Patent Publication Number: US-6671465-B1

Title: Apparatus and methods for improving linearity and noise performance of an optical source

Description:
FIELD OF THE INVENTION 
     The present invention relates generally to optical signal sources for use in optical signal transmission systems, and more particularly to an optical signal source which utilizes a feedback or feedforward technique to provide improved linearity and noise performance without unduly increasing the cost of the source. 
     BACKGROUND OF THE INVENTION 
     In many optical signal transmission applications, it is important for the optical source to exhibit excellent linearity and noise performance. One such application is in high-quality analog optical fiber systems for providing Community Antenna Television (CATV) service. In such a system, an analog CATV signal including several channels of video is modulated onto one or more optical carrier signals for distribution via optical fiber from a cable system head end. Conventional systems for transmitting analog CATV signals over optical fiber generally require highly-linear, low-noise lasers and/or optical modulators. These types of optical signal sources are usually very expensive, and their excessive cost has been a significant impediment to the widespread deployment of fiber-to-the-home transmission systems. The expensive optical signal sources include, for example, analog-grade distributed feedback (DFB) lasers, as well as continuous wave (CW) lasers, such as yttrium aluminum garnet (YAG) and yttrium lanthanum fluoride (YLF) lasers, which require external modulators. 
     Conventional optical transmission systems are described in, for example, U.S. Pat. No. 5,548,436 entitled “Optical Transmission System” and issued Aug. 20, 1996 to Ramachandran et al., U.S. Pat. No. 5,457,557 entitled “Low Cost Optical Fiber RF Signal Distribution System” and issued Oct. 10, 1995 to Zarem et al., U.S. Pat. No. 5,450,508 entitled “Apparatus and Method for Optical Fiber Alignment Using Adaptive Feedback Control Loop” and issued Sep. 12, 1995 to Decusatis et al., and U.S. Pat. No. 5,384,651 entitled “Optical Transmission System” and issued Jan. 24, 1995 to Van de Voorde et al. Unfortunately, none of these conventional systems are configured to permit a low-cost optical source, such as a digital-grade DFB laser diode or a Fabry-Perot laser diode, to be used in place of an expensive highly-linear, low-noise optical source. 
     A number of techniques for improving the linearity or noise performance of an optical source are known. These techniques include the use of pre-distortion circuits, and feedforward approaches in which a second optical source is used. However, conventional pre-distortion circuits generally correct for only source nonlinearity, and an alternative mechanism is therefore required to correct for the source noise. Also, pre-distortion circuits generally require numerous critical adjustments which increase the cost and complexity associated with the source. The second optical source used in conventional feedforward approaches not only involves considerable additional cost and complexity, but introduces wavelength control issues. 
     It is therefore apparent that a need exists for techniques which provide the linearity and noise performance required in analog signal transmission over optical fiber and other important applications, without the excessive cost and complexity associated with conventional highly-linear, low-noise optical sources. 
     SUMMARY OF THE INVENTION 
     The present invention improves the linearity and noise performance of an inexpensive optical source using feedback or feedforward techniques. In accordance with a first aspect of the invention, an inexpensive optical source, such as a digital-grade DFB laser diode or a Fabry-Perot laser diode, has its noise and distortion substantially eliminated by feedback. The optical signal source is provided with a feedback path which corrects for nonlinearity and noise-induced variations in the source output. A modulation signal, such as a broadband analog CATV signal, is applied to the optical source along with a broadband feedback signal. The broadband feedback error signal is generated using a high-speed photodiode in the feedback path to detect a portion of the output optical signal generated by the optical source. The broadband feedback error signal is passed through a delay compensation filter to correct for group delay variations across its bandwidth, and then applied to an input of the optical source to correct source nonlinearity and noise. This aspect of the invention is also particularly well-suited for use with digital quadrature-amplitude modulation (QAM) signals, digital n-level vestigial sideband (VSB) signals, and other digital modulation signals which have a non-constant modulation envelope. 
     In an illustrative embodiment of the invention using the above-described feedback technique, a high-speed photodiode is utilized in a closed feedback loop as a monitoring device to monitor the output of an inexpensive laser diode. The high-speed photodiode is generally substantially more linear than the inexpensive laser diode, and therefore may be used to generate an error signal which can be used to improve the linearity of the laser diode. The high-speed photodiode may have a gain-bandwidth product greater than about 500 MHz, such that the operating bandwidth of the laser diode is substantially increased, while its linearity and noise performance are improved. The feedback loop includes a delay compensation filter which compensates for group delay variations in the feedback error signal across a broad bandwidth. 
     A second aspect of the invention relates to the use of a feedforward technique to improve the linearity and noise performance of an inexpensive optical source. An error signal generated by monitoring the output of the optical source is converted to a frequency band outside of the modulation signal bandwidth before being applied to an input of the optical source. A receiver receiving the optical signal then detects both the converted error signal and the modulation signal, and uses the detected error signal to correct the detected modulation signal for nonlinearity and noise effects of the optical source. 
     An illustrative embodiment of this second aspect of the invention includes an optical signal transmitter in which the output of the high-speed photodiode is first low pass filtered, and then applied to a first signal combiner which also receives a coupled portion of the input modulation signal. The first signal combiner generates an error signal by subtracting the output of the lowpass filter and the coupled portion of the modulation signal. The error signal is then applied to an input of a mixer which mixes the error signal with a carrier signal generated by a local oscillator in order to convert the error signal to a frequency band outside the modulation signal frequency band. The converted error signal is combined with the modulation signal in a second signal combiner, such that both the modulation signal and the error signal are applied to the optical source. An output optical signal generated by such a source thus serves as an optical carrier for both the modulation signal and the error signal. The resulting optical signal is detected in a receiver, and the modulation signal portion and error signal portion of the detected signal are separately processed to recover the respective modulation and error signals. The error signal is then used in the receiver to correct the effects of source nonlinearity and noise on the modulation signal. An optical signal transmission system in accordance with the invention includes the above-described transmitter and at least one receiver, and an optical distribution network for distributing an optical signal from the transmitter to the receiver. The distribution network may include passive splitters, multiplexers, demultiplexers and other types of optical signal routers. Multiple optical signals may be routed within the transmission system using multiple transmitters in conjunction with well-known wavelength-division multiplexing (WDM) techniques. 
    
    
     An optical source configured in accordance with the present invention can provide linearity and noise performance comparable to that heretofore provided only by substantially more complex and expensive optical sources. The invention thus allows inexpensive optical sources, such as digital-grade DFB laser diodes or Fabry-Perot laser diodes, to be used in place of expensive highly-linear, low-noise sources in analog CATV signal transmission and other important applications, without undermining the linearity and noise performance of the system. Compared to conventional pre-distortion circuits, which generally correct for only source nonlinearity, the above-described feedback and feedforward techniques correct for both nonlinearity and source noise while avoiding the numerous critical adjustments required in many predistortion circuits. Compared with other feedforward approaches, the techniques of the invention avoid the need for a second optical source and any wavelength-control issues associated with a second source. These and other features and advantages of the present invention will become more apparent from the accompanying drawings and the following detailed description. 
     BRIEF DESCRIPTION OF THE DRAWINGS 
     FIG. 1A shows an exemplary embodiment of the invention in which feedback is applied directly to the optical source. 
     FIG. 1B shows a frequency allocation graph for television signals in a CATV system, a DBS system or other similar signal distribution system. 
     FIG. 1C shows plots of exemplary delay characteristics as a function of frequency for the delay compensation filter in the embodiment of FIG.  1 A. 
     FIG. 2 shows a feedforward embodiment of the invention implemented in a transmitter and receiver of an optical signal transmission system by generating, transmitting and receiving an error signal which is characteristic of the output of an inexpensive optical source. 
     FIGS. 3A,  3 B and  3 C illustrate various signal spectra in the optical signal transmission system of FIG.  2 . 
    
    
     DETAILED DESCRIPTION OF THE INVENTION 
     The present invention will be illustrated below in conjunction with exemplary optical signal sources and signal transmission systems. It should be understood, however, that the invention is not limited to use with any particular type of optical signal source or system, but is instead more generally applicable to any optical signal transmission system in which it is desirable to improve the linearity and noise performance of the optical source without unduly increasing its cost and complexity. Moreover, the invention is suitable for use in many applications other than the illustrative optical fiber-based analog signal transmission system to be described below, including digital signal transmission applications. For example, the invention is particularly well-suited for use with digital quadrature-amplitude modulation (QAM) signals, digital n-level vestigial sideband (VSB) signals, and other digital modulation signals which have a non-constant modulation envelope. 
     The term “optical source” as used herein is intended to include digital-grade DFB laser diodes, Fabry-Perot laser diodes and any other source capable of generating an optical signal. An “inexpensive” optical source is an optical source, such as a digital-grade DFB laser diode or Fabry-Perot laser diode, which is generally less complex and therefore less costly than a highly-linear, low-noise optical source, such as an analog-grade DFB laser, utilized in a conventional optical signal transmission system. The term “feedback” refers generally to the process of supplying an error signal generated from an optical source output to an input of the optical source. The term “feedforward” as used herein refers generally to the process of generating an error signal from the output of an optical source, and supplying it to a receiver for use in correcting a signal received from the optical source. The terms “convert” or “converter” in the context of error signal frequency conversion are intended to encompass both upconversion and downconversion of the error signal. For example, although the illustrative feedforward embodiments described in conjunction with FIG. 2 herein utilize upconversion of an error signal in a transmitter and downconversion of the error signal in a receiver, other embodiments of the invention could utilize downconversion of the error signal in the transmitter and upconversion of the error signal in the receiver. 
     FIG. 1A shows an exemplary apparatus  10  in accordance with the present invention for generating a highly-linear, low-noise optical signal using an inexpensive optical source. The apparatus  10  includes an input  12  which receives a digital or analog input electrical signal to be modulated onto an optical carrier signal. The input signal may be an analog RF video signal, a stream of digital data, or any other suitable modulation signal. The input signal is applied via a resistor R to an input of an amplifier  14 . In accordance with the present invention, the amplifier  14  is configured as a single-stage amplifier or other suitable low-delay amplifier. The amplifier  14  converts the input signal to a current signal which drives a laser diode optical source  16 . Although not shown in FIG. 1, those skilled in the art will recognize that laser diode  16  will be configured to include appropriate bias circuitry. The optical source in this embodiment may be a digital-grade DFB laser diode, a Fabry-Perot laser diode, or another type of inexpensive optical source. As noted above, such inexpensive optical sources generally do not exhibit sufficient linearity or sufficiently low noise to be suitable for use in analog signal transmission and other important applications. These applications have heretofore been required to utilize a substantially more expensive highly-linear, low-noise optical source. The apparatus  10  of FIG. 1A is configured such that linearity and noise performance of an inexpensive optical source, such as the laser diode  16 , is improved to the point that the source can be utilized for analog signal transmission. 
     The laser diode optical source  16  generates an optical carrier signal which is coupled onto an optical fiber  18  as illustrated in FIG.  1 A. The optical carrier signal is modulated by the signal applied to the input  12 . A portion of the optical signal generated by laser diode  16  is also coupled to a high-speed positive-intrinsic-negative (PIN) photodiode  20  arranged adjacent to the laser diode  16 . The photodiode  20  is biased by a voltage source  22 , and generates a current in a feedback path  24  which is proportional to the amplitude of the optical signal from laser diode  16 . This current is supplied as a broadband feedback signal to the input of the low-delay amplifier  14 , such that it is subtracted from the input signal applied to the laser diode  16 . The feedback path  24  also includes a delay compensation filter  26  arranged between the photodiode  20  and the input of the low-delay amplifier  14 . The delay compensation filter  26  compensates for group delay variation across the broad bandwidth of the feedback signal in a manner to be described in greater detail below. 
     The photodiode  20  monitors the linearity of the laser diode  16  by detecting changes in the amplitude of the optical signal output of laser diode  16 . The feedback path  24  ensures that the drive current supplied to the laser diode  16  is adjusted in accordance with the monitored optical signal amplitude, such that if the amplitude of the optical signal generated by laser diode  16  increases, the current generated by photodiode  20  increases, and the drive current supplied to laser diode  16  decreases. Conversely, if the amplitude of the optical signal decreases, the current generated by photodiode  20  decreases, and the drive current supplied to laser diode  16  increases. The feedback loop including low-delay amplifier  14 , photodiode  20  and feedback path  24  thus substantially increases the linearity of the laser diode source  16 , and allows it to operate over a much broader bandwidth than would otherwise be possible. 
     In accordance with the invention, the high-speed photodiode  20  may have a gain-bandwidth product greater than about 500 MHz. The high-speed photodiode  20  may also have a linearity which is on the order of 20 dB better than that of the laser diode  16 , such that the linearity of laser diode  16  is improved by about 20 dB. Furthermore, the feedback loop also acts to eliminate the effects of noise generated by the laser diode  16 . It should be noted that relatively inexpensive high-speed photodiodes, with gain-bandwidth products of as much as 2 GHz or more, are readily available. Such a photodiode when used with the low-delay amplifier in the configuration of FIG. 1A can provide laser diode  16  with an operating bandwidth on the order of several hundred MHz or more. These improvements in linearity and operating bandwidth permit an inexpensive optical source such as laser diode  16  to be utilized in a broadband analog signal transmission system, as well as in other applications which would otherwise require an expensive highly-linear, low-noise optical source. 
     As noted above, the delay compensation filter  26  is used to correct for group delay variations of the feedback signal in applications in which the analog signal modulating the laser diode  16  is a broadband signal. FIG. 1B shows a frequency allocation graph for a broadband television signal distribution system such as a CATV system, indicating the frequencies assigned to particular system channels. It is apparent from FIG. 1B that the required bandwidth increases substantially linearly with the number of channels supported by the system. A CATV system configured to distribute on the order of 75 channels requires a total bandwidth on the order of 550 MHz. This broad bandwidth requirement of analog fiber transmission systems necessitates the use of the delay compensation filter  26  in the feedback path  24 . 
     The compensation provided by filter  26  will now be described in greater detail. It will be assumed for simplicity of illustration that the signal applied to input  12  is a single frequency of the form sin (ωt) and that the feedback signal is of the form −sin(ωt−ωτ), where τ is the delay of the signal path including amplifier  14 , diodes  16  and  20 , and filter  26 . The combined signal E(t) applied to the input of amplifier  14  is then given by:          E        (   t   )       =         sin        (   ωt   )       -     sin        (     ωt   -   ωτ     )         =       -   2                     sin        (     ωτ   2     )                       cos        (     ωt   -     ωτ   2       )                           
     Without the delay compensation filter  26 , a delay τ on the order of 300 psec will allow the feedback path  24  to provide a 10 dB improvement in the linearity of source  16  over a broad bandwidth for input signal frequencies ƒ c  up to about 160 MHz, given that 20 log(2 sin(ωτ/2)=−10 yields ωτ=0.31 and ƒ c =0.31/(2πτ) or 160 MHz. The delay of the feedback path thus limits the degree to which the source nonlinearity can be corrected over a broad bandwidth. The delay compensation filter  26  is used to overcome this delay-related limitation for the “comb” of higher frequency signals used in CATV signal distribution. The CATV signal comb is generally composed of a number of distinct narrowband signals, one corresponding to each channel of the system, although the entire signal comb may collectively occupy a broad bandwidth on the order of 500 MHz or more. The delay compensation filter  26  provides an amount of delay sufficient to equalize the feedback signal path for each of the individual narrowband signals of a broadband CATV system. 
     It will now be shown that the filter  26  is able to provide this delay compensation in the typical case in which the modulation bandwidth of the individual narrowband channel signal is small relative to its carrier frequency ƒ c . Assume that each of the narrowband signals of the CATV system at the input  12  are single sideband versions of a simple amplitude modulated (AM) signal of the form: 
     
       
           V ( t )=sin(ω m   t )sin(ω c   t ) 
       
     
     where ω m  is the modulation frequency and ω c  is the angular carrier frequency. The equation for the corresponding single sideband AM signal, which is the type of signal typically utilized for television signal distribution, is given by: 
     
       
           V ′( t )=sin((ω c +ω m ) t ) 
       
     
     The filter  26  is designed to compensate for the delay at carrier frequency ƒ c  by setting the value of τ in accordance with the following equation:        τ   =       2                 π                 n       ω   c                       
     where n is greater than or equal to one. The delayed version V d ′(t) of the single sideband signal V′(t) is given by: 
     
       
           V   d ′( t )=sin((ω c +ω m )( t −τ)) 
       
     
     The combined signal E(t) at the input of amplifier  14  may then be expressed as: 
     
       
           E ( t )= V ′( t )− V   d ′( t )=sin((ω c +ω m ) t )−sin((ω c +ω m )( t −τ)) 
       
     
     which may be rewritten as:          E        (   t   )       =       -   2                     sin        (       (       ω   c     +     ω   m       )                     τ   2       )                       cos        (         (       ω   c     +     ω   m       )        t     -       (       ω   c     +     ω   m       )          τ   2         )                         
     Assuming ω c &gt;&gt;ω m  and setting τ=2πn/ω c =n/ƒ c  yields E(t)≈0, which indicates that error attributable to non-linearity and noise in the laser diode  16  in FIG. 1A can be corrected by the above-described feedback arrangement for a given narrowband input signal. In accordance with the invention, this type of equalization is provided for each of the narrowband signals in a given broadband CATV signal comb by altering the amount of delay provided by filter  26  at each of the narrowband signal frequencies. 
     FIG. 1C shows two exemplary delay characteristics for the delay compensation filter  26 . The characteristics plot τ=2πn/ω c =n/ƒ c  as a function of frequency for values of n=1 and n=2. These delay characteristics of filter  26  are designed such that the above-noted condition of E(t)≈0 is satisfied for each of a plurality of narrowband signals making up a broadband CATV signal spectrum. The amount of delay provided by the filter  26  at a given narrowband signal frequency takes into account the delay of the other elements in the signal path. It can be seen from the FIG. 1C characteristics that in order to provide a uniform delay equalization over a broadband comb of narrowband signals, the largest amounts of additional delay are required at the lowest signal frequencies. It should be noted that it may not be necessary to provide an extremely precise delay value at each of the narrowband frequencies. For example, consider a narrowband frequency of 500 MHz, and assume that a delay τ of 2.0 nsec produces E(t)≈0. If the filter  26  is configured such that a delay of 2.05 nsec is used at 500 MHz instead of the 2.0 nsec delay, the resulting error may be computed as −2 sin(ω c τ/2) or 0.15, which still provides an approximately 16 dB improvement in source linearity. Suitable techniques for designing filters with delay characteristics such as those shown in FIG. 1C are well known to those skilled in the art of filter design, and are therefore not described in detail herein. The above-described feedback delay compensation techniques may be used to improve optical source linearity and noise performance in a wide variety of other broadband signal transmission systems, including CATV systems configured with frequency allocations other than that shown in FIG. 1B, and direct broadcast satellite (DBS) systems such as those described in, for example, F. Baylin, “Miniature Satellite Dishes: The New Digital TV,” 2 nd  Edition, Baylin Publications, which is incorporated by reference herein. 
     FIG. 2 shows another exemplary embodiment of the present invention, implemented in an optical fiber-based analog signal transmission system  50 . This embodiment of the invention utilizes a feedforward technique to improve source linearity and noise performance in an optical system which includes an inexpensive optical source. The transmission system  50  includes a transmitter  52  and a receiver  54 . The transmitter  52  may be located in a head end of a CATV system, such that it modulates an input CATV signal onto an optical carrier signal which is supplied via an output fiber  56  to an input of an optical signal router  58  in an optical signal distribution network used to deliver CATV signals from the head end to one or more remote receivers. The optical signal router  58  may be a passive optical splitter or another type of optical signal router. In applications in which multiple optical signals from multiple transmitters or other optical sources are multiplexed or otherwise combined for distribution, the distribution network may utilize conventional wavelength-division multiplexing (WDM) techniques. The optical router  58  directs the modulated optical signal from transmitter  52  to an optical fiber  60  connected to an input of the receiver  54 . The receiver  54  demodulates the input optical carrier signal to recover the original CATV signal, which can be supplied to a CATV receiver for demodulation into one or more video or television signal channels. 
     FIG. 3A illustrates a frequency spectrum P 1  of an exemplary CATV signal which may be applied to a CATV input  62  of the transmitter  52  of FIG.  2 . The CATV signal in this example occupies a frequency band between a first frequency ƒ 1  and a second frequency ƒ 2  which may be, for example, 50 MHz and 550 MHz, respectively. The input CATV signal is applied via a signal combiner  64  to an inexpensive laser diode  66  or other type of optical source. As noted previously, conventional optical transmitters for analog CATV signals are generally required to utilize expensive highly-linear, low-noise optical sources such as analog-grade DFB lasers. An optical transmitter configured in accordance with the present invention, as will be described in greater detail below, is able to operate using an inexpensive optical source such as a digital-grade DFB laser diode or Fabry-Perot laser diode. The output of the laser diode  66  is an optical signal modulated by the analog CATV input signal. The modulated output optical signal is coupled onto an optical fiber  67 . 
     A portion of the output signal on optical fiber  67  is coupled via an optical coupler  68  to a detector  70 . The detector  70  may utilize a high-speed photodiode such as photodiode  20  of FIG.  1 A. The detector  70  detects the output signal from the laser diode  66  and generates an electrical signal which is proportional to the optical signal amplitude. The detected signal is filtered in a low-pass filter  72 , and is applied to one input of a subtractor  74 . The other input of the subtractor  74  is a portion of the input CATV signal coupled from input  12  via an RF coupler  76 . The subtractor  74  generates an error signal e(t) by subtracting from the output of low pass filter  72  the coupled portion of the input CATV signal. The error signal e(t) in this example is upconverted in a mixer  78  to a frequency ƒ c  generated by a local oscillator  80  and filtered in a filter  81 . The filtered, upconverted error signal  82  is then combined with the input CATV signal in signal combiner  64 . The CATV input signal and the upconverted error signal are thus both applied to the optical source  66 , and both modulate the output optical signal on fiber  67 . 
     FIG. 3B shows an illustrative frequency spectrum P 2  of the upconverted error signal, in an embodiment which utilizes double sideband, suppressed carrier (DSB-SC) modulation of the error signal onto the carrier frequency ƒ c . The FIG. 3B spectrum shows that the upconverted error signal in such an embodiment includes a lower sideband occupying a frequency range from ƒ 3  to ƒ 3 ′, and an upper sideband occupying a frequency range from ƒ 4  to ƒ 4 ′. It is apparent from FIG. 3B that the error signal in this illustrative embodiment is a broadband signal. The upconverted error signal frequency ranges may, but need not, be configured such that one or both of ƒ 3 ′−ƒ 3  and ƒ 4 ′−ƒ 4  are substantially equal to ƒ 2 −ƒ 1 . In the illustrative spectrum of FIG. 3B, the carrier signal at ƒ c  is permitted to leak slightly as shown, in order to facilitate carrier recovery in the receiver  54 . Although the mixer  78  and local oscillator  80  are configured in this embodiment to upconvert the error signal, alternative embodiments may utilize a frequency converter which downconverts the error signal. For example, if the input CATV signal occupies a band between about 400 and 550 MHz, the resulting error signal could be downconverted to a frequency band which is below 400 MHz. 
     FIG. 3C shows an exemplary frequency spectrum P 3  illustrating the complete optical signal spectrum on fiber  56  at the output of the transmitter  52 . It can be seen that the upper sideband of the upconverted error signal, occupying the frequency range from ƒ 4  to ƒ 4 ′ in FIG. 3B, has been removed by filtering in the filter  81 . The filter  81  in this embodiment may thus be configured as a lowpass or bandpass filter designed to reject the upper sideband of the upconverted error signal and to provide an appropriate amount of suppression of the carrier signal at ƒ c , while passing the lower sideband in the frequency range from ƒ 3  to ƒ 3 ′. It should be noted that alternative embodiments of the invention may utilize other types of modulation techniques for the error signal. For example, double sideband techniques may be used in which both the upper and lower sidebands of the upconverted error signal are applied via the signal combiner  64  to the input of the optical source  66 . 
     The receiver  54  receives the output optical signal generated by the transmitter  52 . As noted above, this optical signal is distributed from the transmitter  52  via optical signal router  58 , which may be a passive optical splitter. Other outputs of the signal router  58  may be connected to corresponding inputs of other receivers, which are not shown in FIG.  2 . In alternative embodiments, a given transmitted optical signal may pass through other signal routers, including multiplexers and demultiplexers in a multiple-source WDM embodiment, before arriving at the optical fiber  60  at the input of receiver  54 . The received optical signal is modulated by both the CATV signal and the above-described upconverted error signal generated in transmitter  52 . The receiver  54  includes a detector  84  which, like detector  70  in transmitter  52 , may be a high-speed photodiode. The detector generates an electrical signal which represents the modulation on the incoming optical signal, and has a frequency spectrum of the form shown in FIG.  3 C. The CATV signal portion of the detected electrical signal is recovered by filtering in a low pass filter  86  to remove the error signal portion. After passing through a delay element  88  and a signal combiner  90 , the detected CATV signal appears at the output of the receiver  54 . The delay element  88  provides broadband delay equalization for the detected CATV signal, in a manner generally analogous to that described previously in conjunction with the embodiment of FIG. 1A above, although it will be apparent to those skilled in the art that the sign of the delay is different in the FIG.  1 A and FIG. 2 embodiments. The delay element  88  may be replaced in an alternative embodiment with a suitable delay compensation filter. 
     The error signal portion of the detected electrical signal is processed by first coupling a portion of the detected signal via an RF coupler  92  to a bandpass filter  94 . The bandpass filter  94  is centered at the frequency ƒ c  of the upconverted error signal, and passes the upconverted error signal spectrum while rejecting the CATV signal spectrum. The upconverted error signal at the output of the bandpass filter  94  is applied to an input of a mixer  100 . The other input of the mixer  100  is the carrier frequency ƒ c  which is generated by coupling a portion of the error signal via an RF coupler  96  to a carrier recovery circuit  98 . The mixer  100  downconverts the upconverted error signal, and the resulting downconverted signal is filtered in a filter  102  to recover the error signal e(t). The filter  102  serves to reject undesired mixing products in the downconverted signal at the mixer output. The recovered error signal e(t) from the output of filter  102  is supplied to an input of the signal combiner  90 , and used to correct the CATV signal from the low pass filter  86 . The delay element  88  serves to align the CATV signal and error signal in order to eliminate any differential delay between the CATV and error signal paths over a broad bandwidth. It should be noted that in embodiments in which it is desirable to dither the optical source  66 , the upconverted error signal generated in transmitter  52  could be readily modified to provide a high-frequency dither. It is generally desirable for the dither signal to have a frequency of at least about 4 times the maximum CATV signal frequency. For example, a dither signal on the order of 2 GHz may be used in an embodiment in which the maximum CATV input signal frequency is about 500 MHz. 
     Combining the detected CATV signal with the detected error signal in combiner  90  substantially improves the effective linearity and noise performance of the optical source  66 . As a result, an inexpensive optical source such as a laser diode may be used to deliver the broadband analog CATV signal over an optical fiber distribution system. Possible disadvantages to the approach described in conjunction with FIG. 2 include the additional electronics required in the transmitter and receiver, although the cost of this circuitry could probably be reduced to a very low level using conventional integration techniques. It should also be noted that, because of the high-frequency error signal modulation, the modulation depth of the CATV signal may have to be reduced. Also, in applications in which the optical source  66  generates nonlinear distortion which could fall into the error signal band, the upconverted error signal frequency ƒ c  may need to be placed at a fairly high frequency relative to the highest frequency ƒ 2  of the analog CATV signal. For example, the upconverted error signal frequency ƒ c  may be on the order of about 4 times the frequency ƒ 2 . In order to accommodate such a frequency separation, the detector  84  may have to be fairly broadband. The effects of dispersion in the optical fiber of the distribution network should also be taken into account. For example, in certain applications it may be desirable to operate at or near a zero-dispersion wavelength. 
     The present invention permits expensive optical sources such as analog-grade DFB lasers to be replaced with substantially less expensive sources, such as digital-grade DFB laser diodes or Fabry-Perot laser diodes, without undermining the linearity and noise performance of the system. Compared to conventional pre-distortion circuits, which generally correct for only source nonlinearity, the above-described feedback and feedforward techniques correct for both nonlinearity and source noise. Moreover, the invention avoids the numerous critical adjustments required in many predistortion circuits. Compared with conventional feedforward approaches, it avoids the need for a second optical source and any wavelength-control issues associated with a second source. The above-described embodiments of the invention are intended to be illustrative only. Numerous alternative embodiments may be devised by those skilled in the art without departing from the scope of the following claims.