Dimensional transformation in optical communications
阅读说明：本技术 光学通信中的维度变换 (Dimensional transformation in optical communications ) 是由 K·罗伯特 A·坎达尼 S·奥维斯·加兰 M·雷默 M·奥沙利文 于 2019-05-21 设计创作，主要内容包括：发射器(102,200)对表示符号的初始数字驱动信号应用维度变换,从而产生变换后的数字驱动信号(704),数字驱动信号(704)被设计用于使用光学载波(242)的多个第一维度来表示每个符号,所述第一维度被分布在两个或多个时隙上。初始数字驱动信号被设计用于使用所述载波的多个第二维度来表示每个符号,所述第二维度不同于所述第一维度。发射器使用变换后的信号生成(706)光学信号(260)。接收器(102,300)接收(802)光学信号(360)并确定与所述第一维度相对应的接收的数字信号(804)。接收器对所述接收的数字信号应用逆维度变换以生成与所述第二维相对应的初始数字驱动信号估计(806),从而允许所述符号的估计(808)。所述逆维度变换可以对在所述接收的数字信号中的信号劣化进行平均。(A transmitter (102, 200) applies a dimensional transformation to an initial digital drive signal representing a symbol, thereby generating a transformed digital drive signal (704), the digital drive signal (704) being designed for representing each symbol using a plurality of first dimensions of an optical carrier (242), the first dimensions being distributed over two or more time slots. The initial digital drive signal is designed to represent each symbol using a plurality of second dimensions of the carrier, the second dimensions being different from the first dimensions. The transmitter generates (706) an optical signal (260) using the transformed signal. The receiver (102, 300) receives (802) the optical signal (360) and determines a received digital signal (804) corresponding to the first dimension. The receiver applies an inverse dimensional transform to the received digital signal to generate an initial digital drive signal estimate corresponding to the second dimension (806), thereby allowing estimation of the symbol (808). The inverse dimensional transform may average signal degradation in the received digital signal.)
1. A method performed on an optical receiver (102, 300) side, the optical receiver (102, 300) comprising a polarizing beam splitter (344), an optical mixer (358), a light detector (362), an analog-to-digital converter (324, 326, 328, 330), and a processor (314), the method comprising:
receiving an optical signal (360) over an optical communication channel (104) established between the optical receiver and an optical transmitter (102, 200), wherein the received optical signal comprises a degraded version of a modulated optical signal generated at the optical transmitter side;
the polarizing beam splitter splitting the received optical signal into polarized components (354, 356);
the optical mixer processes the polarization components to produce processed components (346, 348, 350, 352);
the photodetector converts the processed component into a received analog signal (332, 334, 336, 338);
the analog-to-digital converter converting the received analog signal into a received digital signal (316, 318, 320, 322) corresponding to a plurality of first dimensions of the received optical signal, wherein the first dimensions correspond to dimensions of an optical carrier (242) modulated to represent a multi-bit symbol (212) at the optical transmitter side, wherein the first dimensions are distributed over two or more time slots;
the processor applying (806) an inverse dimensional transform to the received digital signal to produce initial digital drive signal estimates (370, 372, 374, 376) corresponding to a plurality of second dimensions; and
the processor processes (808) the initial digital drive signal estimate to produce an estimate of the multi-bit symbol.
2. The method of claim 1, wherein the inverse dimensional transformation averages signal degradation in the received digital signal caused by one or more of noise, nonlinear effects, polarization dependent loss or gain (PDL), and analog imperfections.
3. The method of claim 1 or 2, wherein the inverse dimensional transformation comprises a matrix, and wherein the matrix is substantially linear and substantially unitary.
4. The method of any of claims 1-3, comprising processing the received optical signal using an adaptive equalization circuit to compensate for linear impairments in the optical communication channel.
5. A method performed on an optical transmitter (102, 200) side, the optical transmitter (102, 200) comprising a processor (214), a digital-to-analog converter (224, 226, 228, 230), an electro-optic modulator (250, 252), and a beam combiner (258), the method comprising:
the processor generates (702) an initial digital drive signal representative of a multi-bit symbol (212);
the processor generating (704) a transformed digital drive signal (216, 218, 220, 222) from the initial digital drive signal, wherein the transformed digital drive signal is designed to represent each multi-bit symbol using a plurality of first dimensions of an optical carrier (242), the first dimensions being distributed over two or more different time slots, and wherein the initial digital drive signal is designed to represent each multi-bit symbol using a plurality of second dimensions of the optical carrier, the second dimensions being different from the first dimensions; and
generating (706) an optical signal (260) transmitted over an optical communication channel (104) established between the optical transmitter and optical receiver (102, 300), comprising:
said digital-to-analog converter converting said converted digital drive signals into corresponding analog signals (232, 234, 236, 238);
the electro-optic modulator modulates a polarization component (246, 248) of the optical carrier using the analog signal to produce a modulated polarization signal (254, 256); and
the beam combiner combines the modulated polarized signals to form an optical signal.
6. The method of claim 5, wherein the transformed digital drive signal is generated by applying a dimensional transform to the initial digital drive signal.
7. The method of claim 6, wherein the dimensional transformation comprises a matrix, and wherein the matrix is substantially linear and substantially unitary.
8. The method of claim 5, wherein the transformed digital drive signal is generated from the initial digital drive signal using a look-up table.
9. The method of any of claims 5 to 8, further comprising:
the processor applies frequency domain processing (906) to the transformed digital drive signal.
10. The method of any of claims 1-9, wherein the plurality of second dimensions are smaller than the plurality of first dimensions.
11. The method of any one of claims 1 to 10, wherein the two or more time slots are discontinuous.
12. The method of any one of claims 1 to 11, wherein the first dimension is distributed over two polarizations.
13. The method of any one of claims 1 to 12, wherein the first dimension is distributed over an in-phase (I) component and a quadrature (Q) component of at least one polarization.
14. An optical receiver (102, 300) comprising a polarizing beam splitter (344), an optical mixer (358), a light detector (362), an analog-to-digital converter (324, 326, 328, 330) and a processor (314), wherein the optical receiver is configured for performing the method of any one of claims 1-4, or the method of any one of claims 10-13 when claims 10-13 are dependent on any one of claims 1-4.
15. An optical transmitter (102, 200) comprising a processor (214), a digital-to-analog converter (224, 226, 228, 230), an electro-optic modulator (250, 252) and a beam combiner (258), wherein the optical transmitter is configured to perform the method as claimed in any one of claims 5 to 9, or any one of claims 10 to 13 when claims 10 to 13 are dependent on any one of claims 5 to 9.
Technical Field
This document relates to the technical field of optical communication.
Background
In an optical communication system, a transmitter may encode client data bits as follows: the client data bits are mapped to multi-bit symbols, and one or more optical carriers are modulated with the symbols using a particular modulation scheme to generate an optical signal to be transmitted via a communication signal to a receiver, where the optical signal represents digital information. A receiver may process an optical signal received via a communication channel to recover an estimate of the multi-bit symbol, an estimate of the client data bits, or both.
The optical signal received at the receiver may comprise a degraded version of the optical signal generated at the transmitter side. Signal degradation may result from various components of the optical communication system, including optical fibers, optical amplifiers, filters, isolators, and the like. Effects such as amplifier noise, optical nonlinearity, polarization dependent loss or gain (PDL), Polarization Mode Dispersion (PMD), and the like may introduce noise and/or distortion into the signal. The amplitude of the noise relative to the amplitude of the optical signal may be characterized by a signal-to-noise ratio (SNR) or alternatively by a signal-to-noise ratio (NSR). NSR may be convenient when profiling noise sources. High NSR may result in noisy symbol estimatesThis may in turn produce erroneous estimates of the client data bits. The probability that the client data bit estimates recovered at the receiver side will differ from the original client data bits encoded at the transmitter side can be characterized by a bit error rate or Bit Error Rate (BER). A given application may have a maximum BER margin. For example, an application may require BER not to exceed 10-16。
Forward Error Correction (FEC) techniques may be used to reduce BER. Instead of the transmitter mapping the original client data bits directly to multi-bit symbols, the client data bits may first undergo FEC encoding based on the selected FEC scheme. The resulting FEC encoded bits include redundant information such as parity bits or check bits. The bit estimates recovered at the receiver will be estimates of the FEC encoded bits generated at the transmitter. These estimates may be subject to FEC decoding at the receiver based on the selected FEC scheme. FEC decoding utilizes redundant information contained in the FEC encoded bits to detect and correct bit errors.
FEC coding is advantageous in that it may allow error control without resending data packets. However, this comes at the cost of increased overhead. The amount of overhead or redundancy added by FEC coding can be characterized by an information rate R, where R is defined as the ratio of the amount of input information to the amount of data output after FEC coding (which includes overhead). For example, if FEC encoding adds 25% overhead, then for every 4 information bits to be FEC encoded, FEC encoding would add one bit of overhead, resulting in 5 FEC encoded data bits to be transmitted to the receiver. This corresponds to an information rate R of 4/5 of 0.8.
Disclosure of Invention
According to one broad aspect, an optical receiver is operable to receive an optical signal over an optical communication channel established between the optical receiver and an optical transmitter, wherein the received optical signal comprises a degraded version of a modulated optical signal generated at the optical transmitter. The optical receiver is operable to determine a received digital signal corresponding to a plurality of first dimensions of the received optical signal, wherein the first dimensions correspond to dimensions of an optical carrier modulated at the optical transmitter, the dimensions of the optical carrier representing a multi-bit symbol, and wherein the first dimensions are distributed over two or more time slots. The optical receiver is operable to determine an initial digital drive signal estimate using an inverse dimensional transform and the received digital signal, the initial digital drive signal estimate corresponding to a plurality of second dimensions. An optical receiver is operable to determine an estimate of the multi-bit symbol using the initial digital drive signal estimate.
According to some embodiments, the plurality of second dimensions are smaller than the plurality of first dimensions.
According to some embodiments, the two or more time slots may be contiguous or non-contiguous.
According to some embodiments, the plurality of first dimensions are distributed over two polarizations.
According to some embodiments, the plurality of first dimensions are distributed over an in-phase (I) component and a quadrature (Q) component of at least one polarization.
According to some embodiments, the inverse dimensional transformation averages signal degradation in the received digital signal, the signal degradation being caused by one or more of noise, non-linear effects, polarization dependent loss or gain (PDL), and analog defects.
According to some embodiments, the inverse dimensional transformation comprises a matrix, wherein the matrix is substantially linear and substantially unitary.
According to some embodiments, the received optical signal is processed using an adaptive equalization circuit to compensate for linear impairments in the optical communication channel.
According to one broad aspect, an optical transmitter is operable to generate an initial digital drive signal representative of a multi-bit symbol. The optical transmitter is operable to generate a transformed digital drive signal from the initial digital drive signal, wherein the transformed digital drive signal is designed to represent each multi-bit symbol using a plurality of first dimensions of an optical carrier, the first dimensions being distributed over two or more different time slots. The initial digital drive signal is designed to represent each multi-bit symbol using a plurality of second dimensions of the optical carrier, the second dimensions being different from the first dimensions. The optical transmitter is operable to generate an optical signal using the converted digital drive signal, the optical signal being transmitted over an optical communication channel established between the optical transmitter and the optical receiver.
According to some embodiments, the plurality of second dimensions are smaller than the plurality of first dimensions.
According to some embodiments, the two or more time slots may be contiguous or non-contiguous.
According to some embodiments, the plurality of first dimensions are distributed over two polarizations.
According to some embodiments, the plurality of first dimensions are distributed over an in-phase (I) component and a quadrature (Q) component of at least one polarization.
According to some embodiments, the transformed digital drive signal is generated by applying a dimensional transformation to the initial digital drive signal. The dimensional transformation may comprise a matrix. The matrix may be substantially linear and substantially unitary.
According to some embodiments, the transformed digital drive signal is generated from the initial digital drive signal using a look-up table.
According to some embodiments, the optical transmitter is operable to apply frequency domain processing to the transformed digital drive signal. The frequency domain processing may comprise applying a matched filter to the transformed digital drive signal.
Drawings
FIG. 1 illustrates an example optical communication system in accordance with the techniques disclosed herein;
FIG. 2 illustrates an example transmitter in accordance with the techniques disclosed herein;
FIG. 3 illustrates an example receiver in accordance with the techniques disclosed herein;
FIG. 4 shows a graph of Bit Error Rate (BER) as a function of linear noise to signal ratio (NSR) for a 64-level quadrature amplitude modulation (64-QAM) scheme;
FIG. 5 shows an enlarged portion of the graph shown in FIG. 4, with example points A and B;
FIG. 6 shows the second derivative of BER versus NSR of FIG. 4 plotted as a function of BER;
FIG. 7 illustrates an example method for implementing dimensional transformations at the transmitter side;
FIG. 8 illustrates an example method for implementing an inverse dimensional transform at the receiver side;
fig. 9 is a schematic diagram showing an implementation of a dimension transformation at the transmitter side according to a first example;
FIG. 10 is a schematic diagram showing example details for implementing a dimension transformation according to a first example;
fig. 11 is a schematic diagram showing an implementation of an inverse dimensional transformation at the receiver side according to a first example;
fig. 12 is a schematic diagram showing example details for implementing an inverse dimensional transformation according to the first example.
Fig. 13 is a schematic diagram showing an implementation of a dimension transformation at the transmitter side according to a second example;
fig. 14 is a schematic diagram showing an implementation of an inverse dimensional transformation at the receiver side according to a second example; and
fig. 15 is a histogram of received values that have undergone an inverse dimensional transform according to a fifth example.
Detailed Description
Fig. 1 illustrates an
For purposes of this disclosure, it is convenient to treat the transmitted optical signal, such as a signal transmitted over the
The signal transmitted via the
Random defects in the fiber may cause the two orthogonal polarizations to propagate at different speeds. This effect is called Polarization Mode Dispersion (PMD), which causes two polarization components of the signal (denoted X)PMDAnd YPMD) Slowly separating over the entire length of the fiber, causing pulse broadening and overlap. The PMD of a signal may be characterized by the number M of time slots in which overlap occurs. M may be referred to as PMD "memory". PMD compensation may be implemented at the receiver side using an adaptive filter, such as a Least Mean Square (LMS) circuit. However, the LMS circuit may increase the correlation between the noise components of the symbols at different times. This noise correlation can be observed in the same M slots where the PMD memory is observed.
Measurement and mitigation techniques for PDL and/or PMD are described, for example, in the following patent documents: U.S. Pat. No. 7,305,183 to Roberts et al; U.S. Pat. No. 7,382,985 to Roberts et al; U.S. Pat. No. 7,532,822 to Sun et al; U.S. Pat. No. 7,936,999 to Hawryluck et al; U.S. Pat. No. 8,385,747 to Roberts et al; khandani et al, U.S. patent No. 8,718,491; khandani et al, U.S. patent No. 9,602,207; and measurement and mitigation techniques for PDL and/or PMD are also described in the following publications: mumtaz et al, "PDL differentiation in PolMux OFDMSystems Using Golden and Silver Polarization-Time Codes", published in Conference on fiber communication, OSA Technical Abstract (CD) (American Society of optics, 2010), paper JThA7(Optical fiber communication Conference, OSA Technical Digest (CD) (Optical Society of America,2010), paper JThA 7); mumtaz et al, "Space-Time codes for optical communication with polarization multiplexing" published on pages 1-5 of IEEE International Conference on Communications (IEEE,2010), pp.1-5; and "Use of space-time coding in coherent polarization-multiplexed systems from polarization-dependent loss" by Meron et al, which is published in Opt. Lett.35(21),3547-3549(2010), each of which is incorporated herein by reference.
Us patent nos. 8,718,491 and 9,602,207 describe the use of noise whitening matrices to reduce the total noise and equalize the noise variance between orthogonal polarizations. The noise whitening matrix is only applied to the receiver side and may be dynamically updated in response to any changes in the optical line. A transmit jones rotation matrix may be applied at the transmitter side, where the rotation angle attempts to track the changes in the optical line, optimizing the PDL of the received azimuth with respect to noise.
The Mumtaz et al and Meron et al publications describe gold and silver space-time codes that can be used to mitigate the effects of PDL. The implementation of gold and silver codes typically requires complex decoding circuitry.
Fig. 2 is a block diagram illustration of an example transmitter portion 200 ("
The
An Application Specific Integrated Circuit (ASIC)202 is operable to generate I and Q analog drive signals 232, 234 to drive an electro-optic modulator 250. The ASIC 202 is operable to generate I and Q analog drive signals 236, 238 to drive an electro-optic modulator 252.
ASIC 202 is operable to apply FEC encoding 206 to client data bits 204, thereby generating FEC encoded bits 208. The FEC encoded bits 208 may be mapped to multi-bit symbols according to a particular code, as represented by a bit-to-symbol mapping 210. The bit-to-symbol mapping 210 may produce a stream of multi-bit symbols 212.
ASIC 202 also includes a transmit Digital Signal Processor (DSP)214 and a plurality of digital-to-analog converters (DACs). Transmit DSP214 is operable to process symbols 212, for example, by one or more of pulse shaping, subcarrier multiplexing, dispersion pre-compensation, and distortion pre-compensation. The processing by transmit DSP214 may include the application of one or more filters, which may involve the application of one or more Fast Fourier Transforms (FFTs) and one or more corresponding inverse FFTs (iffts).
Based on the symbols 212 and the selected modulation scheme, the transmit DSP214 is operable to generate four digital drive signals corresponding to the four dimensions XI, XQ, YI, YQ at a particular time slot t. For example, digital drive signals 216, 218 may correspond to the I and Q components of the X polarization, respectively, while digital drive signals 220, 222 may correspond to the I and Q components of the Y polarization, respectively. According to this example, the digital drive signals 216, 218 may be represented as S, respectively, at time slot tXI(t)、SXQ(t) and the digital drive signals 220, 222 may be represented as S, respectivelyYI(t)、SYQ(t)。
Digital drive signals 216, 218, 220, 222 may be converted to analog drive signals 232, 234, 236, 238 by respective DACs 224, 226, 228, 230. As previously described, the analog drive signals 232, 234, 236, 238 are used to drive the electro-optic modulators 250, 252, which ultimately results in the generation of the optical signal 260.
Fig. 3 is a block diagram illustration of an example receiver portion ("
ASIC 302 includes analog-to-digital converters (ADCs) 324, 326, 328, 330, analog-to-digital converters (ADCs) 324, 326, 328, 330 operable to sample received analog signals 332, 334, 336, 338, respectively, and generate received digital signals 316, 318, 320, 322, respectively. In one example, received analog signals 332, 334 may correspond to X-polarized I and Q components, respectively, while received analog signals 336, 338 may correspond to Y-polarized I and Q components, respectively. According to this example, the received digital signals 316, 318 may be denoted R at time slot t, respectivelyXI(t)、RXQ(t) and the received digital signals 320, 322 may be represented as R, respectivelyYI(t) and RYQ(t)。
ASIC 302 includes a receive DSP314, and receive DSP314 is operable to process received digital signals 316, 318, 320, 322. For example, receiving DSP314 may be operable to apply one or more filters to digital signals 316, 318, 320, 322, which may involve applying one or more FFTs and one or more corresponding IFFTs. The receiving DSP314 may output digital signals 370, 372, 374, 376 based on the digital signals 316, 318, 320, 322.
ASIC 302 is operable to apply carrier recovery processing 313 to digital signals 370, 372, 374, 376 to derive symbol estimates 312 for the two orthogonal polarizations. Symbol estimate 312 is an estimate of symbol 212 generated by bit-to-symbol mapping 210 at
ASIC 302 is operable to apply symbol-to-bit demapping 310 to symbol estimates 312 to derive bit estimates 308. Symbol-to-bit demapping 310 involves applying the inverse of the code used in bit-to-symbol mapping 210. The bit estimate 308 is an estimate of the bits 208 generated by the FEC encoding 206 at the
ASIC 302 is operable to apply FEC decoding 30 to bit estimates 308 to recover corrected client data bits 304. FEC decoding 306 may include hard decision decoding or soft decision decoding. One example of soft decision decoding is Maximum Likelihood (ML) decoding. If the FEC decoding 306 is able to correct all errors present in the FEC encoded bit estimates 308, the corrected client data bits 304 will be identical to the original client data bits 204. If the FEC decoding 306 is not able to correct all errors present in the FEC encoded bit estimates 308, the corrected client data bits 304 will be different from the original client data bits 204. In this case, the FEC scheme selected for FEC encoding 206 and FEC decoding 306 would be considered to have failed.
The success or failure of a given FEC scheme depends on its strength relative to the degree of error present in the FEC encoded bit estimates. FEC decoding will typically be responsive to an average of FEC encoded bit estimates to which it is appliedThe BER. The average BER observed at the input of the FEC decoding can be expressed as BERFEC_AVG. When BERFEC_AVGOver a certain threshold (expressed as BER)THRESH) Hard decision FEC decoding may not be able to correct all errors in the FEC encoded bit estimates. In other words, when BERFEC_AVG>BERTHRESHThe FEC scheme used for FEC encoding at the transmitter and FEC decoding at the receiver is expected to fail. In one example, BERTHRESHAbout 3.84 × 10-3。
In general, the BER of the FEC encoded bit estimates 308 is expected to increase as the noise in the received optical signal 360 increases. The exact relationship between the noise-to-signal ratio (NSR) and the BER depends on the code used for the bit-to-symbol mapping 210 and the modulation scheme used by the transmit DSP214 to convert the symbols 212 to the digital drive signals 216, 218, 220, 222, and also on the shape of the four-dimensional probability density function of the noise if it is not isotropic gaussian noise.
Fig. 4 shows a graph of BER as a function of linear NSR for a 64-level quadrature amplitude modulation (64-QAM) scheme.
There may be cases where: different streams of bits (or symbols) may experience different noise levels. For example, as previously described, PDL may cause different polarizations to have different noise levels. Thus, for example, symbols transmitted in X-polarization may exhibit different noise levels than symbols transmitted in Y-polarization. Thus, the FEC encoded bit estimates determined from one symbol stream may have a different BER than the FEC encoded bit estimates determined from another symbol stream.
A simple example may be considered in which the first set of FEC encoded bit estimates exhibits a first BER, denoted BERAAnd the second set of FEC encoded bit estimates exhibits a second BER, expressed as BERBWherein BERA≠BERB. If the number of FEC encoded bit estimates in each group is equal, the average BER over the two groups will be BERFEC_AVG＝(BERA+BERB)/2. If hard decision FEC decoding is applied to both sets, then the BER isFEC_AVG＝(BERA+BERB) Per 2 exceeds BER for FEC schemeTHRESHThen the FEC scheme is expected to fail. This is because the performance of FEC depends on the average BER of the FEC encoded bit estimates to which it is applied.
The different BER values of the FEC encoded bit estimates are the result of different noise levels in the symbol estimates from which the FEC encoded bit estimates are determined. As an alternative to applying FEC decoding to sets of bits exhibiting different BERs, it may be advantageous to achieve a more uniform noise level throughout the symbol estimates, so that the FEC encoded bit estimates determined from the symbol estimates have a more uniform BER. By averaging the different noise levels exhibited by different groups of symbol estimates, a more uniform noise level can be achieved across all symbol estimates. Examples of how this noise averaging may be achieved will be described in detail with reference to fig. 7 to 15.
Where noise averaging techniques have been applied, the symbol estimates generated at the receiver may have a substantially uniform noise level, such that the resulting FEC encoded bit estimates have a substantially uniform BER, which may be expressed as BERNOISE_AVG. And by directly aligning the BERAAnd BERBBER determined by averagingFEC_AVGBy contrast, BERNOISE_AVGIs determined using the relationship between BER and symbol noise for the particular modulation scheme used. For example, FIG. 5 shows a magnified portion of the graph shown in FIG. 4, where example points A and B represent two sets of symbol estimates having respective BERsAAnd BERBTwo different noise levels are associated. As shown in fig. 5, the BER can be schematically represented by drawing a straight line between a point a and a point B on the curve and then determining the BER corresponding to the center point of the lineFEC_AVGAnd (4) calculating. Instead, the BER may be determined by first determining the BERAAnd BERBThe associated average linear NSR, and then using the curve to determine the BER corresponding to this average linear NSR to determine the BERNOISE_AVG. As is apparent from the enlarged graph of FIG. 5, BERNOISE_AVGLess than BERFEC_AVG. In other words, the execution pair is at both of theseThe operation of averaging the noise over the group symbols will result in a uniform BER (BER)NOISE_AVG) This uniform BER is less than the average BER (BER) that the FEC scheme would respond to without noise averagingFEC_AVG)。
It may be of interest to ensure that the bit estimates undergoing FEC decoding have as low a BER as possible in order to reduce the likelihood that FEC decoding will fail, or to allow the use of higher rate FEC schemes that require less overhead. Accordingly, for example points a and B in fig. 5, it may be of interest to implement a noise averaging technique such that FEC decoding only needs to respond to lower values of BERNOISE_AVGRather than a higher value of BERFEC_AVGThe higher value BERFEC_AVGFEC decoding would need to be processed in the absence of noise averaging.
However, there are other examples where it may be of interest for FEC decoding to process bit estimates with a range of BER such that FEC responds to BERFEC_AVGRather than using noise averaging to generate a uniform value BERNOISE_AVG. Referring to FIG. 5, BERNOISE_AVGLess than BERFEC_AVGThis is because the points a and B are located in the convex region of the curve in fig. 4. However, it can be shown that there are other points on the curve, in particular those points which lie in the concave region of the curve in fig. 4, for which the BER isNOISE_AVGGreater than BERFEC_AVG。
The convex-concave regions of the curves in fig. 4 can be more easily distinguished from each other by considering the second derivative of BER with respect to linear NSR, which is plotted as a function of BER in fig. 6. Those BER values for which the second derivative is positive correspond to the convex region of the curve in fig. 4, while those for which the second derivative is negative correspond to the concave region of the curve in fig. 4. As is apparent from fig. 6, BER values less than 0.025 are in the convex region, while BER values greater than 0.025 are in the concave region. Although not explicitly illustrated, it can be shown that applying a noise averaging operation may be possible for two points located in the recessed area (i.e., corresponding to two different BER values, each greater than 0.025)Resulting in a single uniform BER valueNOISE_AVGWhich is greater than the value BER for these two pointsFEC_AVG. This is an example where it may be preferable to have the FEC respond to BERFEC_AVGRather than using noise averaging.
Whether noise averaging is chosen may depend on the different noise levels (and BER) in question. A technique known as contrast coding is described in us patent application No. 15/672,434 filed by Oveis-Gharan et al, 8/9/2017, in which noise is redistributed to generate bit estimates of different classes, where each class may be associated with a different average BER. In a given class, the effect of PDL may produce a range of BER values. Whether FEC decoding is chosen to handle this range of BER values or whether noise averaging is chosen instead may depend on the average BER for that category. For example, a low BER category may include a range of BER values that lie within the convex portion of the curve in fig. 4. In this case, it may be advantageous to process the PDL by using a noise averaging operation to obtain a substantially uniform BER value within the class. In another example, a high BER category may include a range of BER values that lie within the concave portion of the curve in fig. 4. In this case, it may be advantageous to process the PDL by having the FEC decoding respond directly to the range of BER values within the class.
Returning to fig. 2, an optical signal 260 is generated at the
However, rather than limiting the dimensions used to represent a multi-bit symbol to a single slot, it may be advantageous to distribute those dimensions over two or more different slots. The time slots may be contiguous or non-contiguous. Based on interleaving, the time slots may be spread over a longer time span. By representing each multi-bit symbol using a dimension that spans multiple time slots, it is possible to average out signal degradation, including degradation caused by one or more of noise, non-linear effects, PDL, and analog defects.
For the purposes of describing the following examples, the term "dimensional transformation" may be understood as an operation that results in the generation of a transformed digital drive signal that is used at the transmitter side to modulate the dimensions of an optical carrier to represent a multi-bit symbol. According to some examples, the transformed digital drive signal resulting from the dimensional transformation modulates the optical carrier such that each multi-bit symbol is represented using a plurality of first dimensions of the optical carrier, wherein the first dimensions are distributed over two or more different time slots. According to some examples, the transformed digital drive signal is generated as a result of applying a dimensional transformation to an initial digital drive signal that has been designed to modulate the dimensions of an optical carrier according to a particular modulation scheme to represent a multi-bit symbol. According to some examples, the initial digital drive signal may have been designed to modulate the optical carrier such that each multi-bit symbol is represented using a plurality of second dimensions, wherein the plurality of second dimensions is smaller than the plurality of first dimensions. In other words, the effect of the dimension transformation may be to increase the number of dimensions used to represent each multi-bit symbol, resulting in a transformed digital drive signal that causes each multi-bit symbol to be represented by more dimensions than if the initial digital drive signal was used to modulate the optical carrier to represent each multi-bit symbol.
The dimensional transformation may be implemented as one or more serial steps, as one or more parallel steps, or as a combination of serial and parallel steps. In some examples, the dimensional transformation may include application of a matrix transformation. For example, a digital signal corresponding to a particular dimension may undergo matrix multiplication as part of a dimension transform. The matrix transformation may be linear or substantially linear. The matrix transformation may be unitary or substantially unitary. That is, the inverse of the matrix transformation may be equal or substantially equal to the complex conjugate transpose of the matrix transformation. In some examples, the linear operations based on matrix multiplication may be replaced by other forms of linear filtering. In some examples, the dimensional transformation may include using the initial digital signal to determine a corresponding transformed digital signal based on information stored in a database, such as a look-up table (LUT).
For the purposes of describing the following examples, the term "inverse dimensional transform" may be understood as an operation applied to a received digital signal, wherein the received digital signal corresponds to a dimension of an optical signal received at the receiver side. According to some examples, each multi-bit symbol may be represented by a received digital signal corresponding to a plurality of first dimensions of the optical signal, where the first dimensions may be distributed over two or more different time slots. Application of the inverse dimensional transform may result in the generation of initial digital drive signal estimates corresponding to a plurality of second dimensions. According to some examples, the plurality of second dimensions may be smaller than the plurality of first dimensions. In other words, the effect of the inverse dimensional transform may be to reduce the number of dimensions used to represent each multi-bit symbol, resulting in the initial digital drive signal estimate representing each multi-bit symbol using fewer dimensions than the dimensions of the received optical signal used to represent each multi-bit symbol. The reduction in the "dimensionality" of the multi-bit symbols may facilitate soft decoding at the receiver side.
The inverse dimensional transform may be implemented as one or more serial steps, as one or more parallel steps, or as a combination of serial and parallel steps. In some examples, the inverse dimensional transformation may include application of a matrix transformation. The matrix transformation may be linear or substantially linear. The matrix transformation may be unitary or substantially unitary. An advantage of using an inverse dimensional transform that includes a unitary matrix is that the application of such a matrix does not enhance noise.
According to some examples, a dimensional transformation may be applied to the initial digital drive signal on the transmitter side, thereby generating a transformed digital drive signal, which is used to modulate an optical carrier to generate an optical signal. The optical signal may be transmitted by a transmitter to a receiver. At the receiver side, an inverse dimensional transform may be applied to the received digital signal, where the received digital signal corresponds to the dimensions of the degraded version of the optical signal sent by the transmitter. The inverse dimensional transformation may comprise an operation that is substantially the inverse of the dimensional transformation applied at the transmitter side. For example, where the dimensional transformation comprises an application of a first matrix transformation, the inverse dimensional transformation may comprise an application of a second matrix transformation, where the second matrix transformation is substantially the inverse of the first matrix transformation. As a result of applying the inverse dimensional transform to the received digital signal, an initial digital drive signal estimate may be determined at the receiver side. The initial digital drive signal estimate is an estimate of the initial digital drive signal to which the dimensional transformation is applied at the transmitter side.
As will be described in the specific examples that follow, the dimensional transformation and inverse dimensional transformation may include additional operations, such as complex conjugate operations applied to subsets of the signals, or signal interleaving.
When the noise levels of the received signals are in a range such that they correspond to the convex region of the BER versus linear NSR curve, such as the curve in fig. 4. Application of an inverse dimensional transform, such as those described herein, may have the effect of making the noise level more uniform (i.e., by averaging the noise level, as previously described). However, when the noise levels of the received signals are in a range such that they correspond to the concave regions of the curve, the application of the inverse dimensional transform may be designed to have the effect of emphasizing the difference between the noise levels. For some applications, it may be advantageous to enhance the difference between the noise levels. In one example, a multidimensional constellation that is non-prismatic may cover all four dimensions XI, XQ, YI, YQ within one or more time slots. A dimension transform may be used to map the stream of symbols into pure X-polarization and pure Y-polarization dimensions over twice as many slots. PDL may produce unequal noise variance on these streams. Unequal noise variances can be better handled by FEC when the noise levels of the received signals are in a range such that they correspond to the concave regions of the curve. Thus, in this case, it may be of interest to use an inverse dimensional transform to emphasize the inequality.
Referring to FIG. 2, signal processing at transmit DSP214 may include applying dimensional transformations to initial digital drive signals, which may be formed from
Referring to FIG. 3, signal processing at receiving DSP314 may include applying an inverse dimensional transform to a received digital signal, which may be represented by RXI、RXQ、RYI、RYQAnd (4) showing. For simplicity, R may be used throughout this documentXTo represent RXIAnd RXQMay be used throughout this documentYTo represent RYIAnd RYQCombinations of (a) and (b). For received digital signal RX、RYDigital signals can be generated separately by applying inverse dimensional transformations
Applying the dimensional transform at the transmitter side and the inverse dimensional transform at the receiver side is different from the disclosures of Khandani et al in us patent nos. 8,718,491 and 9,602,207, in which the transmit jones rotation matrix is applied at the transmitter side and the noise whitening matrix is applied at the receiver side. The noise whitening matrix is not the inverse of the jones rotation matrix. Furthermore, the dimensional transformation disclosed herein can be used to average noise over polarization without the need to track changing optical lines.
In contrast to gold and silver codes described by Mumtaz et al, the application of the dimensional and inverse dimensional transforms described herein does not require complex circuitry to implement. The multiplication by a unitary matrix involves computations that are simple and inexpensive relative to the computations required for real and silver codes. Thus, the dimension transformation may provide an alternative to gold and silver codes, which is less costly in terms of heat generation and power usage.
In the "filter-tolerant transmission by Walsh-Hadamard transform by the Walsh-Hadamard transform for
In "Twin-Wave Based Optical Transmission with Enhanced Linear and nonlinear performance (Twin-Wave-Based Optical Transmission with Enhanced Linear and nonlinear performance)" of Liu, pp.1037-1043 (2015), Journal of light Wave Technology (Journal of Lightwave Technology) Vol.33, No. 5, a method of converting a Binary Phase Shift Keying (BPSK) signal into a "Twin Wave" QPSK signal using conjugate phase characteristics is described. The method of Liu involves matrix multiplication using unitary matrices. However, the method of Liu does not involve a received digital signal corresponding to a first dimension of the optical signal representing a single multi-bit symbol, where the first dimension is distributed over two or more different time slots. That is, the method of Liu does not involve the application of time-memory (time-memory) or time-to-time conversion. The method of Liu involves BPSK encoding one bit per symbol.
In "practical methods for Trellis-Coded Modulation (A practical Approach to Trellis-Coded Modulation)" by Viterbi et al, IEEE journal of Communications (IEEE Communications Magazine), Vol.27, pp.7, pp.11-19 (1989), techniques for Trellis or convolutional coding are described in which the effect of symbols can be distributed over multiple slots. In order to decode a bit stream that has been encoded using a trellis code, a Viterbi (Viterbi) decoder may be used. The decoding of the trellis-encoded bit stream does not involve any inverse dimensional transformation, which has the effect of reducing the dimensionality of the symbols.
U.S. patent No. 3,388,330 to Kretzmer et al describes a partial response, multi-level data system in which the channel response to a single symbol extends over more than one symbol interval. Kretzmer et al do not describe any inverse dimensional transformation that has the effect of reducing the dimensionality of the symbols.
Fig. 7 illustrates an example method 700 for implementing a dimensional transformation at the transmitter (e.g., transmitter 200) side. Method 700 may be implemented by a DSP of a transmitter, such as transmitting DSP 214.
At 702, based on a particular modulation scheme, a transmitter may determine an initial digital drive signal to be used to modulate a dimension of an optical carrier to represent multi-bit symbols of a symbol stream. Each multi-bit symbol may be represented by an initial digital drive signal corresponding to a plurality of dimensions, including a particular combination of dimensions XI, XQ, YI, YQ in a single slot. For simplicity, the dimension used to represent each multi-bit symbol using the initial digital drive signal is denoted herein as the "second dimension". The initial digital drive signal at time slot t may be represented as
At 704, the transmitter may determine a transformed digital drive signal based on the dimensional transform and the initial digital drive signal determined at 702. In one example, the transmitter may generate the transformed digital drive signal by directly applying a dimensional transformation to the initial digital drive signal determined at 702. In another example, the transmitter may generate the transformed digital drive signal by applying a dimensional transformation to a digital signal based on the initial digital drive signal determined at 702. In another example, the transmitter may use a LUT corresponding to the dimensional transformation to determine the transformed digital drive signal.
Application of the dimensional transform may result in a transformed digital drive signal being generated that is designed to modulate the optical carrier such that each multi-bit symbol is represented by multiple dimensions of the optical carrier, denoted herein as "first dimensions", to distinguish them from the dimensions used to represent each multi-bit symbol using the initial digital drive signal. The first dimension is different from the second dimension. The first dimension comprises a particular combination of dimensions XI, XQ, YI, YQ at two or more different time slots. According to some examples, the plurality of second dimensions is smaller than the plurality of first dimensions. Given an initial digital drive signal at time slot t, it is denoted asThe converted digital drive signal at the same time slot t can be correspondingly denoted as SX(t)、SY(t)。
At 706, the transmitter may generate a modulated optical signal using the transformed digital drive signal determined at 704. For example, as described with respect to fig. 2, the digital drive signal S may be generated by converting the converted digital drive signal SX(t)、SY(t) conversion to a corresponding analog drive signal, driving an electro-optic modulator with the analog drive signal to produce a modulated polarized optical signal, and combining the modulated polarized optical signals to form an optical signal (e.g., optical signal 260). Instead of the modulated optical signal which has been generated using an initial digital drive signal designed to represent each multi-bit symbol using a plurality of second dimensions, a transformed digital drive signal is used to generate the modulated optical signalEach multi-bit symbol is represented using a plurality of first dimensions, wherein the first dimensions are distributed over two or more different time slots.
At 708, a transmitter may transmit the modulated optical signal over a communication channel. As a result of the modulation having been performed using the transformed digital drive signal, each multi-bit symbol may be represented using a first dimension of the optical signal, wherein the first dimension is distributed over two or more different time slots.
Fig. 8 illustrates an example method 800 for implementing an inverse dimensional transform at a receiver side, such as
At 802, a receiver may receive an optical signal. The received optical signal may represent a stream of multi-bit symbols. According to some examples, the received optical signal may include a degraded version of the modulated optical signal generated at the transmitter side according to method 700. That is, the received optical signal may have been generated by modulating a plurality of first dimensions of the optical carrier to represent each multi-bit symbol. The first dimension may include a particular combination of dimensions XI, XQ, YI, YQ in two or more slots.
At 804, the receiver may determine a digital signal corresponding to a dimension of the received optical signal. For example, as described with respect to fig. 3, a received optical signal, such as signal 360, may be split into orthogonally polarized components using a polarizing beam splitter. The optical mixer may process the components with respect to an optical signal, and the optical detector may convert an output of the optical mixer into an analog signal, which may be converted into a received digital signal. In a specific time slot t, the received digital signal can be represented by RX(t)、RY(t) represents.
At 806, the receiver may determine an initial digital drive signal estimate based on the inverse dimensional transform and the received digital signal determined at 804. In one example, the receiver may generate an initial digital drive signal estimate by directly applying an inverse dimensional transform to the received digital signal determined at 804. In another example, the receiver may generate an initial digital drive signal estimate by applying an inverse dimensional transform to the digital signal (which is based on the received digital signal determined at 804).
The application of the inverse dimensional transform results in each multi-bit symbol being represented by an initial digital drive signal estimate corresponding to a plurality of dimensions, denoted herein as "second dimensions", to distinguish them from the dimensions used for each multi-bit symbol represented using the received digital signal. The second dimension may correspond to the second dimension described with respect to method 700. The second dimension is different from the first dimension. The second dimension includes a particular combination of dimensions XI, XQ, YI, YQ in a single slot. According to some examples, the plurality of second dimensions are smaller than the plurality of first dimensions. Given a received digital signal at time slot t, denoted RX(t)、RY(t), the initial digital drive signal estimates at the same time slot t may be expressed as
At 808, the receiver can determine an estimate of the multi-bit symbol using the initial digital drive signal estimate determined at 806. For example, this determination may include comparing the digital signal generated at 804 to a predetermined threshold value
The remainder of this document provides example techniques for implementing dimensional transformations on the transmitter side and corresponding inverse dimensional transformations on the receiver side. In the following example, the dimensional transformation is applied by the DSP of the transmitter, such as by transmit DSP214 of
The application of the dimensional transformations and corresponding inverse dimensional transformations described in the following examples may be used to average signal degradation over multiple signal dimensions, including degradation caused by one or more of noise, non-linear effects, PDL, and analog defects.
According to some examples, matched filtering may be applied at the transmitter and receiver sides in order to achieve a low noise level. The substantially zero intersymbol interference may be implemented, for example, using a matched filter selected from the raised cosine family.
According to some examples, adaptive equalization circuitry may be employed at the receiver side to correct for PMD, PDL, and other linear variations. This equalization may be done in the time domain or the frequency domain or both, or by other transformations. Common methods of controlling this equalization include Recursive Least Squares (RLS) equalization, Constant Modulus Algorithm (CMA) equalization, Least Mean Square (LMS) equalization, and Decision Feedback Equalization (DFE). LMS equalization may provide an advantageous tradeoff between complexity and performance. The LMS circuit may cause noise correlations to be generated between symbols within a certain number N of integer time slots with respect to each other and/or symbols on different polarizations. As noted previously, the application of the dimensional transformation and the inverse dimensional transformation may involve a set of signals representing at least a first time slot and a second time slot, where the time slots are separated by an integer T. In the case where an LMS circuit is used in such an example, it may be interesting to choose T to be greater than the number of time slots M over which the LMS circuit produces noise-related and/or non-uniform noise enhancement. In this way, the noise averaging achieved by the dimensional transformation (and the inverse dimensional transformation) may not be hindered as a result of the noise correlation caused by the LMS circuit. Furthermore, dimensional transformations may be applied over dimensions with different noise levels to ensure an average noise level over the different dimensions.
Example 1
Fig. 9 is a schematic diagram illustrating an implementation of the dimension transformation at the transmitter side according to the first example. In this example, the dimensional transformation includes the matrix transformation H provided in equation 11：
Can be used for the initial digital driving signal
Signal SX(T-T) and SY(T-T) represents the converted digital drive signal at the first time slot T-T. The converted digital drive signal, i.e. S, in the second time slot tX(t) and SY(t) by taking the signals separatelyAnd
As shown in fig. 9, matrix transformation H1Combining subsequent partial complex conjugates is represented by a dimension transform 902. A dimensional transform 902 is applied to the initial digital drive signal 901 to generate a transformed digital drive signal 903. The converted digital drive signal 903 may undergo further processing before being converted to an analog drive signal. For example, FFT 904 may be applied to transformed digital drive signal 903, thereby producing frequency domain signal 905, which frequency domain signal 905 may then undergo frequency domain processing 906 to produce processed frequency domain signal 907. Frequency domain processing 906 may include the application of a matched filter. The processed frequency domain signal 907 may be converted to a corresponding time domain signal 909 by an IFFT 908.
Fig. 10 is a schematic diagram showing example details for implementing a dimension transformation according to a first example. That is, the dimension transform 902 described with respect to fig. 9 may be implemented using the operations performed in fig. 10.
Given an initial digital drive signal
As shown in block 1004, an initial digital drive signalAre divided into pairs so that the signalsAnd signalPairing, and signaling
As shown in block 1006, an initial digital drive signalAndundergo a rotation of 45 degrees, which respectively result in the generation of a signal SX(T-T) and
as shown in block 1008, an initial digital drive signal
signal SX(T-T) and SY(T-T) is the converted digital drive signal at the first time slot T-T. SignalAnd
Accordingly, the operations performed in fig. 10 are performed by an initial digital drive signal 901 (e.g., as shown in fig. 10) that will be at a particular time slot t) Converted into a converted digital drive signal 903 (e.g., S as shown in fig. 10) at the same particular time slot tX(t) and SY(t)), may be used to implement the dimension transform 902 described with respect to fig. 9. The operations in FIG. 10 illustrate but one example of how the dimension transform 902 is implemented.
Fig. 11 is a schematic diagram illustrating an implementation of an inverse dimensional transformation at the receiver side according to a first example. In this example, the inverse dimensional transformation comprises the inverse matrix transformation provided in equation 3
Inverse matrix transformation at the receiver sideIs included as part of an inverse
Signal
The received
The parameters for
Fig. 12 is a schematic diagram showing example details for implementing an inverse dimensional transform according to a first example. That is, the inverse
Given a received digital signal RX(t)、RY(T) applying a delay of T time slots results in the generation of the received digital signals R, respectivelyX(t–T)、RY(T-T). This delay is represented by block 1202.
As shown in block 1204, a received digital signal RX(t)、RY(t)、RX(t–T)、RY(T-T) is divided into pairs such that the signal RX(T-T) and the signal RY(t) pairing, and signal RX(t) with the signal RY(T-T) pairing.
Signal RX(t) and RY(t) may undergo complex conjugate operations, represented by block 1206, to generate signals, respectively
as shown in block 1208, the signal RX(T-T) andmay undergo a 45 degree rotation resulting in a separate generation of a signal
as shown in block 1210, a signalAnd RY (T-T) may also undergo 45 degree rotation, which results in separate generation of signals
signal
Accordingly, the operation performed in FIG. 12, by the Jockey, isReceived
It can be shown by calculation that the aggregate NSR of the initial digital drive signal estimate 1105 is equivalent to the aggregate NSR of the received
Example 2
According to a second example, the dimension transformation comprises the matrix transformation H provided in equation 52：
Can be used for the initial digital driving signalAndapplying a matrix transformation H2To respectively generate converted digital driving signals SX(T-T) and SY(T), where T-T represents a first integer time slot and T represents a second integer time slot. This is shown in equation 6.
Signal SX(T-T) represents the converted digital drive signal in the X-polarization of the first time slot T-T, and the signal SY(t) denotes the transformation on the Y polarization of the second time slot tThe latter digital drive signal.
Fig. 13 is a schematic diagram showing example details for implementing a dimension transformation at the transmitter side according to a second example.
As shown in block 1302, an initial digital drive signal
As shown in
As shown in
Processed frequency domain signal S'X(f) And S'Y(f) Can be respectively converted into corresponding time domain signals represented as S by IFFT 1308X(T-T) and SY(t)。
Accordingly, the operation performed in FIG. 13 is performed by applying the initial digital drive signal
According to a second example, the inverse dimensional transformation comprises the inverse matrix transformation provided in
Can be applied to the received digital signal RX(t) and RY(T-T) applying an inverse matrix transform
Fig. 14 is a schematic diagram illustrating an implementation of the inverse dimensional transformation at the receiver side according to the second example.
Given the received digital signal R in the second time slot tX(t) and RY(T), a delay of T slots, such as
As shown in block 1404, the signal RX(T-T) and RY(t) may undergo a 45 degree rotation, which respectively results in a signal being generated
Accordingly, the operation is performed in fig. 14 by receiving the digital signal RX(t-T)、RY(t) separately converting to initial digital drive signal estimatesCan be used to implement the inverse dimensional transformation represented by equation 8. The operations in FIG. 14 may be implemented instead of the inverse dimension transform 1108 in FIG. 11. In this case, the operations shown in FIG. 13 would be implemented in place of the dimension transform 902 in FIG. 9.
The dimensional transformation of example 2 (see equation 6 and fig. 13) is a linear time-invariant operation. Accordingly, it may be inverted using an adaptive equalizer circuit, which may be implemented in the receiving DSP314 as part of the channel impairment compensation, for example. In practice, the dimensional transformation of example 2 can be considered as an example of a time-invariant linear transformation, such as that applied by the channel itself, but which is intentionally applied at the transmitter side. Thus, the adaptive equalization performed at the receiver side may be able to invert the dimensional transformation together with the channel linear impairments. In contrast, the dimensional transformation of example 1 (see equation 2 and fig. 10) is a time-varying transformation because it involves dividing time samples into pairs. Accordingly, the channel equalizer at the receiver side may not be able to reverse this operation.
As a result of I/Q power imbalance or timing skew, the noise power may vary between dimensions XI, XQ, YI, and YQ at a given time slot. Example 3 and example 4 below describe matrix transformation H, respectively1And H2Which may average impairments that have different effects on the I and Q components of the X and Y polarizations.
Example 3
According to a third example, a matrix transformation H comprising the first example1The dimensional transformation of the modified version of (2) may be implemented at the transmitter side. In this third example, the matrix transformation is provided by equation 9For, the matrix transform is represented as H3：
Matrix transformation H3Can be used instead of the matrix transformation H in equation 21Thus,
as described with respect to equation 2, the signal SX(T-T) and SY(T-T) represents the converted digital drive signal at the first time slot T-T. The converted digital drive signal, i.e. S, in the second time slot tX(t) and SY(t) may be respectively passed through the fetch signalAnd
According to a third example, the inverse dimensional transformation comprises the inverse matrix transformation provided in equation 11
Inverse matrix transformationCan be used instead of the inverse matrix transformation in equation 4
as described with respect to equation 4, the signalAnd
Given the impairments at the transmitter side that have different effects on the I and Q components of the X and Y polarization, it can be shown to include a matrix transformation H3The implementation of the dimensional transformation of (c) may average the impairment over the entire dimension.
Example 4
According to a fourth example, comprising the matrix transformation H of the second example2The dimensional transformation of the modified version of (1) may be implemented at the transmitter side. In a fourth example, the matrix is transformed (denoted as H)4) Provided by equation 13:
matrix transformation H4Can be used instead of the matrix transformation H in equation 62To obtain equation 14:
as described with respect to equation 6, the signal SX(T-T) represents the converted digital drive signal in the X-polarization of the first time slot T-T, and the signal SY(t) represents the converted digital drive signal on the Y-polarization of the second time slot t.
According to a fourth example, the inverse dimensional transformation comprises the inverse matrix transformation provided in equation 15
Inverse matrix transformationCan be used instead of the inverse matrix transformation in equation 8
as described with respect to equation 8, the signal
Given the impairments at the transmitter side that have different effects on the I and Q components of the X and Y polarizations, it can be shown that the matrix transformation H is involved4The implementation of the dimensional transformation of (a) may average the impairment over the whole dimension.
Example 5
According to a fifth example, the dimension transformation may comprise a pair of four-dimensional signalsUsing a 4 × 4 Hadamard matrix followed by interleaving of different dimensions, e.g.Such asOn the transmitter side, a 4 × 4 real matrix multiplied by a matrix such as an adama matrix may be applied, which will differ from the 2 × 2 complex matrix mentioned in equation 6.
At the receiver side, the inverse of the interleaving matrix may be applied followed by the inverse real hadamard matrix transformation, such as that provided in
Fig. 15 is a histogram of received values that have undergone inverse dimensional transformation in combination with dimensional de-interleaving and application of the inverse of the real 4 x 4 hadamard matrix as described with respect to example 5. The received values are based on multi-bit symbols that have been generated at the transmitter based on a Dual Polarization (DP) -16QAM modulation scheme, which symbols have undergone a dimensional transformation at the transmitter side.
Each of the horizontal and vertical axes shows a particular dimension in time, such asThe received histogram includes a cloud of received symbols centered around an ideal transmitted symbol. The difference between the received point and the closest ideal DP-16QAM point determines the channel noise. The horizontal and vertical dashed lines represent the square of the minimum Euclidean distance equal to 1 (i.e., d)2 min1) direction. Solid diagonal arrow d2 min2 direction. The graph of fig. 15 demonstrates that applying the inverse dimensional transformation results in more nonlinear noise being distributed along the diagonal and less along the vertical and horizontal lines. By having the non-linear noise distributed in this way, the likelihood of detecting erroneous symbols during carrier recovery may be reduced, which may ultimately result in a lower BER.
In the previous example, soft FEC decoding (such as ML decoding) may be used to recover the corrected client data bits. Soft decoding may be performed in multiple dimensions. By increasing the number of dimensions used for soft decoding, it is possible to improve performance by exploiting correlation and using higher dimensional geometries in constellation design. However, this improvement may come at the cost of increased circuit complexity.
In the foregoing example, the delay T is described as an integer number of slots. More generally, however, the delay T included as part of the dimensional transformation or inverse dimensional transformation may be a non-integer or fractional number.
The scope of the claims should not be limited by the details set forth in the examples, but should be given the broadest interpretation consistent with the description as a whole.
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