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| United States Patent |
5,416,628
|
|
Betti
, et al.
|
May 16, 1995
|
Multilevel coherent optical system
Abstract
A multilevel coherent optical system, including a heterodyne transmitter
and receiver, in which a multilevel signal with a coherent optical carrier
is provided by modulating the phase and the polarization of the
electromagnetic field propagating through a single-mode optical fiber. The
transmitter comprises a coherent light source providing the optical
carrier, a phase modulator modulating the phase of the carrier, a
polarization modulator, and a modulation signal generator providing
control signals to the phase modulator and the polarization modulator. The
receiver comprises a first stage carrying out the heterodyne detection of
the phase component and the phase quadrature component of the polarization
of the signal received through an optical fiber, a second stage
demodulating the received signal to provide the multilevel signal, and a
processing circuit comparing the received multilevel signal with
predetermined reference signals. Such a system exploits the four degrees
of freedom of the electromagnetic field propagating through the optical
fiber so as to more closely approach the theoretical Shannon limit
compared with conventional systems.
| Inventors:
|
Betti; Silvello (Rome, IT);
Curti; Franco (Rome, IT);
De Marchis; Giancarlo (Rome, IT);
Iannone; Eugenio (Rome, IT)
|
| Assignee:
|
Fondazione Ugo Bordoni (Rome, IT)
|
| Appl. No.:
|
946333 |
| Filed:
|
November 9, 1992 |
| PCT Filed:
|
May 6, 1991
|
| PCT NO:
|
PCT/IT91/00036
|
| 371 Date:
|
November 9, 1992
|
| 102(e) Date:
|
November 9, 1992
|
| PCT PUB.NO.:
|
WO91/18455 |
| PCT PUB. Date:
|
November 28, 1991 |
Foreign Application Priority Data
| Current U.S. Class: |
398/185; 398/184; 398/188 |
| Intern'l Class: |
H04B 010/06 |
| Field of Search: |
359/156,192,181,183,188
|
References Cited [Referenced By]
U.S. Patent Documents
| 3752992 | Aug., 1973 | Fluhr | 359/183.
|
| 4436376 | Mar., 1984 | Fergason | 359/156.
|
| 4831663 | May., 1989 | Smith | 359/192.
|
| 5008958 | May., 1991 | Cimini | 399/192.
|
| Foreign Patent Documents |
| 0277427 | Aug., 1988 | EP.
| |
| 0280075 | Aug., 1988 | EP.
| |
Other References
Niblock, "Polarization and Demodulation of Light", Applied Optics, 2-64,
vol. 3 #2, pp. 277-279.
Hodgkinson, "Polarization Insensitive Heterodyne Detection Using
Polarization Scrambling" Electronic Letters, vol. 23 #10 pp. 513-514.
Benedetti, et al., "Performance Evaluation of Multilevel Polarisation Shift
Keying Modulation Schemes", Electronics Letters, vol. 26, No. 4, pp.
244-246, Feb. 15, 1990, Stevenage, GB.
|
Primary Examiner: Pascal; Leslie
Attorney, Agent or Firm: Staas & Halsey
Claims
What is claimed is:
1. A method of providing a multilevel signal on a coherent optical carrier
in order to transmit information through a single-mode optical fiber by
modulating the phase and the polarization of the carrier, comprising the
steps of:
coding a first, second, and third control signal by coding a binary
succession representing information to be transmitted and formed of a
plurality of symbols each representing a predetermined state of the
multilevel signal to be transmitted;
modulating the phase of the carrier with the coded first control signal;
dividing the modulated carrier into two signals having the same
polarization;
modulating the phase of a first of the two signals with the coded second
control signal;
mixing and dividing the modulated first signal and a second of the two
signals into two orthogonal signals representing the polarization state;
modulating the phase of a first of said two orthogonal signals with the
coded third control signal; and
coupling the modulated first orthogonal signal and a second of the two
orthogonal signals to produce an optical signal modulated in phase and in
polarization.
2. The method of claim 1, further comprising the step of determining the
predetermined states of the multilevel signal to be transmitted, each
represented by components of a four-dimensional vector defining a
reference point on a surface of a sphere of the four-dimensional Euclidean
space having a radius equal to a square root of a transmitted optical mean
power, by selecting the respective reference points to minimize a
multi-variable function correlating a bit error probability with
coordinates of said reference points.
3. An optical receiver for receiving a multilevel optical signal,
comprising:
a first stage including an optical local oscillator to generate a coherent
optical signal, a 90.degree. optical hybrid to receive said multilevel
optical signal and said coherent optical signal and to output a first
signal, corresponding to a sum of the multilevel optical signal and said
coherent optical signal, and to output a second signal, corresponding to a
sum of the multilevel optical signal and said coherent optical signal with
a phase of one of said multilevel optical signal and said coherent optical
signal shifted by 90.degree., two beam splitters, each to separate said
first and second signals, respectively, into orthogonal polarization
component signals, and four photodiodes each to detect said separated
component signals, said first stage coupled to an optical fiber to carry
out a heterodyne detection of the phase terms and the phase quadrature
terms of a beat signal generated from a polarized signal received by the
optical fiber and the coherent optical signal, said first stage further
including four bandpass filters centered about the intermediate frequency
of the respective component signals detected by said four photodiodes;
a second stage coupled to said first stage to demodulate the received
signals and to provide a multilevel signal, including means for converting
the intermediate frequency signals of said four bandpass filters to
respective four base band signals; and
a processing circuit coupled to said second stage to compare said
multilevel signal with predetermined reference signals.
4. The optical receiver of claim 3 for receiving a multilevel signal,
wherein said processing circuit is based upon the evaluation of the
inverse Jones matrix and comprises;
four circuits, each for respectively receiving at their inputs the four
base band signals from the converting means, for calculating the time
averages of said signals in time periods much longer than the symbol
period and much shorter than the characteristic periods of the
polarization fluctuations, and for supplying at their respective outputs
four signals representing said time averages;
an inverse Jones matrix circuit for receiving at its input the four base
band signals and supplying at its output corresponding estimated values of
the transmitted multilevel signal; and
a calculation circuit for receiving at its input the four signals
representing the time averages of the base band signals and for comparing
said time average signals with the feasible transmitted symbols forming
the predetermined reference signals stored in the calculation circuit to
calculate the coefficients of the Jones matrix and to supply them to the
inverse Jones matrix circuit; and
a comparing circuit for receiving at its input the estimated values of the
transmitted multilevel signal and for comparing said estimated values with
the feasible transmitted symbols stored in the comparing circuit to assign
to each estimated value one of the feasible transmitted symbols.
5. The optical receiver of claim 3 for receiving a multilevel signal,
wherein said processing circuit comprises:
first circuit means for initially determining the reference signals by an
initialization sequence; and
second circuit means for calculating time averages of the base band signals
in time periods much longer than the symbol period and much shorter than
the characteristic period of the polarization state fluctuations, and for
storing and updating the components of the reference signals,
the first circuit means further comparing the time averages of the base
band signals with the reference signals and assigning to each of them one
of the feasible transmitted symbols, the updating time period being much
shorter than the characteristic period of the polarization fluctuations
and much longer than the symbol period.
6. An optical transmitter for transmitting a multilevel optical signal
modulated in phase and polarization, to transmit information through a
single-mode optical fiber, comprising:
a coder to code a first, second and third control signal by coding a binary
succession representing information to be transmitted and formed of a
plurality of symbols each representing a predetermined state of the
multilevel signal to be transmitted;
a coherent light source to generate an optical carrier;
a first phase modulator, connected to said coherent light source and said
coder, to modulate a phase of the carrier with the coded first control
signal;
a polarization selection beam splitter, connected to the first phase
modulator, to split the modulated carrier into two components of the
polarization state of the carrier;
a first polarization rotator, connected to the polarization selection beam
splitter, to rotate the polarization of a first of the two components by
90.degree.;
a second phase modulator, connected to the polarization selection beam
splitter and said coder, to modulate a phase of a second of said two
components with the coded second control signal;
a directional first coupler, connected to both the first polarization
rotator and the second phase modulator, to superimpose the rotated first
component with the modulated second component and to output a first and a
second output signal, respectively;
a second polarization rotator, connected to the directional first coupler,
to rotate the polarization of the first output signal by 90.degree. so
that the rotated first output signal is orthogonal to the second output
signal;
a third phase modulator, connected to the directional first coupler and
said coupler, to modulate a phase of the second output signal with the
coded third control signal; and
a second coupler, connected to the second polarization rotator and the
third phase modulator, to couple the modulated second output signal with
the orthogonal first output signal to produce an optical signal modulated
in phase and polarization.
7. An optical transmitter for transmitting a multilevel optical signal
modulated in phase and polarization, to transmit information through a
signal-mode optical fiber, comprising:
a light source to generate a carrier;
a coder to code a plurality of control signals based on a binary succession
of information to be transmitted and a predetermined state of the
multilevel signal to be transmitted;
polarization and modulation means for modulating a phase of the carrier
with one of said plurality of coded control signals, and for generating a
first and a second signal from the modulated carrier, the first signal
being orthogonal to the second signal and the second signal being further
modulated with another one of said plurality of coded control signals; and
a coupler to couple the first and second signals to generate an optical
signal modulated in phase and polarization.
8. A method for transmitting a multilevel optical signal modulated in phase
and polarization, to transmit information through a single-mode optical
fiber, comprising the steps of:
generating a carrier;
coding a plurality of control signals based on a binary succession of
information to be transmitted and a predetermined state of the multilevel
signal to be transmitted;
modulating a phase of the carrier with one of said plurality of coded
control signals;
generating a first and a second signal from the modulated carrier, the
first signal being orthogonal to the second signal and the second signal
being further modulated with another one of said plurality of coded
control signals; and coupling the first and second signals to generate an
optical signal modulated line in phase and polarization.
Description
BACKGROUND OF THE INVENTION
1. Field of the Invention
The present invention relates to the communication systems using optical
signals propagating through single-mode optical fibres and, in particular,
a method of and an apparatus for generating, transmitting and receiving a
multilevel optical signal.
2. Description of the Related Art
Reliable and economically competitive, coherent optical transmission
systems which can be made available at short and medium terms allow novel
network architectures to be provided regarding long-distance and
high-performance connections and multi-user LAN (Local Area Network) and
MAN (Metropolitan Area Network) connections as well. In particular, the
very large bandwidth of the single-mode optical fibres (thousands of GHz)
can be suitably exploited by providing optical FDM-systems (Frequency
Division Multiplexing) in which the selection of the desired channel can
be obtained by shifting the frequency of the local oscillator. This allows
passive optical networks with very high traffic capacity (thousands of
gB/s) to be carried out. However, two important aspects restrict on one
hand the bandwidth of the single channel and limit on the other hand the
maximum number of channels which can be tuned by the user. In the first
instance, in fact, the main restriction is due to the bandwidth of the
photodiodes and the electronic circuits, while regarding the second
instance it should be considered that the frequency range which can be
tuned by the user depends on the tunability characteristics of the laser
used as local oscillator.
In order to increase the information rate of any channel, systems have been
provided in which the information to be transmitted is coded with more
than two levels instead of being coded using only the two binary levels as
it is customary for providing a high signal reception sensitivity. By
transmitting multilevel signals an improvement of spectrum efficiency
expressed in terms of information rate per unit of occupied band is
obtained at the cost of a reduction of the sensitivity. The known systems
with two or more levels resort to the digital amplitude and phase keying
(APK) or to the digital phase shift keying (PSK) or polarization shift
keying (SPSK) of the electrical component of the electromagnetic field
associated to a coherent optical wave generated by a laser source.
In particular, according to the previous state of art, EP-A-0 277 427
discloses methods of an devices for processing an optical signal by
altering the polarization state thereof under control of a signal at a
predetermined scrambling frequency.
EP-A-0 280 075 discloses an optical low-noise superheterodyne receiver for
modulated optical signals in which a received light signal is coupled to a
coherent light signal having the same polarization. Then such signals are
combined so as to provide two pairs of optical signals, the signal of each
pair having the same polarization perpendicular to that of the other pair,
and fed to photoelements which provide electrical signals. Such electrical
signals are then summed to each other after demodulation and after at
least a phase shifting of one of such signals.
In "Electronics Letters" Vol. 26, No. 4 of 15 Feb. 1990 there is disclosed
the performance of coherent optical transmission systems using multilevel
polarization modulation based upon equipower signal constellations at the
vertices of regular polyhedra inscribed in to the Poincare's sphere.
SUMMARY OF THE INVENTION
The present invention seeks to provide a method of generating a multilevel
signal with a better performance than the known systems with regard to the
signal reception sensitivity on the same number of employed levels. Within
such general aim the invention seeks to provide in particular a
transmitting and a receiving apparatus carrying out the above mentioned
method.
BRIEF DESCRIPTION OF THE DRAWINGS
Such aims are achieved by the invention defined and characterized in
general in the claims attached to the following description in which the
present invention is disclosed by way of a non-limitative example with
reference to the accompanying drawing, in which:
FIG. 1 is a block diagram of a transmitting apparatus for a multilevel
optical signal according to the present invention;
FIG. 2 is a block diagram of the detecting stage and the intermediate
frequency stage of a receiving apparatus according to the invention;
FIG. 3 is a block diagram of a multilevel signal processing stage based on
the determination of the coefficients of the inverted Jones matrix in a
receiving apparatus according to the invention;
FIG. 4 is a block diagram of a multilevel signal processing stage based
upon an algorithm for providing and uptodating the values of the
components of the reference vectors in the receiving apparatus of the
invention;
FIG. 5 is a block diagram of the circuit of the stage of FIG. 4 for
uptodating the values of the components of the reference vectors;
FIG. 6 is a diagram of the logarithm of the error probability P.sub.e
versus the number of the received photons per bit F for different values
of the level number N;
FIG. 7 is a graph for the comparison of the sensitivity of the receiving
apparatus (N-4Q) according to the invention, expressed in terms of the
logarithm of the number of received photons per bit F versus the level
number N, with the sensitivity of a N-PSK apparatus (N-level Phase Shift
Keying), a N-APK apparatus (N-level Amplitude and Phase Keying), and a
N-SPSK apparatus (N-level Polarization Shift Keying with detection by
Stokes parameters); and
FIG. 8 is a graph for the comparison of the sensitivity of the receiving
apparatus according to the invention, expressed in terms of the logarithm
of the number of received photons per bit F versus the level number N,
with the limit performance of the transmitting apparatus defined by the
Shannon expression of the transmitting channel capacity.
DETAILED DESCRIPTION OF THE PREFERRED EMBODIMENTS
The electrical field E(t) of an electromagnetic wave having angular
frequency .omega..sub.o and propagating through a single-mode optical
fibre can be written as follows:
E(t)=E.sub.x (t)x+E.sub.y (t)y=(x.sub.1 +ix.sub.2)x+(x.sub.3 +ix.sub.4)y
e.sup.i.omega. o.sup.t
where the phase terms x.sub.1 and x.sub.3 and the phase quadrature terms
x.sub.2 and x.sub.4 are the components on the reference axes x and y of
the polarization state, i.e. the vector representing the electrical field
according to a given polarization. Vector X=(x.sub.1, x.sub.2, x.sub.3,
x.sub.4) can be associated to any state of such electromagnetic field, the
components of which being such that:
x.sub.1.sup.2 +x.sub.2.sup.2 +x.sub.3.sup.2 +x.sub.4.sup.2 =P
where P is the transmitted optical power;
The schematic block diagram of a transmitter according to the invention is
shown in FIG. 1: a laser source 1 generates a linearly polarized optical
carrier having a frequency, for example, of 10.sup.14 Hz, so as to form an
angle of 45.degree. with respect to the reference axes x and y. The phase
of such optical field is modulated by a phase modulator 2 with a message,
for example a voltage having a time variable amplitude .alpha.(t), which
is generated by a coder 10 from a binary sequence m(t) representing an
information to be transmitted. After the phase modulation the components
of the polarization state on axes x and y are split by a polarization
selection beam splitter 3. It should be noted that the reference axes x
and y are defined by the orientation of splitter 3. In the upper branch
the polarization of the signal is rotated by 90.degree. by a polarization
rotator 4 so as to align it with that of the signal in the lower branch.
The phase of the latter signal is modulated by a modulator 5 with a
message .beta.(t) also generated by coder 10. The two signals having the
same polarization are mixed by a directional coupler 6, the outputs of
which will be as follows:
s.sub.1 (t)=A/2 e.sup.i[.omega. o.sup.t+.alpha.(t)] [e.sup.i.beta.(t)
+e.sup.i.pi./2 ]
s.sub.2 (t)=A/2 e.sup.i].omega. o.sup.t+.alpha.(t)]
[e.sup.i.beta.(t)+i.pi./2 +1]
where A.sup.2 is proportional to the transmitted optical power. The
polarization state of signal s.sub.1 is then rotated by 90.degree. by a
polarization rotator 7' so as to make it orthogonal to that of signal
s.sub.2, the phase of which is modulated by a modulator 8 with a message
.gamma.(t) generated by coder 10. The resulting signals are then coupled
by a polarization selection directional coupler 9 to provide the optical
signal to be transmitted through the fibre, the x and y polarization
components of which have the following phase terms and phase quadrature
terms:
##EQU1##
where the function .alpha.(t), .beta.(t) and .gamma.(t) can have values
between 0 and 2.pi. according to the selected codification method.
In particular, such functions are generated by coder 10 according to the
following criteria. A succession of bits representing the information to
be transmitted are fed into coder 10. Such succession is divided in groups
of bits, each group of bits representing a symbol of the alphabet used by
the coder. Thus the succession of bits is transformed in a succession of
symbols. In case a N-level signal is transmitted and, for the sake of
semplicity, under the assumption that N is a power of 2, each symbol is
formed by m bits where m=2 log N. Each symbol can be univocally associated
to a point of the sphere in the four-dimensional space in which the
electromagnetic field is represented, such point being determined by the
vector X=(x.sub.1, x.sub.2, x.sub.3, x.sub.4) or by a tern of generalized
spherical coordinates .alpha., .beta. and .gamma. and by the radius of the
sphere, i.e. the square root of the transmitted optical power. Therefore,
the transmission of a symbol corresponds to the transmission of a well
defined state of the electrical field. As the succession of bits m(t) are
fed into the coder, an association between symbols and points at the
coordinates .alpha., .beta. and .gamma. is effected; the latter are then
entered into a digital-to-analog converter and transformed to the voltages
.alpha.(t), .beta.(t) and .gamma.(t) which are the control signals of the
demodulators 2, 5 and 8. It should be noted that the states of the
electrical field are completely determined by the three angular
coordinates as the transmitted optical power in the apparatus of FIG. 1
remains constant.
The block diagram of the stage detecting the optical signal and of the
intermediate frequency stage of a receiving apparatus according to the
invention is shown in FIG. 2.
The optical signal modulated in phase and polarization and generated by a
transmitter of the type shown in FIG. 1 and transmitted through a
single-mode fibre 11 is entered into a "90.degree. optical hybrid" 13
along with a coherent optical signal generated by a laser source operating
as local oscillator 12. Such signal of the local oscillator having a
frequency which differs from that of the transmitted signal carrier by a
predetermined amount between 10.sup.8 and 10.sup.9 Hz is linearly
polarized at 45.degree. with respect to the reference axes x and y. The
90.degree. optical hybrid 13 is a known device having two inputs and two
outputs and providing at one output the sum of the input signals and at
the other output the sum of one input signal and the other input signal
the phase of which is shifted by 90.degree.. In such a case, therefore,
the output signals are the phase component and the phase quadrature
component of the beat signal.
The x and y components of the polarization state of the output signals of
the optical hybrid 13 are then split by polarization selection beam
splitters 14 and 15 defining with their orientations the reference axes x
and y, and separately detected by four photodiodes 16, 17, 18 and 19. The
four electrical intermediate frequency signals are then filtered by
bandpass filters 20, 21, 22 and 23 centered about the intermediate
frequency and having a double as high bandwidth as the figure rate
R.sub.s, i.e. the inverse of the transmission time of a symbol. A phase
locked loop (PLL) 28 and four multipliers 24, 25, 26 and 27 allow the four
intermediate frequency signals y.sub.1, y.sub.2, y.sub.3 and y.sub.4 at
the outputs of the filters 20-23 to be translated to base band. Such
signals are then fed to four lowpass filters 29, 30, 31 and 32 having the
same bandwidth as the figure rate R.sub.s so as to provide four base band
signals z.sub.1, z.sub.2, z.sub.3 and z.sub.4 proportional to the
estimated values of the components of vector X which are mainly impaired
by the detection noise.
Two preferred embodiment of the processing apparatus have been proposed for
providing and updating the estimated values of the components of vector X
from the base band signals z.sub.1, z.sub.2, z.sub.3 and z.sub.4. Such
apparatus allow the fluctuations of the polarization state of the optical
signal due to the propagation through a single-mode fibre to be
compensated by merely electronic techniques.
The operation of the first apparatus, the block diagram of which is shown
in FIG. 3, is based on the determination of the inverse Jones matrix. As
it is known, the effects due to the propagation through a single-mode
optical fibre can be taken into account by the Jones unit operator
providing the input-output relation between the polarization states of the
optical field. Since such relation is linear, the application of the
inverse Jones operator to the received signal allows the polarization
state of the transmitted optical signal to be determined. Vector Z having
the base band signals z.sub.1, z.sub.2, z.sub.3 and z.sub.4 as components
is multiplied in Unit 33 by the inverse Jones matrix U.sup.-1 so as to
provide the estimated values of the components of vector X. The
coefficients of the matrix are determined by an algorithm based upon the
consideration that the fluctuations of the polarization state (0, 1-1 Hz)
due to the fibre birefringence are much slower than the figure rate
(10-1000 Hz). The algorithm is implemented on the base of the calculation
of the time averages of the signals z.sub.1, z.sub.2, z.sub.3 and z.sub.4
at coefficient units 34, 35, 36 and 37 in time intervals much longer than
the symbol period. i.e. the transmission time of a symbol, and much
shorter than the characteristic period of the polarization fluctuations.
The elements of the Jones matrix depend linearly on the averages of the
signals z.sub.1, z.sub.2, z.sub.3 and z.sub.4, as the coefficients of such
linear relation are the averages of the four coordinates of the reference
points evaluated in the set of the N feasible transmitted symbols and
stored in calculation unit 38. Therefore, if the averages of the signals
z.sub.1, z.sub.2, z.sub.3, z.sub.4 are known, a linear system of four
equations with four unknown values can be implemented, the solution of
which calculated in calculation unit 38 provides the real and imaginary
parts of the coefficients of the Jones matrix, the inverse of which is
then calculated in unit 33. This algorithm causes the coefficients of the
Jones matrix to be uptodated at the end of any time period at which the
time averages of the signals z.sub.1, z.sub.2, z.sub.3 and z.sub.4 are
evaluated, thus allowing the apparatus to follow the fluctuations of the
polarization state due to the single-mode fibre birefringence. The
decision, i.e. the recognition of the state of the multilevel signal
received at a given time, is effected in comparison unit 39 by comparing
the estimated vector .epsilon. of components .epsilon..sub.1,
.epsilon..sub.2, .epsilon..sub.3 and .epsilon..sub.4 with the reference
vectors corresponding to the feasible transmitted symbols, the components
of which have been stored in unit 39 when adjusting the apparatus. In
particular, such comparison is effected by calculating the distances
between the point on the surface of the sphere in the four-dimensional
space corresponding to the estimated vector .epsilon. and the points
determined by the reference vectors. Among the feasible transmitted
symbols it is selected the symbol corresponding to the point determined by
the reference vector having the shortest distance from the point of
coordinates .epsilon..sub.1, .epsilon..sub.2, .epsilon..sub.3 and
.epsilon..sub.4. The output signal of unit 30 is fed to an User apparatus
50.
The operation of the second apparatus processing the multilevel signal is
on the contrary based upon an algorithm allowing the values of the
coordinates of the reference points to be initially determined and
uptodated. i.e. the components of the reference vectors on the surface of
the sphere in the four-dimensional Euclidean space. The schematic block
diagram of such processing apparatus is shown in FIG. 4. The apparatus
determines initially the reference vectors by means of a suitable
initialization sequence and subsequently effects the continuous uptodating
of the components of such vectors, the values of which are fed to decision
circuit 45 in which a decision is taken by the above described procedure
based upon the calculation of the distance between the point corresponding
to the received symbol and the reference points. The decision circuit 45
in case of a N-level signal has 4N memory cells in which the components of
the N reference vectors are stored. In the time interval between two
successive uptodatings the decision circuit 45 estimates the received
symbol and associates it to any of the N symbols which can be transmitted.
The uptodating of the components of any reference vector is carried out by
calculating the mean value of the vector components which are estimated by
the decision circuit during the uptodating interval as corresponding to
that reference vector. At the end of any uptodating interval, which is
chosen also in this case much shorter than the characteristic periods of
the polarization fluctuations and much longer than the symbol period, the
reference vectors are replaced by those corresponding to the novel
components, the mean values of which calculated by the above described
method have been stored in the 4N memory cells.
In the diagram of FIG. 4 the uptodating operation is effected by updating
40 formed of four circuits 41, 42, 43 and 44, each of them comprises a
switch 46 and N mean value circuits 47 for the calculation of the mean
value of the signal selected by the switch. After having estimated the
received symbol, the decision circuit 45 supplies the control signal
formed of the components of the reference vector corresponding thereto to
the four blocks 41, 42, 43 and 44. Such control signal causes any base
band signal z.sub.1, z.sub.2, z.sub.3 and z.sub.4 to be entered through
switch 46 into circuit 47 for the calculation of the mean value
corresponding to the reference symbol selected by the decision circuit 45
among N feasible symbols which can be transmitted. Therefore, during the
uptodating interval the outputs of the circuits 41, 42, 43 and 44 supply
the signals which are to be used at the uptodating time to calculate the
mean values of the components of the novel reference vectors which are
then stored in the 4N memory cells of the decision circuit 45. The
resulting processing signal of block 45 is supplied to an user apparatus
50.
The performance of the apparatus has been valued in view of the statistics
of the detection noise. In order to optimize the performance, the
reference states of the transmitted optical field have been selected such
as to reduce to a minimum the optical power necessary to achieve a
predetermined error probability. In case of a N-level signal such choise
consists in determining the position of N reference points on the sphere
of the four-dimensional Euclidean space. From an analytical point of view
the optimization of the performance can be achieved by an algorithm which
minimizes the multi-variable function establishing the relationship
between the error probability P.sub.e and the coordinates of the N
reference points. The problem cannot be analytically solved in closed form
so that a numeric algorithm has been used to minimize the above mentioned
multi-dimensional function for 3.ltoreq.N.ltoreq.32.
Some results regarding feasible configurations of N reference points
obtained by the minimization algorithm of multi-variable functions and
using the downhill simplex method are shown in the following tables I, II,
III, IV.
TABLE I
______________________________________
Level .phi..sup.o .psi..sup.o
.theta..sup.o
______________________________________
1 0.00 0.00 0.00
2 182.65 75.52 0.00
3 117.70 124.54 161.56
4 157.16 308.49 295.89
5 298.07 310.91 144.30
______________________________________
TABLE II
______________________________________
Level
Level 1 2 3 4 5
______________________________________
1 0.000 1.581 1.581 1.581
1.581
2 1.581 0.000 1.581 1.581
1.581
3 1.581 1.581 0.000 1.581
1.581
4 1.581 1.581 1.581 0.000
1.581
5 1.581 1.581 1.581 1.581
0.000
______________________________________
TABLE III
______________________________________
Level .phi..sup.o .psi..sup.o
.theta..sup.o
______________________________________
1 0.00 0.00 0.00
2 180.00 0.00 0.00
3 57.43 90.00 0.00
4 113.52 2.43 90.00
5 212.56 270.00 0.00
6 122.57 270.00 180.00
7 211.76 332.02 270.00
8 327.42 90.00 180.00
______________________________________
TABLE IV
______________________________________
Level
Level 1 2 3 4 5 6 7 8
______________________________________
1 0.000 2.000 1.414
1.414
1.414 1.414
1.414
1.414
2 2.000 0.000 1.414
1.414
1.414 1.414
1.414
1.414
3 1.414 1.414 0.000
1.414
1.414 2.000
1.414
1.414
4 1.414 1.414 1.414
0.000
1.414 1.414
2.000
1.414
5 1.414 1.414 1.414
1.414
0.000 1.414
1.414
2.000
6 1.414 1.414 2.000
1.414
1.414 0.000
1.414
1.414
7 1.414 1.414 1.414
2.000
1.414 1.414
0.000
1.414
8 1.414 1.414 1.414
1.414
2.000 1.414
1.414
0.000
______________________________________
In particular Table I shows the values of the angular coordinates .phi.,
.PSI. and .theta. corresponding to the points of the sphere of the
four-dimensional Euclidean space having standardized unit radius which are
associated to the reference states of the electromagnetic field in case of
an optimized five-level configuration. The angular coordinates are bound
to the components x.sub.1, x.sub.2, x.sub.3 and x.sub.4 defining the state
of the electromagnetic field by the following relations:
x.sub.1 =cos .phi. cos .PSI. cos .theta.
x.sub.2 =cos .phi. cos .PSI. sin .theta.
x.sub.3 =cos .phi. sin .PSI.
x.sub.4 =sin .phi.
Table II shows the values of the distances between the reference points on
the sphere of standardized unit radius in case of a five-level
configuration; in this case the distance of any couple of points is the
same, and when that result is obtained, that is the best for simmetry
reasons.
Table III shows the values of the angular coordinates .phi., .PSI. and
.theta. corresponding to the points on the sphere of the four-dimensional
Euclidean space having standardized unit radius which are associated to
the states of the electromagnetic field in case of an eight-level
configuration.
Table IV shows the values of the distances between the reference points on
the sphere having standarized unit radius in case of an eight-level
configuration. In such case it was not possible to arrange the eight
reference points on the four-dimensional sphere in such a way that they
are at the same distance from one another. Nevertheless the optimum
configuration has a high simmetry as any point has six first near points
at a distance equal to the radius of the sphere multiplied by .sqroot.2
and only one second near point at a double as high distance as the radius
of the sphere.
In FIG. 6 the performance of the apparatus is shown by the logarithm of the
error probability P.sub.e versus the photon number per bit F for a number
N of levels equal to 4.8 and 16, respectively.
In FIG. 7 the sensitivity of the apparatus is shown by the logarithm of the
photon number per bit versus the number N of levels at an error
probability of 10.sup.-9. In such figure the performance of the apparatus
according to the invention designated by N-4Q is compared with that of a
N-level heterodyne PSK apparatus (N-PSK, N-Phase-Shift-Keying), a N-level
heterodyne APK apparatus (N-APK, N-Amplitude-Phase-Keying), and a N-level
polarization modulation apparatus with detection by Stokes parameters
(N-SPSK, N-Stokes-Parameter-Shift-Keying), the former two being described
in K. Feher "Digital MODEM Techniques", Advanced Digital Communications,
Prentice-Hall Inc., Eaglewood Cliffs, N.J., 1987, the third one being
described in an article of S. Betti, F. Curti, G. De Marchis, E. Iannone,
"Multilevel Coherent Optical System Based On Stokes Parameters Modulation"
which is being published on the Journal of Lightwave Technology.
In FIG. 8 the limit performance of the transmitting apparatus conditioned
by the Shannon equation regarding the channel capacity is shown. The
apparatus according to the invention suffers from a penalty with respect
to the Shannon limit of 8.5 dB for N=16, 7.4 dB for N=32 and 7.8 dB for
N=64, respectively. The performance of the apparatus according to the
invention with respect to the compared apparatus tends to improve as the
number of levels increases as illustrated in the following Table V showing
the improvement in dB of the performance of the apparatus according to the
invention with respect to that of N-SPSK and N-PSK apparatus.
TABLE V
______________________________________
N N-SPSK N-PSK
______________________________________
8 1.4 3.8
16 2.3 5.4
32 3.0 9.3
64 3.8 10.9
______________________________________
While only one embodiment of the invention has been illustrated and
described, it should be appreciated that several changes and modifications
can be made without parting from the scope of the invention.
* * * * *
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