1. Introduction

For many years, ON–OFF keying has been the only the practical modulation format in highspeed optical fiber communication systems. Recently, progress in optical modulation and detection technologies have promoted more advanced modulation formats. For example, differential phase-shift keying (DPSK) attracts many research groups, and many experimental demonstrations on high-density and long-haul transmissions have been reported [1, 2]. In optical communications, however, high-speed external modulation in the format of minimum-shift keying (MSK) has never been achieved, before. MSK is a well-known modulation format in radio-frequency digital communications, having the following features: the main lobe of the modulation spectrum is more compact than that of DPSK, and sidelobes around higher frequency components fall off sharply. These characteristics are greatly advantageous to long-haul transmissions because such a compact spectrum potentially gives a good dispersion tolerance.

In order to realize such an MSK format, optical frequency should be modulated with phase continuity. We have recently achieved high-speed external modulation for optical continuous-phase frequency-shift keying (CPFSK) format using synchronous control technique [3]. In the modulation scheme, the frequency is shifted at the timing when optical phase is continuous, by using an external LiNbO₃ FSK modulator [4] based on single-sideband (SSB) modulation technology. Before our report, direct modulation on a laser diode (LD) was the only way to form the optical CPFSK signal [5, 6]; therefore, the modulation speed was limited by the response of the LD; and thermal coupling effect in an LD degraded low-frequency components of the CPFSK signal.

In the previously reported CPFSK modulation, however, the minimum zero-to-peak frequency deviation available is at least B/2, where B [bit/s] denotes bit rate of the CPFSK signal [3]. The frequency deviation for the MSK symbols should be B/4 and -B/4 relative to a carrier frequency, (that is, the full deviation in frequency is B/2.) In order to achieve external modulation in the MSK format, in this paper, we propose an initial phase control technique accompanied together with the CPFSK modulation. By using this novel technique, the phase jumps inherent to the external FSK modulation with any frequency deviation is canceled, so that MSK modulation becomes attainable.

The aim of this paper is twofold. First, by numerical analysis, we show that the initial phase control enables external modulation in MSK format. Without initial phase control (or with imperfect control), the modulation signal has undesired high frequency components that broaden the modulation spectrum. Second, we experimentally demonstrate that the initial phase control actually realizes high-speed MSK modulation. 10-Gb/s external modulation in MSK format was successfully demonstrated. The generated MSK signal had 15-GHz spectral width that was much more compact than that of the conventional binary PSK.

2. Principles of initial phase control for optical MSK modulation

In the external CPFSK modulation, the upper-sideband (USB) or lower-sideband (LSB) signal should be synchronously shifted to the other state at the timing when both of the sideband signals have the same phase [3]. This is because phase continuity is not ensured for the external FSK modulation. The following expressions indicate the phase excursion of each sideband component generated from the external FSK modulator, viewing in the coordinate of the phase plane at the frequency of the carrier light,

where f ₀ denotes the frequency deviation; the phase difference between θ _USB and θ _LSB at t = 0 is defined to be zero, which appropriately describes the operation of the FSK modulator based on SSB modulation technology. It is found that the optical phases of each sideband are always shifting in the opposite directions and coincide with one another when

where m is an integer. The synchronous switching between the USB and LSB at these conditions enables external continuous-phase modulation. We call this technique the method of “synchronous control [3].” It should be noted that the achievable frequency deviation using this scheme is discrete: the frequency deviation (f ₀) is related to the bit rate (B) by f ₀ = nB/2 (n: integer) because the optical phase should be shifted by nπ during each bit duration; this relation also suggests that the smallest frequency deviation obtained with this technique is f ₀ = B/2. In optical communication systems, however, it is very important to transmit data with more compact spectrum for the purpose of increasing spectral efficiency and improving dispersion tolerance in the optical links. It is found that the synchronous control technique cannot offer the condition required for the MSK format, where frequency deviation is f ₀ = B/4. In other words, the externally modulated FSK signal under the condition of f ₀ = B/4 cannot help containing phase jumps at the timing of the frequency shift, as shown in Fig. 1(a).

 

Fig. 1. Concept of the initial phase control technique for optical MSK modulation.

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To solve this problem and realize external modulation in MSK format, in this paper we propose an initial phase control technique, which can achieve continuous-phase modulation with narrower frequency deviation (f ₀ = B/4). Figure 1 shows basic structure of an optical MSK transmitter, which consists of two intrinsic sections: one is for FSK modulation and the other is for initial phase control. The section of the FSK modulation has a role to selectively generate USB or LSB components. Clock and baseband data signals are fed to the FSK modulator, and the delay between them controls the timing of the frequency shift. The frequency of the clock (f ₀ [Hz]) and the speed of the baseband data (B [b/s]) determine the frequency deviation and bit rate of the FSK signal, respectively. The initial phase controller, on the other hand, controls the optical initial phase of each sideband synchronously to the bit sequence of the baseband data. Optical MSK modulation is obtained if the initial phase controller compensates for the phase jump induced in the FSK modulator. The details of the control scheme are explained as follows: At the beginning of the kth bit of the modulation data, the phase difference between the USB and LSB generated from the MSK transmitter in Fig. 1 is described as

 

Fig. 2. Calculated modulation spectra: (a) optical phase is discontinued, (b) optical phase is continuous at the timing of frequency shift. f ₀ = 2.5 GHz, B = 10 Gbit/s. (b) corresponds to the case for the optical MSK format. The phase trajectory calculated at the MSK condition is shown in (c).

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where k is an integer; Δθ ₀ denotes the phase difference at the initial 0th bit; and Δϕ_k is the phase shift given by the initial phase controller. For the purpose of continuous phase modulation, Δθ_k should be zero. In the case of MSK, the phase difference yields Δθ_k = kπ - Δϕ_k, substituting f ₀ = $\frac{B}{4}$ and Δθ ₀ = 0 into Eq. (3), where the parameter of Δθ ₀ can be controlled by the delay (τ) between the clock and the data in Fig. 1. If k is even, the optical phase at the beginning of the kth bit becomes continuous by setting Δϕ_k = 0, as illustrated in Fig. 1(b). This means that the optical initial phase of the FSK modulated signal at the k-th bit is not required to be shifted for even k. When k is odd, on the other hand, the initial phase difference between the USB and LSB is π (or -π). Therefore, the amount of phase shift introduced by the initial phase controller should be π if frequency is shifted at this timing. As shown in Fig. 1(c), the optical phase for any timing becomes continuous with this control scheme.

The signal introduced into the initial phase controller is simply encoded from the baseband modulation data, as follows:

where A_k (=0 or 1) is the logical state of the k-th bit of the modulation data. Since the data for the initial phase control is encoded in binary, it is possible to use a conventional binary PSK modulator, such as an LiNbO₃ phase modulator or push-pull Mach-Zehnder modulator.

3. Ideal MSK modulation characteristics

By using numerical calculation, in this section, we show that the initial phase control technique enables external MSK modulation. In this analysis, an optical phase modulator used in the controller is driven with the above-mentioned encoded data (Eq. 5) for the initial phase control. The baseband signal introduced into the modulator has a rectangular waveform and its mark and space levels are aligned to be π and 0, respectively. The FSK modulator cascaded to the initial phase controller ideally generates USB or LSB signal using Eq. (2). The data signal fed to the modulator is in 1024-bit random sequence.

 

Fig. 3. (a) Experimental setup for external modulation in MSK format using the initial phase control; (b) an external FSK modulator. LD: laser diode, OSA: optical spectrum analyzer.

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Figure 2 shows optical modulation spectra. Figure 2(a) shows the case in which the initial phase is not controlled, whereas Fig. 2(b) is obtained with the optimal initial phase control. The modulation spectra are calculated at the following conditions: f ₀=2.5 GHz, B=10 Gbit/s. As shown in Fig. 2(a), FSK modulation without initial phase control generates higher order modulation sidelobes. This is because the phase jump occurring at the frequency shift contains high frequency components. With the optimum initial phase control, the sidelobe components are effectively suppressed in the modulation spectrum [Fig. 2(b)]. The two-sided occupant bandwidth of the main lobe is 15 GHz, and the suppression ratio of sidelobe components is more than 20 dB. The phase trajectory plotted in Fig. 2(c) shows that the signal is actually in MSK format because the phase discontinuity is canceled and the phase is gradually shifted by $\frac{\pi }{2}$ or $-\frac{\pi }{2}$ through each bit duration.

4. Experiments of external MSK modulation

4.1. Experimental setup

Figure 3(a) shows the experimental setup for continuous-phase modulation in the MSK format. The transmitter was equipped with an initial phase controller and an FSK modulator made of LiNbO₃ modulators. The lightwave at 1550 nm generated from a laser diode was injected into the initial phase controller followed by the FSK modulator. The structure of the FSK modulator is illustrated in Fig. 3(b) [4]. The two sub–Mach–Zehnder (MZ) modulators (MZ-a, MZ-b) embedded in the main Mach–Zehnder (MZ-c) were biased at null points, and sinusoidal clocks with 90 deg phase difference were fed to them. The frequencies of the sinusoidal clocks were 2.49 GHz, corresponding to the case of MSK (f ₀ = B/4). The main electrode MZ-c was driven with 9.95-Gbit/s binary non-return-to-zero (NRZ) data in the format of 2⁷–1 pseudorandom bit sequences (PRBS). The clock and baseband signals were phase locked with each other and the delay between them was adjusted by a phase shifter. On the other hand, the initial phase controller was made of a push–pull MZ modulator that was biased at a null point. The modulator was driven with NRZ data encoded from the above-mentioned PRBS data according to Eq. (4). The timing between the encoded data and the baseband modulation data was also aligned with another phase shifter.

 

Fig. 4. Measured optical spectra for 10 Gbit/s MSK and BPSK signals; solid: MSK, dotted: BPSK.

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4.2. Experimental results

The solid line in Fig. 4 shows modulation spectra generated from the MSK transmitter. The modulation spectrum at the condition of the MSK was successfully generated with the following conditions: The two-sided occupant bandwidth of the main lobe in the modulation spectrum was ~15 GHz, and the sidelobe suppression ratio was ~20 dB, which agrees well with the numerically calculated spectrum shown in Fig. 2(b).

As a reference, the modulation spectrum of BPSK, obtained with almost the same experimental setup, is also plotted as a dotted line in the same graph of Fig. 4. The bandwidth of the MSK spectrum was much narrower and sidelobes were highly suppressed as compared with the BPSK spectrum.

5. Conclusion

In this paper we have proposed an initial phase control technique for external continuous-phase modulation in the format of MSK. Numerical calculation showed that external MSK modulation can be achieved. We experimentally confirmed the effectiveness of this modulation scheme. A 10 GHz MSK modulation spectrum with 15 GHz main lobe width was successfully obtained.