10.1.1 Introduction

The demand for high-capacity long-haul telecommunication systems has increased over the recent years. To achieve high throughput of signals with minimum errors, different advanced modulation formats, such as ASK, PSK (coherent and differential in-coherent), and FSK, have been proposed, and comparisons are made to determine which modulation format would offer the best transmission performance. In countering performance degradation, modulation formats aim to narrow down the optical spectrum to enable close channel spacing in the network. They increase symbol duration, so that more uncompensated dispersion accumulates before intersymbol interference (ISI) becomes significant. Furthermore, this format is more resilient to fiber nonlinearities and optical signal distortion.

Modulation format is important in determining the performance of 40 Gbps optical fiber communication systems. DB and continuous phase modulation (CPM) are shown to offer high spectral efficiency [14,15]. DB modulation formats minimize ISI impairments in a controlled way instead of trying to eliminate it. It is possible to achieve a signaling rate of equal to the Nyquist rate of 2W symbols per second in a channel of bandwidth W Hz. Optical DB technique has received much attention due to its high dispersion tolerance and high-frequency utilization efficiency by means of spectral narrowing. DBM format is similar to the non-return-to-zero (NRZ) format, with inclusion of phase coding. The phase characteristics of DBM signals compensate for the group velocity dispersion by reducing the spectral component in conventional NRZ modulation. ISI is reduced, since bit patterns such as 101 are transmitted with the ones carrying the opposite phase. Therefore, if pulses spread out into the zero time slot, due to dispersion, they tend to cancel each other out. The recovering of signals at the receiver is relatively simple. Furthermore, direct detection receiver can be used to simplify and can be offered as a low cost solution. There are two types of DBM schemes, which are constant phase and alternating phase in blocks of logics “1s.”

This chapter presents the models for photonic transmission with optical channels operating under DBM format. This includes the development and implementation of the photonic transmitter, the optical fiber propagation, and the optoelectronic receiver. DBM encodes two-level electrical signal to three-level electrical signal before modulating the lightwave carrier. The transmitter of the Simulink model will consist of a DB encoder and a dual-drive Mach–Zehnder interferometric modulator (MZIM). A baseband modulation is first implemented in the DB encoder, which encodes the binary signal into three levels of signals—“1,” “0,” and “−1.” MZIM is an electro-optic modulator that converts the electrical signal to optical signal.

The DB or phase-shape binary modulation formats can be generated by modulating a dual-drive MZIM with the bias voltage located at the V_π and the amplitude of the signals must be at 0 and 2V_π. Recent works have shown that the driving voltages for the modulator can be reduced to generate variable-pulse-width DB optical signals. However, the pulse width of the DB-DPSK has not been thoroughly investigated under the alternating phase of the “1” coded bits. That means the “0,” “π,” “0,” “π” phases of consecutive “1” in contrary of conventional DB formats. We also present modeling performance of alternating-phase DB modulation with a full-width half mark (FWHM) ratio with respect to the bit period of 100%, 50%, and 33%, and compare with experimental transmission of carrier-suppressed DPSK over 50 km of SSMF and dispersion compensation. For the DB case, the transmission without dispersion compensation over the same SSMF length offers better performance for 50% FWHM DB modulation and slightly poorer for 33%. The transmission performance, the bit error rate versus receiver sensitivity, of these DB modulation formats are compared with the carrier-suppressed DPSK experimental transmission.

Section 10.2 of this chapter describes the fundamental aspects of the DBM format. It is followed by a description of each component of the 40 Gbps DBM photonic transmission system in Section 10.3. Section 10.4 describes the implementation of the Simulink model of the communication system. Next, Section 10.5 gives the simulated results. Finally, comparisons with theoretical analyses and other modulation formats are given.

10.1.2 DBM Formatter

Modulation format aims to modulate one or more field properties to suit system needs. There are four types of field properties, which are intensity, phase, polarization, and frequency. Symbols are constellated in one or more dimensions, in order to carry more information and to travel a further distance. Data modulation format is the information-carrying property of the optical field.

DBM format has become an attractive modulation format over the recent years, compared to other formats, such as NRZ and return-zero (RZ). This is due to the fact that it can overcome the fiber chromatic dispersion in high-capacity transmissions. The characteristics of the DBM format make it the preferred format.

DBM schemes can be described as correlative-level coding or partial-response-signaling schemes. Correlative coding schemes can be implemented by inserting ISI to the transmitted signal in a controlled manner.

A signaling rate equal to the Nyquist rate of 2W symbols per second in a channel of bandwidth W Hz can then be achieved. “Duo” in the word duobinary indicates the doubling of transmission capacity of a conventional binary system. DBM format is, in fact, NRZ modulation with an inclusion of phase coding. The one bits in the data input are phase modulated. For instance, for a bit pattern of 101, this data will be transmitted with the ones carrying opposite phase, 0 and π. If the pulse of the one bits spreads out to the zero time slot in between, they will cancel each other. This effect increases the dispersion tolerance, and allows the signal to be transmitted over a longer distance.

DB coding converts a two-level binary signal of 0’s and 1’s into a three-level signal of “−1,” “0,” and “+1.” This is done by, first, applying the binary sequence to a pulse-amplitude modulator to produce two-level short pulses of amplitudes −1 and +1, with −1 corresponding to 0 and +1 corresponding to 1. This sequence is, then, applied to a DB encoder to produce a three-level output of “−2,” “0,” and “2.”

As shown in Figure 10.1 input sequence, {a_k} of uncorrelated two-level pulses is transformed into {c_k}, which is a sequence of correlated three-level pulses. The correlation between adjacent pulses is equivalent to introducing ISI into the transmitted signal in an artificial manner. The DB encoder is simply a filter involving a single delay element and a summer, as shown in Figure 10.2. However, once errors are made, they tend to propagate through the output. This is because a decision made on the current input a_k depends on the decision made on the previous input a_k−1. Therefore, precoding is needed to avoid this error propagation phenomenon. Binary sequence, {b_k}, is converted into another binary sequence, {d_k}, by modulo-2 addition, exclusive OR of b_k and d_k−1, as shown in Figure 10.3.

The three-level DB output, {c_k}, is then modulated into a two-level optical signal by an external modulator. The most commonly used external modulator is the MZIM. The optical DB signal has two intensity levels, “on” and “off.” The “on” state signal can have one of two optical phases, 0 and π. The two “on” states correspond to the logic states “1” and “−1” of the DB-encoded signal, {a_k}, and the “off” state corresponds to the logic state “0.” Figure 10.4a shows an example of the original binary signal, the DB-encoded signal, and optical DB signal, and then Figure 10.4b shows a summary of the coding rule.

10.1.3 40 Gbps DB Optical Fiber Transmission Systems

Ultra-long terrestrial networks, transmitting signals at a bit rate of 40 Gbps, has matured over recent years. Various advanced modulation schemes, such as RZ, NRZ, NRZ-DPSK, and RZ-DPSK, have been proposed to achieve extended reach and improved capacity of communication systems.

Figure 10.5 shows the typical DWDM optical fiber communication system. Signals are modulated at the transmitters and are multiplexed together at the wavelength multiplexer before transmitting them into the fiber. The fiber link is divided into a number of spans. Each span consists of an SSMF and a dispersion-compensating fiber (DCF). The EDFA is used to compensate for the optical power loss of the transmission span. At the end of the fiber, the signals are demultiplexed and detected at the receivers.

DBM format has become popular compared to other modulation formats because it extends the transmission distance as limited by fiber loss, without regenerative repeaters. It extends the dispersion limit without additional optical components, such as the DCF. Chromatic dispersion has become a main effect that limits the transmission distance. The optical three-level transmission can overcome this limitation since narrowband signals have higher tolerance to chromatic dispersion compared to broadband signals. Furthermore, DB optical fiber communication system can suppress stimulated Brillouin scattering (SBS).

The main modules of the communication system are the transmitter, optical fiber, and the optoelectronic receiver, as shown in Figure 10.6. The transmitter consists of the DB encoder and the MZIM. A series of 0’s and 1’s is modulated under the DBM scheme. These three-level electrical data are then used to modulate the laser source, producing a two-level optical signal. This modulated signal are transmitted along an optical fiber transmission link toward the electro-optic receiver. The signal will be detected using a photodetector, which converts the two-level optical signal back into an electrical signal. Optical amplification can be done at some point along this transmission link to minimize the effect of fiber loss.

10.1.4 Electro-Optic Duobinary Transmitter

A transmitter modulates and converts incoming electrical signals into the optical domain. Depending on the nature of the signal, the resulting modulated light may be turned on and off, or may vary linearly in intensity between the two levels. The output of the DB transmitter is the modulated lightwaves switched on and off at transitional instances of the input electrical signal. In general, a DBM transmitter is shown in Figure 10.7, consisting of a monochromatic laser source, a coder, and a photonic modulator. Binary data are encoded by a DB encoder. This resulting three-level electrical signal is converted into a two-level optical signal using the folding characteristic of an optical MZIM. It is then transmitted into the optical fiber.

There are two types of DB transmitters. The conventional DB transmitter, as previously mentioned, includes a dual-drive MZIM driven by three-level electrical signals in a push–pull configuration. It is proposed that three-level signals may experience significant distortion in electrical amplifiers operating in saturation, leading to penalties for long word lengths. It may also cause the degradation of receiver sensitivity. For these reasons, a second type of DB transmitter has been proposed. This type of transmitter has the MZ modulator driven by only two-level electrical signals. The optical DB signal generated is the same as the DB transmitter type one, that is, constant phase in blocks of 1’s.

10.1.5 DB Encoder

The DB encoder encodes the binary signals, which is a sequence of 0’s to a three-level electrical signal. The DB signal is a fundamental correlative coding in partial response signaling. A DB encoder consists of a precoder and a DB coder. A precoder is used before DB coding to allow for easier recovery of binary data at the receiver, and to avoid error propagation. The precoder is a simple binary digital circuit that consists of an exclusive OR (XOR) and a one-bit delay feedback. The DB coder is a filter consisting of a single delay element and a summer.

Binary data input is precoded, with initialization of the one-bit delay to 0. The output of the DB precoder is, then, modulated by a pulse-amplitude modulator, to produce a two-level electrical signal with amplitude of −1 and 1. The DB signal is produced by adding the data delayed by one-bit period to the present data. This DB signal is a three-level electrical signal of −2, 0, and 2. Finally, it is converted to a level of −1, 0, and 1. The three-level is mapped into the optical domain by modulating both amplitude and phase. The “+1” and “−1” levels have the same optical intensity but opposite optical phase. The DB encoder structure is shown in Figure 10.8.

10.1.6 External Modulator

Although the electro-optic modulator has been described in Chapter 2, it is essential here to revisit the operation of the MZIM for DB operation. In an MZIM, the input optical carrier is split into two paths via a Y junction. This Y junction splits the input signal into E_i/√2 each. The resultant signal is

where V_π is the voltage to provide a π phase shift of each phase modulator, and V(t) is the driving voltage. Note that, in this equation, the term e^jωt (ω = optical angular frequency) indicating the optical wave phase is removed. The transfer relationship between the input and output of this MZIM is as shown in Figure 10.9. It is accompanied by a phase modulation of exp(jφ(t)) with φ(t) = πV(t). For V(t) from 0 to V_π, E_o and E_i have the same phase, and as for V(t) from V_π to 2V_π, E_o and E_i have different phases.

MZIM can be single drive or dual drive. Single-drive x-cut LiNbO₃ MZM has no phase modulation along with the amplitude modulation. It follows the transfer characteristics of Figure 10.9. Dual-drive x-cut LiNbO₃ MZIM, on the contrary, has two paths phase modulated with opposite phase shifts in a push–pull operation. The V_π in Figure 10.9 is reduced by half in this case. For dual-drive y-cut LiNbO₃ MZIM, two paths are driven by complementary signal with V₁ equals to –V₂. The output electric of a dual-drive MZIM is

DB optical signal is generated by driving a dual-drive MZIM with push–pull operation, as shown in Figure 10.10.

One arm is driven by the DB signal and the second arm is driven by the inverted DB signal. Figure 10.11 [6] shows the operation of the MZIM. The output electric field E_o(t) can be expressed as

where E_i is the input electric field, Δϕ(t) is the phase difference between the lightwaves propagating in two optical waveguides, and ϕ₀ is a constant when the MZIM is driven in a push–pull operation.

At point B of Figure 10.11, the phase of the output optical signal is inverted. The optical DB signal is dependent on the biasing point of the driving signal, which is the electrical DB signal. By biasing at point B in Figure 10.11, “−1” and “+1” level of the electrical DB signal will correspond to the “on” state of the optical signal, whereas the “0” level will correspond to the “off” state. To achieve the effect of carrier suppressed, there must be a π phase different between the two arms.

10.1.7 DB Transmitters and Precoder

The transmitter model, generally, consists of the DB coder and the MZIM. The DB coder encodes the incoming binary sequence of 0’s and 1’s to DB electrical signal. This signal is, then, used to drive the arms of the dual-drive MZIM. One arm is driven by the DB signal, and the other arm is driven by the inverted DB signal. The Bernoulli binary generator generates a random sequence of binary electrical signals. It is set to generate the data at a rate of 40 Gbps. This signal is encoded by the DB encoder, which consists of a DB precoder and a DB coder. The first output of the encoder is shifted up by 1 to produce levels of “0,” “1,” and “2.” Figure 10.12 shows a conventional Simulink model of the transmitter for DB. This electrical DB signal is sent to the phase shift block, as shown in Figure 10.13, to represent these levels with a certain phase. This, in fact, represents the biasing point on the transmittance curve. For dual-drive MZIM, the driving signal is biased at V_π/2. The second output of the DB encoder is the inversion of output 1. This output is used to modulate the second arm of MZIM. The output 2 signal is shifted down by −1, to bias at the point −V_π/2 of the transmittance curve. MZIM is an amplitude modulator, accompanied by a shift of phase. This modulation is also called AM-PSK. This lightwave, which is the sine wave produced by the sine wave function, is modulated by the DB signal through the complex phase shift block. The input sine wave is shifted by the amount specified at the Ph input.

The DB coder consists of a precoder and a coder, as shown in Figure 10.14. The precoder is a differential coder, with an exclusive OR (XOR) gate and a one-bit delay feedback path. The addition of −0.5 and division by 2 function as the amplitude modulator, which shifts levels of the signal from “0” and “1” to “−1” and “+1.” The signal is, then, added to its one-bit delay to produce a three-level DB signal of level “−2,” “0,” and “+2,” followed by a conversion to a level of “−1,” “0,” and “+1.” The summation of the signal with its one-bit delay is the DB coder. For the second output, the output of the differential coder is inverted, before going through the same operation as Out1. Zero-order hold is placed before the output of the DB encoder functions to discretize the signals to have a fast-to-slow transition of signals. It holds and samples the signal before transmitting it out. If the signals are transmitted out without the zero-order hold, the transition to “0” level will be overseen. The signal will only have two levels, which are “−1” and “+1.”

10.1.8 Alternative Phase DB Transmitter

Two types of DB transmitter model are proposed. The conventional DB transmitter, as mentioned previously, uses a dual-drive Mach–Zehnder modulator driven by three-level DB electrical signals. The MZIM shown in Figures 10.15 and 10.16 is the DB transmitter type 2, and is usually driven by a two-level electrical signal. In some cases, this three-level driving signal may experience significant distortion in electrical amplifiers operating at saturation. This may lead to penalties for long word lengths. It may also occur that there will be a degradation of receiver sensitivity. Due to these uncertainties, an alternative DB transmitter, as shown in Figure 10.15 and 10.17, is proposed. This second type of DB transmitter has the MZIM driven by two-level electrical signals. It consists of a differential encoder, a one-bit period electrical time delay, and an MZ modulator. One arm of the dual-drive MZ modulator is driven with the signal from the original signal, whereas the other arm is driven by the inverted signal, delayed by a one-bit period. Both DB transmitters produce the same result, which is a constant phase in blocks of 1’s.

10.1.9 Fiber Propagation

As described in Chapter 3, the fiber propagation model models the linear and nonlinear dispersion effects that exist over the entire length of the optical fiber can be represented by the NLSE including the SPM, other nonlinear effects can also be included, given by

With β₁ the lightwave group delay, β₂ and β₃ are the first-order and second-order group velocity dispersions, γ is the nonlinear coefficient, and A is the pulse envelope. NLSE can be solved by the split-step Fourier method (SSFM) that integrates two main steps of the split-step model, the nonlinear effects act alone in frequency domain and then the linear effects in the linear Fourier transform domain.

where L and N represent linear and nonlinear operators, respectively, which can be extracted from the NLSE.

The fiber propagation block, as shown in Figure 10.18, consists of a Gaussian filter, a gain factor, and the single-mode fiber (SMF) model. The SMF model is shown in Figure 10.19. This model is based on the SSF method. It splits the fiber into a number of small sections. All parameters needed for the SSF operations are concatenated into a matrix, before passing it to the MATLAB function. The MATLAB function block solves the NLSE using the SSFM. Linear operation is implemented in all steps. When the peak power is greater than the nonlinear (SPM) threshold, the nonlinear operator is activated. In this fiber propagation model, a buffer is incorporated at various locations along the propagation path. The buffer is used to redistribute the input samples to a new frame size—in this case, a larger frame size than that of the input. Buffering to a larger frame size yields an output with a slower frame rate than the input. The “Unbuffer” block unbuffers the frame-based input into a sample-based output. The buffer used in this model determines the number of bits sent into the fiber, which is the SMF block.

Probes are connected at two different points of the fiber propagation model. These probes determine the sampling time at these points. The sampling time of 2.5e⁻¹¹ indicates down-sampling to baseband. At the baseband, the complex envelope of the signal is extracted and transmitted through the fiber, which is represented by the SMF block shown in Figure 10.18. However, the phase contents of the signal are maintained and are transmitted through the fiber. These phase components of the DB signal are important, because it increases the dispersion tolerance and, thus, allow the signal to travel a longer distance.

10.3.1 DB Encoder

The DB encoder is the first implemented model in this 40 Gbps DB optical fiber communication system for the generation of three-level DB electrical signals. Scopes are probing at various points of the DB encoder, as shown in Figure 10.14. All time scopes are set to the same range to allow for comparisons of the bits within the same range. The temporal sequences at the outputs of the encoder for driving the MZIM are shown in Figure 10.23. Scope 1 shows the data generated by the Bernoulli binary generator. Scopes 2–4 show the output at each arm. A bit “0” is encoded as “+2” or “−2,” while the bit “1” is encoded as 0. This agrees with the DB coding scheme. They also show a three-level electrical signal. Scope 4 is the inverted version of scope, as expected, due to the NOT gate applied to the second arm.

10.3.2 Transmitter

The transmitter includes the DB encoder and MZIM. After the output of the DB encoder is verified and checked to produce the correct signal, the levels of the signal are represented with a phase. This phase is used to shift the laser source, produced by the sine wave function. The testing of the implemented DB transmitter includes observing the eye diagram and power spectrum at the output. Time scopes are attached at various points of the transmitter to observe the signal at these points. Spectrum scopes are connected at the output of the transmitter, which is after the summation of both arms of MZIM and to each arm of the MZIM to observe the power spectrum at these arms. Some adjustments need to be made to the transmitter model in order to observe the power spectrum. The sine wave function is set to produce a wave of 200 GHz, rather than 193 THz. This is to enable the observation of the spectrum centered at a lower frequency, and better spectral resolution. The zero-order hold that functions to hold and sample the incoming signal is set to 1e−12, so that the x-axis of the spectrum scope is in the THz range. The obtained results, as shown in Figure 10.24, reflect the results expected from experiments and theories. The power spectrum for a 5 Gbps DB optical fiber communication system is shown in Figure 10.25a [6]. This is used to verify the power spectrum obtained from the Simulink model. Spectrum (c) of Figure 10.26 corresponds to the Spectrum Scope in Figure 10.18. The obtained spectrum reflects on that in Figure 10.24a, with the shape approximately the same. The bandwidth of the obtained spectrum corresponds to the data rate, as in Figure 10.25a. The spectrums obtained are centered at 200 GHz, which is the carrier frequency of the model. Spectrum (c) is carrier suppressed, while the other two spectrums are not. This is as expected from the DBM format. Due to the π-phase difference in the two arms of MZIM, the output is expected to have its carrier suppressed.

Further verification of the DB transmitter Simulink model is carried out by monitoring the eye diagram at the output of the transmitter. The observation prior to the transmission block in the overall system, shown in Figure 10.27, is used to observe the eye diagram before transmission into the fiber. The eye diagram obtained, as shown in Figure 10.28, has an “open eye” with an amplitude of 0.6. It reflects the one in Figure 10.25. For a range of 100 ps, four “eyes” are obtained, giving one “eye” 25 ps. This proves that the eye diagram is correct, since the data rate is 40 Gbps, which equals 1 bit every 25 ps.

10.3.3 Transmission Performance

The overall performance is observed at the receiver of the 40 Gbps DB optical fiber communication system. The eye diagram and power spectrum are observed by the spectrum scope and vector scope attached inside the receiver. Eye diagrams show the distortion and attenuation of signals at various lengths of the fiber. When the “eye” of the eye diagram closes, the signal is severely distorted and dispersed, and, thus, recovering of the signal will be impossible. The eye diagram can also be used to calculate the received optical power. The Q factor and BER can be obtained by plotting the histogram of the received signal, followed by some calculations to obtain the mean voltage level and the standard deviation of noise.

The eye diagrams of various lengths of the fiber are obtained. It can be observed from Figures 10.28, 10.29 and 10.30 that, as the length of the fiber increases, so do the dispersion and noise. The “eye” of the eye diagram closes eventually. DB signals are expected to be able to travel up to 200 km without the “eye” closing completely. This has been proved by the model. It can be observed that, at the length of 250 km, as shown in Figure 10.30b, the “eye” of the eye diagram is yet to be fully closed. Dispersion effects can be observed, and they progressively increase with the distance of the fiber.

Data obtained from the demodsignals block, shown in Figure 10.31, are used to plot the histogram that determines the Q factor and BER. Q factor is the quality factor of the system. From the Q factor, the BER can be calculated. It is expected that, for a BER of 10⁻⁹, the Q factor is approximately 6. The histograms for 1 and 10 km are shown in Figure 10.32. The two points on the histogram are compared with the histogram at the receiver to obtain the mean value, μ₀ and μ₁, and the standard deviation of noise, σ₀, and the BER, or bit error rate, can be calculated from the Q factor found. Figure 10.32 shows the plot of BER versus distance. It can be observed that, as the distance of propagation of the signal increases, so does the bit error rate. This is as expected, since the linear and nonlinear effects of the fiber introduce noise and errors to the transmitting signal. Figure 10.33 is the plot of BER versus receiver sensitivity. The BER is plotted against the receiver sensitivity for the range from −23 dBm to −20 dBm. Experimental results of the transmissions of the CSRZ-ASK and RZ-ASK formats are also included for system over 328 km SSMF and DCM modules, completely dispersion compensated with five EDFA modules integrated.

10.3.4 Alternating-Phase and Variable-Pulse-Width DB: Experimental Setup and Transmission Performance

10.3.5 Remarks

The effectiveness of DBM formats has been demonstrated over the transmission by simulation. MATLAB and Simulink models are employed for this simulation platform. The system performance is error free, with receiver sensitivity of −60 dBm without receiver electronic noise. The nondispersion compensation transmission can reach 9−10 km for 40 Gbps, equivalent to 150 km for 10 Gbps. The Simulink model is successfully developed. We have also demonstrated both experimentally and in modeling the CSRZ-DPSK transmission. These transmission performances are compared with the noncompensating 50 km SSMF transmission of DBM with a pulse width of 33% and 50%. The later format offers at least 2 dB improvement in terms of the BER and receiver sensitivity over that of CSRZ-DPSK. The 50% and 33% FWHM DB modulation schemes offer simpler driving circuitry for the optical modulators due to its lower swing voltage levels applied to the electrodes of the dual-drive MZIM. This is very important when the bit rate is in the multi-GHz region. Furthermore, the 50% and 33% pulse width and Gaussian profile will further reduce the demand on the bandwidth of optical modulators—that is, a 30 GHz or lower MZIM can be used. A Simulink model has also been developed for simulation of the transmission performance of the DBM formats. Simple driving conditions can be achieved, and its effectiveness demonstrated.

We have demonstrated, both experimentally and in modeling, the CSRZ-DPSK and DB transmissions. These transmission performances are compared with noncompensating 50 km SSMF transmission of DBM with pulse width of 50% and 67% (NRZ). The later formats with 50% and 67% pulse width, offer at least 5 dB and 1.2 dB improvement, respectively, in terms of the BER and receiver sensitivity over that of CSRZ-DPSK. The 67%, 50%, and 33% FWHM DB modulation schemes offer simpler driving circuitry for the optical modulators due to its lower swing voltage levels applied to the electrodes of the dual-drive MZIM. Simpler and narrower bandwidth of the electronic amplifier for 67% DB case would also improve the receiver sensitivity. We thus expect that 33% DB would worst than the case of CSRZ-DPSK, and hence no simulation is conducted for this scenario. This is very important when the bit rate is in the multi-GHz region. Furthermore, the 67% and 50% pulse widths and Gaussian profile will further reduce the demand on the bandwidth of optical modulators—that is, a 30 GHz or lower MZIM can be used. Simulink models have also been developed for simulation of the transmission performance of the DBM formats. The balanced receivers are modeled exactly as a real practical subsystem. This allows a fair comparison with the transmission performance of the CSRZ-DPSK formats. Simple driving conditions can be achieved, and its effectiveness demonstrated.

Although we have not conducted the transmission of DB format pulse sequences of variable pulse width over the multispan optically amplified distance in the power threshold region at which the self-phase modulation effects may occur. It is expected that the CSRZ 67%, RZ 33%, and RZ 50% DB format would outperform their DPSK counterparts. It is also expected that the RZ 33% DB would suffer much less nonlinear distortion effects than its 50% and 67% RZ counterparts. These performances will be reported in the future. Similarly, the effects of the electrical filtering at the transmitter will also be investigated.

10.4.1 Transmission System

The schematic diagram of the optical transmission employing the VSB modulation format is shown in Figure 10.48. An optical source operating in the continuous mode is launched into an external optical modulator that is modulating the lightwave carrier via a random bit pattern generator and associate microwave power amplifiers. The external modulator, an X-cut LiNbO₃ MZ intensity modulator, is used to offer chirp-free modulated output. For 40 Gbps, the stabilization and linearity of the external modulator is critical. Normally, two modulators would be used, one for generating the required NRZ format, and the other for either carrier suppression or phase modulation, if required, depending on the transmission format.

NRZ data format are used in this simulation. The VSB modulation technique is used and generated by the use of an OF that filters the unwanted sideband of the information channel. After the filtering, a number of optical VSB channels can be multiplexed and then transmitted through a number of optically amplified dispersion-managed fiber spans. Each optically amplified dispersion-compensating in-line unit would consist of an in-line optical amplifier followed by a dispersion-compensating module, and then another optical amplification booster that would then enhance the total average optical power for transmission to the next span. Eye diagrams are obtained, and the BER can be deduced. For example, the back-to-back eye diagram is observed when dispersion compensation fibers are used with appropriate dispersion slope for equalization. Naturally, at the end of the transmission line, the multiplexed channels are separated via a demultiplexer. The principal objective of this chapter is to study the effects of the OF on the VSB system performance, and thus we do not include optical amplification noises in our modeling in the preamplifiers and booster amplifiers located at each transmission span. Both RZ and NRZ formats can be used. The main advantage of the NRZ format is that it occupies half of the RZ format’s bandwidth. VSB modulation allows a small amount of the unwanted sideband existing at the output of the modulator. This depends on the roll of passband of the filter. Instead of eliminating the entire second sideband, such as in the case of SSB, the VSB modulation suppresses most of, but not completely, the second sideband. Using this technique, the difficulty in generating a very sharp cutoff can be overcome. The VSB modulation can be implemented with OFs to eliminate most of the second sideband. The spectrum of a VSB signal can be obtained as [23]

where E is the magnitude of the optical field envelope, ω_c is the optical carrier radial frequency, and ω₁ and ω₂ are the arbitrary radial frequencies of the signals. The signal can be demodulated by multiplying with 4cos(ω_ct) and applying the low-pass OF, leading to

The basic characteristics of a VSB OF is illustrated in Figure 10.49. We note that the roll-off bands and passbands are asymmetric.

10.4.2 VSB Filtering and DWDM Channels

To achieve the VSB-modulation-formatted signals, OF is implemented. In this chapter, a number of low-pass elliptic filters (LPEF) are chosen because this filter type offers the steepest transition region between the passband and stopband without stability problems. The elliptic filter is a combination of the Chebyshev Type I and Chebyshev Type II, and exhibit some amplitude response ripples in the passband and stopband. The main advantage of the elliptic filter is that the width of the transition band is minimized for a finite ripple limit in the passband and a minimum attenuation in the stopband. Furthermore, these filters can be implemented using planar circuit technology [24]. The spectral response of the optical LPEF of the order N is given by [24]

where E_N²(ω) is the Chebyshev rational function and can be determined from the specified ripple characteristics. Similarly, the s-domain transfer function of the LPEF of order N can be obtained as

where s = jω, r=N−12 for odd N, and r=N2 for even N. The definitions of all the bands of the filters can be referred to in Figure 10.49. Figure 10.50 illustrates a typical response of the LPEF. The carrier wavelength of 1550 nm is used as the center wavelength corresponding to the optical frequency of 193.41 THz. The characteristic of the elliptic filter is designed with the following properties: passband ripple = 0.5 dB or less; minimum stopband attenuation = 10 dB; passband region = 28 GHz; stopband = 2 GHz; and 20 dB cutoff band = 10 GHz and 20 GHz for the left and right sides, respectively. The filter spectral characteristics are illustrated in Figures 10.50 and 10.51. The eight multiplexed signals at the output of an LPEF filter are plotted in Figure 10.52. This type of OFs can be implemented by using fibers Bragg gratings or multistage silica-on-silicon planar integrated MZDI. We note that the MZDI can also be considered as an al-pass (all-zero) filter that would offer no resonant peaks, and hence its group delay is almost constant and thus no dispersion would be introduced by these OFs. In this work, we would take into account the dispersion characteristics deduced from the group delay of the design filter, and this would be compensated for by the dispersion-compensating module.

The optical transmission system is simulated for eight wavelength channels in which the 1550 nm wavelength is taken as the center wavelength and the frequency spacing of 20, 30, and 40 GHz wavelength grid, and so on. For simplicity, we use 1550 nm as the center wavelength rather than the exact ITU spectral grid. After filtering out the unwanted sideband, the multichannels are then multiplexed and then propagated through the single-mode low nonzero dispersion-shifted fibers (NZ-DSFs). The multiplexing is based on the wavelength division multiplexing (WDM) technique in which multiple optical carriers at different wavelengths are modulated using independent electrical bit streams and then transmitted over the same fibers. Our design employs variable channel spacing of 20–40 GHz. The signal spectra in the frequency and the time domain at the output of the multiplexer are depicted in Figure 10.53. We observe that there are some ripples in the temporal signals. It is believed that these ripples appearing at the output of the multiplexer are due to the crosstalks generated in multichannel transmission. At the output of the LPEF, the ripple is negligible as the channels are filtered independently to each other.

10.4.3 Transmission Dispersion and Compensation Fibers

SMFs, standard or NZ-DSF types, are naturally chosen as the transmission media in this simulation. This section briefly describes the design of the fibers so that their dispersion properties can be specified accurately instead of using the data provided by fiber manufacturers. Due to chromatic dispersion, the GVD is frequency dependent. Consequently, different spectral components of the pulse travel at different velocities and cause pulse dispersion that limits the performance of SMFs. Fiber dispersion consists of two components: material dispersion and waveguide dispersion. The transmission fibers and the matched DCFs as described in Ref. [25] with matched dispersion factors and dispersion slopes for complete compensation of the channels across the signal spectral band. A brief summary of the design can be explained as follows.

For the transmission fiber, the material M(λ) and D_W(λ) waveguide dispersion factors can be calculated by using

The waveguide-dependent factor can be approximated by when the V parameter limited in range of 1.3–2.6 micro-meters for SSMF whose waveguide and dispersion factors have been given in Chapter 2 as

Hence, the total dispersion fibers is given by

In order to obtain nonzero low total dispersion of the SMMF and the DCF over a wide wavelength range, techniques for design of dispersion-flattened fibers are gain considered here, thus the repeat of a number of equations given earlier in Chapter 2. An optimized large-effective-area fiber with pure silica material for the cladding is designed for the transmission medium since it gives the best dispersion slope for matching with those of the dispersion compensation module. The Sellmeier constants for pure silica fibers are: G₁ = 0.696750 and λ₁ = 0.069066e−6; G₂ = 0.408218 and λ₂ = 0.115662e−6; and G₃ = 0.890815 and λ₃ = 9.9900559e−6. The refractive index of pure silica can be expressed as

with c₁ = 1.45084, c₂ = −0.00343 μm⁻², and c₃ = 0.00292 μm², and hence the refractive index [n(λ)] for pure silica fiber is 1.45. For DCF these coefficients would be changed accordingly, even the index profile so that the wave guide and dispersion factors can meet the criteria for compensation over the whole spectral window of the multichannels. We have designed the transmission and dispersion-compensating optical fibers with a specific dispersion factor of 17 ps/nm/km and a dispersion slope of 0.3 ps/(nm²·km) for transmitting several channels. The dispersion and dispersion slope values of the dispersion-compensating fiber are designed with a factor of five times those of the transmission fiber, with a residual dispersion of about 1.5 ps/nm/km for the highest and lowest wavelength channels. These fiber parameters are used in this simulation: fibers radius a = 1.6 μm; relative refractive index difference Δ = 0.0339. The dispersion factors of the centered channel (only channel 5 is illustrated) are indicated in Figure 10.54.

The pulse broadening after transmitting through a fiber of length L can be expressed as

where D(λ) is the fiber’s spectral dispersion (ps/(nm·km)); σ_λ is the signal bandwidth when the laser linewidth is much smaller than that of the VSB signals; and L is the fiber’s transmission distance. Figure 10.54 shows the signals at the output of the demultiplexer for each channel (channels 1 through 8) without dispersion compensation.

From Figure 10.54, the simulation results show that over a 100 km span transmission line, the eye of the transmitted data closes completely, as expected, due to fiber dispersion. It is observed that the eye is still open at a BER of about 10⁻⁹ after 16 km designed fiber transmission. This is a significant improvement over the NRZ format.

We now turn to the DCFs. Since the GVD limits the system performance, it is essential to implement a DCF. The condition of dispersion compensation can be expressed as

where D₁ is dispersion factor of the transmission section (ps/(nm·km)); L₁ is the transmission distance (km); D₂ is the dispersion compensation distance (ps/(nm·km)); L₂ is the dispersion compensation distance (km); and Γ is the dispersion factor contributed by the VSB OF. Obviously, Equation 10.10 shows that the DCF must have its GVD negative at 1550 nm to compensate for the positive dispersion of the transmission fibers and the OF. The parameters of the DCF can be optimized for minimum nonlinear self-phase-modulation effect with: fiber radius a = 1.7 μm; relative refractive index difference Δ = 0.0243. Figure 10.55 shows the transmitted data at the end of the dispersion-managed system with a dispersion compensation for channel 5 (of the eight channels). This shows the effectiveness of dispersion compensation fibers in the improvement of the BER because the received eye diagram is quite close to its original pattern as obtained at the output of the transmitter. The residual ripple of the compensated pulses clearly shows the effects of the filter passband on the time-domain pulses. These ripples contribute the penalty on the eye closure, and hence the Q factor. An optical multiplexer then combines the modulated lightwaves to the transmitting fibers. At the receiver, the channels are separated into different signals by an optical demultiplexer. Figure 10.54 gives the simulation results of transmitted signals at the output of the multiplexer without dispersion compensation, while Figure 10.55 shows the transmitted signals at the output of multiplexers with DCF in cascade with the transmission fibers. We note that the optical amplifiers at the input and booster amplifiers at the output are not included in this simulation.

10.4.4 Transmission Performance

The eye diagram is used to deduce the Q factor and hence the system BER. The random digital optical pulse sequence suffers distortion by noise, pulse broadening and timing jitter errors introduced in the optically amplified fiber link. Assuming that the probability density function of “1”and “0” are equal and Gaussian, the eye diagram can be used to estimate the Q factor by

where μ₁ and μ₀ are the means of the current at the output of the photodetector of the decision circuitry of the receiver at the sampling instant, respectively, for symbols “1” and “0.” While σ₁ and σ₀ are the standard deviations of the current at the decision circuit input at the sampling instant, for the symbols “1” and “0”, respectively.

Figure 10.56a and b shows the eye diagram of the transmitted pulse random sequence at 1550 nm (channel 5) with 40 GHz channel spacing, which depicts the eye diagram at the end of the transmission line without and with dispersion compensation fibers, respectively. The eye diagram of data with dispersion compensation is wide open compared to that without dispersion compensation. The wide-open eye diagram shows that the system performance is good, since the error has been compensated.

10.5.1 Hilbert Transform SSB MZ Modulator Simulation

The Hilbert transform of signal m(t) is defined to be the RF signal whose frequency components are all phase shifted by π/2 radians (Figures 10.61 and 10.62).^* Therefore

Taking the Fourier transform, we have

10.5.2 SSB Demodulator Simulation

The modulated signal is

The demodulated signal is (Figures 10.63 and 10.64)

The low-pass filter is used to filter high-frequency components in the signal. The only component left is the modulating signal (10 Gbps [binary ∗ cosine signal]) after demodulation. It is required to multiply the demodulated signal by in-phase cosine signal and also there is high-frequency signal, so that LPF is required to filter the high-frequency components in the signal.