Abstract:
A compensation function mitigates a substantial portion of the chromatic dispersion imparted to a communications signal by an optical communications system. A digital input signal is digitally processed using the compensation function to generate a predistorted signal. An amplitude and a phase of an optical signal are modulated using a pair of orthogonal signal components to generate a predistorted optical signal for transmission. In one implementation, the pair of orthogonal signal components are components of the predistorted signal. In another implementation, the predistorted signal is processed using a non-linear compensator to generate a further distorted signal and the pair of orthogonal signal components are components of the further distorted signal. In that implementation, the non-linear compensator is configured to substantially compensate for nonlinearities in one or both of an optical modulator of a transmitter of the system and an optical-to-electrical converter of a receiver of the system.

Description:
TECHNICAL FIELD 
       [0001]    The present invention relates to optical communications systems, and in particular to electrical domain compensation of optical dispersion in an optical communications system. 
       BACKGROUND 
       [0002]    Optical communications systems typically include a pair of network nodes connected by an optical waveguide (i.e., fiber) link. Within each network node, communications signals are converted into electrical signals for signal regeneration and/or routing, and converted into optical signals for transmission through an optical link to another node. The optical link between the network nodes is typically made up of multiple concatenated optical components, including one or more (and possibly 20 or more) optical fiber spans (e.g., of 40-150 km in length) interconnected by optical amplifiers. 
         [0003]    The use of concatenated optical components within a link enables improved signal reach (that is, the distance that an optical signal can be conveyed before being reconverted into electrical form for regeneration). Thus, for example, optical signals are progressively attenuated as they propagate through a span, and amplified by an optical amplifier (e.g., an Erbium Doped Fiber Amplifier—IEDFA) prior to being launched into the next span. However, signal degradation due to noise and dispersion effects increase as the signal propagates through the fiber. Consequently, noise and dispersion degradation become significant limiting factors of the maximum possible signal reach. 
         [0004]    Dispersion, also known as Group Velocity Dispersion or Chromatic Dispersion, in single mode fibre at least, occurs as a result of two mechanisms: a) Waveguide dispersion—within a single mode fibre, different wavelengths travel along the fibre at different speeds; and b) Material dispersion—the phase velocity of plane waves in glass varies with wavelength. For the purposes of the present invention, references to “dispersion” shall be understood to mean the sum total of group velocity dispersion effects. 
         [0005]    Mathematically, first order dispersion is the derivative of the time delay of the optical path with respect to wavelength. The effect of dispersion is measured in picoseconds arrival time spread per nanometre ‘line width’ per kilometer length (ps nm −1  km −1 ). The magnitude of waveguide and material dispersions both vary with wavelength, and at some wavelengths the two effects act in opposite senses. The amount of dispersion present in a link can also vary with the temperature of the cable, and if the route is changed (e.g., using optical switches). Dispersion in optical fibre presents serious problems when using light sources whose spectrum is non-ideal, for example broad or multispectral-line, or when high data rates are required, e.g., over 2 GB/s. 
         [0006]    For the purposes of analyzing the effects of dispersion, it is convenient to represent an optical communications system using the block diagram of  FIG. 1 . In this case, the transmitter is represented by an electrical-to-optical converter (E/O)  2  which operates to convert an electrical input signal x(t) into a corresponding optical signal E IN (ω) for transmission to the receiver. The optical fiber span  4 , including all concatenated components, is represented by a transfer function T(ω), which will normally be complex. The receiver is represented by an optical-to-electrical converter (O/E)  6  which detects the optical signal E OUT (ω) received through the optical fiber span  4 , and generates a corresponding output signal y(t). For a linear optical channel, the received optical signal E OUT (ω) will nominally be equivalent to the product of E IN (ω) and T(ω). 
         [0007]    In general, the output signal y(t) represents a distorted version of the input data signal x(t). While it would be highly desirable for T(ω)=≈1, this is rarely the case. Accordingly, it is frequently necessary to utilize at least some form of compensation, so that the original input data signal x(t) can be detected within the distorted output signal y(t). 
         [0008]    One commonly used method of addressing the problem of dispersion in high-bandwidth communications systems is by inserting one or more optical dispersion compensators  8 , represented in  FIG. 1B  by the compensation function C(ω), within the link. Such dispersion compensators may, for example, take the form of a length of fibre, a Mach Zehnder interferometer, an optical resonator, or a Bragg reflector. Some of these compensators can also produce a controllable amount of compensation, which enables mitigation of time-variant dispersion effects. In either case, these compensators are intended to at least partially offset the signal distortions introduced by the system transfer function T(ω). The compensation function C(ω) is a dispersive function that is selected to optimize performance of the link. In a fully linear system, the compensation function C(ω) would preferably be equivalent to the complex conjugate T*(ω) of the transfer function T(ω), in which case T(ω)·C(ω)=1, and the combined effect of T(ω) and C(ω)=T*(ω) would be an undistorted received signal EouT(ω) that exactly corresponds to the original optical signal E IN (ω). However, limitations of optical components, and the time-varying amount of compensation required, make this objective very difficult to achieve. Additionally, optical compensators are expensive and introduce significant optical losses. These losses must be offset by additional optical gain which introduces more optical noise. The additional (or higher-performance) optical amplifiers required to provide this increased gain further increases the total cost of the communications system. In addition, the presence of optical dispersion compensators and high performance amplifiers distributed along the length of the link provides a significant technical barrier to system evolution. For example, implementation of optical switching (e.g. at the Tx and/or Rx ends of the link, or an intermediate site without electrical termination) necessarily requires adjustment of optical amplifiers, in order to accommodate changing energy states within the link. 
         [0009]    These problems can be alleviated by moving the compensation function to the terminal ends (e.g., the transmitter  2  and/or receiver  6 ) of the link. This technique typically involves “preprocessing” the input signal x(t) at the transmitter (Tx) end of the link  4  to improve dispersion tolerance, and/or postprocessing the output signal y(t) detected at the receiver (Rx) end of the link to accurately detect the input signal x(t) within the distorted output signal y(t). 
         [0010]    For example, high bandwidth traffic can be distributed over a larger number of lower-rate channels. The reduced bit-rate of each channel enhances the dispersion tolerance in proportion to the square of the reduction in the bit-rate. However, this approach is expensive, spectrally inefficient, and creates four wave mixing problems. 
         [0011]    The publication “Dispersion Compensation by Active Predistorted Signal Synthesis” Koch et al, Journal of Lightwave Tech, Vol. LT-3, No. 4, August 1985, pp. 800-805, describes a technique for synthesizing a predistorted optical signal at the input end of the optical link. According to Koch et al, an (electrical) input signal is used to drive a set of N parallel optical modulators. Each of the parallel optical signals is subject to a respective predetermined delay, and the delayed signals optically combined to produce a predistorted optical signal. Dispersion of the optical link then processes the predistorted optical signal to generate a substantially undistorted optical signal at the receiver end of the link. This approach uses multiple parallel optical modulators, optical delays and a signal combiner to produce an approximation of the desired “ideal” predistorted optical signal. The accuracy of this approximation can be increased by increasing the number (N) of modulators. However, this solution dramatically increases the cost of the system. In addition, in order to compensate time-varying dispersion, it is necessary to individually control each of the optical modulators and the respective signal delays. This requirement can significantly increase the size and complexity of the control system. 
         [0012]    Koch et al speculate (at page  801 ) that it might be possible to synthesize a predistorted waveform using “ . . . an algorithm at the input which involves all the neighboring bits of information over a time span on the order of that to which dispersion broadens the sharpest features in the absence of any compensation.” However, Koch et al do not provide any teaching regarding how this might be accomplished, and in fact conclude that this solution would be “ . . . difficult to realize, and in general also requires modulation bandwidths fully capable of transporting the undistorted signal.” Accordingly, Koch et al reject this approach in favor of their technique of combining multiple delayed optical signals. 
         [0013]    Dispersion tolerance can be increased by narrowing the spectrum of the transmitted optical signal. Various known techniques may be used for this purpose, such as multilevel coding. However, this requires expensive electronics and significantly reduces the noise tolerance of the communications system. 
         [0014]    Subcarrier multiplexing, which involves transmitting a plurality of lower bit-rate signals over one optical carrier, is another known method of increasing dispersion tolerance. In this case, the dispersion tolerance obtained is equivalent to that of the lower bit-rate subcarrier, However this approach is not cost effective and does not have a good noise tolerance. 
         [0015]    The optical spectrum occupied by a signal can be reduced by use of modulators with reduced chirp, such as a Mach-Zehnder modulator. The amount of chirp can even be tailored to optimize transmission over a particular moderate amount of dispersion. One variation of this technique is referred to as dispersion supported transmission, an example of which is discussed in EP-A-0643  497 . In this case, dispersion produces an FM to AM conversion effect, which can facilitate bit detection and thereby extend transmission distance without controlling or compensating dispersion. The dispersion causes shifting of adjacent signal components of different wavelengths, resulting in either energy voids or energy overlaps at the bit transitions. Constructive interference in an overlap causes a positive peak in the optical signal, while a void produces a negative peak. In principle, these positive and negative peaks represent an AM signal which may be detected to reproduce the original bit stream, This has proved difficult to implement over a reasonable range of practical link dispersions. 
         [0016]    Many transmission formats are known that enable somewhat increased dispersion tolerance, for example, as described in U.S. Pat. No. 5,892,858. However none of these formats provide sufficient dispersion tolerance to allow a wide bandwidth signal to be accurately detected in the presence of large amounts of dispersion. 
         [0017]    It is known that the use of a coherent receiver enables the signal degradation due to dispersion to be removed via linear electrical filtering. However, because of their high cost, very few coherent optical receivers have been installed, and the cost of replacing installed receivers with the high-performance coherent receivers is prohibitive. 
         [0018]    The majority of receivers installed in modern optical communications networks are of the direct detection type. Due to the well known squaring effect in these receivers, electrical processing of the output signal y(t) is capable of compensating only a very limited amount of dispersion. See, for example, “Performance of Smart Lightwave Receivers with Linear Equalization” Cartledge et al, J Lightwave Tech, Vol. 10, No. 8, August 1992, pp. 1105-1109; and “Electrical Signal Processing Techniques in Long-Haul Fiber-Optic Systems” Winters et al, IEEE Trans. Comms, Vol. 38, No. 9, September 1990, pp. 1439-1453. 
         [0019]    In addition to the squaring effect in conventional receivers, optical modulators also frequently display a non-linear performance characteristic. Nonlinearity compensation of modulators can be implemented in the electrical domain (see, for example “Reduction of Dispersion-Induced Distortion in SCM Transmission Systems by using Predistortion-Linearized MOW-EA Modulators”, Iwai et al, Journal of Lightwave Tech., Vol. 15, No. 2, February 1997, pp. 169-177). It is also possible to provide the nonlinear compensation in the optical domain (see “Mitigation of Dispersion-Induced Effects using SOA in Analog Optical Transmission”, Jeon et al, IEEE Photonics Technology Letters, Vol. 14, No 8, August 2002, pp. 1166-1168 and “Predistortion Techniques for Linearization of External Modulators”, Wilson, 1999 Digest of the LEOS Summer Topical Meetings, 1999, pp. IV39-IV40), or via hybrid optical/electrical domains (see, for example “Signal Distortion and Noise in AM-SCM Transmission Systems employing the Feedforward Linearized MQW-EA External Modulator”, Iwai et al, Journal of Lightwave Tech., Vol. 13, No. 8, August 1995, pp. 1606-1612 and U.S. Pat. No. 5,148,503). 
         [0020]    While modulator non-linearity can be compensated, the output signal y(t) detected at the Rx end of the communications system contains distortion components due to non-linearities in both the modulator (transmitter)  2  and the receiver  6 , as well due to optical dispersion within the link  4 . These distortions are compounded, one upon the other, and it is difficult to distinguish distortions of the output signal y(t) due to non-linearity of the modulator  2  from those resulting from non-linearity of the receiver  6 . It is also difficult to distinguish these effects from dispersion. 
         [0021]    Accordingly, a cost-effective technique for mitigating the effects of dispersion on high bandwidth optical signals remains highly desirable. 
       SUMMARY OF THE INVENTION 
       [0022]    Accordingly, an object of the present invention is to provide a technique for mitigating effects of dispersion on high bandwidth optical signals in an optical communications system. 
         [0023]    This object is met by the combination of elements defined in the appended independent claims. Option elements of the invention are defined in the dependent claims. 
         [0024]    Thus an aspect of the present invention provides a method of compensating optical dispersion of a communications signal conveyed through an optical communications system. A compensation function is determined that substantially mitigates the chromatic dispersion imparted to the communications signal by the optical communications system. The communications signal is then modulated in the electrical domain using the compensation function. 
         [0025]    The method of the invention can be implemented at either the Tx or Rx ends of the communications system, or may be divided between both ends, as desired. In cases where the method of the invention is implemented in the transmitter, the communication signal in the form of an input electrical signal (e.g. a substantially undistorted binary signal) is digitally filtered using the compensation function to generate a predistorted signal. The predistorted signal is then used to modulate an optical source to generate a corresponding predistorted optical signal for transmission through the optical communications system. This arrangement is particularly advantageous, because the predistorted signal can incorporate compensation for dispersion and component non-li neariti es throughout the system. Consequently, dispersion compensation can be effectively implemented independently of the type of detection . . direct or coherent) used in the receiver. 
         [0026]    In cases where the method of the invention is implemented in the receiver, the received optical signal is converted into a corresponding received electrical signal, which includes distortions due to dispersion imparted on the optical signal by the optical communications system. The received electrical signal is then sampled (e.g. using an analog-to-digital converter) and digitally filtered using the compensation function to generate an output electrical signal which is a substantially undistorted version of the original communications signal. 
         [0027]    Thus the present invention compensates optical dispersion by digitally filtering a communications signal in the electrical domain. This filtering of the communications signal is governed in accordance with the required compensation function of the communications system transfer function and the non-linearity compensation required. With this arrangement, arbitrary optical dispersion imparted by the communications system can be compensated in such a manner that a comparatively undistorted output signal is generated at the receiving end of the communications system. 
     
    
     
       BRIEF DESCRIPTION OF THE DRAWINGS 
         [0028]    Further features and advantages of the present invention will become apparent from the following detailed description, taken in combination with the appended drawings, in which: 
           [0029]      FIGS. 1A and 1B  are block diagrams schematically illustrating transmission of an input data signal through a conventional optical communications system; 
           [0030]      FIG. 2  is a block diagram schematically illustrating transmission of an input signal through an optical communications system in accordance with an embodiment of the present invention; 
           [0031]      FIG. 3  is a block diagram schematically illustrating principal components and operations of a compensation processor in accordance with a first embodiment of the present invention. 
           [0032]      FIG. 4  is a block diagram schematically illustrating principal components and operations of a compensation processor in accordance with a second embodiment of the present invention; 
           [0033]      FIG. 5  is a block diagram schematically illustrating principal components and operations of a compensation processor in accordance with a third embodiment of the present invention; 
           [0034]      FIGS. 6A and 6B  are block diagrams schematically illustrating principal components and operations of a compensation processor in accordance with a fourth embodiment of the present invention; and 
           [0035]      FIGS. 7A and 7B  are block diagrams schematically illustrating principal components and operations of a compensation processor in accordance with a fifth embodiment of the present invention. 
       
    
    
       [0036]    It will be noted that throughout the appended drawings, like features are identified by like reference numerals. 
       DETAILED DESCRIPTION OF THE PREFERRED EMBODIMENT 
       [0037]    The present invention provides a method and system for compensation of chromatic dispersion in an optical communications system.  FIG. 2  is a block diagram schematically illustrating principal operations in accordance with the method of the present invention. 
         [0038]    As shown in  FIG. 2 , the optical communications system is represented by electrical-to-optical (E/O) and optical-to-electrical (O/E) converters  2  and  6  separated by an optical link  4  represented by a system transfer function T(ω). In accordance with the present invention, signal distortions introduced by the system transfer function T (ω) are compensated by deriving a compensation function C(ω) that optimizes system performance. A compensation processor  10  uses the compensation function C(ω) to filter the input signal x(t) in the electrical domain, thereby producing a predistorted input signal x 1 (t)  12  given by x 1 (t)=x(t) conv C(ω) where “conv” is the convolution function, 
         [0039]    The predistorted input signal x 1 (t)  12  is then converted to a corresponding predistorted optical signal E 1   IN (ω) by the E/O converter  2  and transmitted through the optical link  4  to the receiver. Within the receiver, the incoming optical signal E 1   OUT (ω) is converted by the O/E converter  6  into a corresponding output signal y 1 (t). As may be seen in  FIG. 2 , the received. optical signal E 1   OUT (ω) is the predistorted optical signal E′ IN (ω) multiplied by the transfer function T(ω) of the optical communications system. When the distortions introduced by the compensation function C(ω) exactly counterbalance those introduced by the system transfer function T(ω), the output signal y 1 (t) generated by the O/E converter  6  will be a substantially undistorted version of the original input data signal x(t). Thus the present invention provides a technique of compensating optical distortions impressed upon optical signals traversing the optical link  4 , by predistorting the input data signal x(t) in the electrical domain at the transmitting end of the optical link  4 . Because dispersion compensation is accomplished in the electrical domain, a substantially arbitrary compensation function C(ω) can be implemented, thereby facilitating effective compensation of even severe optical dispersion. 
         [0040]    Various methods may be used to derive the compensation function C(ω). In the example of  FIG. 2 , the optical signal E 1   OUT (ω) at or near the O/E converter  6  is monitored (at  14 ), in order to detect signal quality parameters indicative of dispersion in the optical communications system. in preferred embodiments, the signal quality parameters comprise a direct measurement of dispersion as a function of wavelength across the wavelength band of interest. However, other signal quality parameters such as, for example, the bit error rate or eye closure may be used as proxies for the dispersion. Any of the signal quality parameters may be detected based on an optical signal obtained by tapping the optical link  4  (as shown by solid lines in  FIG. 2 ), or alternatively by analysis of the output signal y(t) generated by the E/O converter  6  (as shown by the dashed line in  FIG. 2 ), In either case, a compensation function C(ω) which optimizes the detected parameters can then be derived (at  16 ) deterministically and/or adaptively, using known techniques. 
         [0041]    It should be noted that the functional step of deriving the compensation function C(ω) can be implemented by any suitable combination of hardware and software, which may be co-located with the receiver, the transmitter, or any other location. In embodiments in which the detected parameters comprise direct measurement of dispersion, the compensation function C(ω) can be derived to minimize (and preferably eliminate) the total dispersion. Where bit error rate and/or eye closure are used as proxies, then the compensation function C(ω) would be derived to optimize these values. 
         [0042]      FIG. 3  is a block diagram schematically illustrating principal elements and operations of the compensation processor  10 , in accordance with a first embodiment of the present invention. As shown in  FIG. 3 , the input signal x(t) is filtered by a digital filter  18  which accepts the compensation function C(ω) as an input. Various known digital filter types may be used to implement the digital filter  18 , such as, for example, Finite Impulse Response (FIR) filters, Infinite Impulse Response (DR) filters, and Fast Fourier Transform (FFT filters). Alternatively, the digital filter  18  may be implemented using a Random Access Memory Look-up Table (RAM LUT), as will be described in greater detail below with reference to  FIGS. 4-7 . In either case, the digital filter  18  generates successive sample values  20  of the predistorted signal x 1 (t)  12 , at a sample rate which is about double the bit-rate of the input signal. A high-speed digital to analog converter (DAC)  22  can then be used to convert these sample values  20  into an analog predistorted signal x 1 (t)  12 . If desired, the analog predistorted signal x 1 (t)  12  can be conditioned, for example by means of a filter  24  and a low noise amplifier (LNA)  26 , in a conventional manner, to remove out-of-band noise and to scale the amplitude of the analog signal to the dynamic range of the E/O converter  2 . In the illustrated embodiment, the E/O converter  2  comprises a tuned optical source  28  such as a narrow band laser coupled to a conventional optical modulator  30 . In this case, the analog predistorted signal x 1 (t)  12  can be used as an input to control the optical modulator  30  in a manner known in the art. 
         [0043]    As mentioned above, the digital filter  18  may be implemented in a variety of ways.  FIG. 4  schematically illustrates an embodiment in which the digital filter  18  is implemented using a RAM LUT  32 . This technique exploits the fact that the input signal x(t) is a substantially undistorted binary signal, in which successive bits can be unambiguously discriminated. This greatly simplifies the problem of digitally filtering the input signal x(t), because a direct relationship can be defined between the input signal x(t) and each sample value  20  of the predistorted signal x 1 (t)  12 . 
         [0044]    As shown in  FIG. 4 , successive bits of the input signal x(t) are latched through a serial-to-parallel converter (SPC)  34  (e.g., a shift register) which converts the serial bit stream into a parallel bit stream  36  having a width of N bits. In the illustrated embodiment N=8, it being understood that other values of N may be used as desired. Each N-bit word of the parallel data stream  36  is then used as an index value to access a random access memory (RAM) look-up table  32  having 2 N  registers (not shown). With this arrangement, one or more M-bit (where M will generally be at least four) sample values  20  of the predistorted signal x 1 (t)  12  corresponding to each N-bit word can be calculated and stored in each register of the RAM LUT. As each N-bit word of the parallel data stream is latched into the RAM LUT, the corresponding M-bit sample value(s) of the predistorted signal x 1 (t)  12  is (are) latched out of the RAM LUT  32 . It should be noted that, in order to facilitate accurate synthesis of the predistorted signal x 1 (t)  12  at the output of the DAC  22 , the Nyquist sampling theorem must be respected. In this case, each register of the RAM LUT  32  will store at least two successive sample values  20  for each N-bit word of the parallel data stream. Because the RAM LUT  32  performs a substantially linear filtering function, it is possible to construct the LUT  32  as a set of two or more Random Access Memory blocks (not shown), if desired. In this case, each RAM block stores a respective portion of the desired numerical value  20  of the predistorted signal component. Thus the outputs generated from each RAM block can be digitally summed, in a conventional manner, to produce the desired numerical value  20 . This arrangement allows the LUT  32  to be larger than can conveniently be accommodated within a single RAM block. 
         [0045]    Various methods may be used to calculate each of the digital values  20  stored in the look-up table  32 . In the example of  FIG. 4 , the compensation function C(ω) (derived at  16 ) is used to calculate (at  38 ) respective M-bit sample values for each of the 2 N  possible N-bit words. Each M-bit sample value can then be stored in the appropriate RAM LUT register indexed by its respective N-bit word. 
         [0046]    Because chromatic dispersion causes a time domain distortion of an input signal, the sample value of the predistorted input signal  12  at a particular instant (t) will necessarily be a function of the analog waveform of the input signal x(t) within a time window that brackets the instant in question. The width of the time window, measured in symbols, will generally be a function of the maximum dispersion (D) for which compensation is to be provided; the bandwidth (B) of the optical signal; and the symbol interval (S) of the optical signal. For example, consider an optical communications system in which the transmitter generates an optical signal having a bandwidth of B nanometers and a symbol interval of S picoseconds/symbol. In this case, the maximum dispersion (D) that can be compensated is given by the equation D=N·(S/B), where N is the width of the time window, measured in symbols. It will be appreciated that the selected value of N will limit the maximum dispersion (D) that can be effectively compensated. In general, the value of N will be selected based on the expected maximum dispersion of the optical communications system. 
         [0047]    In the example of  FIGS. 3 and 4 , the look-up table  32  uses N= 8  successive bits of the input signal x(t) to reference successive sample values  20  of the predistorted signal  12 . In this case, the time window used for calculating each sample value of the predistorted signal spans a total of N=8 symbols. 
         [0048]    Following the discussion above, it will be seen that each sample value  20  stored in the look-up table  32  can readily be calculated (at  38 ) by applying the derived compensation function C(ω) to each one of the  2 . possible N-hit words. For each N-bit word, the calculated sample value can then be stored in the lookup table register that is indexed by the N-bit word in question. This process will result in the look-up table  32  being loaded with pre-calculated sample values  20  of the predistorted signal  12  which will be accessed, in sequence, as successive bits of the input signal x(t) are latched through the serial-to-parallel converter  34 . 
         [0049]    It will generally be advantageous to arrange the RAM LUT  32  to output more than one numerical value  20  of the predistorted signal  12  for each bit of the input signal x(t). This can readily be accomplished by calculating the required numerical values  20  for each N-bit word, and storing the resulting set of numerical values  20  in the appropriate register. As each bit of the input signal x(t) is latched through the serial-to-parallel converter  34 , all of the numerical values calculated for each unique N-bit word will be output, in an appropriate sequence, from the RAM LUT  32 . 
         [0050]    In the foregoing discussion, it was assumed that both the DAC  22  and the optical modulator  30  are fully linear, so that these components do not introduce any distortions beyond those accounted for by the system transfer function T(ω). Depending on how the system transfer function T(ω) is defined, this approach may yield satisfactory results. However, it may be desirable to treat the transfer function T(ω) of the optical fiber span  4  separately from those of the DAC  22  and modulator  30 , in which case the compensation function C(ω) will not account for distortions introduced by these elements. 
         [0051]    In many cases, the performance of the various devices forming the signal path between the DAC  22  and modulator  30 , (i.e. the DAC  22 , filter  24 , LNA  26  and modulator  30 ) are well characterized, and this knowledge can be used to calculate a mapping which adjusts the sample values  20  generated by the RAM LUT  32  to compensate for any non-ideal response of these devices. However, improved performance can be obtained by sampling the optical waveform output from the E/O converter  2 , and comparing the instantaneous amplitude of the optical waveform with the corresponding sample value output by the RAM LUT. Thus, as shown in  FIG. 4 , the optical waveform output from the E/O converter  2  is tapped (at  40 ), converted into a corresponding electrical signal (at  42 ), and sampled by an analog-to-digital (A/D) converter  44 . The digital sample  46  generated by the A/D converter  44  is then supplied to a non-linear processor  48 , which also receives sample values  20  of the predistorted signal  12  from the RAM LUT  32 . By properly accounting for propagation delays, it is readily possible to match each sample value  20  with its corresponding digital sample  46  from the AID converter  44 . Comparison between these two values ( 20  and  46 ) facilitates calculation of a mapping which can be applied to the sample values  20  to compensate any non-ideal response of the entire signal path between (and including) the DAC  22  and the E/O converter  2 , and thereby yield a desired waveform of the predistorted optical signal E 1   IN (ω) at the output of the E/O converter  2 . 
         [0052]    As may be seen in  FIG. 4 , the mapping calculated by the non-linear processor  48  can be used to drive a non-linear compensator  50  implemented as a second RAM look-up table positioned between the digital filter  18  and the DAC  22 . Alternatively, the mapping can be used to adjust (at  52 ) the M-bit sample values  20  calculated (at  38 ) using the compensation function C(ω). In the latter case, sample values  20  output from the digital filter  18  will combine compensation for both dispersion of the link  4  and nonlinearities of the DAC  22  and E/O converter  2 . 
         [0053]    In the embodiments of  FIGS. 3 and 4 , a single compensation path is provided for generating the predistorted signal x 1 (t)  12  based on the input signal x(t). As will be appreciated, such an arrangement is suitable for modulating a single dimension (e.g., either amplitude or phase) of the input signal x(t). Accordingly, the predistorted signal x 1 (t)  12  of the embodiments of  FIGS. 3 and 4  will comprise an amplitude or phase modulated version of the original input signal x(t). However, the system transfer function T (ω) of the optical communications system will normally be complex, so that an optical signal traversing the communications system will suffer distortions in both phase and amplitude. This issue is addressed by the embodiments of  FIGS. 5-7 . 
         [0054]      FIG. 5  is a block diagram schematically illustrating an embodiment of the present invention in which a 2-dimensional compensation processor  10  is used to compensate effects of a complex system transfer function T(ω). In general, the 2-dimensional compensation processor  10  provides an independent compensation path for each dimension of the communications system for which compensation is to be provided. In the embodiment of  FIG. 5 , it is desired to provide compensation for both amplitude and phase distortions. In this case, a pair of compensation paths generate respective output signals I and Q (at  56  and  58 ) that represent respective orthogonal (In-phase and Quadrature) components of the predistorted signal  12 . 
         [0055]    The two output signals I and Q are then supplied to a suitable 2-dimensional optical modulator  30  capable of modulating the amplitude and phase of light generated by the optical source  28 . Various optical modulators capable of providing this functionality are known in the art, such as, for example, Mach Zehnder modulators. 
         [0056]    As will be appreciated, the 2-dimensional compensation processor  10  can be implemented using multiple compensation paths to generate the predistorted signal x 1 (t)  12  in any desired format, such as, for example, polar coordinates. The only limitation here is that a suitable optical modulator  30  must be provided for modulating the appropriate optical components in response to the signal components generated by the 2-dimensional compensation processor  10 . 
         [0057]      FIG. 6A  is a block diagram illustrating an alternative embodiment of the 2-dimensional compensation processor  10  of  FIG. 5 . In this case, the pair of parallel N×M RAM LUTs  32  of the digital filter  18  are replaced by a single N×2M look-up table, which outputs parallel M-bit sample values  20  for each N-bit sequence of the input data x(t). As in the embodiment of  FIG. 5 , these M-bit sample values  20  represent respective orthogonal (e.g. In-phase and Quadrature) components of the predistorted signal x 1 (t)  12 . Similarly, other signal formats, such as polar coordinates, may equally be used, provided only that the optical modulator  30  is capable of modulating the appropriate optical components in response to the signals generated by the multi-dimensional compensation processor  10 . 
         [0058]    In the embodiment of  FIGS. 4-6 , the input signal x(t) is supplied directly to the SPC  34 , which converts the serial bit stream x(t) into successive N-bit words of the parallel data stream  36 . In some cases, however, it may be desirable to provide a converter  64  to map the serial bit stream x(t) into n-bit symbols  66  upstream of the SPC  34 , as shown in  FIG. 6B . This arrangement would be particularly suitable for Quadrature Phase Shift Keying (QPSK) encoded traffic, for example. in such cases, the SPC  34  will operate to convert each bit of the n-bit symbol stream  66  into successive N-bit words of a corresponding parallel data stream  36 . The values stored in each register of the RAM LUT are calculated to implement a complex filtering operation to output appropriate parallel M-bit sample values  20  of the predistorted signal  12 . 
         [0059]    Due to various factors (such as, for example imperfections, or electrical cross-talk) the orthogonal (i.e. In-phase and Quadrature) control signals  56 ,  58  may in fact produce a non-orthogonal response in the ED converter  2 . Accordingly, in the embodiment of  FIG. 6A  the non-linear compensator  50  is provided as a single 2M×2M RAM LUT, instead of separate devices for each compensation path. Each of the 2 2M  registers of the non-linear compensator  50  stores previously calculated output numerical values for both control signals  56 ,  58 . 
         [0060]    These output numerical values may be calculated in accordance with a mapping function derived from the combined lightwave emerging from the E/O converter  2 , as described above with reference to  FIG. 4 , With this arrangement, the non-linear compensator  50  can readily implement a 2-D mapping which adjusts both components of the predistorted signal  12  in a complementary manner, to thereby compensate for any non-orthogonal response of the E/O converter  2 . As mentioned above, the non-linear compensator  50  may be implemented as a separate device (from the RAM LUT  32 ), or may be “embedded within the RAM LUT  32 ” by applying the mapping function to adjust the sample values stored in the RAM LUT  32 . 
         [0061]    As may be appreciated, in order to successfully compensate dispersion of the link  4 , it is important to maintain precise alignment between each of the signal components  56 ,  58  of the predistorted signal x 1 (t)  12  supplied to the optical modulator  30 . However, the effects of independent DACs  22 , filters  24  and LNAs  26  for each signal component may cause differential propagation delays between the non-linear compensator  50  and the optical modulator  30 . Such differential delay can be compensated by means of a digital filter  60  located in at least one of the signal paths. In general, for an n-dimensional compensation processor  10  (i.e. generating n signal components of the predistorted signal  12 ) differential propagation delays can be compensated by providing a respective digital filter  60  in at least (n−1) compensation paths. For convenience, it may be desirable to provide a digital filter  60  in all of the signal paths, as illustrated in  FIG. 6A . In any event, each digital filter  60  can be controlled in a known manner to impose an selected delay, which is calculated to compensate for the differential propagation delays experienced by each of the signal components. 
         [0062]    If desired, the non-linear compensator  50  can also be used to implement a mapping between different signal formats. For example, in the embodiments of  FIGS. 7A and 7B , the digital filter  18  is designed to generate the predistorted signal x 1 (t)  12  in the form of In-phase and Quadrature components. In addition to compensating non-ideal response of the signal paths between the DACs  22  and the E/O converter  2 , the 2M×2M mapping implemented in the non-linear compensator  50  may also be used to convert these I and Q signal components into a corresponding pair of Amplitude A and Phase φ component samples (i.e. following a polar coordinate system), as shown in  FIG. 7A . Subsequent digital-to-analog conversion of the phase sample by the DAC  22   a  yields a phase control signal  56  which can be used to drive a conventional phase shifter  62  to modulate the phase of the optical signal. The amplitude of the optical signal can then be controlled using a conventional optical modulator (such as an electroabsorptive modulator (EAM) or a variable optical attenuator) in accordance with the amplitude control signal component  58 . 
         [0063]    As shown in  FIG. 7B , the digital filter  60   a  can be controlled to calculate the time derivative of the phase component, to yield a frequency sample f(n). In embodiments in which the non-linear compensator  50  is incorporated into the RAM LUT  32 , the digital filter  18  can generate the predistorted signal x 1 (t)  12  in the form of Amplitude and frequency components directly. In either case, subsequent digital-to-analog conversion of the frequency sample f(n) by the DAC  22   a  yields a frequency control signal f(t)  56  which can be used to drive the optical source  28  directly. This operation exploits the known characteristic of many narrow-band lasers, which exhibit a frequency dependence on the input current. Accordingly, within a certain range, the frequency of the optical signal emitted by the optical source  28  can be controlled by varying the input current. Here again, the amplitude of the optical signal can be controlled using a conventional optical modulator (such as an electroabsorptive modulator (EAM) or a variable optical attenuator) in accordance with the amplitude control signal component  58 . 
         [0064]    The embodiment(s) of the invention described above is (are) intended to be exemplary only. The scope of the invention is therefore intended to be limited solely by the scope of the appended claims.