## Abstract

We present a novel method for dispersion compensation based on vestigial-sideband transmission of an orthogonal frequency division multiplexed signal through standard signal-mode fiber with a direct-detection receiver. This technique requires simpler optical components and can withstand greater link attenuation and splitting ratios than similar methods previously studied, making the method ideal for optically unamplified receivers, such as those in passive optical networks. We present simulations as well as experimental measurements to demonstrate its practicality.

© 2014 Optical Society of America

## 1. Introduction

Recent advances in CMOS digital-to-analog converter (DAC) and analog-to-digital converter (ADC) technology have enabled the possibility of low-cost, short-reach links employing advanced modulation techniques, such as orthogonal frequency division multiplexing (OFDM), and direct-detection (DD). Achieving bit rates in the 50–100 Gb/s/wavelength range without polarization multiplexing optics is now possible due to the development of commercial 8-bit, 65 Gsample/s CMOS DAC and ADC cores [1,2].

In optical access networks, where cost is a primary concern, chromatic dispersion must be combated without a coherent receiver. Electronic dispersion compensation in a DD receiver can be enabled through single-sideband (SSB) transmission, in which either the upper or lower sideband of the electric field is eliminated. A recent work has also explored the possibility of dispersion compensation for double-sideband (DSB) transmission by block-wise phase switching [3, 4]. Previously studied SSB-OFDM systems can be classified into one of two types. The first class of systems transmits the OFDM symbol through a modulated laser intensity, in a manner in which the E-field is SSB [5–8]. The second class of systems transmits the OFDM symbol by modulating the complex E-field directly [9–15]. In this second case, the E-field is made SSB either through SSB modulation with an I-Q modulator or by optically filtering a DSB signal. For both classes of systems, the need for the E-field to be SSB is due to the fact that a DSB signal interacts with dispersion and square-law detection to form nulls in the composite channel [16, 17]. Although SSB transmission prevents formation of nulls, the first class of systems is inherently nonlinear in the path from the transmitter’s digital OFDM signal to the received electrical OFDM signal. This is due to the fact that transmitted and detected signals are intensities, but dispersion is only a linear operator on the E-field. In contrast, the second class of systems are linear, because the transmitted and detected signals are E-fields. The complex E-field is recovered at the DD receiver through either self-homodyning or self-heterodyning. The linearity of the channel provides improved sensitivity, since equalization is thus nearly perfect. The system described in this paper resembles those of the second class, in that it transmits and receives the E-field rather than intensity, but it differs in that it transmits a vestigial-sideband (VSB) OFDM signal rather than a SSB signal. This VSB signal is produced by partially suppressing one of the sidebands of a DSB E-field. Although this signal is not SSB, its asymmetrical form prevents formation of channel nulls, as will be shown. However, a VSB signal can be produced with a simpler transmitter than a SSB signal.

As in [3], we add the carrier to the OFDM signal through a separate parallel waveguide. Techniques which add a carrier (or virtual carrier) to the data signal using a modulator [10, 14, 15], inherently attenuate the carrier due to the modulator’s insertion loss and restriction of the modulator’s drive signal to be in the modulator’s linear region. Adding the carrier outside the modulator avoids this intrinsic carrier attenuation, resulting in a much larger received signal. This is advantageous in optically unamplified links, since this allows for greater link attenuation or splitting. For example, in a passive optical network (PON), a single optical line terminal services many optical network units (ONUs) through a common fiber that is split to reach all receiving ONUs. These ONUs must be low-cost and their receivers are thus not optically amplified [18].

These features make the proposed VSB technique advantageous for standard single-mode fiber (S-SMF) links under 80 km with optically unamplified DD. Section II discusses the gain achieved through carrier generation by a separate waveguide and the incorporation of carrier generation in an integrated waveguide transmitter. Section III introduces the technique of VSB transmission for counteracting dispersion-induced nulling. Section IV presents simulations of the VSB system, including effects of component drift. Section V provides measurements of the performance of a VSB implementation using commercial components. Finally, Section VI presents conclusions.

## 2. Increasing transmission reach in optically unamplified links

Most of the previously studied self-homodyning or self-heterodying OFDM systems have utilized the modulator for generation of the carrier. This was done in one of two ways. The first method is to add a DC offset to the data signal driving the modulator [9]. This results in the presence of an unmodulated optical carrier along with the OFDM signal. These two components then mix at the receiving photodiode to perform homodyning. The second method is to apply no DC bias, but instead add a high-frequency RF tone to the OFDM signal. The receiver photodiode then heterodynes this RF tone with the OFDM signal [10]. Thus, this RF tone is a virtual carrier that is offset from the frequency of the transmitting laser.

Both of these methods of inserting a carrier in the transmitted signal rely on the modulator to add the carrier. This is inherently inefficient for two reasons. The first is that the Mach-Zehnder modulator (MZM) transfer characteristic is a cosine of the input drive signal and is only linear near its null. Adding a DC offset moves the MZM bias into a less linear region; thus the DC offset must be small, which results in a small transmitted carrier. Similarly, adding a large virtual carrier increases the peaks of the composite MZM drive signal (although less severely than a DC offset). The second inefficiency of adding a carrier through the modulator is the modulator insertion loss. A typical commercial Lithium niobate MZM has 6 – 10 dB insertion loss.

These inefficiencies can be avoided by instead adding the carrier through a separate waveguide in parallel with the modulator, as depicted in Fig. 1, where the SSB E-field is produced by optical SSB filtering. In [3], this alternate method for adding the carrier was utilized to enable a large carrier-to-signal ratio to reduce the relative influence of signal-signal mixing. In this case, the carrier is not attenuated by the small swing of the MZM drive signal and suffers no insertion loss. Since the detected electrical signal is proportional to the amplitude of the carrier [10], a larger carrier results in a larger detected signal. This is advantageous in passive links without optical amplification, as it allows for a greater link budget. As shown in the appendix, adding the carrier through a parallel waveguide rather than the modulator increases the received electrical signal by a factor

where*R*is the clipping ratio in linear units,

_{cl}*a*is a scaling corresponding to the MZM insertion loss, and

*m*is a scaling corresponding to using only the linear region of the MZM cosine transfer characteristic. We define

*R*=

_{cl}*x*

_{0}/

*σ*, where

*x*

_{0}is the clipping limit and

*σ*is the standard deviation of the MZM drive signal. For example, with 8 dB clipping, 6 dB insertion loss, and a use of

*m*= 1/2 of the MZM’s dynamic range,

*K*= 7.1, or 17 dB. Although, in principle, one could compensate for the attenuation of the modulator with a higher power laser, there are practical limits to the output power of semiconductor lasers.

## 3. Vestigial-sideband transmission

To prevent loss of channel capacity from dispersion-induced nulls in a DD receiver, many past studies have used SSB transmission. This was achieved either through an I-Q modulator or a single MZM combined with an optical SSB filter. Here, we will illustrate an alternative transmitter based on a single MZM combined with an integrated Mach-Zehnder interferometer (MZI), as shown in the complete system diagram of Fig. 2. This technique requires fewer components compared to the method of I-Q modulation (and also does not need to maintain balance and quadrature between I and Q branches) and has less insertion loss compared to the method of SSB optical filtering. The reduced insertion loss compared to an SSB filter is due to the SSB filter’s sharp transition and large stopband attenuation; its implementation as an integrated optical filter will necessarily be of high order, resulting in larger area and higher insertion loss [19] and thus a reduced link budget. As we now show, a simple MZI can be used to replace the SSB filter.

Consider the system depicted in Fig. 2. Let the DSB-OFDM signal be given by *x*(*t*) and the DC offset added to it be *A*. Let the impulse responses of the optical filter and fiber be *f* (*t*) and *g*(*t*), respectively. Let their respective Fourier transforms be *F*(*ω*) and *G*(*ω*). Then the received E-field is

***denotes convolution. Let

*B*=

*A**

*g*(

*t*) =

*AG*(0), a complex constant. Let

*h*(

*t*) =

*f*(

*t*) *

*g*(

*t*) be the composite channel

*x*(

*t*) traverses. Then the intensity at the receiver is

*y*(

*t*) = 2Re{

*B*

^{*}

*x*(

*t*) *

*h*(

*t*)} is the desired signal term. It can be equivalently be expressed as where The corresponding transfer function for this system is When the real OFDM signal

*x*(

*t*) is chosen such that it occupies the frequency bands (−2

*ω*, −

_{B}*ω*) and (

_{B}*ω*, 2

_{B}*ω*), the intermodulation term (caused by signal-signal beating) |

_{B}*x*(

*t*) *

*h*(

*t*)|

^{2}will occupy the band (−

*ω*,

_{B}*ω*). Thus after highpass filtering, the received signal becomes

_{B}*y*(

*t*), so the system between the transmitted OFDM signal and the received signal is linear. It is apparent that the magnitude of the received signal is proportional to |

*A*|, the magnitude of the transmitted carrier. Thus, adding the carrier through the parallel waveguide results in a much larger received signal than if the carrier (or virtual carrier) were generated through the modulator. If the carrier is sufficiently large compared to the signal, the linear signal term

*y*(

*t*) will become large compared to the intermodulation term |

*x*(

*t*) *

*h*(

*t*)|

^{2}, even if

*x*(

*t*) is allowed to occupy the entire band (0, 2

*ω*) rather than just (

_{B}*ω*, 2

_{B}*ω*). Depending on the relative magnitude of intermodulation compared to receiver thermal and shot noise, it may be advantageous to have a reduced guard band or no guard band at all.

_{B}To evaluate the effects of dispersion, consider the case where the fiber is a dispersive channel with E-field transfer function

where*β*

_{2}is the group-velocity dispersion parameter, and

*L*is the fiber length. Suppose the optical filter is absent, or equivalently,

*F*(

*ω*) = 1 for all

*ω*. For simplicity of discussion, we will consider

*B*= 1, but this does not affect the results. Then by (6),

*H*(

*ω*). One can ask whether insertion of an optical filter

*F*(

*ω*) can break this symmetry and prevent formation of nulls. One particular choice of

*F*(

*ω*) which achieves this is

*F*(

*ω*) is equivalent to using SSB modulation with an IQ-MZM and no optical filter present. However, such a sharp filter will be high in order; it would be preferable to use a low-order planar waveguide-based filter which can be integrated with the MZM. In this work, we study the two-branch MZI with a complex-envelope transfer function where

*ω*is the optical carrier frequency (rad/s) and

_{c}*t*is the time-delay difference between the two arms of the MZI. The delay

_{d}*t*can be tuned through temperature control. Such a filter has a periodic spectrum with period

_{d}*f*= 1/

_{FSR}*t*(Hz), the free spectral range (FSR). Figure 3(a) shows a schematic of the MZI and Fig. 3(b) shows a representative transfer function. In this work, we investigate the performance of a system based on such an MZI as the optical filter for preventing formation of nulls in the composite channel transfer function

_{d}*H*(

_{eq}*ω*). Since an MZI will not completely suppress one of the sidebands, we call this method of transmission vestigial-sideband (VSB) OFDM.

Note that according to Eq. (10), the MZI’s transfer function depends on two parameters, *ω _{c}* and

*t*. The FSR depends only on

_{d}*t*, but the frequency offset of the transfer function relative to the carrier depends on the product

_{d}*ω*. However, to tune the MZI to the desired operating point, one only needs to control

_{c}t_{d}*t*, because minute fractional changes in

_{d}*t*will change

_{d}*ω*by 2

_{c}t_{d}*π*. Thus, the frequency-center of the MZI transfer function can be controlled arbitrarily with negligible impact on the FSR. The FSR is essentially determined only by the fabricated length difference of the two waveguides.

The reason the MZI will eliminate channel nulls, as does a SSB filter, can be seen by examining Eq. (6) with *G*(*ω*) being the dispersion transfer function. We can without loss of generality assume *B* = 1. Then the equivalent channel transfer function is

*F*(

*ω*)| ≠ |

*F*(−

*ω*)|.

*H*(

_{eq}*ω*) is the sum of two phasors;

*H*(

_{eq}*ω*) = 0 if and only if these two phasors have the same magnitude and opposite angle. However, since |

*F*(

*ω*)| ≠ |

*F*(−

*ω*)|, these two phasors will have different magnitudes. Thus, the MZI prevents formation of a channel null.

## 4. Simulations

To demonstrate the effectiveness of VSB transmission in combating dispersion-induced channel capacity loss, we compare the achievable bit rates of VSB transmission with an ideal SSB transmitter. Both systems utilized the method of adding the carrier through a separate waveguide, with the laser power split evenly between the two paths. We simulated these two systems under the following conditions: 128 subcarriers with 10 samples as a cyclic prefix, 6-bit, 56 Gsam-ple/s DAC and ADC, 10 dB clipping ratio at the DAC and ADC, 20 GHz transmitter and 20 GHz receiver bandwidth, 16 dBm laser source, 6 dB MZM insertion loss, MZM drive strength of *x*_{0}/*V _{π}* = 1/2 (where

*V*is the MZM switching voltage), fiber dispersion of 18 ps/nm/km and loss of 0.2 dB/km, photodiode responsivity of 0.8 A/W, and receiver thermal noise of $16\hspace{0.17em}\text{pA}/\sqrt{\text{Hz}}$. Shot noise was included but the laser’s relative intensity noise (RIN) was neglected, since a CW laser can be designed for a low relaxation-oscillation frequency and thus a low RIN [20]. For the VSB system, the optical filter was an MZI with 90-GHz FSR and a null near the center of the lower sideband. The target BER for the link was 10

_{π}^{−3}.

To illustrate the creation of the VSB-OFDM signal using the MZI, we show a DSB-OFDM optical spectrum (without any low-frequency guard band) in Fig. 4(a), followed by MZI filtering in Fig. 4(b) and then superposition with the carrier in Fig. 4(c).

One of the unique advantages of OFDM is the ability to optimally allocate power and information among the subcarriers, according to the modified channel capacity formula

where*b*is the number of bits/symbol transmitted by the

_{i}*i*

^{th}subcarrier,

*SNR*is the signal-to-noise ratio (SNR) of the

_{i}*i*

^{th}subchannel, and Γ is the gap constant determined by the desired BER [21]. In our simulations, we chose a BER of 10

^{−3}. To optimize the power and bit allocation among the subcarriers, we employed Campello’s bit-loading algorithm, which is the optimal discrete-bit-allocation algorithm [22]. The performance gained by bit loading is the result of the non-uniform SNR over frequency. A frequency-varying SNR is also present in systems with multi-mode dispersion, resulting in significant gains through bit loading [23].

Due to the large carrier-to-signal ratio, the intermodulation from signal-signal beating was small compared to the receiver’s combined thermal and shot noise after 50 km of fiber. Thus, we eliminated the low-frequency guard band and allowed the bit-loading algorithm to determine optimal use of the entire 0–28 GHz band. In this case, the “noise” caused by signal-signal beating was a signal-dependent noise. Thus, we allocated the bits and power among the sub-carriers iteratively. After the first bit-loading iteration, the signal spectrum changed, which thus changed the signal-signal beating distribution and thus changed the SNR. This changed the optimal bit and power allocation among subcarriers, so the bit-loading process was re-iterated. This process was repeated and converged within a few iterations.

We first show the back-to-back sensitivity performance of VSB-OFDM for fixed bit rates of 56 Gb/s and 112 Gb/s in Fig. 5(a). For a comparison of techniques, we varied the transmission distance and compared the achievable bit rates of VSB and ideal SSB transmission, with the SSB signal generated by an ideal SSB filter with no insertion loss. To take into account the potential drift of the MZI relative to the carrier, the VSB simulations were also conducted for ±3 GHz offsets of the MZI relative to the carrier, as shown in shown in Fig. 5(b). Although an ideal SSB filter provides improved performance, it is only realizable with high insertion loss (or an IQ modulator with two identical MZMs driven by two identical DACs). We see that an MZI drift of ±3 GHz relative to the carrier has little impact on performance. We also compare VSB-OFDM to the straightforward approach of DSB transmission (which will suffer from channel fading) along with bit loading to prevent allocation of data to the nulled frequencies [24].

## 5. Experimental measurements

To experimentally demonstrate the feasibility of high bit rate VSB transmission using existing commercial components, we constructed the VSB transmitter depicted in Fig. 6. Note that this differed from the original VSB transmitter shown in Fig. 2 in that the optical filter was previously placed before the Y-junction. The only difference between the performance of these two configurations is that the modified system of Fig. 6 slightly attenuates the carrier component. We used this configuration in our experiments because it was simpler to construct: the MZM in parallel with a waveguide was implemented in our experiments using an I-Q modulator, with the I-MZM modulated with the DSB-OFDM signal and the Q-MZM unmodulated and biased away from the null. The Q-MZM thus operated as an unmodulated waveguide transporting the carrier. This thus required the MZI to be implemented as an external filter placed after the Y-junction between the MZM and carrier waveguide. The transmitted DSB-OFDM signal consisting of 512 subcarriers was produced offline using MATLAB and loaded into the memory of the Fujitsu LEIA DAC, operated at a sampling rate of 56 Gsample/s. The cyclic prefix length was 16 samples. Due to bandwidth and high-frequency SNR limitations of the DAC, the OFDM signal band was chosen to be the 0 to 19.6 GHz band rather than the 0 to 28 GHz band. Thus, the last 30% of the subcarriers were zeroed. In principle, the system could be implemented with only a 40 Gsample/s DAC if the OFDM signal band is from 0 to 19.6 GHz, but the clocking circuitry of our DAC required a minimum sampling rate of 56 Gsample/s. The modulator was a Sumitomo I-Q modulator with 20-GHz bandwidth, with the I-MZM modulated by the DAC. The MZI was implemented using the Finisar Waveshaper, an arbitrarily programmable optical filter. The MZI emulation had an FSR of 63 GHz, since 70% of 90 GHz (the simulation FSR) is 63 GHz. Its null was placed 13 GHz below the carrier frequency. The fiber channel consisted of 80 km of S-SMF, with a loss of 0.2 dB/km and dispersion of 18 ps/nm/km. The receiver consisted of a Newport InGaAs photoreceiver with 35 GHz bandwidth and an Agilent 80 Gsample/s, 33-GHz bandwidth real-time oscilloscope.

For these experiments, an Amonics Erbium-doped fiber amplifier was used to compensate for the following limitations in the experimental setup: (1) The waveguide for producing the carrier was part of a modulator and thus had insertion loss. (2) The programmable optical filter emulating the MZI had a 5 dB insertion loss. (3) The input-referred thermal noise of the receiver (consisting of a photoreceiver and oscilloscope) was many times higher than the value used in our simulations. The thermal noise value used in the simulations was based on specifications of integrated receivers used in existing commercial 100G transceivers. However, the purpose of these experiments was to demonstrate the practicality of the approach in combating dispersion, including the effects of MZI drift.

As seen in Fig. 7(a), the system is capable of transmitting 72 Gb/s at a BER of 10^{−3}. This provides ample margin for meeting the standard rate of 50 Gb/s/wavelength. Additionally, its performance is insensitive to ±3 GHz drift of the MZI relative to the carrier frequency, as shown in Fig. 7(b). In Fig. 8(a), we show the SNR of the composite channel from the transmitter’s digital output to the receiver’s digital output. In Fig. 8(b), we show the corresponding optimal bit allocation for the case of 72 Gb/s transmission. The 256^{th} subcarrier was zeroed due to strong DAC nonlinearity at that frequency.

## 6. Conclusions

We have presented a new technique of VSB transmission for an optically unamplified DD receiver. The method uses fewer optical components than typical SSB systems and can sustain larger link attenuation and splitting, making it ideal for cost-sensitive systems with link lengths within 80 km. Through simulation and experimental measurements, we have shown its ability to transmit beyond the standard rate of 50 Gb/s/wavelength and also illustrated its resilience to component drift.

## 7. Appendix

Here we compare the received electrical signal strength for the case of virtual carrier transmission and the case where the carrier is added by a separate waveguide. For simplicity, we consider the transmitted optical signal to be SSB in both cases. For the VSB case, this analysis is still approximately correct.

First consider the transmitter based on the virtual carrier. The SSB signal *x*_{+}(*t*) is produced by a summation of a DSB signal *x*(*t*) with its Hilbert transform *x̂*(*t*) [25]:

*C*exp(−

*jω*), where

_{B}t*C*is assumed real without loss of generality. To create this complex carrier, the MZM in the in-phase branch (I-MZM) is modulated with the real signal

*s*(

_{I}*t*) =

*x*(

*t*) +

*C*exp(−

*jω*) +

_{B}t*C*exp(

*jω*). Similarly the Q-MZM is modulated with the real signal

_{B}t*s*(

_{Q}*t*) =

*x̂*(

*t*) −

*jC*exp(−

*jω*) +

_{B}t*jC*exp(

*jω*). For any real system, the output of the DAC will be clipped to some extent; otherwise its dynamic range is wasted [26]. The previous expressions for

_{B}t*s*and

_{I}*s*do not explicitly include a term to represent the added clipping error, but for the following analysis, excluding this extra “noise” term in the expressions will not have much effect, as long as clipping is not extreme. However, it must be noted that clipping will limit

_{Q}*s*and

_{I}*s*to within ±

_{Q}*x*

_{0}, where ±

*x*

_{0}are the most positive and negative DAC output voltages. For convenience, we will choose

*x*

_{0}= 1.

If we consider the MZM transfer characteristic as approximately linear, then the relation between the MZM drive signal *s _{I}* (or

*s*) and E-field output is a constant scaling factor. This scaling factor depends on the magnitude of

_{Q}*s*relative to

_{I}*V*, the switching voltage of the MZM. We will denote this scaling factor by

_{π}*m*. For example, if the MZM drive signal is at its maximum of

*x*

_{0}= 1, then the MZM output will be

*mE*, where

_{in}*E*is the input field into the MZM. However, this neglects the insertion loss of the MZM. We represent the insertion loss with a scaling constant

_{in}*a*. Thus, for the previous example, the MZM output is

*amE*when the drive

_{in}*s*is at its peak.

_{I}Let *A _{cw}* be the amplitude of the CW source of the modulator. Since this source is split evenly between the I-MZM and Q-MZM, the output of the modulator, after summing I and Q branches, is

Since the transfer function of the fiber has a constant magnitude over the entire signal band, it can be neglected in the following comparisons, since it has the same effect on the received signal power in both cases. Then the received electrical signal is the product of the virtual carrier and the data signal:

Now consider a transmitter which adds the carrier through a waveguide parallel to a single MZM. In this case, the data signal *y*(*t*) is a DSB signal and let *E*[*y*^{2}(*t*)] = *E*[*x*^{2}(*t*)]. In order to make a fair comparison with the virtual carrier transmitter, the MZM should be driven with a signal of the same power in both cases. Since no virtual carrier is present here, the MZM should be driven with
$\sqrt{2}y(t)$. For simplicity, we consider an optical filter which generates an ideal SSB output:

*y*(

*t*) is converted to the SSB signal

*y*

_{+}(

*t*).

As before, the amplitude of the field from the CW source is *A _{cw}*. It is split into two paths, one which passes through an MZM and the other unmodulated. It can be easily shown that the receiver’s signal is largest when the split is equal in both paths. Thus, the output of the unmodulated waveguide is

*A*/2 (we can neglect the phase without changing the results) and the output of the modulated and filtered branch is $(1/\sqrt{2}){A}_{cw}am{y}_{+}(t)$. The resulting signal at the transmitter output is

_{cw}Comparing the amplitudes of the signals of (15) and (18), we see that the real carrier transmitter gives a received electrical signal that is larger by the factor

This can be related to the clipping ratio as follows. The clipping ratio is*R*=

_{cl}*x*

_{0}/

*σ*, where

*σ*is the standard deviation of the unclipped signal. Since we chose the normalization

*x*

_{0}= 1, we have

*σ*= 1/

*R*. The driving signal of the I-MZM or Q-MZM consists of a DSB data signal plus a sinusoidal virtual carrier. The optimal splitting of power between the data and virtual carrier is equal power in each [10]. At the MZM, the real sinusoid added to the DSB signal

_{cl}*x*has amplitude 2

*C*; thus, the power of

*x*is 2

*C*

^{2}. Thus,

*σ*

^{2}= 4

*C*

^{2}. This gives which substituting into (19) gives

## 8. Acknowledgments

The authors would like to acknowledge the financial support of Finisar Corporation. The authors also thank Prof. Olav Solgaard of Stanford University for helpful discussions.

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