DC-Informative Joint Color-Frequency Modulation for Visible Light Communications

Transcription

1 1 DC-Informaive oin Color-Frequency Modulaion for Viible Ligh Communicaion Qian Gao, Member, IEEE, Rui Wang, Member, IEEE, Zhengyuan Xu, Senior Member, IEEE and Yingbo Hua, Fellow, IEEE arxiv:151.16v1 [c.i] 9 an 15 Abrac In hi paper, we conider he problem of conellaion deign for a viible ligh communicaion (VLC) yem uing red/green/blue ligh-emiing diode (RGB LED), and propoe a mehod ermed DC-informaive join color-frequency modulaion (DCI-CFM). hi mehod joinly uilize available diveriy reource including differen opical wavelengh, muliple baeband ubcarrier, and adapive DC-bia. Conellaion i deigned in a high dimenional pace, where he compac phere packing advanage over lower dimenional counerpar i uilized. aking ino accoun muliple pracical illuminaion conrain, a nonconvex opimizaion problem i formulaed, eeking he lea error rae wih a fixed pecral efficiency. he propoed cheme i compared wih a decoupled cheme, where conellaion i deigned eparaely for each LED. Noable gain for DCI-CFM are oberved hrough imulaion where balanced, unbalanced and very unbalanced color illuminaion are conidered. Index erm Conellaion deign, viible ligh communicaion, DC-informaive, join color-frequency, IM/DD. I. INRODUCION o aify he increaingly higher daa rae demand, viible ligh communicaion (VLC) ha drawn remendou inere from boh indury and academia a a promiing complemen o radiional radio frequency communicaion (RFC) ha uffer from pecrum auraion [1] [3]. he mauring of LED manufacuring echnique during he recen decade largely boo he rend of replacing radiional lighing yem wih LED alernaive for boh indoor and oudoor illuminaion purpoe, and he reuling infrarucure are ready for deploymen of VLC. I i a low-co echnology where one can ue he imple ineniy modulaion and direc deecion (IM/DD) echnique. In addiion, one can enjoy a bunch of addiional advanage uch a eye-afey, high ecuriy and cauing no elecromagneic inference. VLC i boh unique from and imilar o RFC. Wih regard o he uniquene of VLC, i only allow poiive and real ignal o drive he LED a ineniie (a non-informaive DC-bia i ypically ued); i channel epecially for indoor environmen i much more lower varying han a RFC counerpar; baeband waveform modulae he LED direcly inead of being up-convered fir, ec. A for he imilariy beween VLC and RFC, many exiing RFC echnique can be applied, Q. Gao, Z. Xu are wih he he Univeriy of Science and echnology of China, Hefei, China ( george @gmail.com; xuzy@uc.edu.cn). Rui Wang i wih ongji Univeriy, Shanghai, China ( liouxingrui@gmail.com). Yingbo Hua i wih Univeriy of California, Riveride, California, USA ( yhua@ee.ucr.edu). alhough poibly wih non-raighforward modificaion o VLC yem, e.g. opical muliple inpu muliple oupu (O- MIMO) [4], opical orhogonal frequency diviion muliplexing (O-OFDM) [5] [7], and oher advanced ignal proceing echnique [8] [15]. hee (and relevan) work nicely ake advanage of variou diveriie a VLC yem provide, uch a paial diveriy, frequency diveriy, color diveriy and adapive DC-bia, o improve yem performance. I i worh noing ha he color diveriy and adapive DC-bia configuraion are pecific o VLC. he moivaion behind hi work i o exploi he benefi of variou diveriie joinly for a very power efficien VLC, while he focu of hi paper i on he problem of conellaion deign in high dimenional pace. hi pace i formed by everal dimenion of freedom including adapive DC-bia, baeband ubcarrier and muliple wavelengh correponding o R/G/B LED ligh. According o he fundamenal idea ha phere (i.e., conellaion poin) can pack more compacly in a higher dimenional pace, a conellaion wih larger minimum Euclidean diance (MED) can be expeced in a higher dimenional pace. 1. hi MED maximizaion problem i formulaed in a non-convex opimizaion form, and i hen relaxed o a convex opimizaion problem by a linear approximaion mehod. Key pracical lighing requiremen are aken ino accoun a conrain, e.g., he opical power conrain, average color conrain, non-negaive ineniy conrain, color rendering index (CRI) and luminou efficacy rae (LER) requiremen [17], [18]. For RFC, one well-known horcoming wih uilizing muliple ubcarrier i he exceive peak-o-average power raio (PAPR) problem inroduced, which can caue evere nonlinear diorion o degrade yem performance. Pleny of mehod have been propoed o reduce PAPR (ee [19] and reference herein). In fac, when uing muliple ubcarrier for VLC, high PAPR i alo a very evere iue, due o he limied linear dynamic range of amplifier and LED. hi paper how ha uch diorion can be avoided by formulaing he dynamic range requiremen a (convex) conrain of he opimizaion problem. In uch way diorion conrol become a offline proce or a by-produc of conellaion deign. he remainder of hi paper i organized a follow. In Secion II, we fir provide an overview of DC-informaive modulaion cheme for opical communicaion. DC-informaive mulicarrier modulaion i inroduced a a power efficien 1 he yem ymbol error rae (SER) i governed by he MED for working elecrical SNR for VLC [12].

2 2 alernaive o radiional non-dc-informaive opical OFDM configuraion. In Secion III, we propoe he DCI-CFM mehod for yem wih RGB LED. he key lighing conrain including dynamic range conrol are dicued. he cae of Balanced, Unbalanced and Very Unbalanced yem are inroduced. In Secion IV, we dicu he pro and con of uing dynamic range conrain, hor ime PAPR conrain and long ime PAPR conrain. In Secion V, we provide imulaion reul o verify he ignifican performance gain of he propoed mehod over a decoupled mehod for balance, unbalance, and very unbalanced yem. Finally, Secion VI provide concluion. II. AN OVERVIEW OF DC-INFORMAIVE MODULAION FOR OPICAL COMMUNICAIONS Opical communicaion baed on IM/DD ha a unique feaure of requiring all ignal modulaing he LED o be poiive (and real), o muliple cheme are propoed accordingly uch a he well-know aymmerically clipped opical OFDM (ACO-OFDM), DC-biaed opical OFDM (DCO-OFDM) and opical muliubcarrier modulaion (MSM). hee cheme all dicard he DC-bia a he receiver, which caue ignifican power lo. he DC-informaive modulaion cheme were hen propoed uch ha % opical power i ued for daa ranmiion (ee [] for ingle carrier cae and [12] for muliple carrier elecive fading cae). o be pecific, conider he channel model y() = γη i () h() + v() i [1, N c ], (1) where i () i a ymbol waveform mapped from b i ha conain N b bi of informaion, denoe he convoluion operaor, h() i eiher fla-fading or elecive-fading channel, v() denoe whie noie, y() i he received ignal, η and γ are elecrical-o-opical and opical-o-elecrical converion facor repecively 2, and N c = 2 N b and for he conellaion ize. he key feaure of a DC-informaive modulaion i ha he following bai are ued joinly o carry informaion 1 φ 1 () = Π( ), (2) 2 φ 2k () = co(2πf k )Π( ) k = 1, 2,..., K, (3) 2 φ 2k+1 () = in(2πf k )Π( ) k = 1, 2,..., K, (4) where boh I and Q channel are ued. φ 1 () i he DC-bia bai, i he ymbol inerval, f k = k i he k-h ubcarrier, K i he oal number of ubcarrier, and a recangular pulehaper i ued { 1, if < 1 Π() = (5), oherwie. he relaionhip beween ymbol waveform i () and conellaion poin i = [ 1,i, 2,i,..., 2K+1,i ] i i () = 1,i φ 1 () + 2,i φ 2 () K+1,i φ 2K+1 (). (6) }{{} Adapive Bia And one of he reaonable goal i o minimize he SER ubjec o fixed elecrical/opical power by properly deign he conellaion marix 1,1 1,2... 1,Nc 2,1 2,2... 2,Nc S =......, 2K+1,1 2K+1,2... 2K+1,Nc 2 We aume γη = 1 wih ou lo of generaliy (w.o.l.g). b R MAP_R R P () R R MOD_R R R* y () R _R y R U R Dec_R ˆ R ReMAP_ R bˆ R b G G MAP_G P () G G MOD_G G G* y () G _G y G U G Dec_G ˆG ReMAP_ G bˆ G b B B MAP_B P () B B MOD_B B B* y () B _B y B U B Dec_B ˆ B ReMAP_ B bˆ B (a) MOD_R () R R R* y () R _R y R b _MAP P De_Mix MOD_G () G G G* y () G _G y G Mix U _Dec ˆ _ReMA P bˆ MOD_B () B B B* y () B _B y B (b) Fig. 1. (a). Syem block diagram of a decoupled yem; (b). Syem block diagram of he DCI-CFM. ( (Re)MAP R/G/B : bi and conellaion (Re)mapper for R/G/B unnel; (De)MOD R/G/B : (De)modulaor for R/G/B unnel; R/G/B : Phoo Deecor and color filer for R/G/B unnel; (Re)MAP : join (Re)mapper; Dec : join ymbol deecor )

3 3 where each column of S i a conellaion poin, and he MED of all column hould be maximized o reach he goal. We ypically ack he column ino a ingle vecor inead, i.e. = [ N c ], (7) for implificaion of he formulaion of he opimizaion problem dicued in Secion II. III. DC-INFORMAIVE OIN COLOR-FREQUENCY MODULAION WIH RGB LEDS Baed on he idea dicued in Secion II, we propoe wo conellaion deign mehod aking advanage of he informaive DC-bia for a viible ligh communicaion yem employing one RGB LED a hown by Fig.1. If he inpu ino R/G/B carry independen bi informaion a hown by Fig.1(a), i i ermed a decoupled cheme. In comparion, if he inpu ino R/G/B modulaor only carry informaion joinly, i i a join cheme inead a hown by Fig.1(b). In oher word, alhough for a join cheme ill hree modulaor are ued o creae coninuou domain waveform o drive correponding LED, informaion canno be eimaed hough recovery of a ingle (or any pair) of hem. I i oberved ha he join cheme may uilize four ype of diveriie during per channel ue, including frequency diveriy, color(wavelengh) diveriy, adapive DC, and paial diveriy. Spaial diveriy can be achieved by exending from employing only one RGB LED o include N one, which i ou of cope of hi paper. We only emphaize he fir hree diveriie here. hi cheme i ermed DC-informaive join color-frequency modulaion (DCI-CFM). he decoupled yem hown in Fig.1(a) work a follow: A he ranmier-ide hree independen bi ream b x,i, x [red,green,blue] i [1, N c ], of lengh N x are mapped o correponding conellaion poin x,i of ize (2K + 1) 1 fir, which are modulaed eparaely o generae coninuou ymbol waveform (curren) x,i () by (6) for each unnel. If cro-alk exi for any unnel, a correponding precoder P x need o be applied before modulaion. Waveform x,i () are hen elecrical-o-opical convered o ineniy ignal η x,i () o drive he LED. A he receiver-ide, phoo deecor of each unnel collec he waveform (convolued wih channel and corruped by noie). he received ignal i en hrough red, green, and blue color filer repecively and afer opicalo-elecrical converion waveform y x,i () are obained. hen 2K + 1 mached filer are employed for each unnel o demodulae y x,i () o obain ignal vecor y x,i. hree ymbol deecor follow o provide ŝ x,i, eimae of he ymbol vecor, which are de-mapped eparaely and he eimae of original bi equence b x,i are finally obained. If croalk exi, po-equalizer U x are applied before he ymbol deecor. Syem uing DCI-CFM a hown by Fig.1(b) work differenly. A join bi equence b,i = [b R,i b G,i b B,i], (8) i firly mapped joinly o a conellaion poin,i of ize (6K + 3) 1. hen,i i convered by a join modulaor o he coninuou domain o obain,i hrough 3,i () = (p 1)(2K+1)+1,i φ 1 () + p=1 } {{ } Adapive R/G/B Bia 3 p=1 2K+1 k=2 (p 1)(2K+1)+k,i φ k (). (9) If cro-alk exi, a join precoder P i applied before modulaion. Alo we oberve he expecaion of,i () a follow 3 E[,i ()] = (p 1)(2K+1)+1,i φ 1 (), () p=1 ince all non-dc bai ha zero ime average. herefore, boh he average opical power and average color of yem are deermined olely by hee hree adapive DC-bia. While he dynamic range of waveform, inead, i influenced by all ubcarrier of all LED. For our deign, we will demonrae wih a line-of-igh (LOS) cenario when channel ha cro-alk, due o he imperfecne of receiver color filer. he dicree channel model can be wrien a follow [11] y = H + n y R I O O R = y G = O (1 2ɛ)I ɛi G + y B O ɛi (1 2ɛ)I B n R n G n B, (11) where ɛ [,.5] i ermed he cro-alk index (CI) and n N (, I N ). A. he objecive funcion Wih working SNR for VLC which are ypically mediumo-high, he minimum Euclidean diance beween conellaion pair govern SER. herefore, we eek o minimize he yem SER by maximizing he minimum Euclidean diance, hrough carefully deign he conellaion vecor ubjec o key lighing conrain. For a conellaion conaining N c poin, diance of a oal of N c (N c 1)/2 pair have o be conrained a follow [] where we define and F l d 2 min, (12) F l(p,q) = E pq, (13) E p = e p I Nc, (14) where denoe Kronecker produc, e p i he p-h column of ideniy marix I 6K+3, and E pq = E p E p E p E q E q E p + E q E q, (15) where l = (p 1)N c p(p+1) 2 +q, p, q 1, 2,..., N c, p < q. he diance conrain are nonconvex in. We chooe o ue he follow linear approximaion a poin () F l () = 2 F l () F l () d 2 min, l. (16)

4 4 B. Pracical lighing requiremen For our deign problem, pracical lighing iue conidered include average opical power, average illuminaion color, LER and CRI, non-negaive ineniy, and flickering-free requiremen. he fir hree requiremen can be conrain uing only one equaion wrien a follow P o avg = 1 N c, (17) where P o i he average opical power of a RGB LED, i a elecion marix (conaining only one and zero) adding up R/G/B componen in repecively by a muliplicaion of each row wih i, avg = [ R G B ] i ermed he average color raio vecor and he follow equaion hold R + G + B = 1. (18) hu he opical power and illuminaion color requiremen are conrained ogeher. he luminou efficacy rae and color rendering index requiremen can be aified by properly chooing avg. C. Dynamic range requiremen Since he linear dynamic range of LED are limied, he range of ignal for each LED have o be conrained o avoid nonlinear diorion, i.e. x,i () I U, x, i, (19) where I U i he highe curren level and for impliciy we have aumed ha red, green and blue LED have he ame dynamic range. We propoe o conrain dynamic range of a equence of ampled ignal and n i picked a n = x,i ( n ) I U, x, i, () n 2KN o, n =, 1,..., N, (21) where N o i he overampling rae, N = 2KN o, and N + 1 i he oal number of ample poin. I hould be noed ha alhough () doe no guaranee (19), which mean he coninuou ignal waveform deigned ubjec o () could reul in negaive ampliude in beween he ample inance, he negaive peak i very mall compare o he dynamic range of ignal. We can compenae hi effec by adding a mall po DC-bia afer obaining an opimized conellaion. herefore, we can formulae hi poin-wie dynamic range conrain a follow u n K x i, (x, i, n) (22) u n K x i I u, (x, i, n) (23) where i elec he i-h conellaion poin and K x elec he correponding coefficien for color x, u n = [u n,, u c n,1, u n,1,..., u c n,k, u n,k ], u n, = 1/, u c n,k = 2/ co(2πf k n ), and u n,k = 2/ in(2πf k n ). D. Problem formulaion We fir formulae he opimizaion problem when here i no cro-alk among differen colored LED, i.e. H = I, a follow maximize,d min, d min,.. P o avg = 1 N c 2 () F l () F l () d 2 min, l. u n K x i (x, i, n) u n K x i I u (x, i, n), (24) which i convex in and d min, and pecialized olver uch a CVX oolbox for MALAB can be uilized [21]. Sar from iniial poin (), he cheme can ieraively converge o a local opima wih each run. he be conellaion i choen from local opimal conellaion obained from muliple run. When he channel uffer from cro-alk, we chooe o deal wih i by employing he well-known ingular value decompoiion (SVD) baed pre-equalizer P = VS 1 and po-equalizer U H for our yem, where H = USV H. Conellaion i deigned by an opimizaion wih ranformed conrain a follow maximize,d min, d min,.. P o avg = 1 N c P 2 () F l () F l () d 2 min, l. u n K x i P (x, i, n) u n K x i P I u (x, i, n), (25) where P = I Nc P i defined 3 and apparenly hi opimizaion i convex a well. For he decoupled yem, hree independen problem can be formulaed o find he MED for each color, i.e. maximize R/G/B,d min,r/g/b d min,r/g/b.. P o R/G/B = 1 N c j P R/G/B R/G/B 2 () F R/G/B l R/G/B () F R/G/B l () R/G/B d 2 min,r/g/b l. u n i P R/G/B R/G/B (i, n) u n i P R/G/B R/G/B I u,r/g/b (i, n), (26) where d min,r/g/b, j, P R/G/B, Fl, i, and I u,r/g/b are defined in a imilar manner wih correponding parameer in (25). For breviy we omi he explici definiion. IV. DYNAMIC RANGE VS PAPR CONSRAINS In fac, alhough a hard conrain on he dynamic range of ymbol waveform can help avoid non-linear diorion 3 i he Kronecker produc.

5 5 compleely, i may bring wih ide effec uch a exceive power efficiency decreae. hi i paricularly rue if only one or few ymbol waveform have noably larger dynamic range han he majoriy. In uch cae, one can conider uing cerain PAPR conrain o replace he dynamic range conrain. In oher word, here i a radeoff beween allowable PAPR and power efficiency. wo ype of PAPR conrain (for each LED ligh) can be conidered. One i he o-called long-erm PAPR (L-PAPR), i.e. he raio of he peak power of all waveform and he ime average of hem. Auming no cro-alk, he L-PAPR conrain for LED x can be wrien a Φ x ( ) = [max i,n(u n K x i )] 2 β x /N c = N c[max i,n (u n K x i )] 2 β x, (27) where β x i he required L-PAPR for LED x. hu, a e of conrain can be formulaed a follow u β x n K x i (i, n), (28) N c which i non-convex in. A way o deal wih hi i o ue a imilar linear approximaion a in (16) a he ame iniial poin (). he above conrain are hu ranformed a follow u βx n K x i ( () () N ) 1 () 2 ( () ) (i, n). c (29) he oher i he individual PAPR (I-PAPR), i.e. he raio of he peak power of each waveform and he average power of i. he I-PAPR for i-h waveform for LED x can be wrien a Φ x,i ( ) = [max n(u n K x i )] 2 i i β x,i () he correponding conrain can be wrien a u n K x i β x,i i i n, (31) and a imilar linear approximaion proce i applied o conver hem o convex conrain. o he be of our knowledge, here i no comprehenive comparion on performance of yem applying hoe hree conrain available o far. An inereing obervaion recenly in [23] how ha he non-lineariy miigaion for an IM/DD VLC i a more involved problem han expeced. he reaon i ha he low par of he baeband frequencie are cauing larger non-linear diorion han he higher par. hi effec, if aken ino accoun along wih he hree conrain dicued above, i expeced o make he deign problem even more worhwhile o look ino. V. PERFORMANCE EVALUAION In hi ecion, we compare he performance of he decoupled cheme and DCI-CFM by aeing he maximum MED and bi error rae (BER) under differen channel cro-alk and color illuminaion aumpion 4. Each conellaion poin i 4 A binary wiching (BSA) algorihm i applied for opimally map bi equence o conellaion poin [22]. aumed o have equal probabiliy of ranmiion, and he union bound for SER of boh he cheme can be wrien a [, Eq.25] P e, 2N n N c Q ( d 2 min,z 2N ), (32) where N n i he number of neighbor conellaion pair [] and Q(x) = 1 exp( 2 /2)d (33) 2π x denoe he Gauian Q-funcion, d min,z [,R,G,B] and for he MED of he DCI-CFM and MED for decoupled cheme. he bi error rae i hu calculaed a P e,b = λ N b P e,, (34) where λ i he number of wrongly deeced bi in each bi equence, which can be minimized by employing he BSA mapper. A. Syem comparion wih no channel cro-alk We fir compare he DCI-CFM and he decoupled cheme when channel cro-alk do no exi. o guaranee a fair comparion, he following yem parameer are choen: he number of Mone-Carlo run for each cheme N M =, he lengh of bi equence for each channel ue i N b = 6 for DCI-CFM and N br/g/b = 2 repecively for each unnel of he decoupled yem, he number of ubcarrier for each LED i K = 2 or 3, he average opical power P o =, he ymbol inerval = 1 i ued 5, he upper bound of waveform ampliude I U = 8, he average color raio vecor for a balanced yem for an unbalanced yem and for a very unbalanced yem avg,b = [1/3, 1/3, 1/3], (35) avg,u = [4/9, 3/9, 2/9], (36) avg,v U = [.7,.15,.15]. (37) he MED of he wo cheme for hree yem obained hrough picking he be conellaio from he local opimum are ummarized by able I. From able I, key obervaion include: a. Wih he DCI- CFM, he join MED i much larger han he R/G/B decoupled MED, excep for he cae wih very unbalanced illuminaion. While for he very unbalanced cae he blue and green unnel could uffer from evere performance lo wih he mall MED, and herefore he DCI-CFM i ill expeced o work beer. b. Larger MED are obained wih an increaed number of ubcarrier. We are only liing he cae when K = 2 and K = 3 for breviy, while we have oberved hrough addiional imulaion ha hi gain coninue o grow wih K. c. he more balanced a yem i, he beer performance i expeced. 5 Wih ou lo of generaliy = 1 i choen, ince he deign i rae independen.

6 6 ABLE I MED COMPARISON WIH NO CROSS-ALK, DCI-CFM (ROW 1&2) VS DECOUPLED (ROW 3&4). d min,z Balanced Unbalanced Very Unbalanced K= K= K=2 [13.18,13.18,13.18] [15.9,11.93,7.95] [27.68,5.93,5.93] K=3 [15.3,15.3,15.3] [18.4,13.53,9.2] [31.56,6.76,6.76] Ampliude 7 5 B. DCI-CFM performance wih channel cro-alk Wih K = 2 and oher parameer given he ame value a in he previou ecion for DCI-CFM, we imulae o obain he be MED ubjec o differen cro-alk level, conrolled by CI varying from [,.2] (ince wih only average qualiy color filer CI beyond.2 can be avoided). Fig red ub waveform for DCI-CFM wih K = 2, no cro-alk. ABLE II MED WIH DIFFEREN CROSS-ALK LEVELS, DCI-CFM. d min,z Balanced Unbalanced Very Unbalanced ɛ = ɛ = ɛ = ɛ = ɛ = Ampliude 5 From able II, key obervaion include: a. Wih increaed channel cro-alk, he performance of all yem degrade monoonouly. b. he performance of he balanced yem remain he be wih any level of channel cro-alk. c. he DCI-CFM i kind of robu wih cro-alk, ince wih a evere cro-alk level, i.e. ɛ =.2, he yem performance i ill comparable or even beer han a decoupled counerpar. Fig green ub waveform for DCI-CFM wih K = 2, no cro-alk. 5 C. he deigned ymbol waveform wih DCI-CFM We pick he opimized conellaion deigned for unbalanced yem a an example in hi ecion. If cro-alk do no exi, he correponding ubcarrier ymbol waveform R,i (), G,i (), B,i () i obained wih DCI-CFM are ploed in Fig. 2 - Fig. 4. Wih fixed opical power P = and varying noie power N, Fig. 5 include bi error rae curve of he wo cheme wih differen color illuminaion acro eleced working elecrical SNR, which i defined a SNR = log E( i i) N = log N c N, (38) for he DCI-CFM and SNR for he decoupled cheme i defined imilarly. Significan power gain of he DCI-CFM over he decoupled cheme are oberved. Alo, he more unbalanced he yem i, he wore performance i expeced. If cro-alk exi and ɛ =.1, he correponding ubcarrier ymbol waveform are ploed in Fig. 6 - Fig. 8. Wih each figure, he ymbol waveform are differeniaed by color. In pracice, he ampled verion of hee waveform can be preored in he memory of a high peed waveform generaor. Ampliude Fig. 4. BER Fig blue ub waveform for DCI-CFM wih K = 2, no cro-alk. DCI CFM, Balanced Decoupled, Balanced DCI CFM, Unbalanced Decoupled, Unbalanced DCI CFM, Very Unbalanced Decoupled, Very Unbalanced SNR (db) BER performance of DCI-DCM and he decouple cheme.

7 7 Ampliude Fig red ub waveform for DCI-CFM wih K = 2, ɛ =.1. Ampliude Fig green ub waveform for DCI-CFM wih K = 2, ɛ =.1. Ampliude Fig blue ub waveform for DCI-CFM wih K = 2, ɛ =.1. VI. CONCLUSION We have propoe a join conellaion deign cheme ermed DCI-CFM aking advanage of he wavelengh, frequency, and adapive bia diveriie a he ame ime for indoor viible ligh communicaion yem. By applying he DCI- CFM cheme, waveform ymbol wih a much larger MED can be obained han hoe from a decoupled cheme wih or wihou channel cro-alk. Fuure work will include a comprehenive comparion among hree yem: one applying dynamic range, one wih long-erm PAPR, and one wih inananeou PAPR conrain repecively; comparion of power efficiency of he DCI-CFM and he popular DCO/ACO- OFDM cheme for muli-carrier muli-color VLC yem; and advanced precoder deign o replace he SVD-baed pre and po-equalizer uilized in hi paper. REFERENCES [1]. Komine and M. Nakagawa, Fundamenal analyi for viible ligh communicaion yem uing LED ligh, IEEE ran. Conumer Elecronic, vol. 5, no. 1, pp. - 7, 4. [2] S. Rajagopal, R. Rober, and S. Lim, IEEE viible ligh communicaion: modulaion cheme and dimming uppor, Opic Expre, vol. 16, no. 26, pp , Dec. 8. [3] H. Elgala, R. Meleh, and H. Haa, Indoor opical wirele communicaion: poenial and ae-of-he-ar, IEEE Commun. Mag., vol. 49, no. 9, pp , 11. [4] L. Zeng, D. O Brien, H. Minh, G. Faulkner, K. Lee, D. ung, Y. Oh, and E. Won, High daa rae muliple inpu muliple oupu (MIMO) opical wirele communicaion uing whie LED lighing, ournal on Seleced Area in Communicaion, vol. 27, no. 9, pp , 9. [5]. Armrong, OFDM for opical communicaion,. of Lighw. ech., pp , vol. 27, no. 3, Feb. 9. [6] S. Dimirov, S. Sinanovic, and H. Haa, Clipping Noie in OFDM- Baed Opical Wirele Communicaion Syem, IEEE ran on Commun., pp , vol., no. 4, Apr. 12. [7] D. Bykhovky and S. Shlomi, An Experimenal Comparion of Differen Bi-and-Power-Allocaion Algorihm for DCO-OFDM,. of Lighw. ech., pp , vol., no. 4, 14. [8] R. You and. Kahn, Average power reducion echnique for mulipleubcarrier ineniy-modulaed opical ignal, IEEE ran. Commun., vol. 49, no. 12, pp , Dec. 1. [9] S. eramoo and. Ohuki, Muliple-ubcarrier opical communicaion yem wih ubcarrier ignal-poin equence, IEEE ran. Commun., vol. 53, no., pp , Oc. 5 []. Karou, E. Agrell, K. Szczerba, and M. Karlon, Opimizing conellaion for ingle-ubcarrier ineniy modulaed opical yem, IEEE ran. Inf. heory, vol. 58, no. 7, pp , uly 12. [11] E. Moneiro and S. Hranilovic, Conellaion deign for color-hif keying uing inerior poin mehod, IEEE OWC-WS, pp , Dec. 12. [12] Q. Gao,.H. Manon, G. Chen, and Y. Hua, Conellaion deign for a mulicarrier opical wirele communicaion channel, IEEE ran. Communi., pp , an. 14. [13] G. Cou, A.M. Khalid, P. Choudhury, and E. Ciaramella, 3.4 Gbi/ viible opical wirele ranmiion baed on RGB LED, Opic Expre, vol., no. 26, pp. B51 - B56, 12. [14] B. Bai, Q. He, Z. Xu, and Y. Fan, he color hif key modulaion wih non-uniform ignaling for viible ligh communicaion, he 1 Inernaional Workhop on Opical Wirele Communicaion in China, pp , 12. [15]. Vucic, C. Koke, K. Habel, and K.D. Langer, 83 Mbi/ Viible Ligh WDM Link baed on DM Modulaion of a Single RGB LED Luminary, Opical Fiber Communicaion Conference, Lo Angele, Mar. 11. [16] IEEE Viible Ligh Communicaion ak Group. (, Aug. ). IEEE Documen [Online]. Available: hp://menor.ieee.org/82.15/documen?i group=7. [17] CIE (1999), Colour rendering (C 1-33 cloing remark), Publicaion 135/2, Vienna: CIE Cenral Bureau, ISBN [18] A. Simon, Phoomery and radiomery for engineer, New York: Wiley and Son. [19] S. Han and. Lee, An overview of peak-o-average power raio reducion echnique for mulicarrier ranmiion, IEEE ran. Wirele Commun., vol. 9, no. 2, pp , Apr. 5. [] M. Beko and R. Dini, Deigning good muli-dimenional conellaion, IEEE Wirele Commun. Le., vol. 1, no. 3, pp , 12. [21] cvx Uer Guide - CVX Reearch, Inc. [22] F. Schreckenbach, N. Gorz,. Hagenauer, and G. Bauch, Opimizaion of ymbol mapping for bi-inerleaved coded modulaion wih ieraive decoding, IEEE Commun. Le., vol. 7, no. 12, Dec. 3. [23] Z. Li and Z. Huang, Demonraion of adapive frequency domain preequalizaion for whie-led nonlineariy in OFDM-baed VLC yem, ubmied, Opic Expre, 14.