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Transcript
Chapter 12 Basic Optical Network
 12.1 Basic Networks
 12.1.1 Network Topologies
 12.1.2 Performance of Passive Linear Buses
 12.1.3 Performance of Star Architectures
 12.3 Broadcast-and-Select WDM Networks
 12.3.1 Broadcast-and-Select Single-Hop
Networks
 12.3.2 Broadcast-and-Select Multihop
Networks
 12.3.3 The ShuffleNet Multihop Network 8.3
Demodulation Schemes
國立成功大學 電機工程學系
光纖通訊實驗室 黃振發教授 編撰
Chapter 12 Basic Optical Network
 12.4 Wavelength-Routed Networks
 12.4.1 Optical Cross-Connects
 12.4.2 Performance of Wavelength Conversion
國立成功大學 電機工程學系
光纖通訊實驗室 黃振發教授 編撰
12.1 Basic Networks
 Figure 12-1 shows the three common topologies
used for fiber optic networks: the linear-bus, ring,
and star configurations.
 Access to an optical data bus is achieved by means
of a coupling element.
 An active coupler converts the optical signal on
the data bus (Fig. 12-1(a)) to its electric baseband
counterpart before any data processing is carried
out.
 A passive coupler employs no electronic elements.
It is used passively to tap off a portion of the optical
power from the bus.
國立成功大學 電機工程學系
光纖通訊實驗室 黃振發教授 編撰
12.1 Basic Networks
Figure 12-1(a). Linear bus topology used for fiber
optic networks.
國立成功大學 電機工程學系
光纖通訊實驗室 黃振發教授 編撰
12.1 Basic Networks
 In a ring topology, consecutive nodes are connected
by point-to-point links that are arranged to form a
single closed path.
 Information in the form of data packets is
transmitted from node to node around the ring.
 The interface at each node is an active device that
has the ability to recognize its own address in a
data packet in order to accept messages.
 The active node forwards those messages that are
not addressed to itself on to its next neighbor.
國立成功大學 電機工程學系
光纖通訊實驗室 黃振發教授 編撰
12.1 Basic Networks
Figure 12-1(b). Ring topology for fiber optic networks.
國立成功大學 電機工程學系
光纖通訊實驗室 黃振發教授 編撰
12.1 Basic Networks
 In a star architecture, all nodes are joined at a
single point called the central node or hub.
Using an active hub, one can control all routing of
messages in the network from the central node.
 In a star network with a passive central node, a
power splitter is used at the hub to divide the
incoming optical signals among all the outgoing
lines to the attached stations.
國立成功大學 電機工程學系
光纖通訊實驗室 黃振發教授 編撰
12.1 Basic Networks
Figure 12-1(c). Star topology for fiber optic networks.
國立成功大學 電機工程學系
光纖通訊實驗室 黃振發教授 編撰
12.1.2 Performance of Passive
Linear Buses
 Over an optical fiber of length x (in km), the ratio
Ao of received power P(x) to transmitted power P(0)
is given by
Ao = P(x)/P(0) = 10-ax/10
(12-1)
where a is the fiber attenuation in units of dB/km.
 The losses encountered in a passive coupler in a
linear bus are shown in Fig. 12-2.
 The coupler has four functioning ports: two for
connecting the coupler onto the fiber bus, one for
receiving tapped-off light, and one for inserting
optical signal onto the line after the tap-off to keep
the signal out of the local receiver.
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光纖通訊實驗室 黃振發教授 編撰
12.1.2 Performance of Passive
Linear Buses
Figure 12-2. Losses in a passive linear-bus coupler
consisting of cascaded directional couplers.
國立成功大學 電機工程學系
光纖通訊實驗室 黃振發教授 編撰
12.1.2 Performance of Passive
Linear Buses
 If a fraction Fc of optical power is lost at each port
of the coupler, then the connecting loss Lc is
Lc = -10 log(1-Fc)
(12-2)
 For example, if we take this fraction to be 20%,
then Lc is about 1 dB; that is, the optical power gets
reduced by 1 dB at any coupling junction.
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光纖通訊實驗室 黃振發教授 編撰
12.1.2 Performance of Passive
Linear Buses
 Let CT represent the fraction of power that is removed
from the bus and delivered to the detector port. The
power extracted from the bus is called a tap loss and is
given by
Ltap = 10 log CT
(12-3)
 For a symmetric coupler, CT is also the fraction of
power that is coupled from the transmitting input port
to the bus.
 If Po is the optical power launched from a source flylead,
the power coupled to the bus is CTPo. The throughput
coupling loss Lthru is then given by
Lthru = -10 log(1 - CT)2
= -20 log(1 - CT)
國立成功大學 電機工程學系
光纖通訊實驗室 黃振發教授 編撰
(12-4)
12.1.2 Performance of Passive
Linear Buses
 In addition to connection and tapping losses, there is an
intrinsic transmission loss Li associated with each bus
coupler.
 If the fraction of power lost in the coupler is Fi, then the
intrinsic transmission loss Li is
Li = -10 log(1 - Fi )
(12-5)
 Consider a simplex linear bus of N stations uniformly
separated by a distance L, as shown in Fig. 12-3.
 From Eq. (12-1) the fiber attenuation between any two
adjacent stations is
Lfiber = -10 logAo = aL
國立成功大學 電機工程學系
光纖通訊實驗室 黃振發教授 編撰
(12-6)
12.1.2 Performance of Passive
Linear Buses
Figure 12-3. Topology of a simplex linear bus
consisting of N uniformly spaced stations.
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12.1.2 Performance of Passive
Linear Buses
 NEAREST-NEIGHBOR POWER BUDGET.
 The smallest distance in transmitted and received
power occurs for adjacent stations, such as between
stations 1 and 2 in Fig. 12-3.
 If Po is the optical power launched from a source at
station 1, then the power detected at station 2 is
P1,2 = AoCT2(1-Fc)4(1–Fi)2Po
國立成功大學 電機工程學系
光纖通訊實驗室 黃振發教授 編撰
(12-7)
12.1.2 Performance of Passive
Linear Buses
 The optical power flow encounters the following
loss-inducing mechanisms:
 One fiber path with attenuation Ao.
 Tap points at both the transmitter and the receiver,
each with coupling efficiencies CT.
 Four connecting points, each of which passes a
fraction (1 - Fc) of the power entering them.
 Two couplers which pass only the fraction (1 – Fi) of
the incident power owing to intrinsic losses.
 Using Eqs. (12-2) ~ (12-4) and Eq. (12-6), the losses
between stations 1 and 2 can be expressed as
10 log(Po/P1,2) = aL+2Ltap+4Lc+2Li.
(12-8)
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12.1.2 Performance of Passive
Linear Buses
 LARGEST-DISTANCE POWER BUDGET.
 The largest distance occurs between stations 1
and N. The fractional power level coupled into
the cable from the bus coupler at station 1 is
F1 = (1-Fc)2 CT (1–Fi)
(12-9a)
 At station N the fraction of power from the buscoupler input port that emerges from the
detector port is
FN = (1-Fc)2 CT (1–Fi)
國立成功大學 電機工程學系
光纖通訊實驗室 黃振發教授 編撰
(12-9b)
12.1.2 Performance of Passive
Linear Buses
 For each of the (N - 2) intermediate stations, the
fraction of power passing through each coupling
module (shown in Fig. 12-2) is
Fcoup = (1-Fc)2(1-CT)2(1–Fi),
(12-10)
since the power flow encounters two connector
losses, two tap losses, and one intrinsic loss.
國立成功大學 電機工程學系
光纖通訊實驗室 黃振發教授 編撰
12.1.2 Performance of Passive
Linear Buses
 Combining the expressions from Eqs. (12-9a), (129b), and (12-10), and the transmission losses of the
N – 1 intervening fibers,
 we find that the power received at station N from
station 1 is
P1,N = AoN-1F1FcoupN-1FNPo
= AoN-1(1-Fc)2N(1-CT)2(N-2)CT2(1-Fi)NPo
(12-11)
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12.1.2 Performance of Passive
Linear Buses
 Using Eqs. (12-2) ~ (12-6), the power budget for this
link is
10.log(Po/P1,N) = (N-1)aL +2NLc +(N-2)Lthru +2Ltap +Nli
= N(aL +2Lc +Lthru+Li) –aL -2Lthru +2Ltap
(12-12)
 The losses of the linear bus increase linearly with the
number of stations N.
國立成功大學 電機工程學系
光纖通訊實驗室 黃振發教授 編撰
12.1.2 Performance of Passive
Linear Buses
Example 12-1 :
 Compare the power budgets of three linear buses, having
5, 10, and 50 stations, respectively.
 Assume that CT = 10 %, so that Ltap = 10 dB and Lthru =
0.9 dB. Let Li = 0.5 dB and Lc = 1.0 dB.
 If the stations are relatively close together say 500 m, then
for an attenuation of 0.4 dB/km at 1300 nm the fiber loss
is 0.2 dB.
 Using Eq. (12-12), the power budgets for these three cases
can be calculated as shown in Table 12-1.
 The total loss values given in Table 12-1 are plotted in Fig.
12-4, which shows that the loss increases linearly with the
number of stations.
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光纖通訊實驗室 黃振發教授 編撰
12.1.2 Performance of Passive
Linear Buses
Table 12-1. Comparison of the power budgets of three
linear buses that have 5, 10, and 50 stations, repectively.
國立成功大學 電機工程學系
光纖通訊實驗室 黃振發教授 編撰
12.1.2 Performance of Passive
Linear Buses
Figure 12-4. Total loss as a function of the
number of attached stations for linear-bus
and star architectures.
國立成功大學 電機工程學系
光纖通訊實驗室 黃振發教授 編撰
12.1.2 Performance of Passive
Linear Buses
Example 12-2 :
 For the Example 12-1, suppose that for
implementing a 10-Mb/s bus we gave a choice of
an LED that emits -10 dBm or a LD capable of
emitting +3 dBm of optical power.
 APD receiver with sensitivity of -48 dBm is used
at the destination.
 In the LED case, the power loss allowed up to 5
stations on the bus.
 For the LD, we gave an additional 13 dB of margin,
so we can have a maximum of 8 stations connected
to the bus.
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光纖通訊實驗室 黃振發教授 編撰
12.1.2 Performance of Passive
Linear Buses
DYNAMIC RANGE:
 System dynamic range is the maximum optical
power range to which any detector must be able to
respond.
 The worst-case dynamic range (DR) is found from
the ratio of Eq. (12-7) to Eq. (12-11):
(12-13)
 This could be the difference in power levels
received at station N from station (N - 1) and from
station 1 (i.e., P1,2 = PN-1,N).
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12.1.2 Performance of Passive
Linear Buses
Example 12-3 :
 Consider the linear buses described in Example 12-1.
 For N = 5 stations, from Eq. (12-13) the dynamic
range is
DR = 3[0.2 + 2(l.0) + 0.9 + 0.5] dB = 10.8 dB.
 For N = 10 stations,
DR = 8[0.2 + 2(l.0) + 0.9 + 0.5] dB = 28.8 dB.
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12.1.3 Performance of Star
Architectures
 From Eq. (10-25), for a single input power Pin and N
output powers, the excess loss is given by
Excess Loss = Lexcess
= 10.log(Pin/SNi=1Pouti)
(12-14)
 The total loss of the device consists of its splitting loss
plus the excess loss in each path through the star.
 The splitting loss is given by
Splitting Loss = Lsplit
= -10.log(1/N) = 10.logN (12-15)
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12.1.3 Performance of Star
Architectures
 For power-balance equation, the following
parameters are used:
• PS is the fiber-coupled output power from a source
in dBm.
• PR is the minimum optical power in dBm required
at the receiver to achieve a specific BER.
• a is the fiber attenuation.
• All stations are located at the same distance L
from the star coupler.
• Lc is the connector loss in decibels.
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12.1.3 Performance of Star
Architectures
 The power-balance equation for a particular link
between two stations in a star network is
PS - PR = Lexcess + a(2L) + 2Lc + Lsplit
= Lexcess + a(2L) + 2Lc + 10.logN.
(12-16)
 In contrast to a passive linear bus, for a star network
the loss increases much slower as logN.
 Figure 12-4 compares the performance of the two
architectures.
國立成功大學 電機工程學系
光纖通訊實驗室 黃振發教授 編撰
12.1.3 Performance of Star
Architectures
Figure 12-4. Total loss as a function of the number
of attached stations for linear-bus and star
architectures.
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光纖通訊實驗室 黃振發教授 編撰
12.1.3 Performance of Star
Architectures
Example 12-4 :
 Consider two star networks that have 10 and 50 stations,
respectively. Assume each station is located 500 m from the
star coupler and that the fiber attenuation is 0.4 dB/km.
 Assume that the excess loss is 0.75 dB for the 10-station
network and 1.25 dB for the 50-station network. Let the
connector loss be 1.0 dB.
 For N = 10, from Eq. (12-16) the power margin between
the transmitter and the receiver is
PS - PR = [0.75 + 0.4(1.0) + 2(1.0)10log10] dB
 For N = 50, the power margin is
PS - PR = [1.25 + 0.4(1.0) + 2(1.0)10log50] dB
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光纖通訊實驗室 黃振發教授 編撰
12.1.3 Performance of Star
Architectures
 Using the transmitter output and receiver sensitivity
values given in Example 12-2, we see that an LED
transmitter can easily accommodate the losses in this
50-station star network.
 In comparison, a laser transmitter could not even
meet the 10-station design in a passive linear bus.
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12.3 Broadcast-and-Select
WDM Networks
 Broadcast-and-select techniques employing passive
optical stars, buses, or wavelength routers are used
for LAN applications.
 Active optical components form the basis for
constructing wide-area wavelength-routing networks.
 Single-hop refers to broadcast-and-select networks
where information transmitted without O/E
conversions at any intermediate point.
 Intermediate E/O conversion can occur in a multihop broadcast-and-select network.
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12.3.1 Broadcast-and-Select
Single-Hop Networks
 Figure 12-14 shows N sets of transmitters and
receivers being attached to a star coupler or a passive
bus.
 Each transmitter sends its information at different
wavelength.
 All transmissions from various nodes are combined in
a passive star coupler or coupled onto a bus and the
result is sent out to all receivers.
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12.3.1 Broadcast-and-Select
Single-Hop Networks
Figure 12-14. Alternate physical architectures for
a WDM-based local network : (a) star, (b) bus.
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12.3.1 Broadcast-and-Select
Single-Hop Networks
 Figure 12-15 illustrates the concept of multicast or
broadcast for a star network.
 Workstations at nodes 4 and 2 communicate using l2,
whereas a user at node 1 broadcasts information to
workstations at nodes 3 and 5 using l1.
 The same concepts are applicable to bus structures,
although the losses encountered in the star and bus
architectures are different.
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12.3.1 Broadcast-and-Select
Single-Hop Networks
Figure 12-15. A single-hop broadcast-and-select network.
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12.3.1 Broadcast-and-Select
Single-Hop Networks
 The WDM setup in Fig. 12-15 is protocol transparent.
This means that different sets of communicating
nodes can use different information-exchange rules
(protocols) without affecting the other nodes in the
network.
 This is analogous to TDM telephone lines in which
voice, data, or facsimile services are sent in different
time slots without interfering with each other.
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12.3.2 Broadcast-and-Select
Multihop Networks
 Figure 12-16 shows an example of a four-node
broadcast-and-select multihop network where each
node transmits on one set of two fixed wavelengths
and receives on another set of two fixed wavelengths.
 Stations can send information directly only to those
nodes that have a receiver tuned to one of the two
transmit wavelengths.
 Information destined for other nodes will have to be
routed through intermediate stations.
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12.3.2 Broadcast-and-Select
Multihop Networks
Figure 12-16. Architecture and traffic flow of
a multihop broadcast-and-select network.
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12.3.2 Broadcast-and-Select
Multihop Networks
 As shown in Fig. 12-17, at each intermediate node,
the address header is decoded to examine the routing
information field.
 Using this routing information, the packet is
switched electronically to the specific optical
transmitter.
 The specific optical transmitter will appropriately
direct the packet to the next node in the logical path
toward its final destination.
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12.3.2 Broadcast-and-Select
Multihop Networks
Figure 12-17. Representation of the fields contained
in a data packet.
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12.3.2 Broadcast-and-Select
Multihop Networks
 The flow of traffic can be seen from Fig. 12-16.
 If node 1 wants to send a message to node 2, it first
transmits the message to node 3 using l1.
 Then node 3 forwards the message to node 2 using l6.
 With this scheme there are no destination conflicts
or packet collisions in the network, since each
wavelength channel is dedicated to a particular
source-destination link.
 For H hops between nodes, there is a network
throughput penalty of at least 1/H.
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12.3.3 ShuffleNet Multihop Network
 The extension of perfect shuffle to optical networks
consists of a cylindrical arrangement of k columns,
each having pk nodes, where p is the number of
transceiver pairs per node.
 The total number of nodes is then
N = kpk
with k = 1, 2, 3, ... and p = 1, 2, 3, .…
國立成功大學 電機工程學系
光纖通訊實驗室 黃振發教授 編撰
(12-17)
12.3.3 ShuffleNet Multihop Network
 Given that each node requires p wavelengths to
transmit information, the total number of
wavelengths Nl needed in the network is
Nl = pN = kpk+1
(12-18)
 Figure 12-18 illustrates a (p, k) = (2, 2) ShuffleNet,
where the (k+1)-th column represents the completion
of a trip around the cylinder back to the 1st column,
as indicated by the return arrow.
 In this example, there are eight nodes and sixteen
wavelengths.
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12.3.3 ShuffleNet Multihop Network
Figure 12-18. Logical interconnection pattern and
wavelength assignment of a (p,k) = (2,2) ShuffleNet.
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12.3.3 ShuffleNet Multihop Network
 An important performance parameter for the
ShuffleNet is the average number of hops between
any two randomly chosen nodes.
 Since all nodes have p output wavelengths,
p nodes can be reached from any node in one hop,
p2 additional nodes can be reached in two hops,
and so on, until all the (pk-1) other nodes are visited.
 The maximum number of hops is
Hmax = 2k -1
國立成功大學 電機工程學系
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(12-19)
12.3.3 ShuffleNet Multihop Network
 In Fig. 12-18, consider the connections between
nodes 1 and 5 and between nodes 1 and 7.
 In the first case, the hop number is one.
 In the second case, three hops are needed with the
routes being either 1-6-4-7 or 1-5-2-7.
 The average number of hops of a ShuffleNet is
(12-20)
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12.3.3 ShuffleNet Multihop Network
 As a result of multi-hopping, only part of the capacity of
a particular link directly connecting two nodes is actually
utilized for carrying traffic between them.
 The rest of the link capacity is used to forward messages
from other nodes.
 Since the system has Np = kpk+1 links, the total network
capacity C is
C = kpk+1/H
(12-21)
and the per-user throughput S is
S = C/N = p/H
國立成功大學 電機工程學系
光纖通訊實驗室 黃振發教授 編撰
(12-22)
12.3.3 ShuffleNet Multihop Network
 Different (p, k) combinations result in different
throughputs, so one can make some tradeoffs among
the variables to get a better network performance.
 For example, given that the number of nodes is fixed
at N, one can reduce the average number of hops by
increasing p (which decreases k) to boost the capacity
and the throughput.
國立成功大學 電機工程學系
光纖通訊實驗室 黃振發教授 編撰
12.4 Wavelength-Routed Networks
 Two problems in Broadcast-and-Select networks :
1). More wavelengths are needed as the number of
nodes in the network grows.
2). Without optical booster amplifiers, a large
number of users spread over a wide area
cannot be interconnected.
 Wavelength-routed networks can overcome these
limitations through wavelength-reuse, wavelengthconversion, optical-switching.
國立成功大學 電機工程學系
光纖通訊實驗室 黃振發教授 編撰
12.4 Wavelength-Routed Networks
 Wavelength-routed network consists of optical
wavelength routers interconnected by pairs of
point-to-point fiber links in a mesh configuration,
as illustrated in Fig. 12-19.
 In Fig. 12-19 the connection from node 1 to node 2
and from node 2 to node 3 can both be on l1,
whereas the connection between nodes 4 and 5
requires a different wavelength l2.
國立成功大學 電機工程學系
光纖通訊實驗室 黃振發教授 編撰
12.4 Wavelength-Routed Networks
Figure 12-19. Wavelength reuse on a mesh network.
國立成功大學 電機工程學系
光纖通訊實驗室 黃振發教授 編撰
12.4.1 Optical Cross-Connects
 Consider the OXC architecture shown in Fig. 12-20
that uses space switching without wavelength
conversion.
 The space switches can be cascaded electronically
controlled optical directional-coupler elements or
semiconductor-optical-amplifier switching gates.
 Each of the input fibers carries M wavelengths, any
of which could be added or dropped at a node.
國立成功大學 電機工程學系
光纖通訊實驗室 黃振發教授 編撰
12.4.1 Optical Cross-Connects
Figure 12-20. Optical cross-connect architecture using
optical space switches and no wavelength converters.
國立成功大學 電機工程學系
光纖通訊實驗室 黃振發教授 編撰
12.4.1 Optical Cross-Connects
 At the input, the arriving signal wavelengths is
amplified and passively divided into N streams by a
power splitter or AWG demultiplexer.
 Tunable filters then select individual wavelengths,
which are directed to an optical space-switching
matrix.
 The switch matrix directs the channels either to one
of the eight output lines if it is a through-traveling
signal,
 or to a particular receiver attached to the OXC at
output ports 9 through 12 if it has to be dropped to
a user at that node.
國立成功大學 電機工程學系
光纖通訊實驗室 黃振發教授 編撰
12.4.1 Optical Cross-Connects
 Signals that are generated locally by a user get
connected electrically via the DXC to an optical
transmitter. The switch matrix directs them to the
appropriate output line.
 The M output lines, each carrying separate
wavelengths, are fed into a wavelength multiplexer
to form a single aggregate output stream.
 Contentions arise in the architecture shown in Fig.
12-20 when channels having the same wavelength
but traveling on different input fibers enter the OXC
and need to be switched simultaneously to the same
output fiber.
國立成功大學 電機工程學系
光纖通訊實驗室 黃振發教授 編撰
12.4.1 Optical Cross-Connects
 The contentions could be resolved by assigning a
fixed wavelength to each optical path throughout
the network, or by dropping one of the channels and
retransmitting it at another wavelength.
 In the first case, wavelength reuse and network
scalability are reduced.
 In the second case, the add/drop flexibility of the
OXC is lost.
 These blocking characteristics can be eliminated by
using wavelength conversion at any output of the
OXC.
國立成功大學 電機工程學系
光纖通訊實驗室 黃振發教授 編撰
12.4.1 Optical Cross-Connects
Example 12-5 :
 Consider the 4 x 4 OXC shown in Fig.12-21. The OXC
consists of three 2 x 2 switch elements.
 Suppose that l2 on input fiber 1 needs to be switched to
output fiber 2 and that l1 on input fiber 2 needs to be
switched to output fiber 1.
 This is achieved by having the 1st two switch elements set
in the bar-state and the 3rd elements set in the cross-state,
as indicated in Fig. 12-21.
 Obviously, without wavelength conversion there would be
wavelength contention at both mux output ports.
 By using wavelength converters ahead of the multiplexer,
the cross-connected wavelengths can be converted to
noncontending wavelengths.
國立成功大學 電機工程學系
光纖通訊實驗室 黃振發教授 編撰
12.4.1 Optical Cross-Connects
Figure 12-21. Example of a simple 4x4 OXC architecture
using optical space switches and wavelength converters.
國立成功大學 電機工程學系
光纖通訊實驗室 黃振發教授 編撰
12.4.2 Performance of Wavelength
Conversion
 Assume that there are H links (or hops) between
nodes A and B.
 Take the number of available wavelengths per fiber
link to be F, and let r be the probability that a
wavelength is used on any fiber link.
 Since rF is the expected number of busy wavelengths
on any link, r is a measure of the fiber utilization
along the path.
國立成功大學 電機工程學系
光纖通訊實驗室 黃振發教授 編撰
12.4.2 Performance of Wavelength
Conversion
 In the case of wavelength conversion, a connection
request between nodes A and B is blocked if one of the
H intervening fibers is full.
 The probability Pb’ that the connection request from
A to B is blocked is the probability that there is a
fiber link in this path with all F wavelengths in use,
so that
Pb’ = 1 - (1 - rF)H
國立成功大學 電機工程學系
光纖通訊實驗室 黃振發教授 編撰
(12-23)
12.4.2 Performance of Wavelength
Conversion
 Let q be the achievable utilization for a given blocking
probability in a network with wavelength conversion,
q = [1 - (1 - Pb’)1/H]1/F
= (Pb’/H)1/F
(12-24)
where the approximation holds for small values of
Pb’/H.
 Figure 12-22 shows the achievable utilization q for
Pb’ = 10-3 as a function of the number of wavelengths
for H = 5, 10, and 20 hops.
 The effect of path length is small, and q rapidly
approaches 1 as F becomes large.
國立成功大學 電機工程學系
光纖通訊實驗室 黃振發教授 編撰
12.4.2 Performance of Wavelength
Conversion
Figure 12-22. Achievable wavelength utilization as a
function of the # of wavelengths for a 10-3 blocking
probability in a network using l-conversion.
國立成功大學 電機工程學系
光纖通訊實驗室 黃振發教授 編撰
12.4.2 Performance of Wavelength
Conversion
 The probability Pb that the connection request from A
to B is blocked is the probability that each wavelength is used on at least one of the H links, so that
Pb = [1 - (1 - r)H]F
(12-25)
 Letting p be the achievable utilization for a given
blocking probability in a network without wavelength
conversion, then
p = 1 - (1 - Pb1/F)1/H
= -(1/H).ln(1 - Pb1/F)
(12-26)
 The achievable utilization is inversely proportional to
the length of the path H between A and B.
國立成功大學 電機工程學系
光纖通訊實驗室 黃振發教授 編撰
12.4.2 Performance of Wavelength
Conversion
 Figure 12-23 depicts the achievable utilization p for
Pb=10-3 as a function of the number of wavelengths
for H = 5, 10, and 20 hops.
Figure 12-23. Achievable wavelength utilization as
a function of the # of wavelengths for a 10-3 blocking
probability in a network not using l-conversion.
國立成功大學 電機工程學系
光纖通訊實驗室 黃振發教授 編撰
12.4.2 Performance of Wavelength
Conversion
 Define the gain G=q/p to be the increase in fiber or wavelength utilization for the same blocking probability.
 Setting Pb’=Pb in Eqs. (12-23) and (12-25), we have
(12-27)
 Figure 12-24 shows G as a function of H = 5, 10, and 20
links for a blocking probability of Pb=10-3. The figure
shows that as F increases, the gain increases, and peaks
at about H/2.
 The gain then slowly decreases, since large trunking
networks are more efficient than small ones.
國立成功大學 電機工程學系
光纖通訊實驗室 黃振發教授 編撰
12.4.2 Performance of Wavelength
Conversion
Figure 12-24. Increase in network utilization as a
function of the # of wavelengths for a 10-3 blocking
probability when l-conversion is used.
國立成功大學 電機工程學系
光纖通訊實驗室 黃振發教授 編撰