Motivation

Recently, the wireless communication is focused on millimeter-wave band around 60GHz. The millimeter-wave in this band has some properties for communication such as the short transmission length in the air and broadband bandwidth. It can provide safe communication and transmit high data rate information such as high definition television (HDTV) video signal. However, the electrical components are much more expensive when transmission RF signal is in higher frequency. Hence, the ROF system including frequency multiplication technique and supporting vector signals are required.

                                             

Chapter 2

The Concept of New Optical Modulation System

2.1 Preface

There are three parts in optical communication systems : optical transmitter, communication channel and optical receiver. Optical transmitter converts an electrical input signal into the corresponding optical signal and then launches it into the optical fiber serving as a communication channel. The role of an optical receiver is to convert the optical signal back into electrical form and recover the data transmitted through the lightwave system. In this chapter, we will do an introduction about the external Mach-Zehnder Modulator (MZM), constructing a model of new ROF system.

2.2 Mach-Zehnder Modulator (MZM)

Direct modulation and external modulation are two modulations of generated optical signal. When the bit rate of direct modulation signal is above 10 Gb/s, the frequency chirp imposed on signal becomes large enough. Hence, it is difficult to apply direct modulation to generate microwave/mm-wave.

However, the bandwidth of signal generated by external modulator can exceed 10 Gb/s. Presently, most RoF systems are using external modulation with Mach-Zehnder modulator (MZM) or Electro-Absorption Modulator (EAM).

The most commonly used MZM are based on LiNbO3 (lithium niobate) technology. According to the applied electric field, there are two types of LiNbO3 device : x-cut and z-cut. According to number of electrode, there are two types of LiNbO3 device: dual-drive Mach-Zehnder modulator (DD-MZM) and single-drive Mach-Zehnder modulator (SD-MZM) [6].

2.3 Single-drive Mach-Zehnder modulator

The SD-MZM has two arms and an electrode. The optical phase in each arm can be controlled by changing the voltage applied on the electrode. When the lightwaves are in phase, the modulator is in “on” state. On the other hand, when the lightwaves are in opposite phase, the modulator is in “off ” state, and the lightwave cannot propagate by waveguide for output.

2.4 The architecture of ROF system 2.4.1 Optical transmitter

Optical transmitter concludes optical source, optical modulator, RF signal, electrical mixer, electrical amplifier, etc.. Presently, most RoF systems are using laser as light source. The advantages of laser are compact size, high efficiency, good reliability small emissive area compatible with fiber core dimensions, and possibility of direct modulation at relatively high frequency.

The modulator is used for converting electrical signal into optical form.

Because the external integrated modulator was composed of MZMs, we select MZM as modulator to build the architecture of optical transmitter.

There are two schemes of optical transmitter generated optical signal. One scheme is used two MZM. First MZM generates optical carrier which carried the data. The output optical signal is BB signal. The other MZM generates optical subcarrier which carried the BB signal and then output the RF signal, as shown in Fig. 2-1 (a). The other scheme is used a mixer to get up-converted electrical signal and then send it into a MZM to generate the optical signal, as shown in Fig. 2-1 (b). Fig. 2-1 (c) shows the duty cycle of subcarrier biased at different points in the transfer function.

Maximum transmission point Minimum transmission point Quadrature point

 

Figure 2-1 (a) and (b) are two schemes of transmitter and (c) is duty cycle of subcarrier biased at different points in the transfer function. (LO: local

oscillator)

2.4.2 Optical signal generations based on LiNbO3 MZM

The microwave and mm-wave generations are key techniques in RoF systems. The optical mm-waves using external MZM based on double-sideband (DSB), single-sideband (SSB), and double-sideband with optical carrier suppression (DSBCS) modulation schemes have been demonstrated, as shown in Fig. 2-2. Generated optical signal by setting the bias voltage of MZM at quadrature point, the DSB modulation experiences performance fading problems due to fiber dispersion, resulting in degradation of the receiver sensitivity. When an optical signal is modulated by an electrical

RF signal, fiber chromatic dispersion causes the detected RF signal power to have a periodic fading characteristic. The DSB signals can be transmitted over several kilo-meters. Therefore, the SSB modulation scheme is proposed to overcome fiber dispersion effect. The SSB signal is generated when a phase difference of π/2 is applied between the two RF electrodes of the DD-MZM biased at quadrature point. Although the SSB modulation can reduce the impairment of fiber dispersion, it suffers worse receiver sensitivity due to limited optical modulation index (OMI). The DSBCS modulation is demonstrated optical mm-wave generation using DSBCS modulation. It has no performance fading problem and it also provides the best receiver sensitivity because the OMI is always equal to one. The other advantage is that the bandwidth requirement of the transmitter components is less than DSB and SSB modulation. However, the drawback of the DSBCS modulation is that it can’t support vector signals, such as phase shift keying (PSK), quadrature amplitude modulation (QAM), or OFDM signals, which are of utmost importance in wireless applications.

Figure 2-2 Optical microwave/mm-wave modulation scheme by using MZM.

2.4.3 Communication channel

Communication channel concludes fiber, optical amplifier, etc.. Presently, most RoF systems are using single-mode fiber (SMF) or dispersion compensated fiber (DCF) as the transmission medium. When the optical signal transmits in optical fiber, dispersion will be happened. DCF is use to compensate dispersion. The transmission distance of any fiber-optic communication system is eventually limited by fiber losses. For long-haul systems, the loss limitation has traditionally been overcome using regenerator witch the optical signal is first converted into an electric current and then regenerated using a transmitter. Such regenerators become quite complex and expensive for WDM lightwave systems. An alternative approach to loss

DSB

SSB

_Dual-drive

MZM

DSBCS

Single-drive MZM Single-drive

MZM

man

Laser

Figure 2-4

Fig MZ data

mi

4 The mod

gure 2-5 Th ZM

ixer

BERT

el of receiv

he model of LO

EDFA

LPF

ver in a RO

f ROF syst A OBP

mixe

OF system.

tem.

PF

fib

PD er

LO  

ber

D

2.5 The new proposed model of optical modulation system

In section 2.3.2, there is an introduction of three traditional modulation schemes to generate optical RF signal. In this work, we propose a new modulation approach to generate optical vector signals by frequency multiplication based on a DSBCS scheme and only using a single-electrode MZM. Fig. 2-6 schematically depicts the optical vector signal generation system. The single-electrode MZM driving signals consist of a sinusoidal signal of frequency f1 modulated with a RF signal and a sinusoidal signal of frequency f2, as indicated in insets (a) and (b) of Fig. 2-6, respectively. To realize the DSBCS modulation scheme, the MZM is biased at the null point.

Inset (d) in Fig. 2-6 presents the generated optical spectrum that has two upper-wavelength sidebands (USB1, USB2) and two lower-wavelength sidebands (LSB1, LSB2) with carrier suppression.

At the base station, the LSB2 subcarrier is filtered out for the upstream data link (inset (f)), and the rest of the signal is sent to local users. After square-law photo detection, the cross term of USB2 and USB1 generates the RF signal at the difference frequency (f2-f1). Concurrently, the cross term of LSB1 and USB2 yields the RF signal at the sum frequency (f2+f1). Here we only consider the RF signal at the sum frequency and a frequency multiplication of optical RF signal can be achieved by proper choosing the frequencies of vector signal and sinusoidal signal. The filtering out of LSB2 subcarrier not only provides an upstream light source but also eliminates performance fading. As presented in Fig. 2-7, a two-tone RF single at frequencies of 5 GHz and 10 GHz is used to simulate the performance fading.

After square-law photo detection, the generated RF signals at difference and

sum frequencies of 5 GHz and 15 GHz suffer performance fading before filtering. If an optical filter is utilized to remove anyone of the four optical subcarriers, the fading of both 5-GHz and 15-GHz RF signals can be readily eliminated. Notably, a frequency multiplication (1.5 times after square-law photo detection) scheme is adopted to reduce the cost of the electronic components, especially for RF signals in the millimeter-wave range.

  Figure 2-6 Concept of the proposed system. (LD: laser diode, MZM:

Mach-Zehnder modulator, SMF: single mode fiber, C: circulator, FBG: fiber bragg grating, RSOA: reflective semiconductor optical amplifier)  

   

 

w/o Filtering, 5-GHz RF signal w/o Filtering, 15-GHz RF signal Filtering LSB2, 5-GHz RF signal Filtering LSB2, 15-GHz RF signal

0 20 40 60 80 100

Figure 2-7 Simulation of RF performance fading versus SMF transmission length.

Chapter 3

The theoretical calculations of proposed system

3.1 Introduce MZM

For MZM with configuration as Fig. 3-1, the output E-filed for upper arm is E_U E · a · e^∆φ (1)

∆φ π· π (2)

∆φ  is the optical carrier phase difference that is induced by v , where a is the power splitting ratio.

The output E-filed for upper arm is

E_L E · √1 a · e^∆φ (3)

∆φ  is the optical carrier phase difference that is induced by v

∆φ π· π (4) The output E-filed for MZM is

E_T E · a · b · e^∆φ √1 a · √1 b · e^∆φ (5) where a and b are the power splitting ratios of the first and second Y-splitters in MZM, respectively. The power splitting ratio of two arms of a balanced MZM is 0.5. The electrical field at the output of the MZM is given by

E_T · E · e^∆φ e^∆φ (6) E_T E · cos ^{∆φ ∆φ} · exp j^{∆φ ∆φ} (7) For single electro x-cut MZM. The electrical field at the output is given by E_OUT E · cos ^{∆φ ∆φ} · exp j^{∆φ ∆φ} (8) Add time component, the electrical field is

E_OUT E · cos ∆φ · cos t (9) where E0andωcdenote the amplitude and angular frequency of the input optical carrier, respectively; V t is the applied driving voltage, and ∆φ is the optical carrier phase difference that is induced by between the two arms of the MZM. The loss of MZM is neglected. consisting of an electrical sinusoidal signal and a dc biased voltage can be written as,

cos t (10) where is the dc biased voltage, and are the amplitude and the angular frequency of the electrical driving signal, respectively. The optical carrier phase difference induced by is given by

∆φ Vπ Vπ ·^π (11) Eq. (10) can be written as:

E_OUT E · cos V V cos ωt

V_π ·π

2 · cos ω t E · cos b m · cos ω_RFt · cos ω t E · cos ω t · cos b · cos m · cos ω_RFt

sin b · sin m · cos ω_RFt (12) where  _V π  is a constant phase shift that is induced by the dc biased voltage, and  _V π  is the phase modulation index.

cos x sin θ J x 2 J x cos 2nθ

∞

sin x sin θ 2 J x sin 2n 1 θ

∞

cos x cos θ J x 2 1 J x cos 2nθ

∞

sin x cos θ 2 1 J x cos 2n 1 θ

∞

(13) Expanding Eq. (12) using Bessel functions, as detailed in Eq. (13). The electrical field at the output of the MZM can be written as:

E_OUT E · cos ·

cos · 2 · 1 · m · cos 2

∞

sin · 2 · 1 · · cos 2 1

∞

(14) where is the Bessel function of the first kind of order n. the electrical field of the mm-wave signal can be written as

E_OUT E · cos · J m · cos ω t

E · cos · · cos

∞

2 π

E · cos · · cos 2

∞

E · sin · · cos

∞

2 1

E · sin · · cos

∞

2 1

(15)

Figure 3-1 The principle diagram of the optical mm-wave generation using balanced MZM.

 

3.2 Theoretical calculation of single drive MZM 3.2.1 Bias at maximum transmission point

When the MZM is biased at the maximum transmission point, the bias voltage is set at  0, and  cos 1 and sin 0. Consequently, the electrical field of the mm-wave signal can be written as

 

· · cos

· · cos

∞

2

· · cos 2

∞

(16)

The amplitudes of the generated optical sidebands are proportional to those of the corresponding Bessel functions associated with the phase modulation index . With the amplitude of the electrical driving signal equal to , the

maximum is . As 0 , the Bessel function for 1 decreases and increases with the order of Bessel function and m, respectively, as shown in Figure 3-2. , , , and are 0.5668, 0.2497, 0.069, and 0.014, respectively. Therefore, the optical sidebands with the Bessel function higher than can be ignored, and Eq. (14) can be further simplified to

· · cos

· · cos 2 · · cos 2 · · cos 4

· · cos 4 (17)

0 2 4 6 8 10

-0.5 0.0 0.5 1.0

m

J0 J1 J2 J3

  Figure 3-2 The different order of Bessel functions vs. m.

3.2.2 Bias at quadrature point

When the MZM is biased at the quadrature point, the bias voltage is set at

V , and cos ^√ and sin ^√ . Consequently, the electrical field of the mm-wave signal can be written as

E_OUT 1

√2· E · J m · cos ω t 1

√2· E · J m · cos ω ω_RF t 1

√2· E · J m · cos ω ω_RF t 1

√2· E · J m · cos ω 2ω_RF t π 1

√2· E · J m · cos ω 2ω_RF t π 1

√2· E · J m · cos ω 3ω_RF t π 1

√2· E · J m · cos ω 3ω_RF t π

(18) 3.2.3 Bias at null point

When the MZM is biased at the null point, the bias voltage is set at V , and cos 0 and sin 1. Consequently, the electrical field of the mm-wave signal using DSBCS modulation can be written as

E_OUT E · J m · cos ω ω_RF t E · J m · cos ω ω_RF t E · J m · cos ω 3ω_RF t π E · J m · cos ω 3ω_RF t π E · J m · cos ω 5ω_RF t

E · J m · cos ω 5ω_RF t (19)

3.3 Theoretical calculations and simulation results 3.3.1 The generated optical signal

The theoretical calculations of proposed system, the driving RF signal   consisting of an electrical sinusoidal signal and a dc biased voltage can be written as  

cos t cos t (20)

where is the dc biased voltage, , and , are the amplitude and the angular frequency of the electrical driving signals, respectively. The optical carrier phase difference induced by is given by

· cos

V cos t cos t

· cos cos t cos t (21)

where    is a constant phase shift that is induced by the dc biased voltage, and  _V , _V   is the phase modulation index.

· cos · cos cos t cos t · sin · sin cos t cos t

· cos cos m cos cos cos sin cos sin cos

· sin sin cos t cos cos t

cos cos t sin cos t (22) When the MZM is biased at the null point, the bias voltage is set at V , and cos 0 and sin 1. Consequently, the electrical field of the mm-wave signal using DSBCS modulation can be written as

sin cos t cos cos t

cos cos t sin cos t (23) First, to expand equation sin cos t cos cos t

sin cos t cos cos t

2 1 J cos 2n 1 t

∞

· J 2 1 J cos 2n t

∞

2J cos t 2J cos 3 t

· J 2J cos 2 t 2J cos 4 t (24) The optical sidebands with the Bessel function higher than   can be ignored. Consequently, the electrical field can be written as

sin cos t cos cos t

2J J cos t

2J J cos 3 t

4J J ·1

2 cos 2 t cos 2 t

4J J ·1

2 cos 3 2 t cos 3 2 t

(25) Add time component cos t

sin cos t cos cos t cos t

2J J cos t cos t

2J J cos 3 t cos t

4J J ·1

2 cos 2 t cos 2 t cos t

4J J ·1

2 cos 3 2 t cos 3 2 t cos t

(26)

J J ,  2J J ,  4J J , and  4J J   are

shown in Figure 3-3. Therefore, the optical sidebands with the Bessel function

4J J   can be ignored, and Eq. (14) can be further simplified to

sin cos t cos cos t cos t

J J cos t cos t

J J cos 3 t cos 3 t

J J cos 2 t cos 2 t

J J cos 2 t cos 2 t

(27)

0.0 0.2 0.4 0.6 0.8 1.0 1.2 1.4 1.6 1.8 -0.1

0.0 0.1 0.2 0.3 0.4

m

1

,m

2

J₀J₁ J₀J₃ J₁J₂ J₂J₃

  Figure 3-3 The different order of Bessel functions vs. m.

Second: To expand equation cos cos t sin cos t

cos cos sin cos

2 1 cos 2

∞

· 2 1 cos 2 1

∞

2 cos 2 2 cos 4

· 2 cos 2 cos 3

2 cos

2 cos 3

4 ·1

2 cos 2 cos 2

4 ·1

2 cos 3 2 cos 3 2

(28) Add time component cos

cos cos sin cos cos

2 cos cos

2 cos 3 cos

4 ·1

2 cos 2 cos 2 cos

4 ·1

2 cos 3 2 cos 3 2 cos

cos cos

cos 3 cos 3

cos 2 cos 2

cos 2 cos 2 (29)

The output electrical filed can be rewritten as

cos sin cos cos cos

cos cos sin cos

t ·

cos cos

cos 3 cos 3

cos 2 cos 2

cos 2 cos 2

cos cos

cos 3 cos 3

cos 2 cos 2

cos 2 cos 2

      (30)

  Figure 3-4 Illustration of the optical spectrum at the output of the MZM.

( 6 ) 

The commercial software, VPI WDM-TransmissionMaker^© 5.0, is used to simulate numerically the power ratio. Fig. 3-5 shows the optical power ratio (OPR, _, ) as a function of MI. The _, is defined as

,

(31) where and are the optical powers of the sideband frequency at

1 · 0 · and the sideband frequency at · · ,

respectively. As MI falls from one to zero, the optical power ratios are improved.

0.0 0.2 0.4 0.6 0.8 1.0

0 10 20 30 40 50 60 70 80

MI

Theoretical P

_10,+21

,P

_10,+12

Numerical P

_10,+21

,P

_10,+12

Theoretical P

_10,30

,P

_10,03

Numerical P

_10,30

,P

_10,03

Power (10dB/Div.)

  Figure 3-5 Illustration of the optical spectrum at the output of the MZM.

3.3.2 The generated electrical signal

After square-law detection using an ideal PD with responsivity R, the photocurrent can be expressed as

· | | (32)

The RF signal is E ·

J J 2J J J 2J J 4J J J

· cos 2 t

2J J J J 2J J J J

2J J J J 2J J J J

2J J J J 2J J J J

· cos t cos t

J J 2J J J 2J J

4J J J · cos 2 t

2J J J J 2J J J J

2J J J J

· cos 3 t cos 3 t

2J J J 2J J J

2J J J J 2J J J J

· cos 2 2 t

2J J J 2J J

· cos 4 t

J J 2J J J J

· cos 2 4 t 2J J J J · cos 5 t RF

(33)

Figure 3-6 Illustration of the electrical spectrum of generated BTB mm-wave signals using MZM after square-law PD detection. ( 6 )

Fig. 3-7 shows the RF signal power ratio (RFPR, _, ) as a function of MI.

The _, is defined as

,

(34) where    and    are the RF signal powers of the frequency at  1 ·

1 ·   and the frequency at  · · ,respectively. The RF signal power at sum and subtract frequencies are the same, so do not consider the  _,   term. 

0.0 0.2 0.4 0.6 0.8 1.0 Figure 3-7 The RF signal power ratio (RFPR,  _, ) as a function of MI.

 

Table 3-1 Measure the RF power without optical filtering

Frequency  ^Amplitude 

2   ^{J J 2J J J 2J J}

4J J J  

,   ^{2J J J J 2J J J J}

2J J J J 2J J J J

2J J J J 2J J J J  

2   ^{J J 2J J J 2J J}

4J J J  

3 , 3   ^{2J J J J 2J J J J}

2J J J J  

2 2   ^{2J J J 2J J J}

2J J J J 2J J J J  

4   ^{2J J J 2J J}  

2 4   ^{J J 2J J J J}  

5 , 5   ^{2J J J J}  

3.3.3 Consider dispersion effect

When optical RF signals are transmitted over a single-mode fiber with dispersion, a phase shift to each optical sideband relative to optical carrier is induced. The propagation constant of the dispersion fiber can be expressed as

(35)

where is the derivative of the propagation constant evaluated at . The effect of high order fiber dispersion at 1550-nm band is neglected. For carrier tones with central frequency at , we have

(36)

and

· D (37)

where c is light speed in free space, D is the chromatic dispersion parameter, and is the frequency of the optical carrier. For a standard single-mode fiber, D is 17-ps/(nm.km). The fiber loss is ignored. Therefore, after transmission over a single-mode fiber of length z, the electrical field can be written as

· cos 1

2

cos 1

2

cos 1

2

cos 1

2

(38)

After square-law photo detection, the RF signal can be expressed as

· DC RF

2 · cos 1

2 · cos 1

2

2 · cos 1

The RF signal at the substrate frequency :

I J J J J · The RF signal at the substrate frequency can be written as

I J J J J · cos c d cos c d

The RF signal at the sum frequency :

I J J J J ·

cos t 1 2

1 2

cos t 1

2

1 2

(43) Define

e t

f 1

2

1 2

1 2

(44) The RF signal at the sum frequency can be written as

I J J J J · cos e f cos e f

I 2J J J J · cos e cos f

2J J J J · cos 1 2 · cos t

(45)

Fig. 3-8 and Fig. 3-9 show the numerical simulation and theoretical solutions, the RF fading problem with the same results. Fig. 3-8 RF signal is driving 5 GHz and 30 GHz sinusoidal. Fig. 3-9 shows the results after 50km SMF transmission.

0 10 20 30 40 50 -50

-40 -30 -20 -10 0 10

Transmission Length (km) 25G Numerical

35G Numerical Theoretical

Power (10dB/Div.)

  Figure 3-8 shows the numerical and theoretical solution for RF signal fading

issue after transmission.

30 35 40 45 50 55 60

-50 -40 -30 -20 -10 0 10

Frequency (GHz) Numerical

Theoretical

Power (10dB/Div.)

  Figure 3-9 RF power vs. .

3.4 The generated optical signal using optical filtering 3.4.1 Analysis of the generated signal

When we use fiber grating, the equation for the optical spectrum is

·

J J · cos t cos t

J J cos 3 t cos 3 t

J J cos 2 t cos 2 t

J J cos 2 t cos 2 t

J J · cos t cos t

J J cos 3 t cos 3 t

J J cos 2 t cos 2 t

J J cos 2 t cos 2 t (46)

  Figure 3-10 shows the optical spectrum when the LSB1 is filter out.

 

  Figure 3-11 shows the optical spectrum when the LSB2 is filter out.

After square-law detection, the photocurrent can be expressed as

E ·

· J J 1 · J J J

2J J 2 2 · J J J

· cos 2 t

1 · J J J J

1 · J J J J 1 · J J J J 2J J J J

2J J J J 2J J J J

· cos t

· J J J J

1 · J J J J 1 · J J J J 2J J J J

2J J J J 2J J J J

· cos t

· J J 1 · J J J

2J J 2 2 · J J J

· cos 2 t

1 · J J J J

1 · J J J J 2J J J J

· cos 3 t cos 3 t

1 · J J J 1 · J J J

2J J J J 2J J J J

· cos 2 2 t

1 · J J J 2J J

· cos 4 t

J J 2J J J J

· cos 2 4 t 2J J J J · cos 5 t RF

(47)

Table 3-2 Measure the RF power with optical filtering

Frequency Amplitude

2   · J J 1 · J J J

2J J 2 2 · J J J  

  1 · J J J J

1 · J J J J

1 · J J J J

2J J J J

2J J J J

2J J J J

  · J J J J

1 · J J J J

1 · J J J J

2J J J J

2J J J J

2J J J J

2   · J J 1 · J J J

2J J 2 2 · J J J  

3 , 3   1 · J J J J

1 · J J J J

2J J J J  

2 2   1 · J J J

1 · J J J

2J J J J

2J J J J

4   1 · J J J 2J J  

2 4   J J 2J J J J  

5   2J J J J  

Figure 3-12 Illustration of the electrical spectrum of generated BTB mm-wave signals when the LSB1 is filter out. ( 6 )

     

  Figure 3-13 Illustration of the electrical spectrum of generated BTB mm-wave

signals when the LSB2 is filter out. ( 6 ) 

3.4.2 The effects of fiber dispersion

Consider fiber dispersion effect, the electrical field can be written as

· · J J cos ω t 1 After square-law photo detection, the RF signal can be expressed as

E · DC RF

The RF signal at the substrate frequency : The RF signal at the substrate frequency can be written as

I J J J J The RF signal power at the substrate frequency can be written as

P J J J J · A B 2AB · cos θ

The RF signal at the sum frequency

The RF signal at the sum frequency can be written as

I J J J J

The RF signal power at the sum frequency can be written as

P J J J J · A B 2AB · cos θ

J J J J · 2 cos 1

2 2 2 cos 1

2 · · cos θ

(57) Or

P J J J J · A B 2AB · cos θ

J J J J · 2 cos 1

2 2 2 cos 1

2 · · cos θ

(58) Because grating only filter out LSB1 or LSB2 at the same time, so the equation of the RF signal power at the sum and substrate frequency are the same. The

(58) Because grating only filter out LSB1 or LSB2 at the same time, so the equation of the RF signal power at the sum and substrate frequency are the same. The

在文檔中 高頻譜效率之正交分頻多工技術應用於倍頻光載微波信號系統 (頁 16-0)