optimum bias point in broadband subcarrier multiplexing with optical iq modulators

258 JOURNAL OF LIGHTWAVE TECHNOLOGY, VOL. 33, NO. 1, JANUARY 1, 2015

Optimum Bias Point in Broadband SubcarrierMultiplexing With Optical IQ Modulators

Fernando A. Gutierrez, Philip Perry, Frank Smyth, Andrew D. Ellis, and Liam P. Barry

Abstract—This paper develops a theoretical analysis of the trade-off between carrier suppression and nonlinearities induced by op-tical IQ modulators in direct-detection subcarrier multiplexingsystems. The tradeoff is obtained by examining the influence ofthe bias conditions of the modulator on the transmitted single sideband signal. The frequency components in the electric field andthe associated photocurrent at the output of the IQ modulator arederived mathematically. For any frequency plan, the optimum biaspoint can be identified by calculating the sensitivity gain for everysubchannel. A setup composed of subcarriers located at multiplesof the data rate ensures that the effects of intermodulation dis-tortion are studied in the most suitable conditions. Experimentaltests with up to five QPSK electrical subchannels are performed toverify the mathematical model and validate the predicted gains insensitivity.

Index Terms—Carrier to signal power ratio (CSPR), nonlineardistortion (NLD), optical IQ modulator, subcarrier multiplexing(SCM).

I. INTRODUCTION

O PTICAL subcarrier multiplexing (SCM) relies on the ex-cellent stability and low phase noise of microwave os-

cillators to generate one or more digitally modulated radiofre-quency (RF) signals that are then intensity modulated onto anoptical wavelength before transmission over fibre. SCM can becombined with wavelength division multiplexing (WDM) to in-crease the flexibility of the network. Analogue and digital SCMapproaches have been used in many applications, including ca-ble television (CATV) [1], radio over fibre [2] also focusingon the increasingly important Common Public Radio Interface[3], broadband point to point links [4], access networks [5] and100 Gbit/s local area networks [6]. In such a system it is desiredto guarantee the following features: optical single side band(SSB) to increase spectral efficiency and eliminate dispersivefading [7], low inter channel distortion and an appropriate levelof the optical carrier to optimize the sensitivity at the receiver.

Fig. 1 shows three different possibilities to generateSCM/SSB signals with partial carrier suppression (CS). If a stan-

Manuscript received October 3, 2014; revised December 2, 2014; acceptedDecember 14, 2014. Date of publication December 18, 2014; date of currentversion January 23, 2015. This work was supported in part by the EI CFTDGrant CF/2011/1627, SFI Grants 09/IN.1/12653 and 10/CE/I1853 and EPSRCGrant EP/L000091/1.

F. A. Gutierrez, P. Perry, and L. P. Barry are with the RINCE Institute,Dublin City University, Dublin, Ireland (e-mail: [email protected];[email protected]; [email protected]).

F. Smyth is with the RINCE Institute, Dublin City University, Dublin, Ireland,and also with the Pilot Photonics, Invent Centre, Dublin City University, DublinIreland (e-mail: [email protected]).

A. D. Ellis is with the Aston Institute of Photonic Technologies, Aston Uni-versity, Birmingham B4 7ET, U.K. (e-mail: [email protected]).

Color versions of one or more of the figures in this paper are available onlineat http://ieeexplore.ieee.org.

Digital Object Identifier 10.1109/JLT.2014.2384838

Fig. 1. Three alternatives to generate SCM/SSB/CS.

dard Mach Zehnder modulator (MZM) is used for the electro-optic conversion, an optical double side band signal is obtained,requiring an optical filter to suppress the undesired sidebandand produce SSB. The most linear performance of this systemis achieved by biasing the device at quadrature. As the opticalmodulation index (OMI) must be small to minimize nonlineardistortion (NLD), the carrier to signal power ratio (CSPR) ishigh and significant energy is wasted in the optical carrier. Thepower efficiency of the transmission and the sensitivity in thereceiver can be improved by applying CS. A direct method toachieve CS is biasing the device at a point different to quadrature(Fig. 1(a)) although NLD will increase presenting a trade-offwith the sensitivity of the link [8]. A conventional approach togenerate SCM/SSB without optical filters employs a dual driveMZM whose RF ports are driven by signals with a relative phaseshift of 90 degrees [9]. In this case the device can only be biasedat quadrature so that the optical carrier cannot be suppressedin the modulator and a costly CS block must be included [4]to increase efficiency (Fig. 1(b)). For this technique, differentstudies have presented comprehensive mathematical analysesof the NLD [10] and its tradeoff with CS and the sensitivity ofthe link [11]. An optical IQ modulator (OIQM) is an interestingdevice because it can generate SSB and CS without requiringadditional components. In [12] it was shown that this modulatorallows a wide range of CSPR values to be achieved by adjustingthe bias levels (Fig 1(c)). However, no detailed investigation ofNLD was carried out. As NLD increases while CSPR is reduced,a deeper analysis is required.

OIQMs and SCM are technologies that can be combinedto achieve specific system requirements such as colorless SSBtransmitters, received signals free of dispersive fading [7], and,finally, partial optical carrier suppression. This paper studiesanalytically and experimentally the NLD and the CSPR thatare generated simultaneously by an OIQM as a function of thebias point. The analysis presented in [12] is extended to obtainaccurate CSPR and NLD for any number of RF subchannels.

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GUTIERREZ et al.: OPTIMUM BIAS POINT IN BROADBAND SUBCARRIER MULTIPLEXING WITH OPTICAL IQ MODULATORS 259

Fig. 2. WDM SCM/SSB system consisting of an OIQM and N QPSK electrical subchannels per optical wavelength.

An optimum bias point is identified, optimizing the trade-offbetween NLD and CSPR in the presence of optical noise, whereoverall system performance is maximized. The analysis and re-sults presented can be used to achieve efficient transmissionin any multicarrier SCM link, analog or digital, without theneed for a CS block. Experimental results were obtained in a13.5 Gbit/s SCM/SSB system designed with subcarriers locatedat multiples of the data rate so that the distortion due to in-bandintermodulation products falls in the center of other subchan-nels. Measurements show CSPR and NLD, their impact on theperformance of channels and real gains in sensitivity. The ex-perimental results show good agreement with theory.

II. NLD AND CSPR IN OIQMS

A generic SCM/SSB/WDM scheme based on OIQMs isshown in Fig. 2. In every optical wavelength, N QPSK elec-trical subchannels are multiplexed and transmitted.

In this section, the main frequency components at the outputof the OIQM will be derived. CSPR and NLD will be general-ized for any frequency plan. The analytical study is based oncontinuous waves instead of real data as this approach has beenwidely used and its validity proved [13], producing good agree-ment with experimental data using independently modulatedsubcarriers.

A. Introduction

Initially, some basic concepts that will be employed inSection II are reviewed. Firstly, the bias point of a MZM isdetermined by the total relative phase shift that is applied to theoptical wavelength in the modulator arms before recombination.With a push-pull configuration a total relative phase shift equalto 2φ is obtained by producing opposite delays (φ and −φ) ineach arm. Thus the bias point is defined as the absolute valueof the phase shift φ introduced in each arm by the bias voltageVB :

φ =π · VB

2Vπ(1)

where Vπ is the half-wave voltage of the MZM. When φ = 0 theMZM is biased at peak, when φ = π/4 the device is biased atquadrature and finally when φ = π/2 the modulator is biasedat null. The amplitude of the signal at the RF port of the MZMdetermines the OMI. The root mean square (rms) OMI of amodulating signal composed of one subcarrier of amplitudeVAC is given by [10]:

m =π · VAC

2Vπ. (2)

Secondly, NLD can be divided into two groups: harmonic dis-tortion (HD) and intermodulation distortion (IMD). The mostsignificant are second and third order ones: HD2 , HD3 , IMD2 ,IMD3 (mixing of two frequencies) and IMD3B (mixing of threefrequencies or triple-beat). These terms show the power of anindividual distortion normalized to the power of a desired tone.Every subchannel is interfered by a different number of indi-vidual intermodulation products of each kind, NC SO for IMD2and NC T B for IMD3B , being its associated overall distortionreferred as composite second order (CSO) and composite triplebeat (CTB) respectively. CSO and CTB are the most limitingdistortions in direct detected (DD) systems [10], [14]. In gen-eral NC SO is higher for the lowest frequency channels andNC T B is higher for the channels in the middle of the frequencyplan [14].

Finally, a reference frequency plan is defined. The generaltheoretical results will be particularized for this case so thattheory and experiments can be linked. This plan consists of fiveelectrical subcarriers at the second, third, fourth, fifth and sixthharmonic of a fundamental frequency (2.7 GHz in the case of theexperimental results). The first subcarrier is the most affectedby CSO (NC SO = 3, NC T B = 2) while for a five subcarriersystem the fourth (middle) subcarrier is only affected by CTB(NC SO = 0, NC T B = 4).

B. Theoretical Model

As shown in Fig. 1(b) an OIQM consists of three MZMs:two parallel sub-MZMs are modulated by electrical data and thethird one establishes a phase shift between the optical outputs of


the two parallel sub-MZMs before recombination. Provided thatthe electrical inputs present a relative phase shift of 90 degrees,SSB is achieved by biasing the third MZM to produce an opticalrelative phase shift of 90 degrees, and the two parallel sub-MZMs at the same bias point φ. These are operating conditionsthat are employed in the following analysis.

The study of the CSPR requires the derivation of the math-ematical expression of the electrical field E at the output ofthe OIQM. An analysis based on phasors and Bessel expan-sions can be used to obtain all the frequency components ofthe electric field E, for any number of RF subcarriers N. Thefollowing results were obtained with the phases configured toproduce optical lower side band and with equal values of OMIper subcarrier m. The frequency of the optical carrier is de-noted as ωc . The frequencies and phases of the N subcarriersare written as Ω1,Ω2,....,ΩN and θ1 , θ2,....,θN respectively. Asingle expression can be used to calculate the amplitude ofany fundamental tone, harmonic or intermodulation productEk1,k2...kN whose frequency is (ωc + k1Ω1 + k2Ω2 + . . . . +kN ΩN ), where k1 , k2 , . . . , kN are arbitrary integer numbers re-flecting the nature of the signal in question. This contribution isgiven by:

Ek1 ,k2 ,...,kn= Ei

·(

N∏i=1

Jki(m)

)· cos

(π

4

(1 +

N∑i=1

Ki

))

· cos

(φ +

π

2

(N∑

i=1

Ki

))

·N∏

i=1

ej(ki (θi −π4 )) (3)

where Jn (m) stands for the nth order Bessel function of thefirst kind and Ei is the amplitude of the optical carrier at the in-put of the OIQM. To calculate the total contribution at a desiredfrequency it is necessary to add all the components that fall on it.For the reference frequency plan studied here, the contributionof the first fundamental tone at (ωc − Ω1) would be E−1,0,0,0,0 .

While the contribution produced by (ωc + Ω3 − Ω5), whichwould fall on (ωc − Ω1), would be given by E0,0,1,0,−1 . Pro-ceeding in that way, the individual nonlinear distortions can becalculated and are shown in Table I.

For a direct detection scheme envisaged here it is necessaryto obtain the distortion in the detected photocurrent I, which isproportional to the square of the envelope of the electrical fieldand is given by:

I =E2

i

8

×(

1 +12

(cos(2m · s(t) + 2φ) + cos(2m · s(t) + 2φ)))

(4)

where s(t) is equal to the sum of all the tones (normalized withamplitude 1) that are applied to one RF port and s(t) is its

TABLE INORMALIZED NLD POWER OF THE FIELD AT THE MODULATOR OUTPUT (Ωi ,

Ωj , AND Ωk ARE THREE ARBITRARY SUB CARRIER FREQUENCIES)

Distortion type Distortion frequency Formula

Second harmonic (HD2 ) ωc ± 2Ω i

[J2 (m )√2 · J1 (m )

cot φ

]2

Third harmonic (HD3 ) ωc + 3Ω i

[J3 (m )J1 (m )

]2

ωc − 3Ω i 0

2nd order IM (IMD2 ) ωc ± Ω i ± Ω j

[J1 (m )√2 · J0 (m )

cot φ

]2

3rd order IM (IMD3 ) ωc + Ω i ± 2Ω j

[J2 (m )J0 (m )

]2

ωc − Ω i ± 2Ω j 0

Triple beat (IMD3 B ) ωc + Ω i + Ω j + Ωk

ωc + Ω i − Ω j − Ωk

[J1 (m )J0 (m )

]4

ωc − Ω i − Ω j − Ωk

ωc − Ω i + Ω j + Ωk

0

Formulas valid for m << 1.

TABLE IINORMALIZED NLD POWER FOLLOWING PHOTO-DETECTION (Ωi , Ωj , AND Ωk

ARE THREE ARBITRARY SUB CARRIER FREQUENCIES)

Distortion type Distortion frequency Formula

Second harmonic (HD2 ) 2Ω i 0

Third harmonic (HD3 ) 3Ω i

[J3 (2m ))J1 (2m )

]2

2nd order IM (IMD2 ) +Ω i − Ω j

[√2

J1 (2m )J0 (2m )

cot 2φ

]2

+Ω i + Ω j 0

3rd order IM (IMD3 ) Ω i ± 2Ω j

[J2 (2m )J0 (2m )

]2

Triple beat (IMD3 B ) Ω i ± Ω j ± Ωk

[J1 (2m )J0 (2m )

]4

Formulas valid for m << 1.

Hilbert-transformed pair (s(t) shifted 90 degrees) that is appliedto the other RF port. Again, Bessel expansions can be used toobtain all the frequency components and deduce the nonlineardistortions. They are shown in Table II. Due to the nonlinearityof the photodiode, HD2 disappears while certain IMD3B appearsbalancing all the combinations of subcarriers that give rise totriple beat.

C. CSPR as a Function of the Bias Point

In any DD SCM system, the CSPR will depend on the numberof electrical subchannels N and the OMI. From (3), CSPR canbe calculated including all the significant contributions fromthe fundamental tones and distortions. The accurate CSPR wasobtained for the reference frequency plan and is shown in Fig. 3for two different values of m. A simplified model, neglectingNLD, can be used to obtain an approximate value considering


Fig. 3. Accurate and approximated CSPR for an SCM/SSB system composedof an OIQM and five subcarriers for two different values of subchannel OMI(0.055 and 0.15).

only fundamental tones:

CSPR ≈ E2C

NE2T

=1

2N

[J0(m)J1(m)

cot(φ)]2

(5)

where EC is the electric field of the optical carrier and ET isthe electric field of any fundamental tone. This approximationhas been employed previously [12] but its accuracy was notanalyzed. Table I shows that in the electric field E the main con-tributions of NLD come from HD2 and IMD2, being maximumat peak bias point and canceling while approaching the null.For that reason the approximated CSPR, which is also shownin Fig. 3, diverges clearly around peak. However, for the biaspoints of interest in DD systems, between quadrature and null,the approximation is valid, especially for low values of m (errorless than 0.3 dB from quadrature in this example).

The curves in Fig. 3 also show the CSPR that is obtainedwith the most significant terms of I obtained from (4). Apartfrom the area around the null point, CSPR can be approximatedby measuring the detected photocurrent and adding 3 dB. Thistechnique will be used to measure CSPR in the experimentalsection as direct measurement is not possible.

It can be concluded that, as expected, CSPR decreases whenthe bias point moves towards null. Different bias points producedifferent partial CS while the power of the transmitted tonesremains the same. Thus decreasing the CSPR, and neglectingNLD, the subchannels could be received with the same qualitywith a lower received average optical power, thereby improvingsensitivity. However, as it is explained in the next section, somesubchannels can be severely impaired due to NLD when the biaspoint changes.

D. NLD as a Function of the Bias Point

From Table II it can be confirmed that the most limiting NLDin the detected photocurrent I are second order intermodulationand triple beat (CSO and CTB when all the intermodulationproducts are considered). Fig. 4 shows both distortions for twovalues of OMI. Whereas IMD3B depends only on m, IMD2varies with the bias point cancelling at quadrature and worsen-

Fig. 4. Individual NLD (IMD2 and IMD3B ) at the detected photocurrent ofan SCM/SSB system using an OIQM for two values of OMI.

ing sharply if the bias point changes. In both cases higher valuesof m give rise to higher distortions.

The previous results have illustrated the combined behaviorof CSPR and NLD as a function of the bias point. Both termspresent a relationship that can be manifested in two differentways depending on the nature of the IMD. All the cases can bedivided into two groups: systems where the desired tones areonly interfered by CTB and systems where at least one of thesubchannels is interfered by CSO. The first case happens whenthe frequency plan ensures that CSO is not interfering (NC SO =0 for all the electrical subcarriers), thus NLD is composed onlyof CTB and is constant irrespectively of the bias point. Thisis achieved when there is a guard band between the opticalcarrier and the first subcarrier equal to at least half of the totalspectrum as in DD/OFDM [15] or some CATV schemes [16].This particular case is simpler to analyse and for a given OMI theoptimum bias point would be obtained when CSPR is equal toone, as it has been experimentally shown [17]. Strong clippingappears in the signal but it does not have a detrimental effectbecause its associated distortion translates into CSO and fallsin the part of the spectrum where no desired subcarriers arepresent. A deeper analysis, like the one presented in the nextsection would be required to find the optimum OMI. The secondcase happens when there are low frequency subcarriers as inbroadband SCM [4] or in the reference example. In this casethere is a trade-off between CSPR and NLD: biasing closer tonull improves CSPR but at the same time CSO increases sharply.A mathematical analysis of the system is required to obtain thesensitivity at the receiver as a function of the bias point so thatthe optimum bias can be found.

E. Optimum Bias Point

The study was based on an SCM link composed of N subcar-riers and with a pre-amplified receiver as shown in Fig. 5. Thisreceiver consists of an erbium doped fiber amplifier (EDFA), aphoto-detector and an RF demodulator.

The average optical power PIN at the input of the receiverrequired for a given quality factor QF is mathematically derived


Fig. 5. SCM/SSB scheme with a pre-amplified optical receiver.

Fig. 6. Gains in sensitivity for QF = 6 with respect to quadrature and m =0.055 for a subchannel distorted by NLD (NC S O = 3 and NC T B = 2) in afive subcarrier QPSK SCM/SSB link consisting on an OIQM and a pre-amplifiedreceiver (F = 5 dB, v = 193.4 THz, Be = 2.7 GHz).

in the Appendix A:

PIN =4Q2

F FhvBe

I2φ(1 − Q2

F (NCSOIMD2 + NCTBIMD3B ))(6)

where F is the noise figure of the EDFA, h is Planck’s constant, vis the optical frequency and Be is the electrical bandwidth of thebaseband channel at the receiver. Iφ represents the dependencyof the amplitude of the subcarrier on the bias point:

Iφ =√

2JN −10 (2m)J1(2m) sin(2φ)1 + JN

0 (2m) cos(2φ). (7)

As the only sources of noise and distortion considered are am-plified spontaneous emission (ASE) and NLD, PIN in Eq. (6)represents the minimum sensitivity that is theoretically achiev-able in a QPSK SCM/SSB link implemented with an OIQM anda pre-amplified receiver.

The gain in sensitivity that can be achieved by varying thebias point depends on NLD. This distortion is different for everysubchannel because it is determined by different values of NC SO

and NC T B . Therefore, depending on the nature of the link,the optimum bias point is given by either the average bit errorrate (BER) or the BER of the worst case channel. The secondcondition is the strictest and is used in this analysis.

These results will be particularized for the reference designconsidering only subcarrier 1, as it is the most affected by CSO(NC SO = 3 and NC T B = 2), and subcarrier 4, as it is the mostinterfered of the channels affected only by CTB (NC SO = 0 andNC T B = 4). Considering quadrature and a low value of m asthe initial point, Fig. 6 shows the gains in sensitivity (for QF =

Fig. 7. Gains in sensitivity for QF = 6 with respect to quadrature and m =0.055 for a subchannel distorted by NLD (NC S O = 0 and NC T B = 4) in afive subcarrier QPSK SCM/SSB link consisting on an OIQM and a pre-amplifiedreceiver (F = 5 dB, v = 193.4 THz, Be = 2.7 GHz).

6, BER = 10−9) that can be achieved changing the settings.Moving the bias point towards null, the sensitivity improvesnotably until CSO is comparable to the optical noise floor. Fora value of m = 0.055, there is an optimum bias point (φ =1.1 rad), where a sensitivity gain of almost 4 dB with respect toquadrature is achieved. This gain is very sensitive to changes inφ (it is reduced to 3 dB at φ = 1.175) and m (3.5 dB with m =0.06). From that point sensitivity improves while m increasesand the bias point moves towards quadrature. This effect occursbecause CSPR improves with a higher OMI and CSO tendsto cancel while close to quadrature. A gain in sensitivity of8 dB is observed for m = 0.15 with respect to m = 0.055 atquadrature. However, while m increases, the impact of CTBon subchannel 4 also increases, as shown in Fig. 7. For thatchannel, as CTB is constant regardless of the bias point, a gainin sensitivity is always achieved when moving the bias fromquadrature towards null. For m = 0.055, the gain in sensitivityat the optimum bias point of subchannel 1, φ = 1.1 rad, is 6 dBwith respect to quadrature. When m increases, CSPR reducesand CTB increases, resulting in better sensitivity until the levelof CTB is comparable with the optical noise floor, as it happensat m = 0.2. From that value, further increments of m result in aloss in sensitivity.

The previous analysis can be applied to achieve optimumsensitivity in any SCM link using an OIQM. The influenceof the bias point can be summarized with two effects. Firstly,for a given OMI, it is possible to find a bias point different toquadrature and closer to null where overall sensitivity improves.Secondly, as the OMI increases, this optimum bias point will becloser to quadrature. In the following section a real scheme isused to validate the predicted gains in sensitivity and to showthe described trends. The overall link performance is determinedby the combined behavior of, among others, the OMI, the biaspoint, and the performance of the optical and RF components inthe bands of use. For different system design level objectives,different individual parameters may be required. On many oc-casions OMI is maintained small to guarantee low IMD butthis behavior can cause loss in sensitivity. This effect can be


overcome with an increase in the OMI of the signal, but thatrequires a higher power consumption of the RF components.As power consumption is usually a major issue, a lower valueof OMI can be used accompanied with a bias closer to null toachieve equivalent sensitivity

III. EXPERIMENTAL RESULTS

The experimental setup was a five carrier SCM/QPSK sys-tem with the electrical transmitter and receiver equivalent to thatshown in Fig. 2. The IQ mixers were off-the-shelf monolithicmicrowave integrated circuits. SCM/QPSK has been previouslyreported [18] but employing two regular mixers and microwavecircuitry instead of the integrated IQ mixers used in this work.The baud rate per subcarrier was 1.35 Gbaud, making a totaldata rate of 13.5 Gbit/s for every optical channel. An FPGA wasused to generate patterns of 215 bits. The data streams were lowpass filtered to reduce the spectrum of the signal to the first lobeof a sinc function. Imitating the reference design that was stud-ied in Section II, the employed RF local oscillators were evenharmonics of the data rate (from 5.4 to 16.2 GHz), obtainedusing an electrical comb and appropriate demultiplexing filters.Thus no guard band was introduced between subchannels andthe total energy of any intermodulation product distorted onlyone subchannel. No digital signal processing algorithms wereemployed to compensate the impairments of the analogue com-ponents. The electrical signal was applied to a thin film polymerOIQM [19] with a bandwidth of 20 GHz and Vπ of 2.5 Volts.

The setup was completed in two different configurations de-pending on the parameter to be measured. Both configurationswill be described in the next sections. To make the experimentalresults comparable with theory m has to be redefined for the caseof real data. When a modulated electrical subcarrier presents anrms voltage of VRM S the experimental rms OMI is:

m =π · VRM S

2Vπ. (8)

It should be noted that the peak to average power ratio (PAPR)of the final signal will depend on the OMI, number of subcar-riers and the particular relative phases of the subcarriers whenthey combine. However, theoretically, system performance willbe determined by the rms power or the rms OMI of the finalsignal, m�N, regardless of the individual phases and the PAPRthat arises. Obviously it has to be ensured that the rest of thecomponents in the system can handle that PAPR value withoutincluding additional nonlinearities.

A. Bias Points

The system characterization was carried out by biasing thetwo parallel sub-MZMs of the OIQM to get equal intensity fromthem, and then varying these bias levels between peak and null.Sixteen levels of intensity were selected. For each bias setting ofthese sub-MZMs, the bias point of the third MZM (that combinesthe optical outputs of the parallel ones) was adjusted to achievethe best suppressed side band rejection (SSR). In Fig. 8 theoptical spectrum of one of these realizations is shown, where anSSR of 20 dB can be observed.

Fig. 8. Optical spectrum obtained with m = 0.055 at a one of the sixteen biaspoints analyzed. OLSB with an SSR of 20 dB is achieved. CSPR = 15.7 dB.

Fig. 9. Setup employed in the characterization of the optical modulator.

B. Agreement with the Model: Measured CSPR and IMD2

The theoretical analysis concluded that CSPR and IMD2 arethe two key parameters to determine the optimum bias point inan SCM link implemented with an OIQM. These parameterswere measured experimentally to verify the agreement with themodel obtained with the employed OIQM. For this particulardevice the bias is established with constant current instead ofvoltage, thus the measurements will be presented as a functionof bias current. The tests were performed with the configurationshown in Fig. 9. At the output of the OIQM a variable opticalattenuator (VOA) was included prior to an EDFA. The gain ofthe EDFA was maintained constant and the VOA attenuationwas modified to ensure the same optical power at the input ofthe EDFA for all the bias points that were analyzed. With thismethod the measurements at different bias points were takenunder the same conditions.

To investigate IMD2, a discrete photo-detector with a band-width of 20 GHz was employed. Its output was connected toa spectrum analyzer. In the transmitter only the first (5.4 GHz)and the fifth (16.2 GHz) electrical subcarriers were activatedsuch that the second order intermodulation product for this fre-quency plan falls at 10.8 GHz. Fig. 10 illustrates the measuredand theoretical IMD2 that were obtained for a modulation indexm = 0.15 for the different bias points. A trace from the spec-trum analyzer after the photo receiver is also shown. A goodagreement between theory and measurements is observed. Thediscrepancy with the peak of the theoretical value is due to thefact that the minimum distortion that could be measured was


Fig. 10. Second order intermodulation distortion. Measurements performedactivating only the first and the fifth carrier and measuring the distortion at thethird one. m = 0.15. Electrical spectrum at one of the measurements.

Fig. 11. CSPR: theoretical and measured. Five carriers. m = 0.055 and 0.15.Photocurrent at two different bias points: quadrature and point B.

limited by the noise floor. With lower values of OMI this lim-itation is present in more bias points and for that reason thosemeasurements are not shown. The previous result confirms thatbiasing at a point different to quadrature translates into a mean-ingful increase of CSO. In the next section it will become clearthat this impairment can be balanced with the associated im-provement in CSPR that gives rise to overall sensitivity.

For the measurement of the CSPR, the photo-detector of adigital oscilloscope was used. CSPR was obtained for the de-tected photocurrent as the square of the ratio between the DCcomponent and the rms value of the AC signal. Fig. 3 showedthat a good approximation of the optical CSPR could be ob-tained adding 3 dB to the value obtained with the detected pho-tocurrent (excluding the area around null). Fig. 11 illustrates theaccurate theoretical value and the measurements for m = 0.055and m = 0.15. A good agreement between theory and the ex-periment is observed. For the case of lower OMI, the picturealso shows the photocurrent at two bias points: quadrature (Q

Fig. 12. BER versus Optical input power at the receiver for the first electricalcarrier. Two different bias points, Q and B. Measurements obtained with one orfive active carriers. m = 0.055 and 0.15.

in the figure), where IMD2 presented its lowest value, and pointB, the closest to the optimum that was identified in the theoret-ical section for m = 0.055. The improvement in CSPR at pointB is 5 dB relative to Q, and the optical peak to peak modulationdepth approaches unity (roughly from 2/4 to 4/5), making thispoint more suitable for an efficient transmission.

C. Effects of CSPR and NLD on Channel Performance

This section shows how the CSPR and NLD induced by theOIQM influences the performance of electrical channels in thecommunications system. The results are taken with a setup sim-ilar to that shown in Fig. 5, simulating the losses in the fiber witha VOA so that dispersion effects are removed. The gain of theEDFA in the transmitter is fixed to obtain 10 dBm at the output.The gain of the EDFA at the receiver is regulated to guaranteethe sensitivity in the baseband electrical receivers irrespectiveof the incoming optical power. The measurements were focusedon two carriers, subchannel 1 to observe the effects of CSO andsubchannel 4 to analyse the effects of CTB. The modulationindex was m = 0.055 and two bias points were analyzed: Qand B. BER versus received optical power were obtained in twodifferent situations: activating only one electrical carrier so thatno IMD was produced, and with all the carriers on and NLDpresent in the system.

The performance of the first subchannel can be observedin Fig. 12. As expected, the influence of the intermodulationproducts is more severe when biasing closer to null at point B.At Q, CSO is cancelled, so there is only a minor difference inperformance when all the channels are active (less than 1 dB).However, when biasing at B, the NLD coming from CSO causesa penalty in performance of up to 5 dB. Despite the higherpenalty due to NLD, a sensitivity gain of 3 dB can be observedat point B with respect to Q, for a BER = 10−9 , in agreementwith the theoretical prediction.

A similar analysis was done for the fourth carrier and isshown in Fig. 13. CTB is independent of the bias point, as hasbeen illustrated in Fig. 4. Due to the low value of CTB for this


Fig. 13. BER versus Optical input power at the receiver for the fourth electricalcarrier. Two different bias points, Q and B. Measurements obtained with one orfive active carriers. m = 0.055 and 0.15.

OMI, the difference that can be observed between the single andmulticarrier cases is small and, as expected, is similar at bothbias points. The gain in sensitivity due to the better CSPR atpoint B is 6 dB with respect to Q, as predicted by theory for aBER = 10−7 (similar to the prediction for a BER = 10−9).

D. Effects of Increased OMI

According to the theoretical study for OIQM-based SCMsystems, the behavior of the sensitivity can be summarized withtwo trends. For a given OMI, there can be an optimum biaspoint different to quadrature, where the channel most affectedby CSO determines the gain in sensitivity of the link. Thiseffect has been verified experimentally in the previous section.The second trend shows that it is possible to improve sensitivityby increasing OMI and biasing closer to quadrature, but at somepoint this process will have a detrimental effect for the channelsaffected by CTB. This behavior is showed in this section.

The effects of CSO on subchannel 1 shown in Fig. 12 alsoinclude the performance for the case of increased OMI withm = 0.15 biasing at quadrature. The higher value of m inducesa better CSPR and the bias at quadrature cancels CSO, resultingin a gain in sensitivity of 9 dB with respect to the lower OMI,consistent with the 8 dB predicted by theory. On the other hand,the behavior of channel 4 shown in Fig. 13 includes the samecase of increased OMI while biasing at quadrature. It can be seenthat the increment in CTB associated to the higher OMI resultedin a loss of sensitivity with respect to the case of lower OMI forall BER below 10−5. This penalty occurred with an OMI lowerthan that expected from the theoretical prediction (m = 0.20).This is due to the fact that the model included ideal electrical IQmixers. In practice, as these components are designed for lowerbandwidth signals [20], the use of higher rates translates into asignificant eye closure that can appear like increased NLD.

IV. CONCLUSION

SCM is a reliable multicarrier technique that is employedin multiple schemes, usually combined with SSB to obtain in-

creased tolerance to dispersive fading. The mathematical studyof SCM has been extended by analyzing the OIQM, an idealchoice in the transmitter because, unlike other alternatives, bothSSB and CS can be obtained directly without external compo-nents by adjusting the bias points.

When the frequency plan ensures that the subchannels areonly affected by CTB, CSPR can be modified without addingany impairment in the subchannels. When at least one of thesubchannels is interfered by CSO, a trade-off between CSPRand NLD is present. The developed mathematical model can beused to determine the optimum bias point and predict the gainsin sensitivity that can be achieved for every subchannel.

Experiments have been conducted with a scheme and compo-nents that ensure subcarriers are located at multiples of the datarate, which makes it ideal for an accurate study of the effects ofIMD. The theoretical predictions have been validated measuringCSPR, NLD, and their effect on the performance of channels.The sensitivity gains that can be directly achieved with OIQMprove the suitability of this device to improve the power budgetof SCM/SSB links without incurring additional costs.

APPENDIX A

This appendix shows the mathematical derivation of the sen-sitivity required for a desired quality factor QF in a SCM/SSBlink composed of an optical IQ modulator, a pre-amplified re-ceiver (see Fig. 5) and N QPSK subcarriers.

This receiver consists of an EDFA whose gain is G, a photo-detector whose responsivity is R and an RF demodulator. Theaverage optical power at the input of the receiver can be ob-tained as the DC component of the photocurrent detected witha responsivity of 1. From (4):

PIN = IDC =18(1 + JN

0 (2m) cos(2φ)) (A.1)

where Ei has been normalized to 1. The amplitude of the kthelectrical subcarrier at the detected photocurrent can also beobtained from (4):

Ak = RG

√2

8JN −1

0 (2m)J1(2m) sin(2φ). (A.2)

To calculate the sensitivity of the link, the detected photocur-rent must be rewritten making PIN an independent variable:

I = RGPIN

(1 +

N∑k=1

Iφ cos(Ωk t + θk ) + NLD

)(A.3)

where Ωk and θk are the frequency and phase of the subcar-rier and Iφ represents the dependency of the amplitude of thesubcarrier on the bias point:

Iφ =√

2JN −10 (2m)J1(2m) sin(2φ)1 + JN

0 (2m) cos(2φ). (A.4)

Thus, the amplitude of the kth subcarrier can be written as:

Ik = RGPIN Iφ . (A.5)

In the described link, neglecting NLD, the main source ofnoise will be ASE coming from the EDFA. After demodulation


the contribution of this noise will be [4]:

σ2ASE = 2R2PIN G(G − 1)FhνBe (A.6)

where F is the noise figure of the EDFA, h is Planck’s constant, vis the optical frequency and Be is the electrical bandwidth of thebaseband channel at the receiver. Under a Gaussian approxima-tion the time averaged second and third order intermodulationcurrent power [21], [22] is added like noise as in [11]. Thus theabsolute contribution of NLD is:

σ2N LD = σ2

C SO + σ2C T B

=(NC SO

IM D22 + NC T B

IM D3 B

2

)I2K . (A.7)

The quality factor QF after the RF demodulator for a QPSKSCM system is obtained with the following expression [4]:

QF =√

2IK

2(√

σ2ASE + σ2

N LD ). (A.8)

After some manipulations and for G >> 1, the sensitivity fora desired value of QF can be deduced as:

PIN =4Q2

F FhvBe

I2φ (1 − Q2

F (NC SO IMD2 + NC T B IMD3B )).

(A.9)

REFERENCES

[1] P. M. Hill and R. Olshansky, “A 20-channel optical communication us-ing subcarrier multiplexing for the transmission of digital video signals,”J. Lightw. Technol., vol. 8, no. 4, pp. 554–560, Apr. 1990.

[2] G. H. Smith and D. Novak, “Broad-band millimeter-wave (38 GHz) fiber-wireless transmission system using electrical and optical SSB modulationto overcome dispersion effects,” IEEE Photon. Technol. Lett., vol. 10,no. 1, pp. 141–143, Jan. 1998.

[3] R. P. Almedia, R. S. Oliveira, N. S. Moritsuka, C. R. L. Frances, A.Teixeira, and J. C. W. A. Costa, “Digital radio over fibre transmission basedon SCM and WDM system for C-Ran architecture,” in Proc. Telecommun.Symp., 2014, pp. 1–5.

[4] R. Hui, B. Zhu, R. Huang, C. T. Allen, K. R. Demarest, and D. Richards,“Subcarrier multiplexing for high-speed optical transmission,” J. Lightw.Technol., vol. 20, no. 3, pp. 417–427, Mar. 2002.

[5] B. Charbonnier, S. Menezo, P. O’Brien, A. Lebreton, J. M. Fedeli, andB. Ben Bakir, “Silicon photonics for next generation FDM/FDMA PON,”J. Opt. Commun. Netw., vol. 4, no. 9, pp. A29–A37, 2012.

[6] M. Salter, D. Platt, L. Petterson, L. Aspemyr, and M. Bao, “Circuits andsystems simulations for 100 Gb/s optical SCM transmission,” in Proc. Int.Conf. Electron., Circuits, Syst., 2009, pp. 960–963.

[7] J. Maeda, T. Kato, and S. Ebisawa, “Effect of fiber dispersion on subcarrierQAM signal in radio-over-fiber transmission,” J. Lightw. Technol., vol. 30,no. 16, pp. 2625–2632, Aug. 2012.

[8] J. Leibrich, A. Ali, and W. Rosenkranz, “OFDM transceiver design foroptimizing sensitivity and long-haul performance,” in Proc. IEEE LEOSSummer Top. Meet., 2008, pp. 249–250.

[9] G. H. Smith, D. Novak, and Z. Ahmed, “Overcoming chromatic dispersioneffects in fiber-wireless systems incorporating external modulators,” IEEETrans. Microw. Technol., vol. 45, no. 8, pp. 1410–1415, Aug. 1997.

[10] W. H. Chen and W. I. Way, “Multichannel single-sideband SCM/DWDMtransmission systems,” J. Lightw. Technol., vol. 22, no. 7, pp. 1679–1693,Jul. 2004.

[11] P. Laurencio, S. O. Simoes, and M. C. R. Medeiros, “Impact of the com-bined effect of RIN and intermodulation distortion on OSSB/SCM sys-tems,” J. Lightw. Technol., vol. 24, no. 11, pp. 4250–4262, Nov. 2006.

[12] T. Nakatogawa, M. Maeda, and K. Oyamada, “Optical single sidebandmodulator for distribution of digital broadcasting signals on millimetre-wave band based on self-heterodyne,” Electron. Lett., vol. 40, no. 21,pp. 1369–1370, Oct. 2004.

[13] M.-C. Wu, P.-Y. Chiang, and W. I. Way, “On the validity of using CWtones to test the linearity of multichannel M-QAM subcarrier multi-plexed lightwave systems,” IEEE Photon. Technol. Lett., vol. 12, no. 4,pp. 413–415, Apr. 2000.

[14] W. I. Way, Broadband Hybrid Fiber/Coax Access System Technologies.New York, NY, USA: Academic, 1998.

[15] B. J. C. Schmidt, A. J. Lowery, and J. Armstrong, “Experimental demon-strations of electronic dispersion compensation for long-haul transmissionusing direct-detection optical OFDM,” J. Lightw. Technol., vol. 26, no. 1,pp. 196–203, Jan. 2008.

[16] T. Nakatogawa, M. Maeda, and K. Oyamada, “A novel millimeter wavereceiver using self-heterodyne detection for a digital broadcasting ROFsystem,” in Proc. Int. Top. Meeting Microw. Photon., Oct. 2006, pp. 1–4.

[17] A. J. Lowery and J. Armstrong, “Orthogonal-frequency-division multi-plexing for dispersion compensation of long-haul optical systems,” Opt.Exp., vol. 14, no. 6, pp. 2079–2084, Mar. 2006.

[18] J. Y. Ha, A. Wonfor, R. V. Penty, I. H. White, and P. Ghiggino, “Spectrallyefficient 10 x 1 Gb/s QPSK multi-user optical network architecture,” inProc. Opt. Fiber Commun. Conf., 2007, pp. 1–3.

[19] G. Yu, E. Miller, J. Mallari, C. Wei, B. Chen, H. Chen, V. Shofman, andR. Dinu, “Small form factor thin film polymer modulators for telecomapplications,” in Proc. Opt. Fiber Commun. Conf., 2012, pp. 1–3.

[20] B. E. Olsson, J. Martensson, A. Kristiansson, and A. Alping, “RF as-sisted optical dual-carrier 112 Gbit/s polarization- multiplexed 16-QAMtransmitter,” in Proc. Opt. Fiber Commun. Conf., 2010, pp. 1–3.

[21] R. Olshansky, “Optimal design of subcarrier multiplexed lightwave sys-tems employing linearized external modulators,” J. Lightw. Technol.,vol. 10, no. 3, pp. 378–382, Mar. 1992.

[22] F. Ramos and J. Marti, “Compensation for fiber-induced compositesecond-order distortion in externally modulated lightwave AM-SCM sys-tems using optical-phase conjugation,” J. Lightw. Technol., vol. 16, no. 8,pp. 1387–1392, Aug. 1998.

Authors’ biographies not available at the time of publication.

optimum bias point in broadband subcarrier multiplexing with optical iq modulators

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