U.S. patent application number 12/966991 was filed with the patent office on 2011-09-01 for transmitter frequency peaking for optical fiber channels.
This patent application is currently assigned to CLARIPHY COMMUNICATIONS, INC.. Invention is credited to Thomas A. Lindsay, Norman L. Swenson.
Application Number | 20110211846 12/966991 |
Document ID | / |
Family ID | 36954011 |
Filed Date | 2011-09-01 |
United States Patent
Application |
20110211846 |
Kind Code |
A1 |
Lindsay; Thomas A. ; et
al. |
September 1, 2011 |
Transmitter Frequency Peaking for Optical Fiber Channels
Abstract
Frequency peaking is used in the transmitter to improve link
performance. In one example, frequency peaking improves the
PIE.sub.D or TWDP. The frequency peaking can result in pulse shapes
that have more electrical energy in the receiver (and therefore
higher received SNR) than uncompensated pulses. In addition, due to
the response of typical fibers, boosting the high frequencies
typically will flatten the received spectrum, which will improve
the performance of the equalizer in an EDC receiver.
Inventors: |
Lindsay; Thomas A.; (Brier,
WA) ; Swenson; Norman L.; (Mountain View,
CA) |
Assignee: |
CLARIPHY COMMUNICATIONS,
INC.
Irvine
CA
|
Family ID: |
36954011 |
Appl. No.: |
12/966991 |
Filed: |
December 13, 2010 |
Related U.S. Patent Documents
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Application
Number |
Filing Date |
Patent Number |
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11370655 |
Mar 7, 2006 |
7853149 |
|
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12966991 |
|
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60659924 |
Mar 8, 2005 |
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60677911 |
May 4, 2005 |
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Current U.S.
Class: |
398/194 |
Current CPC
Class: |
H04B 10/541 20130101;
H04B 10/508 20130101; H04B 10/25137 20130101; H04B 10/504
20130101 |
Class at
Publication: |
398/194 |
International
Class: |
H04B 10/04 20060101
H04B010/04 |
Claims
1. An optical transmitter for transmitting data over an optical
fiber at a specified data rate, wherein the optical transmitter
comprises: a laser that exhibits relaxation oscillation; and a
laser driver coupled to drive the laser, the laser driver adapted
to utilize the laser relaxation oscillation to boost the peak
frequency relative to a DC frequency; wherein the laser produces an
optical signal that encodes the data and is suitable for
transmission over the optical fiber, and the optical signal has a
frequency spectrum that has a relative peak at a peak frequency
located in a vicinity of a line rate and the relative peak is
relative to a reference frequency spectrum of a reference optical
signal produced by an ideal rectangular pulse transmitter encoding
the data.
2. The transmitter of claim 1 wherein the peak frequency is between
10% and 100% of the line rate.
3. The transmitter of claim 1 wherein the peak frequency is between
25% and 75% of the line rate.
4. The transmitter of claim 1 wherein the peak frequency is
approximately 35-50% of the line rate.
5. The transmitter of claim 1 wherein the optical pulses encode the
data based on on-off keying.
6. The transmitter of claim 1 wherein the data rate is
approximately 10 G.
7. The transmitter of claim 1 wherein the transmitter complies with
a standard specifying a maximum power penalty.
8. The transmitter of claim 1 wherein the transmitter has a lower
power penalty than the ideal rectangular pulse transmitter.
9. The transmitter of claim 1 wherein the transmitter has a lower
PIE-D power penalty than the ideal rectangular pulse
transmitter.
10. The transmitter of claim 1 wherein the peak frequency is
located in a frequency band that is attenuated by the optical
fiber.
11. The transmitter of claim 1 wherein the optical pulses are
characterized by overshoot at the frequency peak.
12. The transmitter of claim 1 wherein the transmitter complies
with an X2, XFP or SFP+ form factor.
13. A method for transmitting data over an optical fiber at a
specified data rate, the method comprising: receiving the data; and
producing an optical signal that encodes the data and is suitable
for transmission over the optical fiber, wherein the optical signal
has a frequency spectrum that has a relative peak at a peak
frequency located in a vicinity of a line rate and the relative
peak is relative to a reference frequency spectrum of a reference
optical signal produced by an ideal rectangular pulse transmitter
encoding the data, wherein the step of producing the optical signal
comprises utilizing a laser relaxation oscillation to boost the
peak frequency relative to a DC frequency.
14. The method of claim 13 wherein the peak frequency is between
10% and 100% of the line rate.
15. The method of claim 13 wherein the peak frequency is between
25% and 75% of the line rate.
16. The method of claim 13 wherein the step of producing the
optical signal comprises producing the optical pulses based on
on-off keying of the data.
17. The method of claim 13 wherein the data rate is approximately
10 G.
18. The method of claim 13 wherein the optical signal has a lower
power penalty than the ideal rectangular pulse transmitter.
19. The method of claim 13 wherein the peak frequency is located in
a frequency band that is attenuated by the optical fiber.
Description
CROSS-REFERENCE TO RELATED APPLICATION(S)
[0001] This application is a divisional of U.S. patent application
Ser. No. 11/370,655, "Transmitter Frequency Peaking for Optical
Fiber Channels," filed Mar. 7, 2006; which claims priority under 35
U.S.C. .sctn.119(e) to (a) U.S. Provisional Patent Application Ser.
No. 60/659,924, "Transmitter frequency peaking for dispersive
optical fiber channels," filed Mar. 8, 2005; and to (b) U.S.
Provisional Patent Application Ser. No. 60/677,911, "A New Approach
to Measure Tx Signal Strength and Penalty," filed May 4, 2005. The
subject matter of all of the foregoing is incorporated herein by
reference in its entirety.
BACKGROUND OF THE INVENTION
[0002] 1. Field of the Invention
[0003] This invention relates generally to the transmission of data
over optical fibers and, more particularly, to the use of frequency
peaking in transmitters to improve the performance of the
transmission.
[0004] 2. Description of the Related Art
[0005] Optical fiber is widely used as a communications medium in
high speed digital networks, including local area networks (LANs),
storage area networks (SANs), and wide area networks (WANs). There
has been a trend in optical networking towards ever-increasing data
rates. While 100 Mbps was once considered extremely fast for
enterprise networking, attention has recently shifted to 10 Gbps,
100 times faster. As used in this disclosure, 10 Gigabit
(abbreviated as 10 G or 10 Gbps) systems are understood to include
optical fiber communication systems that have data rates or line
rates (i.e., bit rates including overhead) of approximately 10
Gigabits per second.
[0006] Regardless of the specific data rate, application or
architecture, communications links (including optical fiber
communications links) invariably include a transmitter, a channel
and a receiver. In an optical fiber communications link, the
transmitter typically converts the digital data to be sent to an
optical form suitable for transmission over the channel (i.e., the
optical fiber). The optical signal is transported from the
transmitter to the receiver over the channel, possibly suffering
channel impairments along the way, and the receiver then recovers
the digital data from the received optical signal.
[0007] A typical 10 G optical fiber communications link 100 is
shown in FIG. 1. The link 100 includes a transmitter 105 coupled
through optical fiber 110 (the channel) to a receiver 120. A
typical transmitter 105 may include a serializer, or
parallel/serial converter (P/S), 106 for receiving 10 G data from a
data source on a plurality of parallel lines and providing serial
data to a 10 G laser driver 107. The laser driver 107 then drives a
10 G laser 108 which launches an optical signal carrying the data
on optical fiber 110.
[0008] A typical receiver 120 includes a 10 G photodetector 111 for
receiving and detecting data from the fiber 110. The detected data
is typically processed through a 10 G transimpedance amplifier 112,
a 10 G limiting amplifier 113, and a 10 G clock and data recovery
unit 114. The data may then be placed on a parallel data interface
through a serial/parallel converter (S/P) 115.
[0009] In an optical fiber communications system, the optical power
output by a laser is commonly modulated in a binary fashion to send
data over an optical fiber. Nominally, the optical power is high
for the duration of a bit period to send a logical "1," and low to
send a logical "0." This is commonly referred to as on-off-keying,
where "on" means high laser power and "off" means low laser power.
In nonreturn-to-zero (NRZ) modulation, the output power stays at
nominally the same level for an entire bit period. In actuality,
the level is not perfectly constant for the entire bit period due
to various effects. Nonetheless, a common feature of NRZ modulation
is that a long string of zeros or a long string of ones will each
result in an optical signal that tends to a constant steady state
value.
[0010] Standards play an important role in networking and
communications. Since components in the network may come from
different vendors, standards ensure that different components will
interoperate with each other and that overall system performance
metrics can be achieved even when components are sourced from
different vendors. There are a number of standards that relate to
10 G fiber networks. For example, the IEEE 802.3aq committee is
developing a new standard (10 GBASE-LRM) for 10 G Ethernet over
multi-mode fiber over distances of up to 220 meters using
electronic dispersion compensation (EDC). This standard is in a
draft state, currently documented in IEEE Draft P802.3aq/D3.1,
Draft amendment to: IEEE Standard for Information
technology--Telecommunications and information exchange between
systems--Local and metropolitan area networks--Specific
requirements, Part 3: Carrier Sense Multiple Access with Collision
Detection (CSMA/CD) Access Method and Physical Layer
Specifications, Amendment: Physical Layer and Management Parameters
for 10 Gb/s Operation, Type 10 GBASE-LRM, which is incorporated
herein by reference.
[0011] Standards committees define agreed-upon metrics to quantify
performance of various components of the system being standardized.
For example, in the case of optical fiber communications link, a
quantity known as Optical Modulation Amplitude (OMA) is often used
to characterize the signal strength of the transmitted optical
waveform. OMA is the difference in optical power for the nominal
"1" and "0" levels of the optical signal. Another parameter used to
characterize an optical fiber transmission is the extinction ratio
(ER), which is the ratio of the nominal "1" optical power level to
the nominal "0" optical power level. Techniques for measuring both
OMA and ER are defined in the IEEE 802.3aq draft standard. The
technique defined by 802.3aq to measure OMA is to capture samples
of a test waveform using a sampling oscilloscope. The test waveform
is a square waveform consisting of several consecutive 1's followed
by several consecutive 0's in a repeating pattern. The mean optical
power level of an optical 1 is measured over the center 20% of the
time interval where the signal is high, and similarly for 0's when
the signal is low. The frequency of the square wave used to measure
the OMA will be referred to as the "OMA measurement frequency." The
OMA quantity as a measure of transmitter power can be used to
normalize performance metrics relative to a standardized
transmitter power.
[0012] One such performance metric is the optical power penalty.
Assume that some signal quality effect causes a drop in the signal
to noise ratio of a certain amount. The impact of that effect can
be characterized by an optical power penalty. The optical power
penalty is the decrease in optical power (e.g., as measured by OMA
in certain cases) that would result in the same drop in the signal
to noise ratio. All else being equal, a lower power penalty means a
better signal to noise ratio (and better performance) than a higher
power penalty.
[0013] One measure of optical power penalty is referred to as
PIE.sub.D (Penalty for Ideal Equalizer--DFE). See for example, S.
Bhoja, "Channel metrics for EDC-based 10 GBASE-LRM," IEEE 802.3aq
Task Force, July 2004, available online at:
http://grouper.ieee.org/groups/802/3/aq/public/jul04/bhoja.sub.--1.sub.---
0704.pdf, which is incorporated herein by reference. PIE.sub.D is a
calculation for optical power penalty for a type of EDC known as
decision feedback equalization (DFE) and is given in optical dB
by
PIE D = 5 log 10 ( exp ( - 2 T .intg. 0 1 2 T ln ( 1 T H a ( f ) 2
+ .sigma. 2 ) f ) ) ( 1 ) ##EQU00001##
[0014] PIE.sub.D is the ratio of two signal-to-noise ratios (SNRs).
The first signal-to-noise ratio is a matched filter bound SNR,
SNR.sub.MFB-Rect, which is the SNR of a matched filter receiver
that receives a perfect rectangular non-return-to-zero (NRZ) pulse.
The second SNR is SNR.sub.DFE, which is the SNR realized at the
slicer of an ideal infinite-length DFE receiver assuming that the
channel can be modeled as linear. T is the bit period (1/line
rate), .sigma. is 1/SNR.sub.MFB-Rect, and |H.sub.a(f)|.sup.2 is the
folded spectrum defined by
H a ( f ) 2 = 1 T n = - .infin. .infin. H ( f + n T ) 2 ( 2 )
##EQU00002##
where H(f) is the Fourier Transform of h(t), and h(t) is the
response of the normalized channel to a rectangular pulse of
duration T and amplitude 1. In this sense the normalized channel
includes filtering by the transmitter, the fiber channel, and the
front-end filter of the optical receiver. Therefore, h(t) is the
convolution of a rectangular pulse with the impulse responses of
filters characterizing those elements. The channel is normalized
such that H(0) is equal to T. Both SNR.sub.MFB-Rect and SNR.sub.DFE
are computed assuming that the minimum OMA allowed by the standard
is transmitted (which effectively determines .sigma. in Eqn.
1).
[0015] PIE.sub.D is the optical power penalty corresponding to a
given channel response H(f) assuming that the channel is linear.
Other penalty measures include, for example, the transmit waveform
and dispersion penalty (TWDP) as defined in the IEEE 802.3aq draft
standard and described further in N. Swenson et al., "Explanation
of IEEE 802.3, clause 68 TWDP," available online at
http://ieee802.org/3/aq/public/tools/TWDP.pdf, which is
incorporated herein by reference. The TWDP test is a compliance
test for a transmitter and computes a penalty similar to that
computed by PIE-D for a reference fiber channel and reference
receiver. TWDP differs from PIE.sub.D in that TWDP does not assume
that the transmitter is linear and it uses a finite-length
equalizer in the equalizing receiver.
[0016] While in theory it may be possible to overcome a power
penalty by simply increasing the transmitted OMA, it has been
observed in practice that when PIE.sub.D or TWDP exceeds a certain
value, reliable communication with a practical receiver is not
possible, regardless of the transmitted OMA. For this reason, the
802.3aq committee placed an upper bound on the allowable TWDP for a
compliant transmitter. Since TWDP and PIE.sub.D are both based on
normalized OMA, these penalties cannot be reduced by increasing the
OMA of the transmitter. A conventional method of reducing the
transmitter power penalty (TWDP) is to improve the quality of the
transmitted signal such that the signal more closely approximates a
perfect rectangular NRZ waveform. This, however, can add
significant cost to the transmitter. Therefore, a need exists to
reduce the transmitter power penalty (and other penalties) in a
cost effective manner, thus increasing the performance of the
communications link.
SUMMARY OF THE INVENTION
[0017] The present invention overcomes the limitations of the prior
art by using frequency shaping (e.g., frequency peaking) in the
transmitter. Generally speaking, shaping the frequency spectrum of
the transmitter in a manner that increases the AC power of the
electrical signal after photodetection at the receiver can result
in better performance. Moreover, accomplishing this power increase
at the receiver in a manner that does not increase the transmitted
OMA results in lower power penalties, even compared to ideal
transmitters that produce perfectly rectangular pulses. Thus, it is
possible to reduce PIE.sub.D and TWDP by shaping the overall
channel response H(f).
[0018] In one aspect of this invention, frequency peaking is
employed to reduce the PIE.sub.D or TWDP penalty. The frequency
peaking can result in pulse shapes that have more electrical energy
(and therefore higher received SNR) than uncompensated pulses
(i.e., ideal rectangular pulses). In addition, due to the lowpass
nature of the combined frequency response of typical fibers with
the receiver front-end filter, boosting the high frequencies will
generally tend to flatten the received spectrum, which will improve
the performance of the equalizer in an EDC receiver.
[0019] In one aspect, an optical transmitter produces an optical
signal that is suitable for transmission over an optical fiber. The
optical signal encodes data that is being transmitted at a certain
data rate (or line rate). Compared to the frequency spectrum of a
reference optical signal produced by an ideal rectangular pulse
transmitter encoding the same data, the frequency spectrum of the
optical signal produced by this transmitter has a relative peak at
a peak frequency located in a vicinity of the line rate.
Alternately, the transmitter can be modeled as an ideal rectangular
pulse transmitter that produces perfectly rectangular pulses
followed by a transmit filter, where the transmit filter has a
frequency response that peaks at a frequency (the peak frequency)
that is located in a vicinity of the line rate. In various
implementations, the peak frequency can be located between 10% and
100% of the line rate, between 25% and 75% of the line rate, and/or
at approximately 30-50% of the line rate.
[0020] In one implementation, the frequency peaking is achieved by
a pre-emphasis network that boosts the peak frequency relative to
the value of the continuous power spectrum at the DC frequency
(and/or relative to the power spectrum at the OMA measurement
frequency in the case of AC coupling). One example would be a
filter that has a transfer function of (1+x)-xD, where x is a
fraction between 0 and 1 (e.g., x=0.25), and D is a delay equal to
one period of the line rate (or one pulse period for NRZ
transmission).
[0021] In another implementation, the frequency peaking is achieved
by utilizing the relaxation oscillation behavior of a laser. Many
lasers exhibit relaxation oscillation which, if not corrected, can
cause overshoot or ringing in the optical pulses produced. In most
transmitters, the laser transmitter is designed to suppress this
effect, thus producing a well-behaved rectangular pulse. However,
in one aspect of the invention, the laser transmitter instead
utilizes the laser relaxation oscillation in order to boost the
peak frequency relative to the DC frequency and/or relative to the
OMA measurement frequency.
[0022] In another implementation, peaking is achieved by tuning a
matching network located between the laser driver and the laser.
The matching network boosts currents at higher frequencies. The
network is typically passive and can include resistors, capacitors,
inductors, and lengths of transmission line.
[0023] Frequency peaking can be applied to many different
applications. Examples include 10 G communications links. Example
standards include 10 GBASE-LRM. Example transmitter form factors
include X2, XENPAK, XPAK, XFP, SFP+, 300-pin, SFP, SFF, GBIC, etc.
Other aspects of the invention include methods corresponding to the
devices and systems described above, and applications for all of
the above.
BRIEF DESCRIPTION OF THE DRAWINGS
[0024] The invention has other advantages and features which will
be more readily apparent from the following detailed description of
the invention and the appended claims, when taken in conjunction
with the accompanying drawings, in which:
[0025] FIG. 1 (prior art) is a block diagram of an optical fiber
communications link.
[0026] FIG. 2 is a block diagram of a transmitter according to the
invention.
[0027] FIG. 3 is a block diagram of a pre-emphasis network
according to the invention.
[0028] FIGS. 4a and 4b are spectral diagrams of a transmit filter
without, and with, frequency peaking, respectively.
[0029] FIGS. 5a and 5b are time traces of optical pulses produced
by a transmitter without, and with, frequency peaking,
respectively.
[0030] FIGS. 6a and 6b are eye diagrams of the optical pulses in
FIGS. 5a and 5b.
[0031] FIG. 7 is a graph that plots the cumulative distribution
function of an idealistic power penalty for an EDC receiver.
[0032] FIG. 8 is a spectral response of a laser diode, illustrating
relaxation oscillation.
[0033] FIG. 9 is a time trace of optical pulses produced by a
transmitter with frequency peaking based on relaxation
oscillation.
[0034] FIGS. 10a and 10b are eye diagrams of optical pulses
produced by a transmitter without, and with, frequency peaking,
respectively.
[0035] FIG. 11 is a graph of the cumulative distribution function
of the optical power penalty, with and without frequency
peaking.
[0036] The figures depict embodiments of the present invention for
purposes of illustration only. One skilled in the art will readily
recognize from the following discussion that alternative
embodiments of the structures and methods illustrated herein may be
employed without departing from the principles of the invention
described herein.
DETAILED DESCRIPTION OF THE PREFERRED EMBODIMENTS
[0037] The following mathematical discussion shows how a properly
shaped pulse can have significantly more electrical energy than an
ideal rectangular pulse while having the same OMA. This discussion
relates to the Matched Filter Bound SNR, SNR.sub.MFB, which is the
upper bound on the SNR that can be realized by an equalizing
receiver that uses a zero-forcing criterion. (PIE.sub.D and TWDP
are based on the minimum mean-squared error criterion instead of
the zero-forcing criterion, but the performance is nearly identical
for the low-noise channels of interest.) Increasing SNR.sub.MFB at
the receiver will generally improve the SNR at the slicer of the
equalizing receiver, resulting in a reduced penalty. Furthermore,
shaping the transmit spectrum in such a way that the resulting
folded spectrum |H.sub.a(f)|.sup.2 in Eqn. 1 is approximately
constant over the interval from 0 to 1/2T will reduce the gap
between the SNR at the equalizer slicer and SNR.sub.MFB at the
receiver. We refer to this gap as "equalizer loss." Therefore,
frequency peaking can have two beneficial effects: 1) increasing
SNR.sub.MFB at the receiver, and 2) decreasing the equalizer loss.
Both of these effects are achieved without increasing OMA.
Therefore, they reduce PIE.sub.D and TWDP.
[0038] Let an optically modulated signal be given by
y ( t ) = B + A n a ( n ) p ( t - nT ) ( 3 ) ##EQU00003##
where a(n).epsilon.{-1,+1} is the underlying data, p(t) is the
pulse shape, T is the period of the data transmission (i.e., 1/line
rate), and A and B are constants. y(t) is the optical signal power.
Let the energy in the pulse p(t) be defined by
.epsilon..sub.p.ident..intg.p(t).sup.2dt (4)
[0039] If y(t) is converted to an electrical signal (assuming
perfect E/O conversion) and then corrupted by additive white
Gaussian noise with a two-sided power spectral density of
N.sub.0/2, the matched filter bound SNR is given by
SNR.sub.MFB.ident.A(2.epsilon..sub.p/N.sub.0).sup.1/2 (5)
where SNR.sub.MFB is defined in the optical power domain. If
defined in the electrical power domain, SNR.sub.MFB would be the
square of the quantity defined in Eqn. 5. With SNR.sub.MFB defined
in the optical power domain, BER=Q(SNR.sub.MFB) for a matched
filter receiver receiving an isolated pulse, where Q( ) is the
Gaussian error probability function
Q ( y ) = .intg. y .infin. 1 2 .pi. - x 2 2 x ( 6 )
##EQU00004##
[0040] For a perfect square wave modulation with infinite
extinction ratio (i.e., the nominal optical power level of a
transmitted "0" is zero), B is the average power P.sub.ave=OMA/2,
A=OMA/2, p(t) is a rectangular pulse of magnitude 1 and duration T
(a single bit period), .epsilon..sub.p=T, and
SNR.sub.MFB=OMA(T/(2N.sub.0)).sup.1/2 (7)
[0041] Now consider an example channel that can be modeled as shown
in FIG. 2 where
.PI..sub.T(t)=1 for |t|.ltoreq.1/2 and 0 elsewhere. (8)
In this figure, h.sub.Tx(t) is a transmit filter that represents
the response of the transmitter and h.sub.F(t) is a filter that
represents the response of the fiber. The model can also include a
receive filter h.sub.R(t) (not shown in FIG. 2) that represents a
front end electrical filter in the receiver. For the 10 GBASE-LRM
application, this front-end receiver filter can generally be
modeled as a fixed 7.5 GHz 4.sup.th-order Bessel-Thomson filter.
Note that y.sub.1(t) is the optical signal that would be produced
by an ideal rectangular pulse transmitter. Because we are dealing
with modulated optical power, OMA, P.sub.ave, the transmit filter,
and the fiber filter are all constrained such that y.sub.1(t) must
be nonnegative. For example, OMA.ltoreq.2 P.sub.ave. Other
constraints on h.sub.Tx(t) and h.sub.F(t) are less obvious and will
be important later.
[0042] The transmit filter and fiber filter are normalized such
that H.sub.Tx(0)=1 and H.sub.F(0)=1, where H(f) denotes the Fourier
Transform of h(t). With this normalization, the filters conserve
optical power, or alternatively, conserve DC power. The assumption
that H.sub.Tx(0)=1 is not meant to exclude the case of AC coupling
in the transmitter. It is merely a model that simplifies analysis.
Alternatively one could assume that H.sub.Tx(f.sub.OMA)=1, where
f.sub.OMA is the OMA measurement frequency. It can then be shown
that each of the y.sub.1(t) can be written in the form
y i ( t ) = P ave + OMA 2 n a ( n ) p i ( t - nT ) ( 9 )
##EQU00005##
Specifically, p.sub.1(t)=.PI..sub.T(t),
p.sub.2(t)=p.sub.1(t)*h.sub.Tx(t), and
p.sub.3(t)=p.sub.2(t)*h.sub.F(t), where * denotes convolution. Note
that each p.sub.i(t) has the property
n p i ( t - nT ) = 1 ( 10 ) ##EQU00006##
(Any pulse shape generated by filtering a rectangular pulse of
duration T has the property that an infinite train of such pulses
sums to a constant value). Conversely, one can show that any pulse
shape with this property can be generated by filtering a
rectangular pulse. In this sense, the channel model is completely
general for a linear NRZ modulation.
[0043] Let MFB.sub.i denote SNR.sub.MFB for y.sub.i(t) and
.epsilon..sub.i denote the corresponding pulse energy, then
MFB.sub.i=OMA/2(2.epsilon..sub.i/N.sub.0).sup.1/2 (11)
[0044] Note that with h.sub.F(t).gtoreq.0 for all t (as it is with
the LRM model), it follows that
.epsilon..sub.3.ltoreq..epsilon..sub.2, with strict inequality
unless h.sub.F(t)=.delta.(t). Therefore, fiber propagation causes
an unrecoverable reduction in the matched filter bound. This is not
equalizer loss, since it is not due to ISI. It is a reduction in
the theoretically best SNR achievable in the absence of ISI.
[0045] While h.sub.F(t).gtoreq.0 for all t, there is no such
constraint on h.sub.Tx(t). There are, however, other constraints on
h.sub.Tx(t) resulting from constraints on the pulse p.sub.2(t) at
the output of the filter. Let p.sub.2(t)=.PI..sub.T(t)*h.sub.TX(t).
It can be shown that
1/2-P.sub.ave/OMA.ltoreq.p.sub.2(t).ltoreq.1/2+P.sub.ave/OMA
(12)
Note that the lower bound is less than or equal to zero and the
upper bound is greater than or equal to 1, with equality in both
cases for infinite extinction ratio (P.sub.ave=OMA/2).
[0046] Proof: We know that
y 2 ( t ) = P ave + OMA 2 n a ( n ) p 2 ( t - nT ) .gtoreq. 0 ( 13
) ##EQU00007##
where the inequality holds for all t and any sequence a(n).
Consider the sequence a(n)=1 for all n except 0, and a(0)=-1. Then
a(n)=1-2 .delta..sub.n (where .delta..sub.n is the Kroneker delta
function), and
y 2 ( t ) = P ave + OMA 2 ( - 2 p 2 ( t ) + n p 2 ( t - nT ) ) = P
ave + OMA 2 - OMA p 2 ( t ) .gtoreq. 0 ( 14 ) ##EQU00008##
[0047] This gives the upper bound on p.sub.2(t). The lower bound on
p.sub.2(t) is similarly obtained by considering the sequence
a(n)=-1+2 .delta..sub.n. With the lower bound on p.sub.2(t)
determined above, note that p.sub.2(t) cannot go negative unless
P.sub.ave>OMA/2, which is the condition for finite extinction
ratio.
[0048] Precompensation (or predistortion) can be used to improve
the performance of LRM links by boosting high frequencies in the
transmitted pulse p.sub.2(t) by shaping the transmit filter
h.sub.Tx(t). In order to boost high frequencies with respect to DC
(i.e., to implement frequency peaking), a finite extinction ratio
is used to allow p.sub.2(t) to go negative. Show this as follows.
Suppose p.sub.2(t).gtoreq.0 for all t. Letting P.sub.2(f) denote
the Fourier Transform of p.sub.2(t), then
|P.sub.2(f)|.sup.2=.intg. cos(2.pi.f.tau.)R.sub.2(.tau.)d.tau.
(using R.sub.2(.tau.)=R.sub.2(-.tau.)) (15)
where
R.sub.2(.tau.).intg.p.sub.2(t)p.sub.2(t-.tau.)d.tau. (16)
Since p.sub.2(t).gtoreq.0 by assumption, R.sub.2(.tau.).gtoreq.0.
Therefore cos(2.pi.f.tau.) R.sub.2(.tau.).ltoreq.R.sub.2(.tau.),
and
|P.sub.2(f)|.sup.2.ltoreq..intg.R.sub.2(.tau.)d.tau.=|P.sub.2(0)|.sup.2
(17)
[0049] Therefore if p.sub.2(t).gtoreq.0 for all t, |P.sub.2(f)| is
upper bounded by its value at DC, so high frequency boosting is not
possible.
[0050] Aside from changing the spectral shape of the transmit
pulse, precompensation changes the matched filter bound of
y.sub.2(t). For a given P.sub.ave and OMA, p.sub.2(t) is
constrained as determined above. The maximum value possible for
.epsilon..sub.2 is achieved when p.sub.2(t) is set equal to its
maximum allowable absolute value for the maximum duration possible
while maintaining the condition that an infinite train of such
pulses sums to 1. There are several possible pulse shapes that
achieve this. One choice is
p.sub.2(t)=(1/2+P.sub.ave/OMA).PI..sub.T(t)+(1/2-P.sub.ave/OMA).PI..sub.-
T(t-T) (18)
This corresponds to a transmit filter h.sub.Tx(t) of
h.sub.Tx(t)=(1/2+P.sub.ave/OMA).delta.(t)+(1/2-P.sub.ave/OMA).delta.(t-T-
) (19)
With this p.sub.2(t), we obtain the maximum .epsilon..sub.2
achievable for a given OMA and P.sub.ave, i.e.,
2 , max ( OMA ) = T [ ( 1 / 2 + P ave / OMA ) 2 + ( 1 / 2 - P ave /
OMA ) 2 ] = T [ 1 / 2 + 2 ( P ave / OMA ) 2 ] and ( 20 ) MFB 2 ,
max ( OMA ) = OMA ( 2 , max ( OMA ) / 2 N 0 ) 1 2 = OMA ( 1 / 2 + 2
( P ave / OMA ) 2 ) 1 2 ( T / 2 N 0 ) 1 2 = ( OMA 2 + ( 2 P ave ) 2
2 ) 1 2 ( T 2 N 0 ) 1 2 ( 21 ) ##EQU00009##
[0051] This is the maximum value of MFB.sub.2 for a given OMA and
P.sub.ave. This expression leads to three observations:
[0052] 1. When the extinction ratio is finite (that is, when the
nominal optical power for a "0" is strictly positive),
precompensation can always improve the matched filter bound at the
transmitter, i.e., MFB.sub.2,max(OMA)>MFB.sub.1=OMA
(T/2N.sub.0).sup.1/2. This follows from the fact that
OMA<2P.sub.ave when the extinction ratio is finite.
[0053] 2. For a given P.sub.ave, MFB.sub.2 is maximized by
increasing OMA to its maximum value of 2P.sub.ave, which
corresponds to infinite extinction ratio. This results in a
transmitted pulse shape p.sub.2(t) that is rectangular, as can be
seen in Eqn. 18. Therefore, precompensation does not improve over
the MFB obtained with infinite extinction ratio rectangular pulses.
In that case OMA=2P.sub.ave, MFB.sub.2,max(OMA)=2 P.sub.ave
(T/2N.sub.0).sup.1/2=MFB.sub.1, and h.sub.Tx(t)=.delta.(t). While
it may seem that precompensation in this case is not advantageous
in terms of increasing SNR.sub.MFB at the transmitter, there are
still good reasons for using it. First, the penalties defined above
are based on normalized OMA power. Recall that PIE.sub.D is the
ratio of SNR.sub.MFB-Rect to the actual SNR achieved at the slicer
of the equalizer, both computed assuming that OMA.sub.min is
transmitted. Therefore the transmitter is not credited for OMA
greater than OMA.sub.min in the calculation of the penalty. For a
given P.sub.ave>OMA.sub.min/2, the penalty can be reduced by
decreasing OMA from its maximum value of 2P.sub.ave, thereby
decreasing extinction ratio to a finite value, and applying
precompensation as described above. Furthermore, maximization of
MFB.sub.2 by using rectangular pulses and an infinite extinction
ratio is based on the simple linear model of modulation given in
Eqn. 3. With real laser transmitters there are other good reasons
to use a smaller extinction ratio, such as avoidance of
nonlinearities (which improves TWDP) or spectral shaping to
minimize equalizer loss.
[0054] 3. As OMA goes to 0, MFB.sub.2,max does not tend to 0, but
instead approaches a positive value equal to P.sub.ave
(T/N.sub.0).sup.1/2. In the limiting case,
y 2 ( t ) = lim OMA -> 0 P ave + OMA 2 n a ( n ) p 2 ( t - nT )
where ( 22 ) p 2 ( t ) = ( 1 2 + P ave / OMA ) .PI. T ( t ) + ( 1 2
- P ave / OMA ) .PI. T ( t - T ) Hence ( 23 ) y 2 ( t ) = P ave + P
ave 2 n a ( n ) p ~ 2 ( t - nT ) where ( 24 ) p ~ 2 ( t ) = .PI. T
( t ) - .PI. T ( t - T ) ( 25 ) ##EQU00010##
This is equivalent to
y 2 ( t ) = P ave + P ave 2 n a ' ( n ) .PI. T ( t - nT ) where (
26 ) a ' ( n ) = a ( n ) - a ( n - 1 ) ( 27 ) ##EQU00011##
This corresponds to 1-D precoding, where a'(n).epsilon.{-2,0,+2}.
This can be considered a degenerate case of precompensation that
gives a null at DC. Because of the null at DC, it cannot be modeled
as shown in FIG. 2 with a nonzero OMA and H.sub.Tx(0)=1. However, a
slight modification of FIG. 2 that would apply to the limiting case
is readily apparent from Eqns. 24 and 25 with
h.sub.Tx(t)=.delta.(t)-.delta.(t-T). In the limiting case, FIG. 2
would be modified such that P.sub.ave/2 replaces OMA/2, and
P.sub.ave is added after, instead of before, the transmit filter
h.sub.Tx(t).
[0055] The mathematics above show that frequency peaking can
increase the transmitter matched filter bound SNR over that of a
rectangular pulse without increasing the OMA. Provided that this
increased energy is in a frequency band passed by the fiber and
receiver transfer functions, this increased SNR at the transmitter
translates to an increased SNR.sub.MFB at the receiver. As long as
the equalizer loss does not increase more than the increase in
SNR.sub.MFB, the resulting power penalty will decrease. The best
frequency peaking will result in an increase in the received
SNR.sub.MFB and a decreased equalizer loss. The net effect on
PIE.sub.D can be mathematically determined by the effect of the
resulting folded spectrum |H.sub.a(f)|.sup.2 on the penalty in Eqn.
1.
[0056] Frequency peaking can be implemented in the transmitter in a
number of different ways. FIGS. 3-7 illustrate one approach based
on the use of pre-emphasis networks in the laser driver. FIGS. 8-11
illustrate another approach utilizing the opto-electronic overshoot
properties of laser diodes, commonly known as relaxation
oscillation.
[0057] FIG. 3 shows a block diagram of a pre-emphasis network that
can be implemented at 10 GHz. This circuit implements a transfer
function of 1.25-0.25D, where D is a one bit delay (T). The DC
response of this circuit is 1, but it boosts the higher frequencies
in the signal spectrum. The pre-emphasis network can be implemented
in different ways. For example, it can be clocked (in which case
frequency peaking at approximately 50% of the line rate can be
conveniently implemented). Alternately, it can be implemented by a
passive network.
[0058] FIG. 4 shows the frequency response of the pre-emphasis
network plus the receiver front-end filter modeled as a fixed 7.5
GHz 4.sup.th-order Bessel-Thomson filter. The plot in FIG. 4a shows
the response of a conventional transmitter with no frequency
peaking Note that the frequency response if flat and then rolls
off. The plot in FIG. 4b shows the response with pre-emphasis
peaking added in the transmitter. It clearly shows the increase in
the channel response at higher frequencies. The plots are
normalized to the same average optical power or optical modulation
amplitude (OMA). Both are common descriptions used for the signal
strength in a fiber optic link. The vertical axes are in optical
dB, and the horizontal axes are frequency normalized to the bit
rate (10.3125 Gbits/sec for LRM).
[0059] FIG. 5 shows some typical time domain waveforms with and
without pre-emphasis. These waveform figures all assume an ideal
NRZ pulse train and the receiver front-end model, and the waveforms
in FIGS. 5a and 5b have the same average optical power and the same
OMA. The plot in FIG. 5a shows the waveform for a conventional
transmitter with no frequency peaking. The plot in FIG. 5b shows
the waveform with pre-emphasis peaking added in the
transmitter.
[0060] FIGS. 6a and 6b show the same information as FIGS. 5a and
5b, except that the waveform is folded into "eye patterns." Eye
patterns are useful for viewing waveform quality in the way that a
conventional non-EDC receiver would view the waveforms. An eye
pattern that has less jitter and distortion is preferred in a
conventional receiver and should produce a lower bit error rate or
BER. Note that the pre-emphasized eye is actually more distorted
with more jitter when viewed conventionally. However, as shown in
the next paragraph, an EDC receiver can equalize this signal to
have a better resulting SNR than the signal that has no
pre-emphasis.
[0061] LRM uses a fiber path model known as the Cambridge set "108
fiber model," IEEE 802.3aq Task Force, October 2004. Available
online at
http://grouper.ieee.org/groups/802/3/aq/public/tools/108fiberModel.
FIG. 7 plots the cumulative distribution function of an idealistic
power penalty for an EDC receiver for 300 meters of each of the 108
fibers in the Cambridge 2.1 model. Percentage coverage indicates
the percentage of fibers that have a penalty at or below the
penalty indicated on the horizontal axis. The penalty on the
horizontal axis is expressed in optical dB. Both traces include an
NRZ pulse train running at 10.3125 Gbits/sec and the receiver
front-end model mentioned before. The trace 710 on the right shows
the power penalties with a conventional transmitter with no
frequency peaking. The trace 720 on the left shows the power
penalties with frequency peaking added in the transmitter. The
transmitter with pre-emphasis, even though more jittered and
distorted when observed with a conventional eye diagram, shows
power penalties for an EDC receiver that are nearly 1 dB
lower/better than the one without frequency peaking. This is
because an EDC receiver can compensate for the jitter and
distortion and apply all the useful signal energy into improving
the signal to noise ratio and the BER, or even extending link
distance.
[0062] As mentioned above, a laser diode has a natural peaking
phenomenon called relaxation oscillation. FIGS. 8-9 show this with
simulated behaviors in the frequency domain (small signal plot) and
in the time domain, respectively. As before, these figures include
the receiver model. Usually, designers try to avoid relaxation
oscillation near the signal bandwidth because it can "close" the
eye in a non-EDC link, but with EDC, the effect can be beneficial
for the same reasons shown above with pre-emphasis.
[0063] The benefit can also be observed with waveforms from real
transmitters measured in the laboratory. FIG. 10a is a normal laser
eye waveform (folded into an eye pattern) with little or no
overshoot. FIG. 10b is a laser eye pattern with overshoot due to
relaxation oscillation.
[0064] The cumulative distribution function of optical power
penalties for these transmitted waveforms across fibers in the
Cambridge model when received by an EDC system are shown in FIG.
11. The trace 1110 on the right corresponds to FIG. 10a (E03) and
the trace 1120 on the left corresponds to FIG. 10B (E09). E09 shows
approximately 0.5 dB power penalty improvement at the 80.sup.th
percentile coverage level (the targeted Cambridge model coverage
for LRM) compared to E03 for an EDC system. Again, this is in spite
of the appearance of severely greater distortion in the eye
pattern.
[0065] Although the detailed description contains many specifics,
these should not be construed as limiting the scope of the
invention but merely as illustrating different examples and aspects
of the invention. It should be appreciated that the scope of the
invention includes other embodiments not discussed in detail above.
Various other modifications, changes and variations which will be
apparent to those skilled in the art may be made in the
arrangement, operation and details of the method and apparatus of
the present invention disclosed herein without departing from the
spirit and scope of the invention as defined in the appended
claims. Therefore, the scope of the invention should be determined
by the appended claims and their legal equivalents.
* * * * *
References