Orbital-angular-momentum mode-group multiplexed transmission over a graded-index ring-core fiber based on receive diversity and maximal ratio combining

O r b i t a l - a n g u l a r - m o m e n t u m m o d e -g r o u p m u l t i p l e x e d t r a n s m i s s i o n o v e r a g r a d e d - i n d e x r i n g - c o r e f i b e r b a s e d o n r e c e i v e d i v e r s i t y an d m a x i m a l r a t i o c o m b i n i n g J UNWEI Z HANG 1 † , G UOXUAN Z HU 1 † , J IE L IU 1,* , X IONG W U 1 , J IANGBO Z HU 2 , C HENG D U 3 , W ENYONG L UO 3 , AND S IYUAN Y U 1,2 1 State Key Laboratory of Optoelectronic Materia ls and Technologies, School of Electronics a nd Information Techn ology, Sun Yat-Sen University, Guangzhou 510006, China 2 Photonics Group, Merchant Venturers School o f Engineering, University of B ristol, Bristo l BS8 1UB, UK 3 Fiberhome T elecommunication Technologies Co. Ltd,Wuhan, 4 30074, China † These authors contributed equally to this work. Abstract : An orbital-angular-mo mentum (OAM) m ode-gro up multiplexing (MGM) scheme based on a g raded-index ring-core fibe r (GIRCF) is proposed, in which a single-inp ut tw o- output (or receive diversity) a rchitecture is designed for e ach MG channel and simple digital signal processing (DSP ) is util ized to adaptively resist the mode par tition noise resulting from random intra-gro up mod e crosstalk. There is no need of complex multiple-inp ut multiple- output (MIMO) equalizati on in this scheme . Fu rthermore, the signal-to- noise ratio ( SNR) of the received sig nals can be improved if a simple maximal ratio combining (MRC) techniq ue is employed on the receiver side to efficie ntly take advantage of the d iversity gain o f re ceiver. Intensity-mod ulated direc t-detection (IM-DD) systems transmit ting three OAM mod e groups with total 100-Gb/s discrete multi-to ne (DMT) signals over a 1-km GIRCF and two OAM mode groups with total 40 -Gb/s DMT signals over an 18-km GIRCF ar e e xperimentally demonstrate d, respectively, to confirm the feasibility of our proposed OAM- MGM scheme . OCIS codes: (060.2330) Fiber Optics Communicatio ns; (060.2270) Fiber c haracteriz ation; (060.4230) Multiplexing. References and links 1. D. J. R ichards on, J. M. Fini, and L. E. Nelson, “Space-division multiple xing in optical fibres,” Nat. Photonics 7 (5), 354–362 (2013). 2. N. K. Fontaine, R. Ryf, H. Chen, A. V. Beni tez, B. Guan, R. Scott , B . Ercan, S. J. B. Yoo, L. E. Gr üner- Nielsen, Y. Sun, R. Lingle, E. Antonio-Lo pez, a nd R. 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Golowich, “On the scalability of ring fiber designs for OAM multiplexing,” Opt. Express 23 , 3721–3730 (2015). 1. Introduct ion Space-d ivision multiplexing (SDM) in optical fiber ha s re cently been intensively investigated, aiming for solving the current single mod e fib er (SMF) capa city crunch by utiliz ing the spatial or mode domain of light [1]. Among various SDM schemes, mode-div ision multiplexin g (MDM ) techniq ues based on mult i-mode fibers (MMFs) or few-mod e fibers (FMFs) can increase the number o f transmission channels within a limited aperture a nd thus increase the capacity de nsity of a single fiber cor e [2–4]. I n addition, the design of a mplifiers, switches and other inline co mponents in MDM schemes can be highly comp act, which makes the scaling of optical networ ks more cost effective and energy efficient [4, 5 ]. The main limitations of MMF-based MDM systems are the cr osstalk a nd d istortion resulting from mode coupling a nd mod al dispe rsion during fiber transmis sion. In lo ng-haul MDM systems, crosstalk between all mode pairs is non-negligib le [6]. As a result, adap tive full-size multiple- input multiple-output ( MIMO) equalization is required , in which case the fiber in the strong- mode-coup ling regime is e ven more desirable to dec rease the differential group delay (DGD) and t hus r educe the complexity o f MI MO p rocessing in these systems [7]. However, on the other hand, in short -reach ap plications ( e.g. intra-data- center networ k, lo cal area networ k, access networ k, etc.), intens ity-modulated direct-dete ction (IM-DD) schemes without MI MO processing are pre ferred, co nsidering the system cost and p ower co nsumption [8]. Wea kly coupled MDM sch eme can be co nsidered as o ne o f the most pro mising solutions to increase the capac ity of short- reach transmis sion systems, since modal cr osstalk and dispersion can be neglected for sho rt-reach transmissio n and the need of coherent op tical detection and MIMO processing c an thu s be eliminat ed [9, 10]. Ho wever, reducing m ode co upling among all the fiber modes, especially t he (quasi-)degenerate modes, over > 2-km fiber distance still re mains a challenge in these schemes . Given the increasi ng mode co upling in MMFs over d istance, Mode-group multiplexing (MGM) [11] emer ges as an alternativ e for MIMO-fre e MMF transmissio n, in which (q uasi-) degenerate modes w ithin each mode gro up ( MG) a re re garded as one data channel . T he weak- coupling stra tegy can be employed between d ifferent MGs to eliminat e the need of coherent detection and MI MO processing at the receiver s. Several MGM schemes have be en implemente d b ased on conventional MMFs, in which all the de-m ultip lexed intra -group modes should be de tected simultaneou sly at the receiver to avoid the mode partition noise resulting from the r andom intra-group mode crosstalk [12–14]. However, a s the numbe r of intra-gro up mod es of the MMFs linearly increases with the MG order [as shown in Fig. 1(a)], receptio n of high-order MGs will become in creasingly comple x, w hich limits scalability of the MMF-based MGM systems. Fig. 1 . Diagrams of (a) intensity of the linearly polarized (LP) modes i n each mode group (MG) of t he multimode fi ber (MMF); (b) intensity of the LP modes in each MG of the ring-core fiber (RCF); (c) intensity and phase of the OAM modes in each M G of the RCF. Here note t hat each fiber mode shown in this figur e can b e further subdivided into two modes with orthogonal polarizations. Ring-core-fibe r (RCF) based MGM systems have been reported re cently [15–17] . W ith the ring-core profile a llowing for only sin gle-radi al-order mode s, a fixed number o f degenerate modes are supported by the RCFs for each high o rder M G [a s shown in Fig. 1(b) and (c)] , which d ecreases the complexity of the high-order MG detection. In ad dition, the coupling strength between a djacent MG s o f the RC Fs decre ases significan tly with the increasing azimuthal mode order [18]. These characte ristics p rovide RCFs wit h a highe r scalability in the o ptical mode space. Besides, both the linearly polariz ed (LP) and orbital angular momentum (OAM) mode b asis can b e utilized for MGM in RC Fs. MG (de)multip lexing of th e RCF-based MGM schemes that have been reported is main ly b ased on we ighted compo site phase masks, in which the re lative amplitude and phase o f all intra- group mod es should b e measured at the receiving end [15–17]. However, as the relative amplitude and phase of the intra- group mod es change randomly d uring fiber transmission, adaptive measurement or evaluation of the amplitude and phase d istribution of d egenerate modes in optical domain may be quite difficu lt in pr actical impleme ntations. Therefore, in this p aper, an OAM-MG M system over a g raded-index r ing-core fiber (GIRCF) base o n a receive-diversity s cheme is pro posed. In the receive-diversity scheme, a single-input two-outpu t architectu re is designed for each MG channel and simple digital signal pr ocessing ( DSP) is utilized t o ada ptively r esist the mod e pa rtition noise induce by random intra- group mode cro sstalk. There is no need of ad aptive MIMO e qualization in this scheme. Furthermor e, a simple maximal ra tio combining (MRC ) technique can be utilized at the receiver of this sche me to efficiently take ad vantage of the diversity gain o f r eceiver and improve the signal -to-noise ra tio (SNR) of the r eceived signals. In o rder to prove the feasibility of the p roposed OAM -MGM scheme, intens ity-modulated direct-de tection (IM- DD) systems transmittin g three OAM m ode groups with total 100-Gb/s discrete multi-to ne (DMT) signal s over a 1-km GIRCF and two OAM mode groups with to tal 40-Gb/s DMT signals over an 1 8-km GIRCF are exper imentally de monstrated, respe ctively. The meas ured results show that by using the receive-d iversity architectur e and MRC techniq ue, there will be an average of ~3 dB improvement of sensitivity at the B ER of 3 .8×10 -3 for both of the OAM- MGM system o ver 1-km and 18-km GIRCF, compa red with that in the O AM-MGM system based on sin gle-PD detectio n. In add ition, when the rec eive-diversity architectu re is utilized, MRC-based system p erformance is superior to that of the system with equal ratio co mbining (ERC), especia lly in the case that there is a great difference of BER performanc e between the two rec eived branches. 2. Proposed OAM-M GM scheme The block diagram of the pr oposed O AM MGM is shown in Fig. 2. For each MG, op tical light at a fixed waveleng th is intensity modulated by an electrical signal to generate the optical signal at the transmitter. Consider ing the li near or quasi-linear relationship between the optical light intensity and the ele ctrical signal, the electric field o f the intensity modulated optical signal for the i th MG can be expr essed as: 0 ( ) 0 ( ) [ ( )] i j t i i i i i E t A V V t e       (1) where   ,   and   denote the amplitu de, frequency and phase of the op tical carrier, respectively, whil e   is the ratio be tween optica l p ower and electr ical power before a nd after electro-op tic conversion at the tr ansmitter of i th MG and here can b e considered as a constant. V i0 and V i (t) refer to the DC a nd AC components of the electrical signal carried by the i th MG channel, respectively. T he generated o ptical sig nals o f all MGs a re launch ed to their respective SMF input ports of the OAM multiplex er. Here note that, for each OAM MG that includes fou r degenerate OAM mod es < ± l , ± s > ( ± s b eing the left- o r right-hand circular polariza tions and ± l being the azimuthal mode order) [1 9], only one OAM mode is e xcited at the transmit ter, as shown in Fig. 2. Then the op tical signals are O AM mode converted and multiplexed with an OAM multiplexer (OAM mux, e.g. the OAM mode sorter [20] ), and finally couple d to the GIRCF. Since the GIRCF here is d esigned with large inter-g roup effective index d ifferences but very small e ffective inde x differences be tween intra- group modes [ 19], rando m intra-gro up mode crosstalk result ing from strong modal coupling is inevitable during fiber transmission , while there is only low coupling between different MGs. As a result, all the four intra-gro up modes should be simul taneously detecte d at the recei ver to avoid the mode partitio n noise, while small p ower loss due to weak coupl ing between M Gs, which is pr oportional to the fiber length and does not vary with time randomly [21] , can be neglected. The e lectric field of four de generate modes in the i th MG after a certa in–distance GIRCF tra nsmission can b e expressed as: 0 , , ( ) OA M , 0 ( ) [ ( )] l m l m j t jl l m i i i E t A V V t e e          (2) where l equals to ± i (the azimuthal mode order) and m equals to ± s (the left- or right-hand circular p olarizatio ns). ' th and ' th denote the amplitude and p hase of the OAM l,m mode, respectively, whose valu es rando mly change in time because of rando m crosstalk between intra-gro up modes.  is the azimuth al a ngle. As p ower loss o f the i th MG resulti ng from fiber loss a nd inter-g roup crosstalk is rel ated to the fiber length , give n a certa in fiber structure and length, the to tal optic al power of a ll the four mod es of the i th MG: , 2 MG O AM 2 0 , 0 ( ) [ ( )] [ ( )] i l m l i m s i i i l m i i i l i m s P E t V V t A C V V t                     (3) where C is a constant. As a result, the to tal o ptical p ower o f the i th MG is pro portional to the electrical sig nal, which theoretically proves that the mode pa rtition noise due to rando m modal crossta lk can be eliminat ed when a ll the four intra-gro up mode s are simultaneo usly power de tected. After mo de converted and demultiplexed by the OAM demultip lexer (OAM demux), two polariza tion m ultiplexe d f undamen tal modes at e ach SM F output port of the OAM demux, which are converted from the two OAM modes with the same azi muthal mode order but orthogonal po larizations, respectively, a re d etected by one photo de tector ( PD). Co nsidering the different power response of the two received branches, the detected photo current after square-law d etection of the i th MG is , , 2 2 MG OAM OAM 2 2 0 , , ( ) ( ) [ ( )]( ) i i m i m i i m s m s i i i i i m i i m m s m s I S t S t E E t A A                                 (4) where μ +i and μ -i are respo nsivity of the two rec eived br anches, re spectively, conside ring power response of both the opt ical tr ansmission paths and PDs. Here note that op tical b eams from SM F ± i output por ts of the OAM demux a re not dire ctly added together in optical domainand detecte d by a same PD in ord er to avoid o ptical interf erences between non- orthogonal modes. From Eq. (4 ), o ne can see that if signals from the tw o received branches of the i th MG are d irectly combined, the d etected electrical signal is no longer propo rtional to the optical po wer, due to the d ifferent p ower response of the two rec eived bra nches. In ad dition to the po wer response d ifference, there are other two kinds o f channel impairments to the two-branch signal reception of the i th MG: 1 ) the relative delay be tween the two r eceived branches induced by the differential moda l delay, which will de synchronize the rec eived signals from the two different branches; 2) randomly varied signal-to-noise ratio (SNR) of the two received signals caused by the r andom power coupling between the ± i OAM m odes, which will de teriorate SNR per formance of the detected signal if electric al signals of the two received b ranches are d irectly adde d together with equal weight. In order to deal with these pro blems, l ow-complexit y digital signal pro cessing (DSP) should b e employed in the electrical domain, as sho wn in Fig. 2. For each r eceived br anch of the i th MG, electrica l signal from the PD is first d igitalized b y an analog-to-d igital converto r (ADC) and then laun ched to the DSP module. In the DSP mod ule, after resample d and symbol synchronized , sig nal of each rece ived br anch of the i th MG is equaliz ed us ing either time domain equaliz ation (TDE) or frequency domain equalization (FDE) algorithms [8] to compensate the disto rtions resulting from the differential modal d elay and c hromatic dispersion. Here note that the TDE or FDE is implemented for the single-cha nnel equalization rather than MI MO eq ualization , while the former has a much lo wer ca lculation complexity [8, 22]. In or der to max imize the SNR of the received signal r egardless of the po wer fluctuation and the respo nsivity difference of the two received branches , the two equalized and demodulated signals of the same MG are combined by using a simple MRC a lgorithm [23]. The MRC o utput of the n th symbol f or each data frame is ( ) ( ( ) SNR ) / S NR l l l l i l i z n y n         (4) where ( ) z n is the combined signal o f the n th symbol used for final symbol decisio n and demapping to obtain the bit d ata of the i th MG,    with l = ± i a re two eq ualized signals of the n th symbol, and SNR l with l = ± i are the probed SNRs o f the two eq ualized sig nals obtained by training symbo l and assumed to be q uasi-time-inva riant within o ne signal frame . It should be noted that this MRC algorithm can be executed to combine two depe ndent signals, either in the time d omain for p ulse-amplitud e modulatio n (PAM) and carri er-less amplitude and phase (CAP) modulat ion, o r in the frequency do main for DM T modulat ion before final symbol decision at the r eceiver. It is noted that in the proposed OAM-MGM scheme only two received branches rather than four branches for the signal reception o f each high order MG in ord er to d ecrease the rece iver complexity. Alth ough equal-we ight combinatio n o f s ignals carrie d by the two polarization multiplexed modes in each received branch might deterio rate the SNR performance of the rec eived signals , there sho uld be a trade-off between the signal performan ce and the system c omplexity in pra ctical implementa tions. Fig. 2. Block diagram of t he proposed OAM mode-gr oup (de)m ultiplexing scheme. SMF n : the single mode fiber input/output port fo r the n th OAM modes; MG n : the n th OAM mode group including OAM modes < ± l , ± s>; Normal.: Normalization; Resamp.: resampling; demod.: demodulation . 3. Fiber design and characteriz ation For proof-of-concep t demonstratio n of the p roposed OAM-MGM sch eme, a GIRCF supporting mode group ord er up to | l | = 4 is designed and fabricated . As shown in Fig. 3 (a), the GIRCF has a par abolic index p rofile o ver the ring-core width to: 1) p rovide large inter- MG differential effective refractive indices (Δ n eff ) a nd lo w intra-MG Δ n eff thereby de-couplin g MGs and decrea sing d ifferential modal d elay between intra-MG mod es[see Fig. 3(b) and (c)], 2) soften the r adial index gradient thus making the fiber less susceptible to pe rturbations such as micro -bending [2 4], and 3) e liminate the spin-orb it-coupling-induced mode p urity impairment [25 ] by removing the step refractive ind ex (RI) interface . It can be seen from Fig. 3(a) that the maximum mate rial RI d ifference ∆ n is around 0. 027, the ring-core radius is around 6.6 μm and the ring-core width is around 3.3 μm. T he c alculated ef fective RI of all guided OAM modes and the calculate d/measured DGD at the wavelength of 1550 nm are illustrated in Fig. 3(b ) and (c) , respectively. The Δ n eff and DGD between adjacent MGs increase with the to pological order of MGs, and high o rder MGs (| l | > 1), which will be selected for the demonstrati on below, pr omise a higher resistance to inter-M G crosstalk. In addition, the very low intra-MG DGD for all MGs (from both c alculation a nd measureme nts) indicates a lo w memory-siz e requiremen t on channel equalization. Fig. 3. (a) The refractive index profile of GIRCF; (b) effective i ndices of MGs in the GIRCF at the wavelength of 1550nm; (c) calculated and measured DGD at the wavelength of 1550 nm. The GIRCF is f abricate d by using a conventional plasma enhanced c hemical vapor deposition (PECVD) process. The meas ured a verage p ropagation attenuation of this fiber is 0.75 dB /km at 15 50 nm. This high loss might be caused b y the imperfections on two grad ed index interfaces of the ring cor e. The sub-system consisting of t he GIRCF and the OAM (de)multip lexer (Mux/Demux) devices (i.e., the part in the ce ntral dashed box in Fig. 4) is also built to characte rize the c rosstalk amongs t higher order MGs experime ntally. T he measured results o f the 1-km and 18.4-km GIRCF based systems ar e sh own in Table I and II, respectively. It can be deduced consequently that the p ure in-fiber mode-coup ling induced crosstalk between MGs | l | = 3 & 4 over a 17.4-km GIRCF is ~ -9. 65 dB in average, whil e that between MG s | l | = 2 & 3 is ~ -7 .58 dB. Conside ring the rela tively larger inter-MG cr osstalk between MGs | l | = 2 & 3 in the 18.4-km GIRCF based system, the two high-order MGs | l | = 3 and 4 are selected for the OAM-MGM transmission, while three MGs | l | = 2, 3 and 4 in the 1- km GIRCF based system are utilized for data transmission d emonstration (details will b e discussed in next section). Table I. The static inter-MG crosstalk (in dB) o f entire o ptical system with 1-km GIRCF. 1-km GIRCF Destination MG | l |=1 | l |=2 | l |=3 | l |=4 Source MG | l |=1 0 -4.43 -15.03 -18.57 | l |=2 -5.09 0 -11.26 -18.04 | l |=3 -17.36 -11.94 0 -14.05 | l |=4 -20.99 -17.29 -13.8 0 Table II. The static inter-MG c rosst alk (in dB) of entire optical system w ith 18.4-km GIRCF. 18.4-km GI RCF Destination MG | l |=2 | l |=3 | l |=4 Source MG | l |=2 0 -5.19 -7.66 | l |=3 -7.33 0 -8.68 | l |=4 -8.39 -7.9 0 4. Data transmission demo nstration An IM-DD DM T tra nsmission system is built for the d emonstration of the proposed OAM- MGM scheme. The experimental setup is sh own in Fig. 4. A t the transmitte r, the input data bit se quences are firs tly mapp ed into quadr ature amplitude modulation (QAM) symbols. Aft er serial-to-par allel ( P/S) conversio n, the QAM symbols a re c onverted to time domain b y 2536- point inverse FFT (IFFT). In ord er to generate a real-val ued DMT signal, the 9th – 26 4th subcarr iers and the 2 029th – 1774th subcar riers are used to carry the effective payloa ds and their comple x conj ugates, respectively. T hen 48-po int cyclic prefix (CP ) padding, parallel-to- serial (P/S) conversion and hard clip ping are p erformed. For each DMT frame , 11 tr aining symbols ar e inserted at the b eginning o f the data frame, which consist of 1 symbol for timing synchronizatio n and 10 symbo ls for channel estimatio n and SN R p robing. By using an arbitrar y w avefor m generator (AWG) operating at a sample ra te of 60-Gsa/s, the ele ctrical DMT signal with an effective bandwidth of 10-GHz is generate d. Aft er amplification, the electrical signal is utilized to modulate optical l ight a t wavelengt h o f 1550.9 2 nm thou gh a Mach-Zehnde r modulator (MZM) to generate double -sideband op tical signal . T hen the generated optic al signal is split into three branches , ea ch of which is amplified by an erbium doped fiber amplifie r (EDFA) and de layed by a single mode fiber (SMF) wi th large relative length from other two branches for data pa ttern decor relation. Fig. 4. Experimental se tup. AWG: arbitrary wavef orm generator; PC: polarization contro ller; MZM: Mach-Zehnder modulator; OC: optical coupler; SMF: single-mode fiber; LP: linear polarizer ; SLM: spatial light modulator; PBS: polarizing beam splitter; HWP: half-wave plate; QWP: quar ter-wave plate; Col.: collimator; BS: beam sp litter; VPP: vortex phase plate; VOA : variable optical attenuator; EDFA: erbium doped fiber amplifier; BPF: band pass filter; PD: photo detector; OSC: oscilloscope. After being co llimated and linear ly polar ized, the Gaussian b eams from the three SMF branches are co nverted to OAM modes of l = +2, +3 and +4, r espectively, by using the phase- only spatial light modulat ors (SLMs). Here note that d ue to the device limitatio n, conversions of OAM modes of l = +3 and +4 are realized by spatially sharing o ne SL M. By employing a polariza tion bea m splitte r (PBS), the two OAM beams o f l = +3 and +4 possessing orthogonal linear-pola rizations are combined w ith low loss . Then the two multiple xed OAM bea ms ar e combined with the OAM bea m of l = +2 by a beam splitter. The gen erated three coa xial OAM beams ar e converted into circular polarization states thro ugh a quarter-wav e plate (QWP) before coupled into the GIRCF, since the eigen OAM state in ring-core fiber is circular polarize d. After GIRCF tr ansmission, all output modes from the fiber are converted into linear p olarizations and split into two branches . In each b ranch, the OAM beams are converted to the Gaussian beams by a vortex phase plate (VP P) and then c ollimated to the SMF p igtail for photo-electric detection. Here it should be noted that the two received branches are used for dete ction of ± l OAM mo des, respe ctively, for the receptio n of the l th MG. In each received br anch, the o ptical signal is detected by a n optic ally pre -amplified receiver, which co nsists of a variable optical a ttenuator (VOA), an EDFA followed by a n optical band-pass filter and a PD. Then the dete cted elec trical signals are d igitized and stored by a real time oscillosco pe (OSC) with a sampling rate of 100 G sa/s and finally processed b y off-lin e DSP includi ng r esamplin g, timing synchron izati on, seri al-to -paral lel (S/P) con version , FFT, one-tap channel equalizatio n, per-sub carrier MRC [23], demap ping and error counting are used to process the d ata. We pe rformed two sets of MGM transmission over the GIRC Fs: tra nsmission of three OAM M Gs over a 1-km GIRCF and two OAM MGs over an 18-km GIRCF. The back-to- back co nfiguration has also been impleme nted wi th a sh ort length of GI RCF (~2- m) between the OAM MU X and DEMUX for syste m performance comparison, and the BE R for each MG are meas ured and evaluated individuall y. Fig. 5(a)-(c) show the measured BER result s as a function of the r eceived optical power (ROP) of the first MGM transmission system, in which three ad jacent OAM MGs o f | l | = 2, 3 and 4 carr ying 10-Gb aud DMT signals are transmitted over a 1-km GIRCF. Here note that the modulatio n f ormat of the DMT signals c arried by OAM MG of | l | = 2 is quadr ature phase shift keying (QPSK), while that of the signals carr ied by o ther two MGs is 16QAM. The following observatio ns c ould be made fro m Fig . 5 (a)-(c): 1) Compare d with that in the back-to-b ack ca se, power penalty of the MG | l | = 2, 3 and 4 for single-MG transmission by using MRC te chnique b ased on two rec eived branches (| l | = 2 , 3 or 4 only, w/ MRC ) o ver the 1-km GI RCF are 1 1.5 dB, 1 .1 dB and 2.6 d B, resp ectively, at BER of 3.8×10 -3 . The MG | l | = 2 suffers a much higher power p enalty due to relatively stronger inter-MG coup ling between MG | l | = 1 a nd 2 ( see Tab le I). 2 ) Compar ed with the single-MG transmis sion case, power penalty of the MG | l | = 2, 3 and 4 at B ER of 3 .8×10 -3 for three-MG transmission by using MRC tec hnique (| l | = 2, 3 or 4 w/ MRC) over the 1-km GIRCF are 1 dB, 4.5 dB and 0.7 dB, respectively , which im plies th at the MG | l | = 3 suffer more crosstalk from the other two MGs, compared with those of the MG | l | = 2 and 3 . 3) Due to the rece iver-diversity gain and SNR improvement from MRC, there is a ~2 dB and ~5 d B power budget improveme nt at B ER of 3.8×10 -3 for MG | l | = 2 and 4 by using the MRC technique, respectively, compared with the case based on single- PD d etection (| l | = i , r eceive l = + i or l = - i, i = 2 and 4). A s for the MG | l | = 3 , when the receive diversity architectu re (two received branches) and MRC tec hnique are utilized, BER of 3.8×10 -3 for three-MG transmission o ver the 1-km GIRCF can be re alized at ROP of ~-14 d Bm, while the B ER in the case of single-PD detect ion fail to a chieve the 7% hard-decisio n forward error correc tion (FEC) limit of 3 .8 ×1 0 -3 at ROP less than -10 dBm. 4) T he B ER performance of system based on two received branches and eq ual r atio combining (E RC) technique (| l | = 2, 3 or 4 w/ ERC) is also evaluated for compariso n. It can be see n that the there is a simila r BER per formance for the cases w/ MRC and w/ ERC (the case w/ MRC i s slig htly better than that of w/ E RC) when the BER performanc e o f l = + i and – i in the case of single-P D de tection are approximately same [see Fig. 5 (b) and (c) ]. However , when the BE R per formance of l = + i and – i have a great difference, there will b e an improveme nt of B ER pe rformance for the case w/ MRC compared with that o f w/ ERC [ see Fig. 5(a)]. Here note that the BER curves in the case of single-P D d etection have larger fluctua tions, which c an b e ascr ibed to severe p ower fluctuation indu ced by strong coupling a mong intra-MG mod es. It can be deduced fro m the results that the system with MRC has muc h more stable per formance co mpared with that of the system with ERC , considerin g the ra ndom power c rosstalk among intr a-MG mode s. The received constellatio n d iagrams for MG | l | = 3 at ROP of -10.7 d Bm after 1-km RCF transmission a re shown in Fig. 5 (d). H ere three rec eiving schemes are considered, which are single-PD-d etection scheme, two-PD-dete ction scheme w/ ERC and two-P D-detectio n scheme w/ MRC. It can b e seen from the r esults that the scheme w/ MRC has the best performance among the three cases. Fig. 5. Measure d BER versus R OP for (a) MG | l | = 2, (b) MG | l | = 3 , and (c) MG | l | = 4 in the OAM-MGM transmission system over a 1 -km GIRCF; (d ) received constellation d iagrams for MG | l | = 3 at a ROP of -10.69 dBm after 1-km GIRCF transmission. Fig. 6(a) and (b) p resent the measure d BER results as a functio n of the ROP for two mode-group multiplexed tr ansmission over an 18-km GIRCF. In this system, t wo adjace nt MGs | l | = 3 and 4 are utilized to transmit DM T signals with modulatio n format of QP SK. It can be seen from the results in Fig. 6(a) and (b) that: 1) Co mpared with that in the single-MG transmission case, the re is ~2 dB and ~0.9 dB power penalty at BER of 3.8 × 10 -3 for MG | l | = 3 and 4, respectively , in the case of two-MG transmis sion o ver the 18-km GI RCF. 2) By utilizing the two-PD-detect ion architecture and MRC technique, the rece ived sensitivity at BER of 3 .8 × 10 -3 for MG | l | = 3 and 4 can be improved mor e than 2 dB and 4 dB, respectively, compared with the single -PD-detectio n cases. 3) Comp ared with the two-PD- detection scheme w/ ERC, the scheme with MRC has a b etter p erformance for bo th the MGs | l | = 3 and 4 [see Fig. 6(a ) and (b)], especially when BE R pe rformance of l = + i and - i has a great differe nce [see Fig. 6 (a)]. Fig. 6(c) and (d) show the SNRs and B ERs of individual subcarriers of MG | l | = 3 used for carrying effective payload at a ROP of -20.9 dBm after 1 8-km RCF tra nsmission. One can see that the SNR or B ER distributions of two singl e-PD-detec tion cases ar e quite d ifferent d ue to the different received powers result ed random power crosstalk between OA M modes of l = + i and - i and different responses of the two r eceived b ranches. The SNR in the two-PD -detection system w/ MRC outperforms that in the two-PD-d etection system, e specially when the SNR performance for l = + i and - i have a great d ifference, which agree with the results shown in Fig. 6(a ) and (b). It should be noted that the SNRs o f high frequen cy subca rriers are lower than that o f lo w freq uency subcarriers when MRC technique is emplo yed, which results in better BER per formance for lo w frequency subcarrie rs. I n order to achieve a higher capacity, adaptive bit and power loading algorith m, which can flexibly alloca te bits and power for each subcarr ier in terms of SNR distribution, c ould be a ssigned in futur e study. Fig. 6. Measur ed BER versus ROP for (a) MG | l | = 3 and (b) MG | l | = 4 in the OAM-MGM transmission system ov er an 18-km G IRCF; (c) SNRs a nd (d) BERs of i ndividua l subcarriers of MG | l | = 3 used for carrying effective payl oad a t a ROP of -20.9 dBm after 1 8-km RCF transmission. 5. Conclusions In this pap er, we have p roposed and e xperimentally demonstrated an OAM-MGM scheme based o n a GIRCF by utilizing simp le MRC at the re ceivers. To resist the mode partitio n noise resulted from the random intra-g roup mode cro sstalk, a receive-d iversity architectur e has b een designed for each MG channel. M oreover, a simple MRC tec hnique has been employed on the receiver side, in orde r to improve the SNR of the received signals by making use o f the diversity gain o f rece iver, without per forming co mplex M IMO pr ocessing. To confirm the feasibil ity of our propo sed OAM M G multiplex ing scheme , IM-DD scheme s transmittin g thre e OAM mode groups with tota l 100-Gb/s DMT signals over a 1-km GIRCF and t wo OAM mode group s with total 4 0-Gb/s DMT signals o ver an 1 8.4-km GIRCF h ave been experimentally d emonstrated, respectively . The measured results show that the MRC- based system exhibits best BER performance among the three schemes, which are systems with single-PD d etection, with ERC -based two-PD detection (rec eive diversity), as well as with MRC-ba sed two-PD detection. Fundin g SYSU is supporte d by National Basic Resea rch Program of China (973 P rogram) (2014CB 340000), National Natural Science Found ations of China (6 1490715, 61505 266, 613230 01, 1169003 1, 5140324 4), Guangdo ng Natural Science Fo undation (2014A0303 10364, 2016A0303 13289) and Science and Technology Program of Guangzhou (20170702 0017). UoB is supp orted by Euro pean Union Horizon2020 p roject ROAM.