Jul 23, 1991 - the partial financial support of the National Research Council (CNR) in the frame of the ..... bandpass filters of bandwidth W = 2(R, + ~FBL), being BL the sum ..... Systems with the Optical Communication Group. Antonio Maria ...
JOURNAL OF LIGHTWAVE TECHNOLOGY, VOL. IO, NO. 6, JUNE 1YY2
777
An Efficient Multilevel Coherent Optical System: M-4Q-QAM Roberto Cusani, Member, IEEE, Eugenio Iannone, Antonio Maria Salonico, and Maria Todaro
Abstract-In this paper a new coherent multilevel transmission system is presented based on the modulation of all the optical field degrees of freedom (the four quadratures of the optical field). The transmitted symbols are represented in the space of the field quadratures by a square lattice of points, so that both the transmitter and the decision devices can be easily implemented. The proposed modulation formats allow high spectral efficient systems to be designed without paying a great sensitivity penalty with respect to binary systems. For this reason the proposed modulation format seems promising for application in densely spaced very high capacity FDM networks and in high-speed data transmission in parallel computers.
I. INTRODUCTION
I
N the last years some attention has been devoted to multilevel optical coherent transmission systems, using both traditional modulation formats as QPSK [l],[2] novel modulation techniques such as polarization modulation [3], [4] or four quadrature (4Q) modulation [SI. For this kind of systems two main applications are foreseen in high capacity FDM optical networks and in high-speed parallel data transmission. With regards to high capacity optical networks, in local or metropolitan environments (LAN’s and MAN’S), the receiver sensitivity is not the only important system figure and an efficient exploitation of the available transmission bandwidth is crucial. The huge optical bandwidth available on conventional single-mode fiber can be utilized by means of frequency division multiplexing (FDM) techniques. On the other hand, the single channel bandwidth is limited by detectors and electronic components and determines the maximum information rate that can be delivered by the network to a single user. A possible solution to improve the capacity of a single optical channel at the expense of receiver sensitivity is multilevel transmission [6]. Moreover, multilevel transmission allows multiple path to be introduced in the logical network topology [7], [8] increasing the throughput performance of some kind of networks. Manuscript received July 23, 1991; revised December 20, 1991. This work was carried out at Fondazione Ugo Bordoni in the framework of an agreement between Fondazione Ugo Bordoni and the Italian PT Administration and under the partial financial support of the National Research Council (CNR) in the frame of the Telecommunication Project. R. Cusani and A. Salonico are with the University of Rome “Tor Vergata,” via Orazio Raimondo, 00173 Roma, Italy. E. Iannone and M. Todaro are with the Fondazione Ugo Bordoni, Viale Europa 190, 00144, Roma, Italy. IEEE Log Number 9107296.
With regards to high-speed parallel data transmission, at the present in parallel computers the calculation speed bottleneck is often constituted by data transmission between processing units [9]. Within a single unit parallel processing is adopted while, in order to transmit data using a binary optical system, a parallel to serial conversion is needed. This operation is not required if a multilevel transmission system is used. It is to be noted that multilevel coherent optical system tailored for high speed data transmission must fulfil quite different requirements with respect to a system embedded in a standard communication environment. Since the transmission distance is quite short, polarization maintaining fibers can be used so that polarization fluctuations are not present. Moreover, the achievement of a system sensitivity as high as possible is not so important. On the other hand systems with a great number of levels transmitting at a high symbol rate (of the order of 500 Msymbols/s) must be implemented. In this paper a new coherent multilevel transmission system is presented based on the modulation of all the optical field degrees of freedom (the four quadratures of the optical field). The transmitted symbols are represented in the space of the field quadratures by a square lattice of points, so that both the transmitter and the decision device can be easily implemented. In analogy with traditional QAM the proposed system will be named M-4Q-QAM. At the receiver side, the received field is divided into its quadratures, each of which is detected via an heterodyne receiver. After IF filtering the electrical signal is demodulated by means of standard electrical PLL and then sent to the decision device. The polarization fluctuations problem is faced and solved by means of a decision driven electronic algorithm that is an improvement of a similar algorithm presented in [6]. However it is to be noted that the system results quite sensible to the phase noise, due to the coherent demodulation. The proposed scheme exhibits better performance than traditional QAM systems, polarization modulated systems [4] and, when the number of levels is higher than 128, constant power 4Q systems [5]. For this reason it seems to be promising not only for telecommunication networks but also for applications in supercomputer architectures. The paper is organized as follows. In Section I1 two alternative transmitter structures are presented. In Section I11 the analytical model adopted to describe the fibre propagation is shown. The spectra of the transmitted and the received optical fields are derived in Section IV while in Section V the receiver structure is described. In Section VI the analytical model used
0733-8724/92$03.00 0 1992 IEEE
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JOURNAL OF LIGHTWAVE TECHNOLOGY, VOL. 10, NO. 6, JUNE 1992
to calculate the system performance both at the quantum limit and in the presence of lasers phase noise is presented and the
TL
- AM
PM
POLM
Finally, in Section VI11 the main results are summarized. 11. MODULATION FORMATAND TRANSMITTER STRUCTURE
The electrical field of an electromagnetic wave propagating through an optical fiber can be written as follows:
E ( t )= E,(~)z+E,(~= ) @[(XI
+ i x 2 )+~ (x3 + i
I
Y Symbol Stream
q ) ]eiwst ~ (1)
so that it then can be represented by means of a vector X of components s, (z = 1,. . . , 4 ) in an Euclidean four dimensional space: the field space (FS). The Euclidean norm of X coincides with the optical power so that electromagnetic fields having the same power is FS are represented by points on a spherical surface. The proposed modulation format can be described as a multilevel modulation without memory in which the time axis is divided into symbol intervals each of which is devoted to the transmission of a symbol. Each symbol is associated to a value of the optical field and during a symbol interval the transmitted field is constant, equal to the value associated to the symbol to be transmitted. The transitions between subsequent symbol intervals are supposed to be instantaneous. Finally, the values of the optical fields representing the M symbols are associated in FS to M points that form cubic lattice constellation. If the number of transmitted symbols M can be written as M = L4, where L is an even integer, each point of the constellation can be addressed by four indexes: g , h, j, k , each ranging from 1 to L. In particular, denoting by Xg,tL,,,k= [xp).zr), xt),xp)] the generic vector belonging to the constellation, the following expressions hold: X1 ( 9 )=
I
Fig. 1. Block scheme of the first proposed transmitter; TL = transmitting laser, AM = amplitude modulator, PM = phase modulator, POLM = polarization modulator, COM = encoder.
AM
PM To Fibre
+
Fig. 2. Block scheme of the second proposed transmitter; TL = transmitting laser, PBS = polarization beam splitter, AM = amplitude modulator, PM = phase modulator, COM = encoder.
The transmitter is constituted by the cascade of three different modulators: an amplitude, a phase and a polarization modulator, that must be able to provide an arbitrary polarization modulation as performed for example by the scheme presented in [4]. At the end of the modulation chain the transmitted field expression is:
d ( 2 g - L - 1) g E [ L L ]
zr)= d ( 2 h - L
- 1) h E [ l ,L ]
x p = 4 2 3 - L - 1 ) 3 E [l.L] x y ) = d ( 2 k - L - 1 ) k E [l.L ]
( 2 ) where U( t ) represents the amplitude modulation, m(t) the phase modulation and P ( t ) and 6 ( t ) take into account the where d is half the distance between neighbors in the lattice. polarization modulation. The axes unit vectors are indicated If the number of transmitted symbols cannot be written as with Z and $. With reference to the case of M = L4 levels, the modulation L‘ with L integer, the point constellation can be obtained by choosing the smallest power of four greater than M and functions can be easily obtained starting from the expression suppressing the L4-M points with the greater norm. Various of the generic point of the lattice given by (2). In particular, other four-dimensional constellations can be designed, but the see S(a)-5(e). In the other cases the expressions from (Sb) to (Se) can be cubic lattice represented by (2) constitutes the reference case used associating to each point of the constellation four indexes considered in this paper. A possible transmitter block diagram is reported in Fig. 1. on the basis of the original lattice structure. Another transmitter block scheme suitable for the proposed The field generated by the transmitting laser, linearly polarized modulation format is shown in Fig. 2. The laser generated along the x axis, has the expression field, linearly polarized at 7r/4 with respect to the transmitter Eo = & & , ( W S ~ + ~ ) ( 3 ) reference axes, is divided into its polarization components, each of one is amplitude and phase modulated. After the where A0 is the field amplitude, w, the optical frequency and modulation stages the two polarization components are sus’ the x-axis unit vector. perimposed and fed into the fiber.
779
CUSANI et al.: AN EFFICIENT MULTILEVEL COHERENT OFTICAL SYSTEM
A0 = 2 ( L - 1)d
a 2 ( t )=
(2g - L - 1)2
+ (2h - L
+ (2k - L - 1 ) 2
4(L - 1)2 1
7T
1 -
7T
P=/
) -:
29-L-1
m(t)= - arccos
-
+
1)2 ( 2 j - L - 1)2
-
(29 - L - 1 y
+ (2h - L - 1)2
2h-L-1
arcsin
+ (2h - L - 1)2 ( 2 g - L - 1 ) 2 + (2h - L - 1 ) 2 ( 2 g - L - 1)2+ (2h - L + ( 2 j L - 1)2 + (2k (29 - L -
-
2j-L-1
S ( t ) = arccos
+
-
-
$h - " t )
-
$h - 7rm(t).
L
-
1y
( 2 j - L - 1)2 (2k - L - 1 ) 2 2k-L-1
= arcsin
( 2 j - L - 1)*
+ (2k - L - 1)2
The transmitted field has the following expression:
where a,(t), a,(t), m,(t), and m,(t) are the modulating functions. If M = L4 is assumed, d is related to the transmitted field amplitude A0 by (5a), and the modulating functions are given, in all the conditions, by the following equations:
af(t)=
+
(29 - L - 1)2 ( 2 h - L -
(74
4 ( L - 1)2 r
m,(t) =
-I
(29 - L
1
- arccos lr
(29 - L -
-
1)
J -1
+ (2h - L - 1 ) 2
r -
1 -
7r
1
(2h - L - 1 )
arcsin (29 - L
-
+ (21L
L
-
1)2
+
r
m,(t) =
-
(2k - L - 1)2 4 ( L - 1)2
( 2 j - L - 1)2 ai(t) =
1
- arccos 7T
1
- - arcsin 7.r
and the polarization modulators, and it is out of the purpose of this paper. However it can be useful to observe that in the second kind of transmitter the two transmitter branches must be perfectly balanced, requiring perfectly identical modulators. This requirement is quite difficult to fulfil at the present state of the art, particularly for the two amplitude modulators, and is not present in the first scheme. On the other hand, assuming for the polarization modulator the scheme presented in [4], a lower overall transmitted attenuation is expected if the second kind of transmitter is used.
(74
111. FIBERPROPAGATION
Neglecting nonlinear phenomena, the effect of fiber propagation can be evaluated by means of the fiber attenuation CY, the fiber phase-shift h ( w ) and the Jones matrix J , a unitary operator which takes into account the polarization evolution along the fiber due to coupling between the polarization modes [lo], [ I l l . Therefore the received optical fie? can be expressed, as a function of the transmitted field Et, as follows:
7
(2j - L - 1)
+
J -1
( 2 j - L - 1)2 ( 2 k - L - 1)2
(2k - L - 1 )
+
( 2 j - L - 1)2 (2k - L - 1 ) 2 (74
A realistic comparison between the two proposed transmitter schemes is possible only on the basis of technological considerations, mainly related to the characteristics of the amplitude
From (8) a relationship between the representative vector of the received field X' and the transmitted one X t can be derived, SO to obtain
JOURNAL OF LIGHTWAVE TECHNOLOGY, VOL. 10, NO. 6, JUNE 1992
7x0
,,
Control signal from
processor
PBS
where tLJ = u J =~ iu,~( j = l , 2 ) and b(w) is supposed to be independent of w, condition verified for all the practical transmission systems, and therefore neglected without loss of generality. The received number of photons per symbol F, can be computed from (9) obtaining
where A = e-aAg is the amplitude of the received field, T, the symbol interval, R, = T,-l the symbol rate and the input optical power is measured in photons per second.
Fig. 3. Block scheme of the optical front end and of the IF section; LO = optical local oscillator, PBS = polarization beam splitter, HY 90' = 90' balanced optical hybrid, IFF = IF filter, PLL = electronic PLL.
allows an easier design of the IF chain and allows matched filter demodulation that is impossible if the spectrum of the IF currents depends on fibre induced polarization fluctuations. In the case M # L4 generally the spectrum matrix of the transmitted field is not diagonal so that the spectrum matrix of the received field depends on the elements of the Jones matrix. As a matter of fact in this case the quadratures of the transmitted field can be no more independent.
IV. FIELD SPECTRA
V. RECEIVERSTRUCTURE
Assuming M = L4, the spectrum matrix of the transmitted vector X t can be easily calculated by observing that the four components of X t are independent and amplitude modulated according to (2). As a consequence the elements Stj ( U ) of the spectrum matrix S' are given by [12]:
Sf,(w) = F{ (sf.s(t)a.:s(t - T ) ) }
where F{ } indicates the Fourier transform, (*) is the average operator, s ( t ) is the unit-amplitude rectangular function in [O.T,] ( s ( t ) = 1 for 0 < t < T,, otherwise s ( t ) = O), b i j is the Kroneker operator and the constant p, which depends only on the number of levels, is given by
/L
8 L'2 = L ( L - q2j=1
( L + 1)(L + 2 ) 3 ( L - 1)2
- 0: +-3L L-1'
The block scheme of the optical stage and of the IF stage is the same as in [SI and is shown in Fig. 3. The received field polarization components are divided by means of a polarization beam splitter and then are coupled with the corresponding polarization components of the local oscillator, linearly polarized at 7 ~ / 4with respect to the receiver reference axes, by means of two balanced 7 ~ / 2optical hybrids. The four fields at the output of the hybrids are detected by means of four photodiodes so that the obtained electric signals are proportional to the components of the representative vector of the received field. After detection the IF currents are filtered by four identical filters, with pulse response h ~ ~ ( tthat ) , are supposed to be ideal ) , BL bandpass filters of bandwidth W = 2(R, ~ F B Lbeing the sum of the transmitting and local lasers linewidths. The parameter ICF must be chosen in such a way to transmit the signals approximately undistorted through the filters [ 131. After filtering, normalizing the power of the local oscillator to unit on each polarization component, the complex envelopes y k ( t ) of the IF currents are given by
+
3L - 6
E'+
-
A. Optical and IF Stage
(12)
It can be shown that the spectrum matrix 9 at the fiber 5 = eP2" J ; S t J r where the apex output can be obtained as ' ' indicates the transpose operation. From the above formula the elements of 9 are given by
+'
It results from (13) that the spectrum matrix elements are independent of the instantaneous value of the Jones matrix, unlike that of other modulation formats based on polarization modulation or constant power 4Q modulation. This property
+ +
+ +
yl(t) = z:s(t)eip(t) izis(t)eiq(t) nl(t) * hIF(t) y2(t) = z i s ( t ) e i p ( t ) izTs(t)eip(t) n2(t)* hIF(t)
(14)
with:
+
nk(t) * h ~ ~ = ( tni(t)t ) inf(t)
(IC = 1 , 2 , 3 , 4 ) (15)
CUSANI
er U/.: AN
EFFICIENT MULTILEVEL COHERENT OPTICAL SYSTEM
where * indicates the convolution and the signal distortion due to the IF filters is neglected. The detection noises n k ( t ) are supposed to be complex white Gaussian processes with power spectral density for quadrature No equal to 1/2 in the adopted normalization. The filtered signals are coherently demodulated by means of an electrical PLL whose control signal is derived from the baseband processor. Low-pass filtering rejects the terms at double frequency. Under the above assumptions and after suitable normalization, the four baseband signals z k ( t )'s, giving an estimate of the received field representative vector, are given by:
781
Z
z Z
1 -
2 3
z
z l ( t ) = z y s ( t )cos[Acp(t)] + x ; s ( t ) sin[Acp(t)] z z ( t ) = x i s ( t )cos[Acp(t)]
z3(t) =
4
Control signal
+
.rzs(t)cos[Acp(t)] z i s ( t )sin[Acp(t)]
+ z4(t)=
+ xys(t)sin[Acp(t)]
[ni(t) cos +(t)- n y ( t )sin +(t)l L 1
(16)
where $ ( t ) is the PLL estimate of the signal phase, possibly including lasers phase noise, and Acp(t) = @(t)- cp(t) is the PLL phase error process. The noise process in (16) is Gaussian with constant power spectral density in the relevant bandwidth and variance cri. that, with the assumed normalization for the local oscillator power, is equal to W. By sampling the baseband signals given by (14) at the center of their existence interval, the decision variables can be assembled in a vector Z = [ , Z ~ , Z Z2,3 , 2 4 1 with components:
+ r; sin Acp + 01, z2 = x; cos Acp + sin Acp + nZr z j = .r; cos Acp + xi sin Acp + ~ 1 = x2;cos Acp + xjsin Acp + n4, z1 = xi cos Acp
I)
If the four photodiodes or four IF filters are not identical the signal to noise ratio on the four electrical branches is not the same so that the noise distribution at the receiver is no more isotropic in the signal space. This effect induces a dependence of the system performance on the received state of polarization. For example if on the first and on the second branches the signal to noise ratio is lower than on the third and on the fourth a linearly polarized field along the z axis is detected with a greater accuracy with respect to a linearly polarized field along the y axis. The above mentioned phenomena produce a degradation of the system performance with respect to the quantum limit whose quantitative evaluation will be carried out in a future work. B. Baseband Section
3 ~
(17)
where z k , x k , 7 ) k c , and are the samples of z k ( t ) , z k ( t ) , n k ( t ) * h ~ ~and ( t ) A4(t), respectively. The noise terms in (17) are uncorrelated Gaussian, with variance = W . However the noise variance could be reduced by strongly low-pass filtering the signals z k ( t ) in the demodulation process (an ideal integrator operating in the symbol interval constitutes the matched filter). At the end of the description of the optical and IF stages some practical observations are useful. The implementation of the described system require two ideal ~ / balanced 2 optical hybrids and four identical photodiodes and IF filters. If the two optical hybrids are not perfectly balanced a crosstalk effect between the detected quadratures is induced. In this case a power penalty arises that depends on the transmitted symbol. If the hybrids characteristics are perfectly known this effect can be compensated at the decision stage, however this introduces further electronic complexity at baseband.
cri
a
Fig. 4. Block scheme of the baseband section; JME = Jones matrix elements estimator, DD = decision device, PCG = PLL control signal generator.
[ n i ( t )cos ~ ( t- )n y ( t )sin ~ ( t ) ]
rZ;s(t)cos[Acp(t)] + z j s ( t ) sin[Acp(t)]
+
PCG
The baseband section of the receiver, whose block diagram is shown in Fig. 4, has three main functions. First of all the Jones matrix elements are estimated so that the vector Z can be multiplied by the inverse Jones matrix J - l r , in order to compensate the fiber induced polarization fluctuations. The obtained vector E = [$I, &, &, E41 is processed by the decision device in order to detect the transmitted symbol. The estimated transmitted symbol is used to drive both the PLL control signal generator and the Jones matrix elements estimator. The above functions and the associated are described in the following. 1) Polarization Fluctuations Tracking: The polarization fluctuations caused by fiber birefringence and coupling cause a continuous rotation of FS that must be tracked in order to correctly estimate the received symbol. Assuming M = L4, the linear baseband tracking proposed in [5] cannot be adopted, since the average value of each component of X' is zero. On the other hand the Reference Vector Tracking algorithm, proposed in [4] and [5],requires a great amount of circuitry to be implemented when A4 is large
782
JOURNAL OF LIGHTWAVE TECHNOLOGY, VOL. 10, NO. 6, JUNE 1992
r ~
(e.g., M = 256). For these reasons a new tracking algorithm is presented here that is suitable for all 4Q modulation formats. The proposed algorithm is decision driven as the Reference Vector Tracking, but the hardware requirement is almost constant at the increase of M . RC I ) The rotation of FS induced by polarization fluctuations Jones Mavix Elements depends only on three parameters, as shown in (9), taking into account that, for the unitarity of J r , it is U ~ ~ + U : ~ + U ? ~ += U~~ 1. As a consequence this rotation is completely individuated "if it is known the transformation affecting two points that are not in line with the reference system origin. Once the point constellation in FS has been fixed, the 1 proposed algorithm selects two points X1' and X2' with the Control from the Decision Device maximum norm and not in line with the reference system origin. At each updating interval the new position of X1' and S" is estimated, and the new elements of the Jones matrix Fig. 5. Block scheme of the polarization tracking processor; SR = scaling and rotation that transform all vectors in A-'' or A-'', SW = switch, are calculated by solving the following linear system: MC, ( z = 1 . 2 ) compound memory cell, IN = analog integrators, RC =
1m-
H' =:--#
rotation computation device.
where 0 is the 4 x 4 zero matrix, XI' and X2' are the estimated positions of the two reference points at the end of the updating interval, and where
The matrices M iare composed by the coordinates of the points XI'' and .X2' at the beginning of the updating interval. For the above considerations three independent equations are certainly present in the system (18) together the condition ,U?,, 1LlZ U $ = 1. The block scheme of an analog processor able to perform the estimation of X I r and X 2 r during each updating intervals shown in Fig. 5. The symbols and the associated points of the received constellation are divided into two classes of M / 2 elements: C1 and Cp. Every time a symbol of the class C, is received a transformation is applied on the four baseband currents so to obtain an estimate of X", and an analogous transformation is performed when a symb_ol of the class C p is received so to obtain an estimate of X2'. For example, if the point X i E C1 is received the applied transformation is constituted by the product of the components of 2 = [ z 1 . 2 2 . ~ 3 , 2 4 by ] ( X i ]lX1'l and by a rotation, that aligns in FS the vectors X 2 and X1'. The obtained vector is the estimate of XI7.. The estimated components of X" and X2' are accumulated in four memory cells and at the end of the updating interval the obtained values give (after normalization) the value of l?lr and X2'.. If the updating interval Tu is much longer than the symbol interval T, but much shorter than the characteristic time Tp
+ 74,. +
+
/
in which a sensible polarization fluctuation takes place, the tracking algorithm can be considered ideal. As a matter of fact the condition T,
