Embodiments of various systems disclosed herein relate in general to optical signal processing and more specifically to optical multi-rate signal processing.
Multi-rate digital signal processing systems and methods employ multiple sampling rates for processing of digital signals. Upsampling (interpolation) and downsampling (decimation) are performed to change the sampling rates within the system using, for example, filters and filter banks.
All-analog (such as all-optical, all-RF) implementations of filter bank based multi-rate systems require a pulsed carrier complex envelope, such as a pulsed laser used in an all-optical system. Such a multi-rate system is useful, for example, for an all-optical multiplexing/demultiplexing system based on filter banks. Such an implementation is described by Cincotti (“Optical Wavelet Signals Processing and Multiplexing”, Cincotti, G., Moreolo, M. S. & Neri, A. EURASIP J. Adv. Signal Process. (2005)). In Cincotti the input signal is pulsed and the filter bank is based on cascaded unbalanced MZI (Mach-Zehnder interferometer) filters. The pulsed signal requires a pulsed laser having temporal behaviour gp(t) expressed in the time domain as:
where:
The use of a pulsed laser significantly increases the cost of implementing such systems, and such systems have therefore found limited use. Further, launching pulses with the required width and repetition rate from a pulsed laser is quite complex.
Use of continuous wavelength (CW) carriers in optical communications is known. A CW carrier c(t) can be represented using the complex envelope:
c(t)=Re{Aejω
Upon modulation of a CW signal, the resulting modulated signal complex envelope S(t) is represented as:
S(t)=AΣnangcw(t−nT) (3)
where an are the data symbols, T is the symbol duration and gcw(t) is a function describing the CW carrier shape in the time domain. However, there is no known use of CW carriers in an all-optical multi-rate system, because performing multi-rate operations on a modulated signal from a CW carrier will result in intersymbol interference (ISI) and performance degradation, as exemplified by the following example. In this example, the ISI can be seen as an overlap in the summation below:
Assume that S1 and S2 are two consecutive symbols with duration T:
As can be seen, an ISI occurs due to the half symbol time delay.
There is therefore a need for, and it would be advantageous to have systems and methods that overcome the ISI to enable implementation of multi-rate systems based on CW carriers.
The description above is presented as a general overview of related art in this field and should not be construed as an admission that any of the information it contains constitutes prior art against the present patent application.
Embodiments disclosed herein relate to all-optical multi-rate systems using CW carriers. According to some embodiments, an optical multi-rate system disclosed herein comprises a CW light source for generating a CW carrier signal, an optical splitter, a plurality of modulators used each to modulate the CW carrier signal, an inverse filter bank (or “multiplexer”, a filter bank (or “demultiplexer”) and a post distortion filter (PDF) positioned between the inverse filter bank and the filter bank. For example and in a non-limiting way, the modulation may be PAM4 amplitude modulation. In general, the modulation may be of any known type, for example PAM, QAM (Quadrature Amplitude Modulation), DPSK or OOK. For example, the PAM modulation may be PAM4, PAM8 or higher PAM modulation, and the QAM modulation may be QAM4, QAM8, . . . QAM 64 or higher QAM modulation. For example and in a non-limiting way, the multiplexing may be Wavelet Packet Division Multiplexing (WPDM) based on a CW laser. For example and in a non-limiting way, the filter banks may be wavelet or multi-wavelet filter banks. In general, other types of filter banks may also be used for the all-optical multi-rate signal processing and transmission using CW carriers disclosed herein. The post distortion filter resolves the intersymbol interference that may result from the use of a CW carrier in an all-optical multi-rate system and which can lead to system degradation.
In exemplary embodiments, there are provided systems comprising: a CW light source used for providing a CW carrier signal, a plurality of modulators used for modulating the CW carrier signal to form a plurality of modulated optical signals, an inverse filter bank used for multiplexing the plurality of modulated optical signals to form a multiplexed optical signal, and a post distortion filter (PDF) used for obtaining a narrowed multiplexed optical signal and, optionally, for overcoming or eliminating ISI in the narrowed multiplexed optical signal, wherein the system is an all-optical multi-rate system.
In exemplary embodiments, there are provided methods comprising: using a CW light source to provide a CW carrier signal, using a plurality of modulators to modulate the CW carrier signal to form a plurality of modulated optical signals, using an inverse filter bank to multiplex the plurality of modulated optical signals to form a multiplexed optical signal, and using a post distortion filter (PDF) to obtain a narrowed multiplexed optical signal and, optionally, to eliminate ISI in the narrowed multiplexed optical signal.
In some embodiments, a system further comprises a filter bank used for demultiplexing the narrowed multiplexed optical signal into a plurality of demultiplexed modulated optical signals.
In some embodiments, the inverse filter bank and the filter bank are inverse multiwavelet (IMW) filter bank. In some embodiments, the IMW and MW filter banks are Geronimo, Hardian and Massopust IMW filter banks.
In some embodiments, the PDF comprises a 50/50 beam splitter for splitting the multiplexed optical signal into a first 50/50 splitter output and a second 50/50 splitter output, a first phase shifter for receiving the first 50/50 splitter output and for providing a first phase shifter output, a recombiner for combining the first phase shifter output and the second 50/50 splitter output into a recombiner output, a combiner for combining the recombiner output with a phase shifted feedback signal provided by a second phase shifter to provide a combiner output, an amplifier for amplifying the combiner output to provide an amplifier output, an a beam splitter for splitting the amplifier output into a PDF output signal and a feedback signal provided to the second phase shifter. In some embodiments, the PDF is further used for providing chromatic dispersion compensation.
In some embodiments, the modulators are electro-optical modulators.
In some embodiments, the modulators are Mach-Zehnder modulators.
In some embodiments, a system further comprises a plurality of demodulators for demodulating the plurality of demultiplexed modulated optical signals.
In some embodiments, the plurality of modulated optical signals is equal to 2N, where N is the decomposition level of the inverse filter bank.
This summary is provided to introduce a selection of concepts in a simplified form that are further described below in the detailed description. This summary is not intended to identify key features or essential features of the claimed subject matter, nor is it intended to be used to limit the scope of the claimed subject matter.
Embodiments disclosed herein are described, by way of example only, with reference to the following accompanying drawings, wherein:
To implement a system and method disclosed herein, the constant wave source in eq. (3), gcw(t) must be transformed to that of a pulse shape resulting from a pulsed source gp(t). Using linear convolution:
g
cw(t)*h(t)=gp(t) (4)
where gcw(t) is as in equation 6 below and h(t) represents a post distortion filter (PDF). Using known relationships in the frequency domain, equation (4) can be represented as:
where H(jω) is a transfer function. gcw(t) is given by
where:
In a first embodiment, assume that the input signal is a rectangular pulse. Using equations (1) and (6) and inserting into Eq. (5), one obtains
According to some embodiments, the above transfer function H (jω) is implemented optically by a post distortion filter (PDF), by using a differentiator and an amplifier represented as follows:
where x(t)=input signal to the PDF, y(t)=output signal from the PDF, and N is the ratio between the symbol duration and the pulse duration.
In a second embodiment, it is known that a chirped signal can be narrowed using dispersion management. Assume that the input signal is a Gaussian signal. It can be shown that when gcw(t) is a chirped Gaussian signal
the minimal pulse width is
The source electrical data signals are modulated (either by electro-optical (E/O) modulation or by direct modulation) such that chirp is added to the modulated signal for narrowing to the desired line width at the receiver and chromatic dispersion compensation (CDC) is provided by the post distortion filter. The CDC is related to the baud rate and amount of chirp required in a known way. Returning now to the drawings,
Light source 102 is preferably a CW laser i.e. it is not pulsed. Modulators 106 may in some embodiments also be referred to as “external modulators” for being external to light source 102. In some embodiments, modulators 106 may be E/O modulators. In some embodiments, modulators 106 may be Mach-Zehnder modulators (MZM). PDF 114, an exemplary embodiment of which is described in detail with reference to
Optical transmission system 100 may be adapted for transmission of a signal having a rectangular symbol shape or of a signal having a Gaussian symbol shape (also referred to herein as “rectangular signal” and “Gaussian signal”). In use, an unmodulated optical carrier wave λCW generated by light source 102 is split by splitter 104 into N unmodulated optical carrier waves λCW1-λCWn. N source signals S1-SN are used to modulate the N unmodulated optical carrier waves λCW1-λCWn by N modulators 1061-106n to obtain N modulated optical signals λCW1S1-MOB-λCWnSN-MOD. In some embodiments, for multiwavelets, N must be divisible by 23.
Modulated optical signals having the same carrier wave λCW1S1-MOD-λCWnSN-MOD are subjected to (for example) multiwavelet (MW) transformation and filtering by inverse filter bank 108. The resulting processed optical signals are multiplexed or combined into a multiplexed optical output signal λCWSMUX. The multiplexing is performed by means of optical convolution wherein each data stream is convolved with the appropriate filter coefficients. For example, inverse filter bank 108 may be implemented by (for example) a multiwavelet (e.g. GHM MW) filter bank, as a MW filter bank, by cascaded or lattice based directional couplers, or by polyphase filters.
Inverse filter bank 108 is in optical communication with PDF 114. According to some embodiments, the output of inverse filter bank 108 (signal λCWSMUX) is coupled into an optical conduit (e.g. waveguide or optical fiber) 120, which inputs it into PDF 114. PDF 114 implements the transfer function (Eq. 8 above):
According to some embodiments, the output of PDF 114 (signal λCWSPDF) is coupled into an optical conduit (e.g. waveguide or optical fiber) 122.
In use, multiplexed signal λCWSMUX is input into PDF 114 for convolution with PDF 114. Splitter 132 splits signal λCWSMUX into two parts, a first part going to first phase shifter 134 and a second part going to first combiner 136. First phase shifter 134 provides a delay of D where:
where N is the decomposition level of inverse filter bank 108 as above.
The part of signal λCWSMUX coming from splitter 132 and the part of signal λCWSMUX with delay D coming from first phase shifter 134 are recombined in first combiner 136. The recombined signal is fed into combiner 138. The output of combiner 138 is fed into amplifier 140 which amplifies it and outputs and amplifies signal to splitter 144. Splitter 144 returns a first part of the amplified signal to second phase shifter 142. Second phase shifter 142 provides a delay of T as follows:
The gain of amplifier 140 and the splitting ratio of splitter 144 are optionally altered depending on the desired performance of PDF 114, i.e. a split resulting in a higher amplitude output from PDF 114 or a lower amplitude output from PDF 114. When a smaller first part of the amplified signal (larger output from PDF 114) is fed back from splitter 144 via second phase shifter 142, more gain is needed in amplifier 140. Conversely, when a larger first part of the amplified signal (smaller output from PDF 114) is fed back from splitter 144 via second phase shifter 142, less gain is needed in amplifier 140.
To summarize, for a square pulse, an input signal λCWSMUX of width T is transformed by PDF 114 into an output (filtered multiplexed) signal λCWSPDF of width T/N.
Filtered multiplexed signal λCWSPDF is transmitted from PDF 114 to filter bank 110 for demultiplexing to provide N demultiplexed signals λCWS1-MOD-Demux to λCWSN-MOD-Demux·λCWSPDF is subjected to (for example) MW transformation and filtering by filter bank 110. The outputs of filter bank 110 are demultiplexed modulated optical signals λCWS1-MOD-Demux to λCWSN-MOD-Demux. Exemplarily, filter bank 110 may be realized by either cascaded or lattice based directional couplers. For example, filter bank 110 may be implemented by a multiwavelet (e.g. GHM MW) filter bank, as a MW filter bank, by cascaded or lattice based directional couplers, or by polyphase filters.
The original N source signals S1-SN are recovered from λCWS1-MOD-Demux to λCWSN-MOD-Demux by N demodulators 1121-112n. In some embodiments, demodulators 112 may be EO demodulators. In some embodiments, demodulators 112 may be Mach-Zehnder demodulators.
Reference is now made to
In
Method of Use for Gaussian Signal Input with Chirp
In use with a Gaussian-shaped signal, chirp can be added to narrow the signal output to a received to a desired line width.
Reference is now made to
In the claims or specification of the present application, unless otherwise stated, adjectives such as “substantially” and “about” modifying a condition or relationship characteristic of a feature or features of an embodiment of the invention, are understood to mean that the condition or characteristic is defined to within tolerances that are acceptable for operation of the embodiment for an application for which it is intended.
It should be understood that where the claims or specification refer to “a” or “an” element, such reference is not to be construed as there being only one of that element.
In the description and claims of the present application, each of the verbs, “comprise” “include” and “have”, and conjugates thereof, are used to indicate that the object or objects of the verb are not necessarily a complete listing of components, elements or parts of the subject or subjects of the verb.
While this disclosure describes a limited number of embodiments, it will be appreciated that many variations, modifications and other applications of such embodiments may be made. The disclosure is to be understood as not limited by the specific embodiments described herein, but only by the scope of the appended claims.
This application is a 371 application from international patent application No. PCT/IB2019/053293 filed Apr. 21, 2019.
Filing Document | Filing Date | Country | Kind |
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PCT/IB2019/053293 | 4/21/2019 | WO | 00 |