A SVD-Based Optical MIMO Precoding Scheme in Indoor Visible Light Communication

Transcription

1 Internatonal Journal of Future Computer and Communcaton, Vol. 3, No. 6, December 0 A SVD-Based Optcal MIMO Precodng Scheme n Indoor Vsble Lght Communcaton Qng-Feng Lu, Shua-Fang Xao, Ka-Zh uang, and Zhou Zhong Abstract A novel cal precodng scheme based on sngular value decomposton (SVD s proposed to solve the problem that strong channel correlaton causes low spatal multpleng gan n ndoor vsble lght MIMO communcaton. Ths scheme frst ensures a nonnegatve sgnal after precodng through mappng the transmt bts nto a specfc smbol constellaton. Then t elmnates the nter-channel nterference b decomposng the MIMO channel through SVD. Fnall, t reduces the b mall allocatng power among the sub-channels wth the object to make the condton of each sub-channel equal. The smulaton results show that SVD-based cal precodng scheme can sgnfcantl reduce the compared to ZF algorthm. And wth the enhancement of channel correlaton, the performance remans n a relatvel low level, so t can obtan hgh spatal multpleng gan under the strong correlaton channel. Inde Terms Indoor vsble lght communcaton, cal MIMO, precodng, SVD, power allocaton. I. INTRODUCTION Vsble Lght Communcaton (VLC s a novel knd of communcaton technolog whch s able to acheve hgh speed data transmsson n ndoor communcaton. Thus, VLC attracts etensve attentons worldwde. The cal wavelengths of lght s used as the carrer of nformaton n VLC, and the Lght Emttng Dodes (s emt hgh speed flcker cal sgnals to transmt nformaton, whle the Photodetector ( or other oelectronc transform devces receve the modulated cal sgnal and transform t to current sgnal. Compared to the tradtonal rado frequenc communcaton and other cal communcatons, VLC has man advantages such as hgh transmtted power, non-electromagnetc nterference, safet, and green. From what has dscussed above, we can draw the concluson that VLC has a great prospect for development []-[3]. The goal of ndoor VLC s to acheve hgh speed data transmsson [], but the modulaton bandwdth of whte s just about 0 Mz [5], whch s too lmted to realze hgh speed data transmsson n Sngle Input Sngle Output (SISO sstem. When Multple Input Multple Output (MIMO technque s appled n ndoor VLC, t could Manuscrpt receved Januar 0, 0; revsed Ma 3, 0. Ths work was supported b Natonal gh Technolog Research and Development Program of Chna (No. 03AA03603, and Open Research Fund of State Ke Laborator of Moble Communcatons (No. 03D09. Shua-Fang Xao s wth the Natonal Dgtal Swtchng Sstem Engneerng & Technologcal Research Center, Zhengzhou 5000, Chna (e-mal: aoshuafang@gmal.com. Qng-Feng Lu, Ka-Zh uang, and Zhou Zhong are wth the Natonal Dgtal Swtchng Sstem Engneerng & Technologcal Research Center, Zhengzhou 5000, Chna. potentall ncrease the scope of the communcaton lnk, overcome the nterrupton whch s caused b personnel walks or shadows of the furnture n the room, and mprove the relablt of the lnk. Meanwhle, the spectrum effcenc can be ncreased wthout the enhancement of bandwdth or transmt power [6], and the hgh data transmsson wll be acheved. In addton, ndoor llumnaton needs man whte s, whch provde rch spatal resources for VLC. Free space cal MIMO s frst researched b Wlson n [7]. Indoor VLC MIMO sstem s frst appled b O Bren n [8]-[0], a non-magng recevng sstem and a magng recevng sstem are ntroduced. And the eperment verfes that the ndoor VLC MIMO sstem can obtan hgh spatal multpleng gan. The performance of Repetton Codng (RC, Spatal Multpleng (SMP and Spatal Modulaton (SM are analzed and compared n []. Whle the lterature [8] and [] ndcate that ndoor VLC MIMO channels have a strong correlaton because of the Intenst Modulaton (IM and Drect Detecton (DD, whch leads to the lack of frequenc and phase components. So t s dffcult to obtan hgh spatal multpleng gan, and the data transmsson can t be fast enough. Lterature [] proposes a modulaton scheme of VLC based on precodng matr,but t doesn t consder the correlaton of MIMO channels. ow to obtan hgh spatal multpleng gan and better use the rch spatal resources of ndoor VLC s stll a hot ssue. In order to solve ths problem, ths paper proposes an ndoor cal precodng scheme based on Sngular Value Decomposton (SVD, we call t SVD-based Precodng. Frst, the nformaton transmtted must be mapped from a specfc smbols constellaton to ensure that the sgnals are nonnegatve after precodng. Then, we decompose the ndoor VLC MIMO channels b SVD, whch can obtan the ndependent sub-channels to elmnate nter-channel nterference. Fnall, we solve the mzaton problem amng at the mnmum sstem and subjectng to the lmted total power to get the mal power allocaton matr, and allocate the power among the sub-channels accordng to the matr to reach the equal performance of each sub-channel, whch can decrease the sstem. The recever emplos Mamum Lkelhood (ML algorthm to decode the receved smbols after shapng process, and recovers the nformaton b nverse smbols mappng. The sstem smulaton results ndcate that the of proposed SVD-based Precodng s sgnfcantl lower than ZF algorthm under dfferent correlaton channel. And wth the enhancement of channel correlaton, the performance remans n a relatvel low level, so t can obtan hgh spatal multpleng gan under the strong correlaton channels. DOI: /IJFCC.0.V3.30

2 Internatonal Journal of Future Computer and Communcaton, Vol. 3, No. 6, December 0 II. SYSTEM MODEL In our VLC MIMO sstem, the number of whte and s N and M, respectvel, M N. Usng the seral-to-parallel converter, the nformaton bts are transmtted through the whte s. The transmtted sgnal vector s denoted b s ( s s s,,,, T = N, N. s go through the ndoor VLC channel, and fnall reach the recever. At the recever, s turn the cal power sgnal nto current sgnal, and then add the whte Gauss nose sgnal n, (,,,, T n = n nj nm, j M the output current sgnal = ( j M. Thus we get,,,, T. j s the output current sgnal of the j th whch s gven b: N =r h s + n ( j j j = r s the photoelectrc converson factor, h j s the Drect Current (DC channel gan from the th whte to the j th. Thus, the matr s represented as: = rs+ n ( matr s the DC channel gan, and the dmenson s M N. In the ndoor envronment, lght sgnals generated b the whte lamp reach the recever through drect path and dffuse path. Through the eperment, lterature [3] fnds that more than 90% of the cal sgnal power at the recever comes from the drect component, and that from the dffuse component can be gnored. So we consder onl the drect path here. We use Lambert radant model to descrbe the lumnescence mechansm of whte lght. The Lambert radant ntenst can be epressed as: ( = ( m+ R0 φ /π cos m φ (3 φ s the emsson angle, m s the order of Lambert emsson. m ln / ln ( cosψ ψ = /, / s the half power emsson angle. Thus the DC channel gan from the th whte to the j th can be epressed as: h j A R 0 ( φj T f ( ϕj g ( ϕj cos ( ϕj, 0 ϕj ϕc = d j ( 0, ϕj > ϕc A s the collecton area for the j th recever, d j s the dstance between the th and the j th recever, φ j s the emsson angle, ϕ j s the angle of ncdence of the lght at the recever, ϕ c s the Feld-of-vew (FOV of the recever, Tf ( ϕ j s the gan of the flter, ( j g ϕ s the gan of the cal concentrator. From Equaton (, the ndoor VLC MIMO channel s determnstc, lacks of frequenc and phase components, and suffers serous nterferences among sub-channels. All these above lead to strong channel correlaton, and then lmt the transmsson rate of the sstem. To solve ths problem, SVD precodng technolog s appled to ndoor VLC MIMO sstems n our artcle. We decompose the MIMO channel nto several ndependent parallel sub-channels through SVD, and allocate more power n the sub-channels whch have smaller DC channel gan. In ths wa, the SNR of these weak sub-channels s mproved, and fnall the performance of the entre sstem. III. SVD-BASED OPTICAL PRECODING SCEME Ths secton descrbes the SVD-based cal precodng scheme n ndoor VLC MIMO sstem. Frst, we map the transmt bts nto a specfc smbol constellaton at the transmtter. After that, we decompose MIMO channel through SVD, and allocate power among the sub-channels wth the object that mnmze the performance. Fnall, the sgnal at the recever wll pass through the shapng process, and the transmtted sgnal could be recovered b ML decodng algorthm. A. Precodng Scheme at the Transmtter As ndoor VLC ads IM modulaton, the transmtted sgnal must be non-negatve, that s s 0, =,,, R (5 R mn N, M. To ensure the transmsson sgnal s become non-negatve, the smbol constellaton of s should be determned frstl. Consderng the common used OOK modulaton n ndoor VLC sstem, the smbol constellaton of s s taken as R represents the rank of, and ( Θ = { a, a,, a } (6 R L =, al s a N dmensonal vector, and satsfes a l ( l, l, l, R = a, a,, a,0,,0, l =,,, L, and the value of a ln,, n =,,, R, s 0 or. Assume s the sgnal to be transmtted. To ensure that the transmtted sgnal s n the smbol constellaton Θ, the smbol constellaton of s taken as Ξ = V Θ = { b, b,, b } (7 b l s a N dmensonal vector, and (,,, l l l l R T b = b, b,, b,0,,0, l =,,, L. As V s a untar matr, sgnal can be transformed nto s n smbol constellaton Θ after precodng b the V matr. Assum s known to the transmtter and recever, then perform SVD decomposton on : L T L

3 Internatonal Journal of Future Computer and Communcaton, Vol. 3, No. 6, December 0 = UΣV (8 ( represents conjugate transpose, V s a N N dmensonal untar matr, Σ s a M N dmensonal dagonal matr: O Σ = R O O ( =,,, R s the th largest sngular value. As ndoor VLC MIMO channel has a strong correlaton, the condton number cond ( of DC channel gan matr s ver large, that s (9 R (0 Therefore, when usng SMP technolog, sub-channels wth smaller sngular value have poor channel condtons. When usng the average power allocaton, the SNR of these sub-channels are lower, and resultng n a hgher sstem. In order to reduce the of the whole ndoor VLC MIMO sstem, when desgnng the power allocaton matr, more power can be allocated on the sub-channels wth smaller sngular values to mprove the receved SNR. P 0 s the total transmt power, and the allocated power of dfferent sub-channels s P = ρ P;0< ρ < ; =,, R ( 0 Set as the nose varance of each sub-channel, and then the recevng SNR of the th sub-channel can be epressed as SNR ( rρ P rp = ρ = ( 0 0 So the sstem wth OOK modulaton can be epressed as the functon Q s rp (3 R 0 = Q ρ R = Q( = e d ( π In order to obtan the mal power allocaton matr, the followng constrant equatons s establshed mnmze subject to ρ = (5 known As the Q s monotoncall decreasng, the followng equaton must be satsfed to get the mnmum rp0 rp0 ρ = ρjj; j (6 Combnng (6 wth (5, we get ρ =, R j = j (7 Thus the mal power allocaton matr under mnmum sstem crteron s Λ ρ, O = ρr, O O (8 And the mal precodng matr whch meets the mnmum sstem crtera can be epressed as Ξ F = VΛ (9 Fg.. Transmsson processng flow of SVD-based cal precodng scheme n ndoor VLC MIMO sstem. The whole processng flow of the transmsson scheme s shown n Fg.. Steps are as follows: Mappng each R bts transmtted nformaton nto sgnal n smbol constellaton Ξ. Perform SVD decomposton on, and get the untar matr V and sub-channel gan matr Σ. Accordng to Σ, solve the mzaton sub-channel power allocaton matr Λ wth the target of mnmzng the sstem. Usng V and Λ to calculate the mal precodng matr F. Λ F Preprocess the sgnal b transmsson sgnal s. s F V Σ, and get the B. Decodng Scheme at the Recever At the recever, we use untar matr U to shape the receved sgnal, and get 3

4 Internatonal Journal of Future Computer and Communcaton, Vol. 3, No. 6, December 0 = U = Δ+ n (0 U Σ Λ Σ Ξ n = U n ( Δ ρ, O = ΣΛ = ρr, R O O ( Then we can recover the sgnal to be transmtted b ML decodng algorthm, and get Fg.. Recevng processng flow of SVD-based cal precodng scheme n ndoor VLC MIMO sstem. = arg mn rσb (3 l l F Σ = U F = ΣΛ ( ( d /,0, d d ( d /,0, dh h ( d /,0, 0 d ( d /,0,0 Fnall, the messages can be recovered through the nverse smbol mappng of. The whole processng flow at the recever s shown n Fg.. Steps are as follows: Perform SVD decomposton on, get the untar matr U and V, and the sub-channel gan matr Σ. Accordng to Σ, solve the mzaton sub-channel power allocaton matr Λ wth the target of mnmzng the sstem. Usng Σ and Λ to calculate mzed sub-channel gan matr Σ. Shape the receved sgnal b untar matr U, and get sgnal. Recover n constellaton Ξ b means of ML decodng algorthm. Recover the source nformaton through the nverse smbol mappng of. Fg. 3. Spatal dstrbuton for ndoor VLC MIMO sstem. ( d /, d /, dh d ( 00d,, h ( d /, d /, dh ( d /, d /, d ( d /, d /, dh h ( d /, d /, 0 ( 000,, ( d /, d /, 0 d ( d /, d /, 0 ( d /, d /, 0 Fg.. Spatal dstrbuton for ndoor VLC MIMO sstem. IV. SYSTEM SIMULATION RESULTS The channel correlaton of MIMO channels n ndoor VLC s related to the dstance between s and s, when d h s fed, the smaller d and d s, the stronger channel correlaton and the greater the condton numbers of wll be. The performance of the sstem wth dfferent channel correlaton can be analzed b changng d or d to get wth dfferent condton numbers. For MIMO and MIMO scenaros wth dfferent dstance spacng of s and s, Monte Carlo smulaton s emploed to smulate the performance of the proposed SVD-based cal precodng scheme of ndoor VLC MIMO sstem. MIMO spatal multpleng s emploed for the smulatng sstems. The spatal dstrbuton of MIMO and MIMO scenaros are shown n Fg. 3 and Fg., the smulaton parameters are shown n Table I, the confguraton of parameters derves from the lterature [5]. TABLE I: SIMULATION PARAMETERS Parameters Values Parameters Values Room Sze 5m 5m 3m d h.5m T(ψ r 0.A/W FOV 60 g(ψ.5 Ψ / 70 A.0cm Settng d = 0.8m, d = 0.8m, then the DC channel gan matr under MIMO and MIMO scenaros are descrbed as follows: = ( = 0 (6 The condton numbers of the DC channel gan matr are

5 Internatonal Journal of Future Computer and Communcaton, Vol. 3, No. 6, December 0 descrbed as cond( = 9.58 and ( cond = 6.5, and n ths case the correlaton of MIMO channel s relatvel weak, and the correlaton of MIMO channel s stronger than that n MIMO scenaro. When d = 0.m and d = 0.m, the DC channel gan matr under MIMO and MIMO scenaros are descrbed as follows: = ( = 0 ( The condton numbers of the DC channel gan matr are descrbed as cond ( = and cond ( = 87.88, and n ths case the correlaton of MIMO channel s relatvel strong. We further reduce d and d, settng d = 0.m and d = 0.m, and then the DC channel gan matr under MIMO and MIMO scenaros are descrbed as follows: = ( = (30 The condton numbers of the DC channel gan matr are descrbed as cond ( = 39.0 and cond( = 67, and n ths case the correlaton of MIMO channels s ver strong. We smulate the performance of the proposed SVD-based cal precodng scheme and compare t wth the ZF algorthm under MIMO and MIMO scenaros wth dfferent spacng of s and s. The smulaton results are shown n Fg. 5. The curve of MIMO scenaro concdes wth that of MIMO scenaro based on the proposed SVD-based cal precodng scheme n ths paper, and what s more the are both sgnfcantl lower than MIMO sstems emplong the ZF algorthm, ths s because the proposed SVD-based cal precodng scheme makes the performance of all sub-channels become smlar b mal power allocaton process. Under the MIMO scenaro, the proposed SVD-based cal precodng scheme n ths paper can acheve 5dB ~ 0dB SNR gan than ZF algorthm when the of the sstem s 0-3 (the mnmum that the forward error correcton process can correct. Whle under the MIMO scenaro, we can acheve a SNR gan above 30dB than ZF algorthm. And what s more, when SNR s 60dB, the wll be greater than 0. and we can t demodulate the source nformaton emplong ZF algorthm. owever, onl about 0dB of SNR s needed to acheve a 0-3 emplong the proposed SVD-based cal precodng scheme. The performances of the MIMO and MIMO sstems almost keep the same wth the channel correlaton gettng stronger, even under channels wth strong correlaton, the proposed scheme stll has a good performance MIMO ZF algorthm 0-5 MIMO SVD-based Precodng MIMO ZF algorthm MIMO SVD-based Precdong SNR(dB d d = 0.8m d = 0.8m MIMO ZF algorthm 0-5 MIMO SVD-based Precodng MIMO ZF algorthm MIMO SVD-based Precdong SNR(dB = 0.m d = 0.m MIMO ZF algorthm 0-5 MIMO SVD-based Precodng MIMO ZF algorthm MIMO SVD-based Precdong SNR(dB c. d = 0.m d = 0.m Fg. 5. Comparson of performance n MIMO sstem under dfferent channel correlaton. Accordng to the smulaton of sstem under dfferent channel correlaton, t s observed that the performance of the proposed SVD-based cal precodng scheme can acheve a SNR gan more than 5dB comparng to the ZF algorthm. Ths s because the proposed SVD-based cal precodng scheme can mprove the SNR of the sub-channels wth poor performance through effectve power allocaton and thus mprovng the performance of the overall sstem. Meanwhle, the performance of sstems emplong ZF algorthm decrease sgnfcantl as the channel 5

6 Internatonal Journal of Future Computer and Communcaton, Vol. 3, No. 6, December 0 correlaton ncreases. When d = 0.m and d = 0.m, the MIMO sstem emplong ZF algorthm wll be unable to demodulate the source nformaton, whle the performance of sstems based on the proposed SVD-based Precodng almost keep the same wth the channel correlaton gettng stronger, and hgh spatal multpleng gan under strong correlaton channels s concevable. V. CONCLUSION In ths paper, we propose an cal precodng scheme based on SVD to solve the problem that t s dffcult to obtan hgh spatal multpleng gan under the strong correlaton MIMO channels n ndoor VLC sstem. Frst, the nformaton transmtted must be mapped from a specfc smbols constellaton to ensure that the sgnals are nonnegatve after precodng. Then, we decompose the ndoor VLC MIMO channels b SVD, whch can obtan the ndependent sub-channels to elmnate nter-channel nterference. Fnall, we solve the mzaton problem amng at the mnmum sstem and subjectng to the lmted total power to get the mal power allocaton matr, and allocate the power among the sub-channels accordng to the matr to reach the equal performance of each sub-channel, whch can decrease the sstem. The recever ads Mamum Lkelhood (ML algorthm to decode the receved smbols after shapng process, and recovers the nformaton b nverse smbols mappng. The sstem smulaton results ndcate that the of proposed SVD-based cal precodng scheme s sgnfcantl lower than ZF algorthm under dfferent correlaton channel. And wth the enhancement of channel correlaton, the performance remans n a relatvel low level, so t can obtan hgh spatal multpleng gan under the strong correlaton channels. Indoor VLC sstem has great nteror spatal resources. But the strong correlaton channels make t dffcult to acheve hgh spatal multpleng gan, whch becomes a lmtng factor to ncrease the data transmsson speed. The proposed SVD-based cal precodng scheme s just one wa to acheve hgh spatal multpleng gan. ow to make better use of nteror spatal resources n VLC sstem to obtan hgher spatal multpleng gan stll needs further stud. REFERENCES []. Elgala, R. Mesleh, and. aas, Indoor cal wreless communcaton: potental and state-of-the-art, IEEE Communcatons Magazne, vol. 9, no. 9, pp. 56-6, Sep. 0. [] M. Saad, L. Wattsuttkulkj, Y. Zhao et al., Vsble lght communcaton: opportuntes, challenges and channel models, Internatonal Journal of Electroncs & Informatcs, vol., no., pp. -, Feb. 03. [3] S. Schmd, G. Corbelln, S. Mangold et al., -to- vsble lght communcaton networks, n Proc. the fourteenth ACM Internatonal Smposum on Moble Ad oc Networkng and Computng, Bangalore, 03, pp. -0. [] J. Vucc and K. D. Langer, gh-speed vsble lght communcatons: State-of-the-art, n Proc. IEEE Optcal Fber Communcaton Conference and Eposton, and the Natonal Fber Optc Engneers Conference, Los Angeles, 0, pp. -3. [5] T. Q. Wang, Y. A. Sekercoglu, and J. Armstrong, Analss of an cal wreless recever usng a hemsphercal lens wth applcaton n MIMO vsble lght communcatons, IEEE Journal of Lghtwave Technolog, vol. 3, no., pp. 7-75, June 03. [6] M. D. Renzo,. aas, and P. M. Grant, Spatal modulaton for multple-antenna wreless sstems: a surve, IEEE Communcatons Magazne, vol. 9, no., pp. 8-9, Dec. 0. [7] S. G. Wlson, M. B. Pearce, and Q. Cao et al., Free-space cal MIMO transmsson wth q-ar PPM, IEEE Transactons on Communcatons, vol. 53, no. 8, pp. 0-, Aug [8] D. O'Bren, Mult-nput mult-output (MIMO ndoor cal wreless communcatons, n Proc. the Fort-Thrd IEEE Aslomar Conference on Sgnals, Sstems and Computers, Pacfc Grove, 009, pp [9] L. Zeng, D. O'Bren,. Mnh et al., gh data rate multple nput multple output (MIMO cal wreless communcatons usng whte lghtng, IEEE Journal on Selected Areas n Communcatons, vol. 7, no. 9, pp , September 009. [0] D. O'Bren, Optcal mult-nput mult-output sstems for short-range free-space data transmsson, n Proc. IEEE Internatonal Smposum on Communcaton Sstems Networks and Dgtal Sgnal Processng, Newcastle, 00, pp [] T. Fath and. aas, Performance comparson of MIMO technques for cal wreless communcatons n ndoor envronments, IEEE Transactons on Communcatons, vol. 6, no., pp , Feb. 03. [] L. Wu, Z. C. Zhang, and. P. Lu, Modulaton scheme based on precoder matr for MIMO cal wreless communcaton sstems, IEEE Communcatons Letters, vol. 6, no. 9, pp , September 0. [3] T. Kome, Fundamental analss for vsble lght communcaton sstem usng lghts, IEEE Transactons on Consumer Electroncs, vol. 50, no., pp , Feb. 00. [] T. A. Tran and D. O'Bren, Performance metrcs for mult-nput mult-output (MIMO vsble lght communcatons, n Proc. IEEE Internatonal Smposum on Communcaton Sstems Networks and Dgtal Sgnal Processng, Psa, 0, pp. -3. [5] L. Zeng, D. O'Bren,. L. Mnh et al., Improvement of date rate b usng equalzaton n an ndoor vsble lght communcaton sstem, n Proc. IEEE Internatonal Conference on Crcuts and Sstems for Communcatons, Shangha, 008, pp Qng-Feng Lu s currentl an assocate professor and a supervsor of postgraduate Student. Now, he s the assstant drector of Moble Communcaton Department for Natonal Dgtal Swtchng Sstem Engneerng & Technologcal R&D Center. s research nterests nclude wreless moble communcaton network and nformaton secrec. Shua-Fang Xao receved hs B.E. degree n electronc engneerng Department from Tsnghua Unverst. e s currentl a M.S. canddate at Natonal Dgtal Swtchng Sstem Engneerng & Technologcal Research Center. s research nterests are moble communcaton, sgnal processng and vsble lght communcaton. Ka-Zh uang was born n 973, who receved the Ph.D. degree n communcaton and nformaton sstem from Tsnghua Unverst. She s currentl a professor and supervsor of postgraduate students. Now, she s the assstant drector of Moble Communcaton department for Natonal Dgtal Swtchng Sstem Engneerng &Technologcal R&D Center. Dr. uang s servng as a leader of enan wreless moble communcaton nnovaton technolog team and ecellent technolog nnovaton group of General Staff eadquarters. er research nterests nclude wreless moble communcaton network and nformaton secrec. Zhou Zhong receved hs B.E. and M.S. degrees n 005 and 008 respectvel, from the Department of Communcaton Engneerng, Zhengzhou Informaton and Scence Insttute. Currentl, he s a Ph.D. canddate at the Natonal Dgtal Swtchng Sstem Engneerng & Technologcal Research Center. s research nterests le n the feld of codng theor, sgnal processng and phscal laer securt n wreless communcaton. 6