MIMO decorrelation for visible light communication based on angle optimization

Transcription

1 MIMO decorrelation for visible ligt communication based on angle optimization Haiyong Zang, and Yijun Zu Citation: AIP Conference Proceedings 80, (07); View online: ttps://doi.org/0.03/ View Table of Contents: ttp://aip.scitation.org/toc/apc/80/ Publised by te American Institute of Pysics Articles you may be interested in Wite LED visible ligt communication tecnology researc AIP Conference Proceedings 80, (07); 0.03/

2 MIMO Decorrelation for Visible Ligt Communication Based on Angle Optimization Haiyong Zang a) and Yijun Zu b) Institute of Information System Engineering, te PLA Information Engineering University, Zengzou 45000, Cina. a) Corresponding autor: b) Abstract. Recently, many researcers ave used te normal vector tilting to solve te problems about low rate of multiplexing and cannel strong correlation in Visible Ligt Communication Multiple-Input Multiple-Output (VLC- MIMO) system, but tey all lack of te teoretical support. In tis paper, we establis a cannel model about VLC- MIMO, ten translate te communication problem about vector tilting optimal angle in a certain range into a matematical problem about seeking te minimum value of function. Finally, we deduced te matematic expressions about te optimal tilting angles of corresponding LEDs and PDs, and tese expressions will provide a teoretical basis for te furter study. Key words: Visible Ligt Communication (VLC); Cannel Decorrelation; Angle Optimization; Teoretical Derivation. INTRODUCTION Visible ligt communication (VLC) uses te ligt-emitting diodes (LEDs) to transmit information by ig-speed ligt and dark flasing, and expands te wireless spectrum wic up to 400THz. Wit te popularity of LED, indoor VLC raises many inspiring discussions in te past few years [, ]. For te LEDs wit limited bandwidt in VLC system, multiple-input multiple-output (MIMO) is one of te most effective ways to increase te transmission rate [3]. But for te system about VLC-MIMO, te interference between signals is very large wen te distance between te transmitting array and receiving array decreases, te transmission distance becomes faraway, te receiver mobility increases and so on. In recent years, many scolars ave focused on tis problem about reducing te interference between te spatial signals by optimizing te normal vector element direction. In [4-], te normal vector directions of te PDs are distributed according to te pyramid and te emisperic. Tis sceme will reduce te interference between te signals and improve te mobility of te receiving array; In [7-8], a PD wit normal vector inclination angle of 45 revolves around te Z axis to get directions about four PDs, ten te elevation angle of eac PD is adaptively adjusted from 0 to 45 to maximize te rank of te cannel matrix; In [9], several different PDs wit small field of view angle replace a PD wit big field of view angle. Tis metod reduces te background noise and te multipat effect as muc as possible, owever it doesn t reduce te overall field of view angle. In order to reduce te correlation of MIMO cannels, researcers proposed a lot of metods about altering te array element normal vector distribution. But tey didn t deduce te optimal tilting angle of te element normal vector by teoretical analysis, so te metods lack of teoretical support. In order to facilitate te furter study and perfect te teoretical system of te normal vector tilting, tis paper deduces te expressions of te optimal tilting angles about te normal vectors of VLC-MIMO system by teoretical analysis. Advances in Materials, Macinery, Electronics I AIP Conf. Proc. 80, ; doi: 0.03/ Publised by AIP Publising /$

3 CHANNEL MODEL Assuming tat te VLC-MIMO system as M LEDs to transmit signals X x, x,, x M receive signals,,, T Y y y y N Were =,,, T, M and N PDs to,, te cannel gain matrix is H. Te signal vector Y can be expressed as Y HX X N () XN n n,n n T N denotes independent identically distributed (i.i.d.) AWGN. From (), we can observe tat te i-t, i =,... N, receiving signal can be rewritten as follows M i ii i j, ij ij j i () y x x n were ii represents te diagonal element of te cannel matrix or te cannel matrix after elementary transformation, te tree sum items represent a useful signal, te sum of all te spatial interference signals and noise respectively. Te bit error rate (BER) of communication system is reduced by optimizing te vector direction of te array element, namely, tis metod reduces te signal power ratio of te second part and te first part in(), tereby reduces te biggest Interference-to-Signal Ratio (ISR) of te received signal. We assume tat te average power of eac LED is equal, and ten, te ISR of eac PD can be expressed as i M j, i j ij ii i N (3) In tis paper, te electrical modulation is unipolar K-PAM (Pulse Amplitude Modulation); te receivers adopt zero-forcing detection, tereby te received signal vector can be expressed as xˆ EqZF y, were H H EqZF ( H H ) H ( ) is te zero-forcing equalizer. MIMO multiplexed cannels in AWGN can be considered as parallel AWGN cannel, ten te teoretical BER can be expressed as [0]: BER r K 3iRSNRlog K Q rk i K K (4) Were r is te rank of H, is te i-t eigenvalue of H H H, i Qu t dt. antenna, and exp u THEORETICAL ANALYSIS R SNR is te average electrical SNR per transmit Te MIMO wit large-scale array will be te future development of VLC. So reducing te array size and improving te number of elements is very important, but tey lead to tat te VLC cannel as strong correlation. Based on VLC-MIMO, tis paper derives te teoretical optimal tilting angles of te array elements by minimizing te biggest ISR. Tis paper establises te VLC-MIMO model, suc as Fig.. We assume tat tere is a lot of parameters be known, suc as d represents te separation distance between LEDs, m represents te order of te Lambertian LED

4 emission, dpd represents te separation distance between PDs, represents te receiver area of te PD, represents te vertical transmission distance, represents te deviation angle between te LED array and te PD array and so on. A LED dled LED ω ω α ω ω d d d d PD dpd PD FIGURE. Te cannel model of VLC-MIMO. We optimize te tilting angle of te element normal vector base on VLC-MIMO. Te expression of te cannel matrix can be written as H (5) Were ij represents te MIMO cannel gain between te j-t transmitter antenna and te i-t receiver antenna, and it can be written as m A cos cos, i j m ij j ij i ij dij () Were j and i represents te tilting angle of j-t LED and i-t PD respectively. Tilting te normal vector reduces te interference between te spatial signals by adjusting te j and i, and ten, reduces te ISR. Terefore, te communication problem about reducing signal interference can be seen as te functions,,, and,,, taking minimal value, were te domain of definition about variables -, - FOV, FOV can be written as and. -, - FOV, FOV Wen te average power of eac LED is equal, te ISR can be written as m d cos cos = m d cos cos m d cos cos = m d cos cos (7)

5 ,,, and,,, follows. take extreme value in te feasible domain, ten we can get two cases, as () We only optimize te PD normal vector tilting angles, i.e. = =0, tereby we ave 4m d cos = sin 4 m d cos d cos 4m = sin 4m d cos (8) -FOV a) If te PD array is on te rigt side of te center of te LED array, we ave ; FOV FOV b) If te PD array is on te left side of te center of te LED array, we ave ; -FOV FOV c) If te PD array is under te LED array, we ave. FOV () We only optimize te LED normal vector tilting angles, i.e. = =0, te best tilting angles of LEDs can be written as or or or. Te optimal tilting angles of LEDs are determined by comparing te biggest ISR wit te above angles, in oter words, te optimal tilting angles make te biggest ISR smaller. Proofs see Appendix. SIMULATION EXPERIMENT In te VLC system, te separation distance between te PD elements and te relative position of te transceivers influences te result of te optimization normal vector tilting angle. So we will simulate te teoretical optimal value of te tilting angles wen altering te factors, ten we can see tat te teoretical optimal value bring some advantage about te BER of te communication system. Simulation conditions: te LEDs spacing is.5m, te alf-power angle of LED is 0, te PD effective pysical area is mm, and te vertical transmission distance is.5m. In order to demonstrate te validity of te angle expressions, we compare te teoretical optimal angles wit te exaustive searc optimal angles ten get a lot of data as sown in Table and Table. From te tables, we can see tat te teoretical optimal value equals te exaustive searc optimal value approximately, tereby te correctness of te expressions can be verified. In VLC system, tere are two objects can be tilted, i.e. LED array element and PD array element. In tis paper, we compare te improvement of BER after optimization to determine te best optimization object. As sown in Fig., wen te separation distance between PDs is 0cm and te PD array is sifted by 40 to te rigt of te LED array, te BER can be improved by 5dB wen optimizing te tilting angles of PDs, but tere is almost uncanged wen optimizing te tilting angles of LEDs. So tis paper optimizes te PD array elements. Comparing te Fig. wit Fig.3, we can see tat te performance improvement becomes greater wen decreasing te separation distance between PDs. If te PD normal vector direction is perpendicular to te orizontal plane, te BER is gradually becoming larger wen increasing te deviation degree of PD array, suc as Fig.4. It also can be seen from te Fig.4 tat te performance improvement becomes greater by optimizing te tilting angles of PDs wen increasing te PD array deviation degree

6 TABLE. Te tilting angles of PDs Deviation angle α Exaustive searc optimal value, (40,40 ) (-,4 ) (-85,0 ) Teoretical optimal value, (43.88, ) (-0.79, ) ( ,9.45 ) TABLE. Te tilting angles of LEDs Deviation angle α Exaustive searc optimal value, (-0,-0 ) (-3,-4 ) (-48,8 ) Teoretical optimal value, (-0.955, ) ( , ) ( ,-8.80 ) Notation: Minus represents tat te tilting direction is contrary to te direction from te luminous beam to normal vector. 0 0 =40 o, d PD =0 cm 0 - BER vertical incline-pd incline-led SNR(/dB) o FIGURE. Compare te BER wen =40 and d 0cm. PD 0 0 =40 o, d PD =5 cm 0 - BER vertical incline-pd incline-led SNR(/dB) o FIGURE 3. Compare te BER wen =40 and d 5cm. PD

7 0 0 d PD = 5 cm 0 - BER 0 - vertical(=0 o ) 0-3 inclinepd(=0 o ) vertical(=0 o ) inclinepd(=0 o ) vertical(=40 o ) inclinepd(=40 o ) SNR(/dB) FIGURE 4. Compare te BER about different FOV. CONCLUSION In order to solve te problem tat te tilting angles lack of teoretically supported in VLC-MIMO, tis paper transforms te communication problem into a matematical problem, tereby deduces te matematic expressions about te optimal tilting angles of te PD array elements and te LED array elements in VLC-MIMO. However, tis paper only deduces te tilting angle expression about te element normal vector of a simple VLC- MIMO system wit two transmitters and two receivers. Te number of array element is too few to satisfy te development of VLC-MIMO. So our next step will increase te number of transceiver elements, ten deduce te best normal vector tilt angles. ACKNOWLEDGMENTS Tis work was supported by te national natural science fund under Grant 753 and Grant REFERENCES. H.Elgala, R. Mesle, and H. Haas, Indoor optical wireless communication: Potential and state-of-te-art, IEEE Commun. Mag., vol. 49, no. 9, pp. 5-, Sept. 0.. Jovicic, J. Li, and T. Ricardson, Visible ligt communication: opportunities, callenges and te pat to market, IEEE Commun. Mag. 5(), 3 (03). 3. L. Zeng, D. O Brien, H. Min, G. Faulkner, K. Lee, D. Jung, Y. O, and E. T. Won, Hig data rate multiple input multiple output (MIMO) optical wireless communications using wite LED ligting, IEEE J. Sel. Areas Commun. 7(9), 54 (009). 4. Nuwanpriya A, Ho S W, Cen C S. Indoor MIMO Visible Ligt Communications: Novel Angle Diversity Receivers for Mobile Users [J] Nuwanpriya A, Ho S W, Cen C S. Angle diversity receiver for indoor MIMO visible ligt communications[c]//globecom Worksops (GC Wksps), 04. IEEE, 04: Saff E B, Kuijlaars A B J. distributing many points on a spere [J]. Te matematical intelligencer, 997, 9(): Faamuel P, Tompson J, Haas H. Improved indoor VLC MIMO cannel capacity using mobile receiver wit angular diversity detectors[c]// Global Communications Conference (GLOBECOM), 04 IEEE. IEEE, 04: Cen Z, Serafimovski N, Haas H. Angle Diversity for an Indoor Cellular Visible Ligt Communication System[C]//Veicular Tecnology Conference (VTC Spring), 04 IEEE 79t. IEEE, 04: CAO Jia-nian, LIU Zuo-yue. Angle diversity and effective ig speed indoor optical communication [J]. Journal of Harbin Engineering University, 009 (): J. G. Proakis, Digital Communications [M]. 5t ed. McGraw-Hill,

8 For te VLC-MIMO system, from Fig., we ave d dled dpd tan d dled + dpd tan and d dled + dpd tan d dled dpd tan can be expressed as So ij APPENDIX arccos( d ) arccos( d ). arccos( d ) arccos( d ) m A cos cos, (9) i j m ij j ij i ij dij Were j and i represents te tilting angle of j-t LED and i-t PD respectively. In tis paper, te optimal tilting angles of te array elements are deduced by minimizing te biggest ISR of PDs, i.e. min max,,,,. Ten te optimization problem can be transformed into a minimum value problem of d cos cos = matematics, namely, te function d cos cos ( m ) find te minimum value in d cos cos = d cos cos te domain of definition -, and - FOV, FOV respectively. -, - FOV, FOV () Wen we only optimize te PD normal vector tilting angles, i.e. = =0, tereby we need to solve te mat problem about finding te minimum value for - FOV, FOV. - FOV, FOV By taking te derivative, we ave d cos cos = d coscos d coscos = d cos cos witin d cos = sin( 3 ), =0 d cos d cos = sin( 3 ), =0 d cos (0)

9 From te Fig., we can see tat te PD array is on te rigt side of te center of te LED array, tereby we ave () From (0) and(), witin te domain of definition, we ave >0 =0 <0 =0 () So te optimal tilting angles of PDs can be written as -FOV FOV (3) Te same procedure may be easily adapted to obtain te optimal tilting angles for any oter cases. Wen te PD array is on te left side of te center of te LED array, we ave So (4) FOV -FOV (5) Wen te PD array is under te LED array, we ave () So FOV FOV (7) () Wen we only optimize te LED normal vector tilting angles, i.e. = =0, tereby we need to solve te mat problem about finding te minimum value for -, witin. -, By taking te derivative, we ave d cos cos d cos cos d cos cos d cos cos

10 d = cos sin 3 d cos d = cos d cos sin d = cos sin d cos d = cos 3 d cos sin (8) (9) Making (8)and (9) equals to 0. We can get te stationary point of, and,, as follows: and. In order to make te and be minimum, tere are four possible values, i.e. or or or. Taking te four points into te function to compare te corresponding and, and ten, te best tilting angles equal to te angles wic make te maximum ISR smaller