Cascaded distortion compensation for analog optical systems

A cascaded distortion compensation arrangement is disclosed which utilizes a plurality of pre-distortion components disposed in a series arrangement at the input to the transmitter and a plurality of post-distortion components disposed in a series arrangement at the output of the receiver. The various components may be modified, added and/or deleted to provide an arrangement suitable for the particular system.

BACKGROUND OF THE INVENTION 
1. Technical Field 
The present invention relates to cascaded distortion compensation for 
analog optical systems and, more particularly, to an arrangement using a 
series connection of a plurality of separate pre- and/or post-distortion 
compensation components, each component capable of providing specific 
functionality. 
2. Description of the Prior Art 
A growing area for analog optical communication systems is the common 
antenna television (CATV) network. In particular, recent advances in long 
wavelength distributed feedback (DFB) laser technology have made possible 
the transport of multiple CATV channels over one single mode fiber at 
.lambda.=1.3 .mu.m. See, for example, "Lightwave subcarrier CATV 
transmissions systems", by T. E. Darcie et al. appearing in IEEE Trans. 
Microwave Theory Tech., Vol. MTT-38, p. 524, 1990. The low levels of 
analog distortions and noise from the DFB lasers have been found to 
satisfy the system requirements such that the presence of many channels 
over a common communication path does not noticeably affect the reception 
of any particular channel. 
It has been well documented, however, that nonlinearities of the DFB laser 
affect the composite second order (CSO) distortion of the system. 
Pre-distortion circuits have been developed to compensate for the laser 
nonlinearity, one exemplary arrangement being disclosed in U.S. Pat. No. 
4,992,754 issued to H. A. Blauvelt et al. In this particular arrangement, 
the distortion is compensated by applying a pre-distorted signal equal in 
magnitude and opposite in sign to the distortion introduced by the DFB 
laser. The input signal is split into two paths with the primary part of 
the signal applied directly to the device, including a time delay to 
compensate for delays in the secondary path. A pre-distorter in the 
secondary path generates harmonic signals, the amplitude of which are 
adjusted to match the amplitude of the distortion. A tilt adjustment is 
made to compensate the amplitude of the pre-distortion for the frequency 
dependence of distortion. A fine adjust of the delay is also included so 
that the phase of the predistortion signal is properly related to the 
phase of the primary signal. 
Additional sources of nonlinearities not discussed in the Blauvelt et al. 
reference, for example, the interaction of FM chirp intrinsic to a DFB 
laser with fiber dispersion, can also affect the system performance, as 
discussed in the article "Dispersion-Induced Composite Second-Order 
Distortion at 1.5 .mu.m", by E. E. Bergmann et al. appearing in IEEE 
Photonics Tech. Lett., Vol. 3, No. 1, January 1991, at p. 59. As discussed 
in the Bergmann et al. reference, dispersion nonlinearity can be 
counteracted by utilizing dispersion-shifted fiber, reducing laser chirp, 
or limiting applications to relatively short spans (e.g., &lt;3 km). 
Exemplary predistortion compensation for this combination is discussed in 
an article entitled "Electrical predistortion to Compensate for Combined 
Effect of Laser Chirp and Fibre Dispersion", by H. Gysel et al. appearing 
in Electronic Letters, Vol. 27, No. 5 at pp. 421-3. Gysel et al. discusses 
the utilization of a varactor diode/inductor combination to "build in" the 
inverse of the expected distortion in the signal as applied to the optical 
transmitting device. 
Recently, doped fiber amplifiers have become available which can be used in 
a CATV network to significantly increase the link loss budget. In 
particular, the erbium doped fiber amplifier (EDFA) is an attractive 
component since it exhibits high saturated output power, polarization 
independent amplification, and low intrinsic optical noise. The high 
saturated output power of an EDFA is of particular importance to CATV 
transport and distribution applications. Furthermore, its saturated gain 
characteristic does not respond to input signal variations at speeds 
faster than a few kilohertz because of the small absorption and stimulated 
emission cross sections, as well as the long metastable lifetime of the 
erbium ions. However, when an EDFA is used to amplify an analog optical AM 
CATV multiple carrier signal from a directly modulated DFB laser, an 
increase in the system distortion is observed. 
In general, the combination of the above-noted dispersion sources, along 
with other nonlinear components contained within the communication system, 
such as external modulators and/or erbium-doped fiber amplifiers, results 
in an overall system-based nonlinear effect which may distort the system 
performance. Prior art compensation techniques, which address distortion 
at the component level (i.e., prior to installation in a communication 
system), cannot provide adequate compensation for the overall analog 
communication system. 
Thus, a need exists for reducing the signal distortion attributed to the 
system-level nonlinearity present within an operating analog optical 
communication system. 
SUMMARY OF THE INVENTION 
The need remaining in the prior art is addressed by the present invention 
which relates to cascaded distortion compensation for analog optical 
systems and, more particularly, to an arrangement using a series 
connection of a plurality of separate pre- and/or post-distortion 
compensation components. 
In accordance with an exemplary embodiment of the present invention, a 
distortion compensation arrangement comprises a plurality of series 
cascaded pre-distortion compensation components (each component configured 
to compensate for a particular type of system distortion present at a 
transmitter) and a plurality of series cascaded post-distortion 
compensation components (each component configured to compensate for a 
particular type of system distortion present at a receiver). The input 
signal i(t) thus passes in series through each compensation component such 
that all distortion is essentially canceled. 
In one arrangement, the pre-distortion components may include a first 
component for compensating laser-based intrinsic distortion and a second 
component for compensating distortion associated with an optical amplifier 
and/or external modulator located at the transmitter. The post-distortion 
components may include a first component for compensating transmission 
fiber dispersion distortion and a second component for compensating 
higher-order (e.g., composite triple beat) distortion. 
An advantage of the cascaded series arrangement of the present invention is 
the modularity of the arrangement wherein the individual compensation 
components are independent correction factors and may be added to or 
deleted from an individual analog communication system as necessary. In 
general, the system may be "field programmable" in that the system user 
may adjust the types and degree of compensation associated with each 
compensation component, in accordance with changes in system requirements. 
Other and further advantages of the present invention will be apparent 
during the course of the following discussion and by reference to the 
accompanying drawings.

DETAILED DESCRIPTION 
FIG. 1 illustrates an generalized block diagram of an exemplary analog 
optical communication system 10 utilizing cascaded series distortion 
compensation in accordance with the teachings of the present invention. In 
general, system 10 comprises a laser transmitter 12 which is utilized to 
form an optical communication signal which propagates over optical fiber 
14 to an optical receiver 16 (e.g., PIN-FET receiver). In accordance with 
the teachings of the present invention a plurality of n pre-distortion 
compensation components 18 are disposed in a cascaded series arrangement 
before the input to laser transmitter 12. A plurality of N post-distortion 
compensation components 20 are illustrated in FIG. 1 as disposed in a 
cascaded series arrangement after the output of receiver 16 (where n may 
or may not be equal to N). In operation, an electrical (RF) message signal 
i(t) is applied as an input to the series arrangement of pre-distortion 
components 18 and is modified as it passes therethrough to provide at the 
output thereof a pre-distorted input signal i" . . . ' (t). Pre-distorted 
signal i" . . . ' (t) is then applied as an input to transmitter 12 which 
then generates an optical signal which is sufficiently pre-distorted so as 
to be essentially linear over the bandwidth of interest. The optical 
signal subsequently propagates along optical fiber 14 and is applied as an 
input to optical receiver 16. Optical receiver 16, which may comprise a 
PIN-FET receiver, then converts the optical signal into an electrical 
representation I(t). Electrical signal I(t), as converted, contains 
distortions introduced both by optical fiber 14 (chromatic dispersion) and 
optical receiver 16. Post-distortion compensation components 20 are thus 
coupled to the output of receiver 16 and utilizes to substantially 
compensate for these distortion elements. 
Pre-distortion compensation arrangement 18 comprises a plurality of n 
separate distortion compensation components 18.sub.1, 18.sub.2, . . . , 
18.sub.n, where each component is utilized to correct for a different 
distortion factor associated with laser transmitters. For example, the 
distortion associated with the laser device itself may be corrected by an 
exemplary component 18.sub.i. Various other elements, for example, optical 
amplifiers and/or external modulators, may be located with the laser 
transmitter and the distortion associated with these elements compensated 
as required. Similarly, post-distortion compensation arrangement 20 
comprises a plurality of N separate distortion compensation components 
20.sub.1, 20.sub.2, . . . , 20.sub.N, where each component is utilized to 
correct for a different distortion factor. dispersion along optical fiber 
14 may be compensated by an exemplary component 20.sub.i. 
As mentioned above, an advantage of the series cascaded arrangement of the 
present invention is the modularity of the arrangement, that is, the 
ability to modify separate components without disturbing the compensation 
characteristics of the remaining compensation components. For example, if 
a different laser source is substituted for transmitter 12, a different 
distortion compensation component 18.sub.i may be substituted. Likewise, 
if the receiver is moved to a fiber of different length, for example, the 
post-distortion component 20.sub.i associated with compensating fiber 
dispersion may be altered without adjusting the remaining post-distortion 
components. Therefore, the arrangement of the present invention may be 
altered as need be by the user to accommodate changes in the environment 
of the deployed system. 
FIG. 2 illustrates an exemplary plurality of n=2 predistortion compensation 
components which may be utilized in system 10 as illustrated in FIG. 1. In 
particular, a first component 18.sub.1 is utilized to compensate for the 
inherent nonlinearities of laser transmitter 12 (FIG. 1 ). As shown, 
component 18.sub.1 includes a splitter 30 which functions to direct the 
incoming (electrical) signal i(t) along a first signal path 32 and a 
second signal path 34. First signal path 32 includes delay means 36 which 
functions to provide a time delay .tau..sub.1 to signal i(t) which is 
substantially identical to the delay associated with second signal path 
34. Second signal path 34 includes a compensation element 38, for example, 
a signal squarer, which essentially duplicates (in amplitude, phase and 
frequency) the particular nonlinearity associated with transmitter 12. The 
details of such a compensation scheme are well-known in the art and need 
not be discussed here. The output from element 38 is subsequently inverted 
in magnitude within an inverter 40. A summing element 42 is then used to 
add the original (delayed) signal to the distortion compensation signal to 
form a first distortion compensated signal i'(t). 
As mentioned above, another influence on system nonlinearity may be 
attributed to the presence of a doped fiber amplifier which is co-located 
with transmitter 12 (not shown). The contribution to the composite second 
order (CSO) distortion from such an amplifier has been found to result 
from inadvertent FM to AM conversion within the doped region of the fiber 
amplifier. Alternatively, the utilization of a external modulator with the 
laser transmitter 12 may form a similar type of distortion. In either 
case, when a laser source is directly modulated through injection current, 
its optical frequency varies likewise. When this frequency modulated 
signal passes through a fiber amplifier (or external modulator), which has 
wavelength dependent gain G(.nu.), the signal experiences unwanted 
amplitude modulation, which is then superimposed upon the desired 
amplitude modulation of the input signal. Therefore, the effective L-I 
curve from the combination of the laser and amplifier (or modulator) is 
either super-linear or sub-linear, thus resulting in the unwanted second 
order distortion. The second order distortion, denoted 2HD, related to the 
presence of a doped fiber amplifier can be represented as: 
##EQU1## 
where .differential.G/.differential..nu. is defined as the slope of the 
doped fiber amplifier curve, d.differential./dI is the frequency chirp, 
I.sub.m is the amplitude of the modulation current, and G(p,.nu..sub.o) is 
defined as the time invariant gain. The CSO distortion related to the 
second order distortion of the j-th channel of a CATV system can be 
expressed as follows: 
EQU CSO.sub.j =c.sub.j [2HD].sup.2. 
The CSO distortion attributed to such amplifiers as described above may be 
corrected using a pre-distortion component 18.sub.2, as shown in FIG. 2. 
In particular, component 18.sub.2 is responsive to the first pre-distorted 
signal i'(t) output from first pre-distortion component 18.sub.1. As 
shown, second pre-distortion component 18.sub.2 includes a splitter 50 for 
providing pre-distorted signal i'(t) along a pair of signal paths 52 and 
54. Signal path 52 contains a delay element 56 for provide a predetermined 
time delay .tau..sub.2 which essentially equals the time delay along 
second signal path 54. Second signal path 54 contains a squaring element 
58, an attenuator 60 and time delay means 62 to form a distortion signal 
of the form ai.sup.k (t-.tau..sub.2). A summing element 64 is used to add 
this distortion signal to the first (delayed) distortion signal i'(t) 
along path 52 to form a second pre-distorted signal i"(t). Signal i"(t) 
may then be subsequently applied as the input to laser transmitter 12 of 
FIG. 1. As mentioned above, various other pre-distortion components may be 
added to those described above. 
FIG. 3 illustrates an exemplary plurality of N=2 post-distortion elements 
20.sub.1 and 20.sub.2. As discussed above, another source of distortion in 
analog optical communication system 10 is the chromatic dispersion 
introduced by optical fiber 14. Studies have indicated that the CSO 
becomes increasingly large as the length of the fiber increases, and also 
as the channel frequency increases. Additionally, it has been found that 
the CSO is worse for lasers with larger chirp. Theoretically, the CSO 
attributed to the laser chirp-fiber dispersion combination for a 
particular channel "j" can be represented as follows: 
##EQU2## 
c.sub.j is the number of CSO components, .omega..sub.j is the angular 
frequency at which distortion occurs, m is the modulation index, p is the 
average optical power, dp/dI is the optical slope efficiency, 
.alpha..sub.s is the system attenuation, D is the fiber dispersion, L is 
the fiber length, d.nu./dI is the laser chirp, .lambda. is the average 
signal wavelength, and c is the speed of light. 
First post-distortion compensation component 20.sub.1, as illustrated in 
FIG. 3, may be utilized to compensate for the chromatic dispersion 
described above. In particular, component 20.sub.1 includes a signal 
splitter 70 which receives as an input the electronic output signal I(t) 
from optical receiver 16 (FIG. 1). The output from splitter 70 is 
subsequent inserted along a first signal path 72 and second signal path 
74. Similar to the pre-distortion components discussed above in 
association with FIG. 2, first signal path 72 includes a delay means 76 
for providing an equalizing time delay .tau..sub.1 with second signal path 
74. As shown, second signal path 74 includes a number of elements which 
are utilized to compensate for chromatic dispersion. In particular, second 
signal path 74 includes a squaring means 78, which is utilized to form the 
second harmonic of the signal, and a differentiator 80, used to form the 
j-th derivative of the signal, where in the case of fiber dispersion 
correction, the first derivative is utilized. An attenuator 82 is disposed 
in second signal path 74 and may be adjusted by the user to provide the 
correct level of distortion compensation. The output from second signal 
path 74 is defined by the term 
##EQU3## 
assuming the first derivative signal is used. This distortion compensation 
signal is subsequently summed with the signal I(t) propagating along first 
signal path 72 within a summing element 84 to form as an output a first 
post-distortion signal I'(t). 
A second post-distortion compensation component 20.sub.2, disposed at the 
output of first component 20.sub.1, may be used to provide higher-order 
correction factors to the received signal. For example, this component may 
be used to compensate for composite triple beat (CTB) distortion. In 
particular, component 20.sub.2 may comprise a signal splitter 90, 
responsive to first post-distorted signal I'(t), for providing this signal 
along a pair of signal paths 92 and 94, where first path 92 includes delay 
means 96. Second signal path 94 contains a compensation element 98 which 
functions to form a cubed representation of the applied signal. A summing 
element 100 is used to combine the signals propagating along paths 92 and 
94, thus forming as an output a second post-distorted signal I"(t). 
It is to be understood that the embodiments described above are exemplary 
only, and any desired pre- and/or post-distortion compensation component 
may be used in the cascaded series arrangement of the present invention. 
As mentioned above, an advantage of the cascaded series arrangement of the 
present invention is the ability to modify, add and/or delete the various 
pre- and post-distortion components as the system needs change.