ⊕ C 2 ⊕ C 3 ⊕ · · · ⊕ C J . (6) T o improve the detection performan ce, we aim to m aximize the minimum Euclidean distance (MED) in the designed codebo ok [1 9]. The pro blem can be formulated as follows, min S X m k s m k 2 s.t. k s i − s j k 2 ≥ 1 , 1 ≤ i ≤ j ≤ M J . (7) The orig inal optimization problem (7) is the no nconve x problem , which is gener a lly difficult to solve. Howe ver , ther e are some good design method s fo r such optimization problem giv en in [20]. Such optimization pr oblem c an be relaxed to a conv ex second-order cone prog ramming (SOCP) problem . W e reshape m atrix S as a vector r by colum n. Then the pro b lem can be reformulated as min k r k 2 s.t. 2 r T 0 E ij r − r T 0 E ij r 0 ≥ 1 , 1 ≤ i ≤ j ≤ M J , (8) where r 0 denotes the initial feasible solu tion; E ij = E T i E i − E T i E j − E T j E i + E T j E j , E i = u T i ⊗ I N ; u i represents the i -th column of identity matrix I M ; and I N denotes an N order id entity m atrix. Note tha t the elements in r need to be masked by the map ping matrix via settin g the cor respond ing positions to be zer o, in order to guar antee sparsity . W e can guaran tee r T E ij r ≥ 1 since ( r − r 0 ) T E ij ( r − r 0 ) ≥ 0 . The result k r k 2 ≤ k r 0 k 2 is obviou s since r is a feasible solution to o ptimization problem (8). T he codebo ok design can b e co nducted via iterativ ely setting r to be r 0 and solving op timization pro blem (8). The pr o cedure for solv ing the multi-dim ension constellation de sign f or SCMA is shown in Algorithm 1 . Algorithm 1 Iterati ve solution to co deboo k design 1: Rand om generate spa r se r 0 from the mapping matrix; 2: if r T 0 E ij r 0 ≤ 1 ; t hen 3: go to step 1 ; 4: end if 5: Solve op timization prob lem (8) , and ob tain solution r ∗ ; 6: if k r ∗ − r 0 k ≥ 0 . 01 ; then 7: Set r 0 = r ∗ , and go to step 5 ; 8: end if 9: Return r ∗ as the ou tput cod ebook design. The transmitted signa ls of each user ar e mu ltiplexed based on different predefined c o deboo ks, and the d e sign comp lexity grows exponen tially with the num b er of users. T herefor e, the main challen ge o f codeb ook design for SCMA is to d ecrease the comp lexity due to th e multiplexing of different users’ codebo oks. B. Re duced Complexity De sign for S ymmetric Constellatio n W e define D i = C i ⊖ C i as d ifference of arbitrar y two codewords in the codebo ok for user i , and merge th e repeated column vectors of matr ix D i . Theref o re m atrix D for the difference betwe e n arbitrary two column vectors s i − s j from S can be rep resented as the fo llowing dire c t sum of ma trices, D = D 1 ⊕ D 2 ⊕ D 3 ⊕ · · · ⊕ D J . (9) W e aim to obtain reduced complexity design via in troducin g certain symme tr y to the codebook. Consider a simple example of four co dew ords in th e codebook fo r each u ser . Let c ij denote absolu te value of signals fo r user i and reso urce block j . Our design structur e is to fix the a b solute value of sign a ls, giv en by c i = [ c i 1 , c i 2 , · · · , c iK ] T . Then codebo ok C i can be represented as C i = 1 − 1 1 − 1 1 − 1 1 − 1 1 − 1 − 1 1 1 − 1 − 1 1 ⊙ ( c i ⊗ e T 4 ) , (10) where ⊙ deno te the element-wise pr o duct. The computation al complexity of codebook design can be significantly reduced since th e numb er of variables and constraints to be op tim ized can b e red uced. The difference matrix D i for our symmetric constellation design c a n be given by D i = 0 2 − 2 − 2 2 2 − 2 0 0 0 2 − 2 − 2 2 2 − 2 0 0 0 2 − 2 2 − 2 0 0 2 − 2 0 2 − 2 2 − 2 0 0 2 − 2 . (11) 4 A more g eneral case for the codebo ok design can be condu c te d as f ollows. Let D r i = D 1 ⊕· · ·⊕ D i − 1 ⊕ D i +1 · · ·⊕ D J denote the d irect sum except for D i . Then we can get D = D r i ⊕ D i . Note that maximizing MED o f matrix D i is the subp roblem of maximizin g MED of matrix D i because there is an a ll- zero column vector in matrix D r i . Based on the af oremen tio ned c riterion, we pr o pose a Har dmard- based structure for generatin g the symm etric ma trix H i for each user , which can guarantee the MED of matrix C i , given by H i +1 = H i H i H i − H i . (12) The basic matrix H 0 is repre sen ted as H 0 = 1 − 1 1 − 1 . (13) Then the construc tio n can be ach ieved v ia the element-wise produ ct of matrix H i +1 and c i ⊗ e T h , whe re h denotes the column num ber of c i . C. Co mplexity Ana lysis for Design and Detection Note that the comp utational complexity mainly results from solving th e optimization prob lem (8). Obviously , the d esign may suffer sign ificant co mputation al complexity if a gener a l structure on the codebook n e eds to b e designed. Consider scheme 1 , where we express the difference as s i − s j for each pair of elements in S . Then the size of S set is M J , and then the nu mber o f con straints is giv en by M J ( M J − 1) 2 , since each s i needs to be comp ared with all other colu mns in the matrix S . Consider scheme 2 , wh ere we expr ess the difference as D for the co n ventional structu re. Then the size of set D i is given by P = M ( M − 1) + 1 , since each co lumn of C i needs to be compar ed with a ll o th er columns, which leads to the size of M ( M − 1) , an d each colu mn also co mpares with itself, resulting in iden tical all-zero vector . Thus we obtain another size o f 1 . The co mplexity can be gi ven by P J − 1 since all combinatio ns of J users need to be incorporated , where we need to subtract 1 from the final size due to removing the all-zero co deword. Howev er , such numb er is still h ig h for the designing problem . For our pro posed scheme, we express the difference as D for our symmetr ic structu r e. T h en the size can be significantly redu c ed due to sharp de crease of P . Th e computatio nal c o mplexity of the above th ree schemes is shown as T ABLE I for M = 4 and J = 6 . W e can see that our design scheme can g reatly red u ce th e com putation a l complexity . T ABLE I: Complexity mea surement. Scheme Number of v aria bles P Number of constra ints Scheme 1 96 \ 8386560 Scheme 2 96 13 4826808 Proposed scheme 24 9 531440 MP A is applied for multiu ser detectio n fo r SCMA, which has significantly lower complexity than the op timal maximum a posterio ri (MAP) d ecoder, due to the spar sity of codeb ook that ca n for m a T an ner g raph. It is an iterative p ropag ation o f message amon g VN s and RNs, sho wn as fo llows, I ( t ) r k → u j ( x j ) = X ∽ x j ( 1 2 π σ 2 exp( − 1 2 σ 2 y k − X m ∈ V ( k ) h k,m x k,m 2 ) Y p ∈ V ( k ) \ j I t − 1 u p − r k ( x p ) ) ; (14) I ( t ) u j → r k ( x j ) = Y m ∈ R ( j ) \ k I ( t ) r m → u j ( x j ) , (15) where V ( k ) represents the set o f all VNs connected to k - th RN r k ; R ( j ) represen ts the set of all RNs conn ected to j -th VN u j ; t denotes the number of iter ation; and ∽ x j denotes the taking marginal function for variables except x j for factor graph. Fixing th e ma ximum iteration numb er t max , the decod ing output can b e expressed a s Ou tput ( x j ) = Y k ∈ R ( j ) I ( t max ) r k → u j ( x j ) . (16) Note that sparsity can re d uce the decodin g co mplexity f or SCMA, w h ile our design stru cture can fu rther re d uce the detection comp lexity . Note th a t the de c oding complexity of MP A mainly comes from Eq uation (14), where for computing the pro b ability of all users’ signa l combinatio n, we need to compute P m ∈ V ( k ) h k,m x k,m . Ho wev er , since e very resource block only h as two different v alues for each user in our design structure, the complexity of prob a bility calculation can be reduced to 2 J , com pared with M J for the g eneral app roach. I V . N U M E R I C A L R E S U LT S Simulation results are p resented to comp are o ur design method with conv entional schemes via BER perform ance. The typical parameters for SCMA are shown in T ABLE II, same a s the parameters adopted in refe rences [ 8] [10] [11]. Note that the nu mber of r esources is defined in c o mplex c o deboo k, while we need to double it when replacing a complex codebook with a real codeb ook, and the factor graph matrix is repre sen ted as [ F ; F ] via matrix repeatin g. Th e codew ords in the designed codebo ok is sho wn in the Appendix. T ABLE II: System parameter s. Parame ters V alue Number of resources K 4 Number of all users J 6 Codebook size M of eac h user 4 Number of act i ve users d r 3 Number of activ e resource N 2 Overl oad factor λ 150% Number of Iteration for MP A 5 Channel model A WGN Number of frame 50 Length bit eac h frame 1024 The BERs versus SNR fo r different codebook design ap - proach e s are shown in Figure 4, wher e LDS [2], shuffling- SCMA [8], MD-SCMA [10], and starQAM-SCMA [11] are modified to accomm o date the real an d p o siti ve signals for visible light communic a tio n. Symmetric-SCMA denotes the 5 symmetric co d ebook de sig n approach pro posed in this p aper . Performan ce imp rovement o f our design is obser ved comp ared with the a b ove fou r b enchmar k schemes. 0 5 10 15 10 −4 10 −3 10 −2 10 −1 10 0 SNR BER LDS shuffling−SCMA MD−SCMA starQAM−SCMA Symmetric−SCMA Fig. 4: BER compar iso n b e tween the prop osed symmetric design and the benchmar k design approaches. 0 5 10 15 10 −4 10 −3 10 −2 10 −1 10 0 SNR BER 1 2 3 4 Fig. 5: The detection bit error prob ability for dif ferent num bers of iteration s f o r MP A de c o ding. Figure 5 shows the detection b it err or pro bability for the MP A under dif ferent nu mber of itera tio n for the p roposed design structu re. Increasing the numbe r of iterations can reduce the d e te c tion er ror prob ability , and the p erform ance improvement beyon d three iteration s is smaller than that below three iterations, i.e., three iterations suffice to provide a reasonably good perform ance. Further increasing the number of iteration s can hardly provid e additio nal BER reductio n. The co deboo k power k r k 2 versus the number o f iterations for Algorithm 1 is shown in Fig ure 6. It is seen tha t a f ter te n iterations, the codebo ok power be comes saturated and clo se to zero, wh ich implies tha t solving the problem ( 8) via ten iterations suffices to provide a good codebo ok de sign. 0 5 10 15 20 25 10 0 10 1 10 2 10 3 10 4 10 5 Iteration number Codebook Power Fig. 6 : Th e c o deboo k p ower k r k 2 versus the nu m ber of iterations for Algorithm 1 . V . C O N C L U S I O N S In this paper, we have investigated the red uced co mplexity codebo ok design for SCMA for VLC systems. W e have pro - posed a symmetric co deboo k d esign structur e, and optimized the multi-dimen sional constellation desig n , which can m a xi- mize the minimum Euclidean distance between codewords in the co debook . W e hav e also proposed symmetric code book to redu ce the design com plexity when considering the co mbi- nation of different users. The p roposed symme tr ic code book design can r educe the design and detection co mplexity simul- taneously . Simu lation results show that our design o utperf o rms the design th at simply m odifies the existing app roaches f or visible light communication . V I . A P P E N D I X The codebo oks used in the simulations for six users are shown as follows, C 1 = 0 . 7071 0 . 707 1 − 0 . 7071 − 0 . 7071 0 . 0000 0 . 000 0 0 . 0000 0 . 00 00 0 0 0 0 0 0 0 0 0 . 3536 − 0 . 353 6 0 . 3536 − 0 . 3536 0 . 3536 − 0 . 353 6 0 . 3536 − 0 . 3536 0 0 0 0 0 0 0 0 . (17 ) C 2 = 0 . 3536 0 . 353 6 − 0 . 3536 − 0 . 3536 0 0 0 0 0 . 3536 0 . 353 6 − 0 . 3536 − 0 . 3536 0 0 0 0 0 . 7071 − 0 . 707 1 0 . 7071 − 0 . 7071 0 0 0 0 0 . 0000 − 0 . 000 0 0 . 0000 − 0 . 0000 0 0 0 0 . (18 ) 6 C 3 = 0 . 0000 0 . 000 0 0 . 0000 0 . 0000 0 0 0 0 0 0 0 0 0 . 5000 0 . 500 0 − 0 . 500 0 − 0 . 5000 0 . 3536 − 0 . 3536 0 . 3536 − 0 . 35 36 0 0 0 0 0 0 0 0 0 . 3536 − 0 . 3536 0 . 3536 − 0 . 35 36 . (19) C 4 = 0 0 0 0 0 . 3536 0 . 353 6 − 0 . 353 6 − 0 . 3536 0 . 3536 0 . 353 6 − 0 . 353 6 − 0 . 3536 0 0 0 0 0 0 0 0 0 . 0000 0 . 000 0 0 . 0000 0 . 0000 0 . 5000 − 0 . 5000 0 . 5000 − 0 . 50 00 0 0 0 0 . (20) C 5 = 0 0 0 0 0 . 6036 0 . 603 6 − 0 . 603 6 − 0 . 6036 0 0 0 0 0 . 2500 0 . 250 0 − 0 . 250 0 − 0 . 2500 0 0 0 0 0 . 7071 − 0 . 7071 0 . 7071 − 0 . 70 71 0 0 0 0 0 . 0000 0 . 000 0 0 . 0000 0 . 0000 . (21) C 6 = 0 0 0 0 0 0 0 0 0 . 7071 0 . 707 1 − 0 . 707 1 − 0 . 7071 0 . 0000 0 . 000 0 0 . 0000 0 . 0000 0 0 0 0 0 0 0 0 0 . 2500 − 0 . 2500 0 . 2500 − 0 . 25 00 0 . 6036 − 0 . 6036 0 . 6036 − 0 . 60 36 . (22) R E F E R E N C E S [1] A. Osseiran, F . Boccardi, V . Braun, K. Kusume, P . Marsch, M. Maternia , O. Queseth, M. Schellmann, H. Schotten , H. T aoka et al. , “Scenarios for 5g mobile and wireless communicatio ns: the vision of the METIS project , ” IEEE Communications Ma gazine , vol. 52, no. 5, pp. 26–35, May 2014. [2] R. Hoshyar , F . P . W athan, and R. T afazoll i, “Novel low-de nsity signature for synchrono us CDMA systems over A WGN channel, ” IEEE T ransac- tions on Sig nal Pr ocessing , vol. 56, no. 4, pp. 1616–1626, Apr . 2008. [3] J. V an De Beek and B. M. Popovic, “Multipl e access with lo w-density signature s, ” in IEE E Global T elecommuni cations Confer ence , 2009. [4] H. Nikopour and H. Bal igh, “Sparse code multiple acc ess, ” in IEEE 24th International Symposium on P ersona l Indoor and Mobile Radio Communicat ions (PIMRC) , 2013. [5] J. Z hang, L. Lu, Y . Sun, Y . Chen, J. Liang, J. Liu, H. Y ang, S. Xing, Y . W u, J. Ma et al. , “PoC of SCMA-based uplink grant-free transmission in UCNC for 5G, ” IEEE Journa l on Selecte d Areas in Co mmunicati ons , vol. 35, no. 6, pp. 1353–1362, J un. 2017. [6] L . Y ang, X. Ma, and Y . Siu, “Lo w complexi ty MP A detector based on sphere decoding for SCMA, ” IEEE Communicatio ns Letter s , v ol. 6, no. 8, pp. 1855 – 1858 , Aug. 2017. [7] H. Mu, Z. Ma, M. Alh aji, P . Fan, and D. Chen, “ A fixed low comple xity message pass algorithm dete ctor for up-lin k SCMA system, ” IEEE W ire less Communication s Lett ers , vol. 4, no. 6, pp. 585–588, Dec. 2015. [8] M. T aherzade h, H. Niko pour , A. Bayesteh, and H. Baligh, “SCMA codebook design, ” in IE EE 80th V ehicul ar T echnol ogy Confere nce (VT C F all) , 2014. [9] J. Boutros, E . V iterbo, C. Rastell o, and J. -C. Belfiore, “Good latti ce constel lation s for both rayleigh fading and gaussian channel s, ” IEEE T ransaction s on Info rmation Theory , vol. 42, no. 2, pp. 502–518, Mar . 1996. [10] D. Cai, P . Fan, X. Lei, Y . Liu, and D. Chen, “Mu lti-di mensional SCMA codebook design based on constellat ion rotation and interl ea ving, ” in IEEE 83rd V ehicular T ech nolog y Confer ence (VTC Sprin g) , 2016. [11] L. Y u, X. L ei, P . Fan, and D. Chen, “ An optimized design of SCMA codebook based on star-QAM signaling constella tions, ” in IEEE Inter- national Confere nce on W ir eless Communications & Signal Proce ssing (WCSP) , 2015. [12] J. Peng, W . Chen, B. Bai, X. Guo, and C. Sun, “Joint optimization of constel lation with mapping m atrix for SCMA codebook design, ” IEEE Signal Proce ssing Letters , vol. 24, no. 3, pp. 264–26 8, Mar . 2017. [13] A. Jovic ic, J. Li, and T . Richard son, “V isible light communication: opportuni ties, chall enges and the path to marke t, ” IEEE Communica tions Magazi ne , v ol. 51, no. 12, pp. 26–32, Dec. 2013. [14] Q. Gao, R. W ang, Z. Xu, and Y . Hua, “DC-informati ve joint color- frequenc y m odulati on for visi ble ligh t communicat ions, ” IEEE J ournal of Lightwave T echnol ogy , vol. 33, no. 11, pp. 2181–2188, Jun. 2015. [15] L. Feng, R. Q. Hu, J. W ang, P . Xu, and Y . Qia n, “ Applyin g VLC in 5G netw orks: Archi tect ures and key technologies, ” IE EE Network , v ol. 30, no. 6, pp. 77–83, Dec. 2016. [16] H. Marshoud, V . M. Kapinas, G. K. Karagi annidi s, and S. Muhaidat, “Non-ortho gonal multiple a ccess for visible light communications, ” IEEE Photonics T echn ology Letters , vol. 28, no. 1, pp. 51–54, Jan. 2016. [17] J. Armstrong and A. Lowery , “Powe r ef ficient optical OFDM, ” Elec- tr onics Letter s , vol. 42, no. 6, pp. 370–372, Mar . 2006. [18] O. Gonz ´ alez, R. P ´ erez-Jim ´ ene z, S. Rodr iguez, J. Raba d ´ an, and A. A y- ala, “OFDM ov er indoor wireless optica l channe l, ” IEE P r oceed ings- Optoele ctr onics , vol. 152, no. 4, pp. 199–204, Aug. 2005. [19] G. D. Forne y and L.-F . W ei, “Mult idimension al constellati ons. i. intro- duction , figures of merit, and generali zed cross constella tions, ” IEE E J ournal on Selec ted Areas in Commun icatio ns , vol. 7, no. 6, pp. 877– 892, Aug. 1989. [20] M. Beko and R. Dinis, “Desig ning good m ulti-di mensional constel la- tions, ” IEEE W ire less Communicati ons Letters , vo l. 1, no. 3, pp. 221– 224, Jun. 2012.
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