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A novel electronic dispersion pre-compensation scheme for a directly modulated laser is described and experimentally demonstrated for transmission distances beyond 200 km using a low-cost laser packaged for 2.5-Gb/s while operated at 10.709-Gb/s. A single look-up-table (LUT) for the drive current is designed to mitigate the effects of fiber dispersion, the intrinsic nonlinear modulation response of the laser, and the laser package. Experimental results show that an 11-bit LUT can compensate the dispersion of 202 km of standard single mode fiber with a required optical-signal-to-noise-ratio of 18.61 dB at a bit error ratio of 3.8 × 10−3.
©2011 Optical Society of America
1. Introduction
A directly modulated laser (DML) provides a low cost transmitter for metropolitan systems operating at OC-192 (9.953-Gb/s) while offering a small footprint, low power dissipation and high output optical power in comparison to an externally modulated laser. Unfortunately, the transmission distance of DMLs is limited to about 30 km in the absence of inline dispersion compensation due to their significant wavelength chirp. Several solutions have been proposed to address this problem. Negative dispersion fibers can enhance the transmission limit to over 100 km [1], however, this solution requires replacing the existing metro fiber base. A transmission distance of 250 km can be achieved using dispersion supported transmission (DST) [2] or a chirp managed laser (CML) [3]. The former employs a tunable low-pass electrical filter at the receiver to compensate the fiber transfer function, while the latter uses an optical filter at the output of the transmitter. DST requires optimizing the receiver for each transmission distance, while the CML uses an additional wavelength specific component.
A more adaptive solution is to compensate for dispersion in the electrical domain at the transmitter. Electronic dispersion pre-compensation (EDC) has been successfully applied to externally modulated systems for compensating the effects of dispersion [4] and narrow optical filtering [5]. For transmitters that use a dual-drive or dual-parallel LiNbO3 Mach-Zehnder modulator, the determination of the pre-compensating drive voltages is relatively straightforward since a simple model of the modulator is sufficiently accurate for the back-calculation and the two drive voltages can be used to generate the required amplitude and phase of the transmitted optical signal. Digital signal processing (DSP) is then used to control both the phase and amplitude of the pre-compensated optical field enabling a transmission distance of 3840 km using the differential phase shift keying modulation format at 10-Gb/s [4]. The pre-compensated drive signals are synthesized by two 21.418-GSa/s digital-to-analog converters (DACs) with 6 bit resolution implemented within a single application specific integrated circuit [4]. However, for a DML the description of the modulation dynamics is more complicated and the amplitude and phase of the transmitted optical signal cannot be generated independently by a single drive current. A solution involves shaping the drive current through a nonlinear processing unit with the control variables optimized for a minimum bit error ratio (BER) at a specified transmission distance. This approach has been adopted in [6], where a particle swarm optimization algorithm was used to select the coefficients of an artificial neural network.
In this paper, we develop a novel optimization scheme for EDC using a DML operating at 10.709-Gb/s. A look-up-table (LUT) for the optical power is utilized as a nonlinear processing unit, followed by reversal of the large signal rate equations to obtain the pre-compensated drive current. We extend our previous work [7,8], to include a single LUT to accommodate the nonlinear mapping between the drive current and the desired output optical power. Using this LUT the pre-compensated drive current can be practically synthesized using a 21.418-GSa/s DAC. We have successfully applied this scheme to a commercially available DML transmitter packaged and specified for 2.5-Gb/s transmission, while operated at 10.709-Gb/s.
2. Electronic dispersion pre-compensation
A schematic of the pre-compensating transmitter is shown in Fig. 1 . The system employs the non-return-to-zero (NRZ) intensity modulation format. The input data bit stream is mapped to digital samples of the pre-compensating signal, with 2 samples per bit, using a LUT as part of a DSP block. The LUT entries are pre-calculated using offline processing for a specific target distance. The generated digital samples are sent to a 21.418-GSa/s DAC with 6-bit resolution. The analog output of the DAC is then amplified and applied to a distributed feedback DML.The task of calculating the entries of the LUT in Fig. 1, must include the effects of:
- 1. the DML adiabatic and transient chirp on pulse propagation,
- 2. the nonlinear mapping between the input current and the output optical power, and
- 3. the limited bandwidth of the DML transmitter packaged for 2.5-Gb/s operation.
- 1. find the near optimum powerat the output of the DML which results in a low BER at the receiver,
- 2. determine the appropriate drive current needed to generate the required while mitigating the nonlinear response of the DML, and
- 3. factor in the DML package response when calculating.
At this stage it is important to note that there are two distinct types of LUTs used in this study. The first is a hypothetical LUT containing the optical power samples used for optimization purposes only as in subtask one, and is referred to as the power LUT. The second is a larger LUT which contains current samples and is the outcome of the entire offline processing, including subtasks two and three. This LUT is accessed by the DSP block depicted in Fig. 1 and is referred to as the current LUT.
2.1 Mitigating dispersion
As there is no closed-form expression of the required optical power at the output of the DML for dispersion pre-compensation, optimization methods are needed. Initially, we start with the expression of the optical field at the output of the DML [9]:
where г denotes the mode confinement factor, V is the active layer volume, ε is the gain compression factor, η0 is the differential quantum efficiency, h is Planck’s constant and v is the photon frequency. It is clear from Eq. (1), that the optical field is a complex nonlinear function of the output power. The interaction of the optical field with fiber dispersion causes intersymbol-interference resulting from the impact of bits before and after the detected bit. As a consequence, a LUT for the output power is an appropriate choice for a nonlinear processing unit. The LUT approach has been previously used in compensating dispersion and self-phase modulation in externally modulated systems [10,11]. In general, a LUT with 2m entries and n samples per entry can be defined for the optical power. An example of power LUT entries for m = 3 and n = 2 is illustrated in Fig. 2 . The input bit sequence is stored in a 3-bit sliding shift register, which is used to address the LUT, generating 2 samples per bit. The information-bearing power signal is a result of the interpolation of the power samples, emulating the output of an ideal 21.418-GSa/s DAC.The LUT entries are initialized using a 27 de Brujin bit sequence (DBBS) with a raised-cosine (RC) NRZ optical power profile. The schematic illustrating the process of establishing and optimizing the LUT is shown in Fig. 3 . The optimization is aimed at finding the power profile and its associated chirp at the output of the DML, which results in a minimum log10(BER) for a specific fiber length, while treating the optical phase at the receiver under direct detection as a degree of freedom. The optical field is subsequently propagated down a single mode fiber (SMF) with a dispersion parameter D = 16 ps/km/nm (nonlinearities are neglected). The system is loaded with additive white Gaussian noise (AWGN) before the receiver, which is composed of a 20 GHz second-order Gaussian optical band-pass filter (OBPF), followed by an ideal photodiode with square-law detection and a 5 GHz fifth-order Bessel electrical low pass filter (ELPF). Finally the BER is estimated using the Karhunen-Lòeve method [12]. The LUT entries (optical power samples) are directly optimized using MATLAB’s nonlinear constrained multi-variable minimization function fmincon.
Fig. 3 Scheme for establishing and optimizing the power LUT. AWGN: additive white Gaussian noise; OBPF: optical band-pass filter; ELPF: electrical low pass filter; BER: bit error ratio.
The advantages of using an optical power LUT as oppose to optimizing a current LUT directly are two-fold. Firstly, the optical field at the output of the DML is readily available using Eq. (1), rather than solving the DML rate equations, which is computationally intensive, as the optimization method would need to re-evaluate the output optical field for every perturbation of the parameter space. Secondly, excluding the DML rate equations relaxes the requirements on the optimization method as it does not need to compensate for the nonlinear distortions appearing at the output of the DML, which is treated in the next subsection.
3.2 Laser nonlinear response
In the case of externally modulated systems, the nonlinear response of the Mach-Zehnder modulator can be compensated through an inverse cosine transfer function. However, for DMLs the nonlinear mapping between the drive current and the optical power is described by large signal rate equations. These equations relate the carrier density, photon density and optical phase to the modulating current. In general, DMLs exhibit damped periodic relaxation oscillations due to the intrinsic resonance in the laser cavity. It is possible to reverse the large signal rate equations through algebraic back-calculation and find the required input current that produces a specific target output power profile [13]. However, the exact expression for is rather complicated and cannot be formulated directly as an analytical function of [13,14]. Here, approximations are performed through removing terms with small numerical contributions yielding the following closed-form expression for the required input current as a function of the target power [14]:
A, B, C, and D are constants, which depend on the laser rate equation parameters and are given by: N0 is the carrier density at transparency, τp and τe are the photon and electron lifetimes, respectively, vg is the group velocity, a0 is the active layer gain coefficient, βsp is the fraction of spontaneous emission coupled into the lasing mode and q is the electron charge. Using Eq. (2) it is theoretically possible to fully linearize the DML response through carefully tailoring the modulating current.Once the optimum optical power LUT is found using the procedure outlined in section 3.1, a longer DBBS sequence (to accommodate the DML nonlinear memory) is used to address the power LUT and generate the target power sample values Ptar(k), where k is the sampling time. After upsampling to increase the numerical bandwidth, the back-calculation procedure in Eq. (2) is used to reverse the laser rate equations and obtain the required input drive current.
3.3 Laser package
For metro-area optical links, it is of interest to achieve 10.709-Gb/s transmission using low-cost 2.5-Gb/s DML transmitters, while fulfilling the requirements for extended reach [15]. In this paper, the small signal intensity modulation (IM) frequency response of the DML is used to extract and alleviate the effect of the laser package [16]. The rate equations parameters are extracted through subtracting (in dB) the measured IM responses just above threshold and well above threshold and employing a curve fitting procedure [16]. Since the subtracted IM response depends solely on the intrinsic response of the DML, the effect of the package response can be isolated. Once the DML rate equation parameters are determined the frequency response of the laser package can be extracted and compensated for when calculating the required drive current obtained in section 3.2. Examples of the measured IM responses of the 2.5-Gb/s DML used in the experiments with a threshold current Ith = 21.1 mA and bias currents of 1.18 Ith and 3.55 Ith are shown in Fig. 4 , with the back-to-back received electrical eye-diagram as an inset.
Fig. 4 Measured and simulated (dashed lines) IM response at 1.18 Ith and 3.55 Ith (inset back-to-back eye-diagram, Timebase = 30 ps/div).
4. Offline processing
To practically generate the pre-compensating drive signal for the DML, Eq. (2) must be implementable in real-time. As this is difficult to attain with analog or digital circuits, we define a single current LUT for EDC. The contents of this current LUT are determined through offline processing as shown in Fig. 5 . Here, a 211 DBBS is used to address a 3-bit optimized optical power LUT. The power samples are interpolated at a higher sampling rate, to increase the numerical bandwidth, followed by the back-calculation procedure to determine the required input current. The effect of the DML package is reduced through multiplying the spectrum of the current with the inverse transfer function of the package. The resulting drive current is then band-limited to 10.709-GHz, sampled at 21.418-GSa/s and quantized to 64 levels. Finally an 11-bit sliding shift register is used to address an 11-bit current LUT. The need to increase the size of the current LUT in comparison to the optical power LUT is due to the pattern dependent nonlinear memory needed to inverse the DML response.
The offline processing depicted in Fig. 5 has been performed for target distances of 152 km, 202 km and 252 km using 3-bit, 3-bit and 5-bit optical power LUTs, respectively. The size of the current LUT was set to 11-bits, with a total memory requirement of 3 KBytes assuming a DAC with 6 bit resolution [17]. The DML used in the offline processing and experiment is a DFB laser with a multi-quantum-well active layer operating at 1531.5 nm. The rate equation parameters are reported in Table 1 .
Table 1. DML rate equation parameters
5. Experimental set-up
The experimental set-up is shown in Fig. 6 . An integrated circuit was used that includes a memory block and a 21.418-GSa/s DAC with 6 bit resolution allowing arbitrary waveform generation (AWG). The experiment was performed using a 214 DBBS. There was no feedback from the receiver to the transmitter for further optimization of the LUT values or offset filtering at the receiver to mitigate the combined effect of laser chirp and fiber dispersion [15]. The per-span launch power was 4 dBm. A broadband source (BBS) with a variable optical attenuator (VOA) was used to load AWGN and facilitate measuring the dependence of the BER on the optical-signal-to-noise-ratio (OSNR) (0.1 nm noise bandwidth). The receiver was composed of a pre-amplifier, direct detection photodiode, low pass filter, RF amplifier and clock-recovery (CR) module. The BER was measured using direct error counting. The current LUT resulting from the offline processing was used to generate pre-distorted digital samples, which were stored in the AWG memory. To assess the limitation due to the 11-bit current LUT implementation, the back-calculation procedure of Eq. (2) was calculated for the entire 214 DBBS and stored in the AWG memory, in effect, mimicking an infinite size current LUT.
Fig. 6 Experimental setup. DAC: digital-to-analog converter, DML: directly modulated laser, EDFA: erbium doped fiber amplifier, OBPF: optical band-pass filter, BBS: broadband source, VOA: variable optical attenuator, OSA: optical spectrum analyzer, CR: clock recovery and ELPF: electrical low-pass filter.
6. Results
The dependence of the measured BER on the OSNR (0.1 nm noise bandwidth) for back-to-back, 152 km and 202 km transmission with the infinite size and 11-bit current LUT is shown in Fig. 7 . A forward error correction (FEC) coding limit of BER = 3.8 × 10−3 is assumed. For comparison, the back-to-back performance was evaluated by driving the laser with a RC pulse train (roll-off factor of 1.0) and a current swing between 1.18 Ith and 3.55 Ith.
Fig. 7 The dependence of the measured BER on the OSNR (0.1 nm noise bandwidth) for the back-to-back case, 152 km and 202 km transmission with an infinite-size and 11-bit current LUT. (FEC limit BER = 3.8 × 10−3 dashed line).
The BER before forward error correction decoding at full OSNR and the required OSNR for a BER of 3.8 × 10−3 for the transmission distances of 152 km, 202 km and 252 km with an infinite size and 11-bit current LUT is reported in Table 2 . The results indicate that using a single 11-bit current LUT, EDC with a DML at 10.709-Gb/s can reach a transmission distance of 202 km with a required OSNR of 18.61 dB. This is a remarkable improvement given the dispersion limit of this particular DML is below 20 km. Implementing the back-calculation as an 11-bit LUT results in a ~1.3 dB OSNR penalty at the FEC limit of BER = 3.8 × 10−3. A distance of 252 km can be reached with a required OSNR of 25.36 dB using an 11-bit LUT.
Table 2. Measured performance of EDC for 10.709-Gb/s using a 2.5-Gb/s DML
The simulated and measured eye-diagrams of the transmitted and received signal for the target distances of 152 km and 202 km with Eq. (2) calculated for the entire 214 DBBS and stored in the AWG memory (infinite size current LUT) are shown in Fig. 8 . Both simulated and measured eye-diagrams indicate a remarkable eye-opening after 202 km with an OSNR penalty of 2.46 dB with respect to back-to-back performance. Although experiments show the promise of applying this method for compensating 252 km, simulations show that distances up to 350 km, can be compensated using a laser with a lower linewidth enhancement factor and a DAC with higher sampling rate [8].
Fig. 8 The eye-diagrams of the transmitted and received signal for the target distances of 152 km and 202 km when an infinite size current LUT is used. (Timebase for experimental results 30 ps/div, simulation results 93 ps/div).
7. Conclusion
In this paper, a novel EDC technique was developed and demonstrated for enhancing the performance of low cost 2.5-Gb/s DMLs operated at 10.709-Gb/s. A single current LUT was designed to mitigate the effects of fiber dispersion, the DML nonlinear response, and the laser package. A tenfold increase in the dispersion limited transmission distance has been demonstrated using a single 11-bit LUT for the drive current and a 21.418-GSa/s 6-bit DAC. Experimental results show that an 11-bit LUT can compensate the dispersion of 202 km of standard single mode fiber with a required OSNR of 18.61 dB at a BER of 3.8 × 10−3.
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