Sub-sampled carrier phase recovery

Presented herein are sub-sampled carrier phase recovery techniques. In accordance with one example, a plurality of consecutive symbols associated with a received optical signal is obtained. Carrier phase recovery of the optical signal is performed using one or more carrier phase estimation stages. At each of the one or more carrier phase estimation stages, a subset of the plurality of consecutive symbols is selected for use in carrier phase estimation. The subset of symbols selected for use in carrier phase estimation at each of the one or more stages comprises symbols that provide the most phase recovery information for each of the one or more stages.

TECHNICAL FIELD

The present disclosure relates to carrier phase recovery in an optical receiver.

BACKGROUND

In recent years there has been an increase in the use of optical fiber communication networks. In an optical fiber communication network, an optical transmitter takes an electrical input and converts it to an optical output using a light source (e.g., laser diode, Light Emitting Diode (LED), etc.). The light from the transmitter is coupled into an optical fiber and is transmitted through the optical fiber to an optical receiver. The optical receiver converts the light back into an electrical signal.

Early optical fiber communication networks used transmission of one bit of information per data symbol. However, due to the need for high-capacity communications, there is an increasing demand for higher bit rates. This has led to the use of higher order modulation schemes for optical transmissions. Modulation schemes that have been implemented include, for example, Quaternary Phase Shift Keying (QPSK) and M-Quadrature Amplitude Modulation (M-QAM), wherein M is an integer with the power of 2 (i.e., 2, 4, 8, 16, 32, 64, etc.). In such modulation schemes, the optical transmitter includes an optical modulator that modulates the optical signal to carry the additional data.

DESCRIPTION OF EXAMPLE EMBODIMENTS

Overview

Presented herein are sub-sampled carrier phase recovery techniques. In accordance with one example, a plurality of consecutive symbols associated with a received optical signal is obtained. Carrier phase recovery of the optical signal is performed using one or more carrier phase estimation stages. At each of the one or more carrier phase estimation stages, a subset of the plurality of consecutive symbols is selected for use in carrier phase estimation. The subset of symbols selected for use in carrier phase estimation at each of the one or more stages comprises symbols that provide the most phase information about the optical signal that is relevant for phase error estimation in each of the one or more stages.

EXAMPLE EMBODIMENTS

FIG. 1is a block diagram illustrating part of a coherent optical receiver10configured to perform sub-sampled carrier phase recovery techniques in accordance with examples presented herein. The illustrated portion of optical receiver10comprises a chromatic dispersion (CD) filter module12, a polarization-mode dispersion (PMD) filter module14, a carrier phase recovery module16, and a Forward Error Correction (FEC) decoder18. The optical receiver10is a Polarization Multiplexed 16-Quadrature Amplitude Modulation (PM-16-QAM) optical receiver. That is, optical receiver10is configured to process and decode optical signals modulated in accordance with a modulation scheme that uses four in-phase (I) and four quadrature (Q) values that yield four bits per symbol, creating 16 possible states.

Complex-valued digital input data20is received and processed by the chromatic dispersion filter module12and the polarization-mode dispersion filter module14. As shown, the complex-valued digital input data20comprises X-polarized components in a scattered arrangement22and Y-polarized components in a scattered arrangement23. The chromatic dispersion filter module12may comprise one or more filters21for application to the X-polarized and Y-polarized components to compensate for the chromatic dispersion in the complex-valued digital input data20. Similarly, the polarization-mode dispersion filter module14may comprise one or more filters30for application to the X-polarized and Y-polarized components to compensate for the polarization-mode dispersion in the complex-valued digital input data20.

Filtered data35(i.e., data processed by the chromatic dispersion filter module12and the polarization-mode dispersion filter module14) is provided to the carrier phase recovery module16. The filtered data35includes X-polarized components in a ring-shaped pattern24and Y-polarized components in a ring-shaped pattern25.

The carrier phase recovery module16comprises two carrier phase estimation (CPE) blocks40each of which are associated with one of the X-polarized components and Y-polarized components. The X-polarized components and Y-polarized components may exchange phase estimation results to increase the overall estimation accuracy. The carrier phase estimation blocks40each comprise a Viterbi-Viterbi carrier phase estimation stage (Viterbi-Viterbi stage)45and a Maximum-Likelihood carrier phase estimation stage (Maximum-Likelihood stage)50. The Viterbi-Viterbi stages45each comprise Viterbi-Viterbi sub-sampling selection logic55, while the Maximum-Likelihood stages50each comprise Maximum-Likelihood sub-sampling selection logic60.

In general, phase error is induced by an optical channel and phase noise associated with the finite line width of the transmit laser and local-oscillator laser receiver. The carrier phase recovery module16is configured to estimate the phase error and use that phase error to generate phase recovered data65. That is, the carrier phase recovery module16is configured to use the estimated phase error to convert the ring shaped patterns24and25in the filtered data35to respective 16-QAM constellations (i.e. constellations from which the phase error has been removed)26and27.FIG. 1illustrates the standard 16-QAM constellations26(corresponding to the X-polarized components) and27(corresponding to the Y-polarized components) forming part of the phase-recovered data65. The phase-recovered data65is provided to Forward Error Correction (FEC) decoder18.

Certain conventional techniques perform carrier phase estimation based on all received symbols. These conventional methods are accurate and provide good tolerance to laser phase noise, non-linear phase noise, and local oscillator (LO)-frequency offset. However, these methods are also complex and may consume significant amounts of power. Presented herein are techniques that select a subset of symbols for use in one or more carrier phase estimation stages in order to reduce the power requirements associated with the carrier phase recovery. The techniques presented herein select the subset of symbols in a manner that substantially maintains a high level performance achieved with techniques that use all received symbols for carrier phase recovery.

More specifically, as described further below, the carrier phase estimation blocks40ofFIG. 1are configured to implement sub-sampling selection techniques in which only certain symbols (i.e., a subset of the received symbols) are used during carrier phase recovery (e.g., in each of the Viterbi-Viterbi carrier phase estimation stages45and the Maximum-Likelihood carrier phase estimation stages50). The symbols selected for use in each stage are, in general, the symbols with the highest ratio between the measured signal phase error and additive noise. That is, the symbols that provide the most phase information about the received optical signal that is relevant for a specific stage are selected for use in that stage. The “most phase information about the received optical signal that is relevant for a specific stage” refers to the most available phase recovery information for a given stage. For instance, the Viterbi-Viterbi carrier phase estimation is unable to use constellation points in the 2ndring, whilst constellation points in the outer rings give the minimum phase error for a given amount of additive noise.

Reference is now made toFIGS. 2A,2B, and3.FIG. 2Ais a schematic diagram illustrating sub-sampling selection techniques in an example Viterbi-Viterbi carrier phase estimation stage45in accordance with examples presented herein. As shown, the Viterbi-Viterbi stage45comprises a ring partitioning segment80, the aforementioned sub-sampling selection logic55, a 4th-power function segment85, an adder tree segment90(for moving average filtering), an unwrapping segment95(vector-to-angle conversion, unwrapping, phase-to-vector conversion), and a symbol rotation segment100.

In operation, optical signals are received at an optical receiver at a high rate (e.g., at a rate of 32 giga-baud (GBAUD), but the application-specific integrated circuit (ASIC) of the optical receiver and/or other hardware components are typically clocked at a lower rate (e.g., they operate with a 500 Megahertz (MHz) clock). Therefore, the Viterbi-Viterbi stage45operates on a plurality of symbols in parallel. In the example ofFIG. 2A, 16 symbols are received and processed in parallel and are referred to as symbols R1through R16. It is to be appreciated that the use of 16 symbols is merely illustrative and that different numbers of symbols (e.g., 12, 32, 96, 108, etc.) could be processed in parallel, depending on the capabilities of the ASIC and/or other hardware components.

The parallel processing of a plurality (e.g., 16) of symbols through the entire Viterbi-Viterbi stage45may consume significant power. The sub-sampling selection techniques presented herein reduce the number of symbols processed at various segments of the Viterbi-Viterbi stage45, thereby reducing the power consumed by the Viterbi-Viterbi stage45.

A 4th-power function is an operation applicable to Quaternary Phase Shift Keying (QPSK) signals for phase error estimation. The 4th-power function segment85is used to remove the QPSK signals, thereby leaving only the phase error and additive noise. That is, the 4th-power function segment85generates a vector from which the data has been removed. For 16-QAM the 4th-power function cannot be directly applied in the same way as with QPSK signals. Therefore, a so-called “ring partitioning” approach is used in which, as shown inFIG. 3, a 16-QAM constellation is generally divided into three rings, namely a first (inner) ring110, a second (middle) ring115, and a third (outer) ring120. The rings, sometimes referred to herein as constellation radius rings, are used to group constellation points (symbols) into classes based on their distance from the center of the constellation.

More specifically, the first ring110is set a first distance from the center of the constellation (i.e., the first ring has a first radius representing the distance from the center of the constellation to the first ring). A number of symbols positioned less than this first distance from the center of the constellation will fall within the first ring110. The second ring115is set a second distance from the center of the constellation (i.e., the second ring has a second radius representing the distance from the center to the second ring). A number of symbols positioned less than the second distance from the center of the constellation, but greater than the first distance will fall within the second ring115. The third ring120is set a third distance from the center of the constellation (i.e., the third ring has a third radius representing the distance from the center to the third ring). A number of symbols positioned less than the third distance from the center of the constellation, but greater than the second distance will fall within the third ring120.

The first ring110and the third ring120are both QPSK-like because they each include four symbol points. The second ring115is not QPSK-like because it includes eight symbol points (with unequal angular spacing). In the example configuration of the Viterbi-Viterbi stage ofFIG. 2A, the ring partitioning is performed on the 16 received (original) symbols R1through R16at ring partitioning segment80. That is, when a symbol is received, the ring partitioning segment80determines within which of the three rings110,115, or120the symbol falls.

As noted above, symbols R1through R16are received at ring partitioning segment80.FIG. 2Aillustrates, in ring partitioning segment80, one box corresponding to each of these received symbols R1through R16that includes a number “1”, “2”, or “3” therein. The number within the box indicates the ring to which the received symbol belongs. For example, symbol R1is associated with a box that includes the number “3” therein, indicating that symbol R1falls in the third ring120(i.e., the ring partitioning segment80has classified symbol R1as a member of the third ring120). Symbols R2and R3are associated with boxes that include the number “2,” indicating that symbols R2and R3fall within the second ring115; symbol R4is associated with a box that includes the number “1,” indicating that symbol R4falls within the first ring110; and so on. Table 1, below, illustrates the received symbols ofFIG. 2Aand within which ring each of those symbols fall.

The sub-sampling selection logic55is connected between the ring partitioning segment80and the 4th-power function segment85. The sub-sampling selection logic55is configured to select a subset of the received symbols R1through R16for processing by the subsequent segments in the Viterbi-Viterbi stage45. In general, the symbols selected for subsequent use are the symbols that provide the most phase information about the optical signal that is relevant for phase error estimation in the subsequent Viterbi-Viterbi operations. More specifically, the 4th-power function results in a vector of the phase of a symbol. Additive Gaussian noise on a symbol will cause a greater phase error for symbols which fall within lower rings. Therefore phase estimates from symbols in outer rings have more valuable information than those in inner rings and should be selected preferentially. In addition, the 4thpower operation results in a longer vector for outer rings and hence weights those phase estimations preferentially. Other techniques involve normalizing the 4thpower vectors so that all are of the same length, and then applying a scaling (e.g. ×2, ×3, ×4) afterwards. The 4th-power function may only be used with symbols that fall within the first ring110or the third ring120(i.e., cannot be applied to second ring symbols). As such, with regards to the application of the 4th-power function to received symbols, the most phase information about the optical signal that is relevant for phase error estimation in a Viterbi-Viterbi stage can be obtained using third ring symbols, while the second most phase information for phase error estimation in a Viterbi-Viterbi stage can be obtained using first ring symbols, and no information can be obtained from second ring symbols.

In the example ofFIG. 2A, the 16 received symbols R1through R16are organized (divided) into eight (8) groups130(1)-130(8) that each comprises two sequential symbols (i.e. pairs of symbols). For example, group130(1) includes symbols R1and R2, group130(2) includes symbols R3and R4, and so on. As such,FIG. 2Aillustrates a sub-sampling factor of 2 that has approximately half of the complexity of a conventional approach that processes all parallel symbols. The sub-sampling logic55is configured to evaluate the symbols within a group to select the symbol in that group that, when the 4th-power function is applied thereto, will provide the most phase information about the optical signal that is relevant for phase error estimation in a Viterbi-Viterbi stage (i.e., identify the symbol with the highest ratio between the measured signal phase error and additive noise and which is useable in the Viterbi-Viterbi stage. For example, as noted, group130(1) comprises symbols R1and R2. R1falls within the third ring120, while R2falls within the second ring115. Third ring symbols provide the most information for phase error correction (i.e., have the highest ratio between the measured signal phase error and additive noise). Second ring symbols have the second highest ratio between the measured signal phase error and additive noise, but cannot be used with the 4th-power function and thus do not provide any information for phase error correction in the Viterbi-Viterbi stage45. As such, from group130(1) symbol R1is selected for subsequent processing by the 4th-power function segment85, while symbol R2is discarded (i.e., omitted for use in processing by the 4th-power function segment85).

As a further example, group130(4) comprises symbols R7and R8. R7falls within the first ring110, while R8falls within the third ring120. Third ring symbols have the highest ratio between the measured signal phase error and additive noise, while first ring symbols have the lowest ratio between the measured signal phase error and additive noise. As such, from group130(4), symbol R8is selected for subsequent processing by the 4th-power function segment85, while symbol R7is discarded.

Furthermore, group130(5) comprises symbols R9and R10that both fall within the second ring115. As noted, second ring symbols cannot be used with the 4th-power function and thus do not provide any information for phase error correction in the Viterbi-Viterbi stage45. As such, no symbols from group130(5) are selected for subsequent processing by the 4th-power function segment85. That is, both symbols R9and R10are discarded.

The symbols that are selected from each group130(1)-130(8) are circled inFIG. 2A. Additionally, Table 2 below illustrates each of the groups130(1)-130(8), the symbols in each group, the symbol that is selected for subsequent Viterbi-Viterbi stage operations, and the selected symbol ring classification.

As noted above, the ring partitioning segment80determines within which ring a received symbol falls. The sub-sampling selection logic55comprises one or more hardware elements (e.g., switches, multiplexers, etc.) that use the ring partitioning segment information to select the appropriate symbols. Further details of the sub-sampling and symbol selection logic55are provided below with reference toFIG. 2B. In essence, the sub-sampling selection logic55is configured to perform a comparison of the symbols within a group130(1)-130(8) to determine which one has the highest relative ratio between the measured signal phase error and additive noise and is useable for phase error estimation in the subsequent Viterbi-Viterbi operations.

FIG. 2Aillustrates an example in which the groups130(1)-130(8) each have two members and where one symbol is selected from each group. It is to be appreciated that these examples are merely illustrative and that other group sizes (e.g., groups of 4 symbols) are possible.

In the example ofFIG. 2A, as a result of the sub-sampling selection logic55, seven symbols are selected for processing by the 4th-power function segment85. As noted, the 4th-power function segment85produces vectors from which the original data has been removed. These vectors are then provided to the adder tree segment90.

Each of the received symbols has some noise associated therewith. The adder tree segment90is configured to use the vectors provided by the 4th-power function segment85to generate, for each group130(1)-130(8), an averaged vector over a sliding/moving window. This process reduces noise in the vectors.

It should be noted that the group130(5) associated with R9and R10does not provide any symbol to the 4th-power function segment85. Accordingly, the 4th-power function segment85does not provide a vector to the adder tree segment90. However, due to the averaging function of the adder tree segment90, an output for group130(5) is still produced (using the surrounding vectors) by the adder tree segment90that may be used for subsequent processing.

The averaged vectors for groups130(1)-130(8) produced by adder tree segment90are provided to the unwrap segment95to remove occasional phase jumps because of the 90 degree phase ambiguity (4thpower function). Using the averaged vectors, the unwrapping segment95generates a Viterbi-Viterbi estimated phase correction (offset)132(1)-132(8) for each group. At the symbol rotation segment100, the Viterbi-Viterbi estimated phase corrections132(1)-132(8) are then applied to the original symbols in the respective group.

More specifically, at the symbol rotation segment100, each of the original symbols R1through R16are provided to an associated processing block135(1)-135(16). Each block also receives a Viterbi-Viterbi stage phase error correction for the corresponding group. For example, blocks135(1) and135(2) receive the original symbols R1and R2, respectively. The blocks135(1) and135(2) also receive the Viterbi-Viterbi stage phase error correction132(1) corresponding to group130(1) to which symbols R1and R2belong. That is, the Viterbi-Viterbi stage phase error correction132(1) generated from R1is used for the phase error correction of both symbols R1and R2at the symbol rotation segment100. Table 3, below, illustrates the Viterbi-Viterbi stage phase error correction signal that is used to correct each of the symbols R1through R16at the symbol rotation segment100.

The symbol rotation segment100is configured to output a plurality of Viterbi-Viterbi phase error corrected signals, shown inFIG. 2Aas symbols R1′ though R16′. These symbols R1′ through R16′ may then be provided to the Maximum-Likelihood stage50of the phase error correction module40for additional phase correction, as described further below.

It should be noted that if the subsequent Maximum-Likelihood stage50is also sub-sampled, it is sufficient to apply the symbol rotation segment only to those symbols that will be used in the Maximum-Likelihood stage50. This further reduces complexity and power dissipation.

As noted,FIG. 2Bis a schematic diagram illustrating further details of the sub-sampling selection logic55and ring portioning segment80. As shown, symbols R1through R16are received and provided to the ring portioning segment80and a timing segment57. The ring portioning segment80includes a vector length calculation block81that feeds a ring decision block82. The output from the ring decision block82is provided to selection block58. The sub-sampling selection logic55also comprises a multiplexer59connected to the timing block57and the selection block58that uses the signals from these blocks to generate an output (Xselect) representing the selected symbol for a group of symbols.

FIG. 4is a schematic diagram illustrating sub-sampling selection techniques in an example Maximum-Likelihood stage250connected to a Viterbi-Viterbi stage245. As noted above, optical signals are received at an optical receiver at a high rate (e.g., at a rate of 32 GBAUD, but the receiver ASIC and/or other hardware components are typically clocked at a lower rate (e.g., they operate with a 500 MHz clock). Therefore, the Viterbi-Viterbi stage245and Maximum-Likelihood stage250operate on a plurality of symbols in parallel. In the example ofFIG. 4, 12 symbols are received and processed in parallel and are referred to as received (original) symbols R1through R12. It is to be appreciated that the use of 12 symbols is merely illustrative and that different numbers of symbols (e.g., 12, 32, 96, 108, etc.) could be processed in parallel, depending on the capabilities of the ASIC and/or other hardware components.

The parallel processing of a plurality (e.g., 12) symbols through the Viterbi-Viterbi stage245and Maximum-Likelihood stage250may consume significant power. The sub-sampling selection techniques presented herein reduce the number of symbols processed at various segments of both the Viterbi-Viterbi stage245and the Maximum-Likelihood stage250, thereby reducing the power consumed at the optical receiver.

In the example ofFIG. 4, the Viterbi-Viterbi stage245operates substantially the same as described above with reference toFIG. 2Ato generate a plurality of Viterbi-Viterbi phase error corrected signals, shown inFIG. 4as symbols R1′ though R12′. More specifically, the Viterbi-Viterbi stage245includes a ring partitioning segment280configured to determine within which of the three rings110,115, or120(as shown inFIG. 3) each of the received symbols R1through R12falls.FIG. 4illustrates, in ring partitioning segment280, one box corresponding to each of the received symbols that includes a number “1”, “2”, or “3” therein. The number within the box indicates the ring to which the received symbol belongs. Table 4, below, illustrates the received symbols R1through R12ofFIG. 4and which ring each of those symbols fall within.

As shown, sub-sampling selection logic255is connected between the ring partitioning segment280and a sub-sampled Viterbi-Viterbi phase estimation and correction block205. The sub-sampling selection logic255is, similar to the sub-sampling logic55of FIG.2A, configured to select a subset of the received symbols R1through R12for processing by the subsequent segments in the Viterbi-Viterbi stage245. In general, the symbols selected for subsequent use are the symbols that provide the most phase information about the optical signal that is relevant for phase error estimation in the subsequent Viterbi-Viterbi operations.

More specifically, as noted above, the 4th-power function results in a vector of the phase of a symbol. Additive Gaussian noise on a symbol will cause a greater phase error for symbols which fall within lower rings. Therefore phase estimates from symbols in outer rings have more valuable information than those in inner rings and should be selected preferentially. In addition, the 4thpower operation results in a longer vector for outer rings and hence weights those phase estimations preferentially. Other techniques involve normalizing the 4thpower vectors so that all are of the same length, and then applying a scaling (e.g. ×2, ×3, ×4) afterwards. The 4th-power function may only be used with symbols that fall within the first ring110or the third ring120(i.e., cannot be applied to second ring symbols). As such, with regards to the application of the 4th-power function to received symbols, the most phase information about the optical signal that is relevant for phase error estimation in a Viterbi-Viterbi stage can be obtained using third ring symbols, while the second most phase information for phase error estimation in a Viterbi-Viterbi stage can be obtained using first ring symbols, and no information can be obtained from second ring symbols.

In the example ofFIG. 4, the 12 received symbols R1through R12are divided into three (3) groups220(1),220(2), and220(3) that each comprises four sequential symbols. For example, group220(1) includes symbols R1-R4, group220(2) includes symbols R5-R8, and group220(3) includes symbols R9-R12. The sub-sampling logic255is configured to evaluate the symbols within each of the groups220(1)-220(3) to select the symbol in that group that, when the 4th-power function is applied thereto, will provide the most information for phase error correction. The symbols that are selected from each group220(1),220(2), and220(3) are circled inFIG. 4. Additionally, Table 5 below illustrates each of the groups220(1),220(2), and220(3); the symbols in each group, the symbol that is selected for subsequent Viterbi-Viterbi stage operations, and the selected symbol ring classification.

The sub-sampled Viterbi-Viterbi phase estimation and correction block205represents the operations/functions that are performed to generate Viterbi-Viterbi phase error corrected signals, shown inFIG. 4as symbols R1′ though R12′. In this example, the sub-sampled Viterbi-Viterbi phase estimation and correction block205corresponds to the 4th-power function operations, the adder tree operations, the unwrapping operations, and the symbol rotation operations described above. As noted elsewhere herein, in certain examples only symbols that will used for the sub-sampled Maximum-Likelihood stage250are rotated before the Maximum-Likelihood stage250to reduce complexity.

As a result of the processing described above, the plurality of Viterbi-Viterbi phase error corrected symbols R1′ though R12′ (or a subset thereof) are provided to the Maximum-Likelihood stage250. The Maximum-Likelihood stage250comprises sub-sampling selection logic225, a sub-sampled Maximum-Likelihood phase estimation block226, and a symbol rotation segment234.

Sub-sampling selection logic225is configured to receive the Viterbi-Viterbi phase error corrected symbols R1′ though R12′ and is configured to select a subset of these symbols R1′ through R12′ for processing by the subsequent segments in the Maximum-Likelihood stage250. The sub-sampling selection logic225may be implemented in a manner similar to the arrangement ofFIG. 2B. In general, the symbols selected for subsequent use are the symbols that provide the most phase information about the optical signal that is relevant for the subsequent Maximum-Likelihood operations. More specifically, depending on the constellation symbol a certain phase error (angle) translates into error vectors with varying length. First ring symbols translate into the shortest length vector, second ring symbols translate into a medium length vector, and third ring symbols translate into the longest vector. The Additive white Gaussian noise that impairs the phase error estimation is independent of the constellation symbol. Consequently, the ratio between the measured signal phase error and additive white Gaussian noise varies with the diameter of each ring, where first ring symbols provide a weak phase estimate, second ring symbols provide a medium phase estimate, and third ring symbols provide a strong phase estimate. In other words, outer constellations have better phase information.

In the example ofFIG. 4, the 12 Viterbi-Viterbi phase error corrected symbols R1′ though R12′ are divided into six (6) groups230(1)-230(6) that each comprise two sequential symbols (i.e., symbol pairs). For example, group230(1) includes symbols R1′ and R2′, group230(2) includes symbols R3′ and R4′, and so on. The sub-sampling logic225is configured to evaluate the symbols within a group to select the symbol in that group that will provide the most phase information about the optical signal that is relevant for the subsequent Maximum-Likelihood operations (i.e., the symbol having the highest ratio between the measured signal phase error and additive noise). For example, as noted previously, group230(1) comprises symbols R1′ and R2′. R1′ falls within the third ring120, while R2′ falls within the second ring115. Third ring symbols have the highest ratio between the measured signal phase error and additive noise, while second ring symbols have the second highest ratio between the measured signal phase error and additive noise. As such, symbol R1′ is selected from group230(1) for subsequent processing, while symbol R2′ is discarded (i.e., omitted for use in processing by the sub-sampled Maximum-Likelihood phase estimation block226).

As a further example, group230(2) comprises symbols R3′ and R4′. R3′ falls within the second ring115, while R4′ falls within the third ring120. Second ring symbols have the second highest ratio between the measured signal phase error and additive noise, while first ring symbols have the lowest ratio between the measured signal phase error and additive noise. As such, from group230(2) symbol R3′ is selected for subsequent processing, while symbol R4′ is discarded.

The symbols that are selected from each group230(1)-230(6) are circled inFIG. 4. Additionally, Table 6 below illustrates each of the groups230(1)-230(6), the symbols in each group, and the symbol that is selected for subsequent Maximum-Likelihood stage operations, and the selected symbol ring classification.

The sub-sampling selection logic225comprises one or more hardware elements (e.g., switches, multiplexers, etc.) that use the ring partitioning segment information to select the appropriate symbols. In essence, the sub-sampling selection logic225is configured to perform a comparison of the symbols within a group230(1)-230(6) to determine which one has the relative highest ratio between the measured signal phase error and additive noise. If both the Viterbi-Viterbi and Maximum-Likelihood stages are sub-sampled, the vector-length and ring decisions do not need to be made again within the sub-sampling logic225(as they were already completed in sub-sampling logic255). In such examples, only the symbol selection block changes.

FIG. 4illustrates an example in which the groups230(1)-230(6) each have two members and where one symbol is selected from each group. It is to be appreciated that these examples are merely illustrative and that other group sizes (e.g., groups of 4 symbols) are possible.

In the example ofFIG. 4, as a result of the sub-sampling selection logic225, six symbols are selected for processing by the sub-sampled Maximum-Likelihood phase estimation block226. In general, the sub-sampled Maximum-Likelihood phase estimation block226is configured to perform Maximum-Likelihood operations using the six selected symbols (symbols R1′, R3′, R5′, R7′, R10′, and R11′) to generate a Maximum-Likelihood phase estimates (offset)232(1)-232(6) for each group. Details of an example Maximum-Likelihood phase estimation block are provided below with reference toFIG. 6.

At the symbol rotation segment235, the Maximum-Likelihood phase estimates232(1)-232(6) are applied to the Viterbi-Viterbi phase error corrected symbols R1′ though R12′ in the respective group. More specifically, at the symbol rotation segment235, each of the Viterbi-Viterbi phase error corrected symbols R1′ though R12′ are provided to an associated processing block235(1)-235(12). Each block235(1)-235(12) also receives a Maximum-Likelihood phase estimate for the corresponding group. For example, blocks235(1) and235(2) receive the Viterbi-Viterbi phase error corrected symbols R1′ and R2′, respectively. The blocks235(1) and235(2) also receive the Maximum-Likelihood phase estimate232(1) corresponding to group230(1) to which symbols R1′ and R2′ belong. That is, the Maximum-Likelihood phase estimate232(1) generated from R1′ is used for the phase error correction of both symbols R1′ and R2′ at the symbol rotation segment235. Table 7 below illustrates the Maximum-Likelihood phase estimate that is used to correct each of the symbols R1′ through R12′ at the symbol rotation segment235.

In certain embodiments, to reduce the overall complexity of the two stage carrier recovery, the Viterbi-Viterbi phase estimate is only applied to symbols that will be considered in the Maximum-Likelihood stage (R1′, R3′, R5′, R7′, R10′ and R11′) behind the Viterbi-Viterbi stage. And after Maximum-Likelihood phase error estimation the sum of the Viterbi-Viterbi estimate and the Maximum-Likelihood estimate is applied to all corresponding uncorrected symbols (R1-R12). Such an arrangement is shown below inFIG. 6.

The symbol rotation segment235is configured to output a plurality of complete phase error corrected signals, shown inFIG. 4as symbols R1″ though R12″. These symbols R1″ through R12″ represent fully phase recovered symbols (i.e., symbols that have undergone both Viterbi-Viterbi and Maximum-Likelihood phase error recovery). The fully phase recovered symbols may be provided to a Forward Error Correction decoder for subsequent processing.

FIG. 5is a schematic diagram illustrating alternative sub-sampling selection techniques in a Maximum-Likelihood stage350connected to Viterbi-Viterbi stage245. Viterbi-Viterbi stage245operates as described above with reference toFIG. 4to generate the plurality of Viterbi-Viterbi phase error corrected symbol R1′ though R12′. As a result, the plurality of Viterbi-Viterbi phase error corrected symbols R1′ though R12′ are provided to the Maximum-Likelihood stage350. The Maximum-Likelihood stage350comprises sub-sampling selection logic325, a sub-sampled Maximum-Likelihood phase estimation block326, and a symbol rotation segment334.

Similar to sub-sampling selection logic225ofFIG. 4, the sub-sampling selection logic325is configured to select a subset of the received symbols R1′ through R12′ for processing by the subsequent segments in the Maximum-Likelihood stage350. In general, the symbols selected for subsequent use are the symbols that have the highest ratio between the measured signal phase error and additive noise. However, in addition to selecting the symbols that have the highest ratio between the measured signal phase error and additive noise, the sub-sampling selection logic325is also configured to only select symbols for which a precursor to that symbol was not used in the Viterbi-Viterbi stage operations. In other words, if a symbol is used in the Viterbi-Viterbi stage245, the sub-sampling selection logic325is configured to eliminate the Viterbi-Viterbi phase error corrected version of that symbol for use in the Maximum-Likelihood stage350. In essence, the sub-sampling selection logic325performs a two-stage selection process that eliminates Viterbi-Viterbi phase error corrected versions of symbols used in the Viterbi-Viterbi stage245and that, from the remaining symbols, selects the one that has the highest ratio between the measured signal phase error and additive noise. This guarantees maximum utilization of the available information about the actual phase error, since the previously unused symbols will contain the phase-error and an uncorrelated noise component which can be averaged.

In the example ofFIG. 5, the 12 Viterbi-Viterbi phase error corrected symbols R1′ though R12′ are divided into six (6) groups330(1)-330(6). The groups330(1)-330(6) in this each comprise two sequential symbols (i.e., a pair of symbols). For example, group330(1) includes symbols R1′ and R2′, group330(2) includes symbols R3′ and R4′, and so on.

As noted, the sub-sampling logic325performs a two-stage selection process to evaluate the symbols within a group to select a symbol in that group that will provide the most phase information about the optical signal that is relevant for phase error estimation in the subsequent Maximum-Likelihood operations. For example, group330(1) comprises Viterbi-Viterbi phase error corrected signals symbols R1′ and R2′. R1′ falls within the third ring120, while R2′ falls within the second ring115. Again, third ring symbols have the highest ratio between the measured signal phase error and additive noise, while second ring symbols have the second highest ratio between the measured signal phase error and additive noise. However, symbol R1(the precursor to symbol R1′) was selected from group220(1) in the Viterbi-Viterbi stage245. As such, sub-sampling selection logic325eliminates symbol R1′ from use in the Maximum-Likelihood stage350. Accordingly, sub-sampling selection logic325selects symbol R2′ for subsequent processing.

As a further example, group330(2) comprises symbols R3′ and R4′. R3′ falls within the second ring115, while R4′ falls within the third ring120. Neither of the precursors for symbols R3′ or R4′ (i.e., symbols R3or R4) were used in the Viterbi-Viterbi stage. As such, since second ring symbols have the second highest ratio between the measured signal phase error and additive noise, while first ring symbols have the lowest ratio between the measured signal phase error and additive noise, symbol R3′ is selected from group330(2) for subsequent processing and symbol R4′ is discarded.

In another example, group330(5) comprises symbols R9′ and R10′. R9′ falls within the second ring115, while R20′ falls within the third ring110. Third ring symbols have the highest ratio between the measured signal phase error and additive noise, while second ring symbols have the second highest ratio between the measured signal phase error and additive noise. However, symbol R10(the precursor to symbol R10′) was selected from group220(3) in the Viterbi-Viterbi stage245. As such, sub-sampling selection logic325eliminates symbol R10′ from use in the Maximum-Likelihood stage350. Accordingly, sub-sampling selection logic325selects symbol R9′ for subsequent processing.

The symbols that are selected from each group330(1)-330(6) are circled inFIG. 5. Additionally, Table 8 below illustrates each of the groups330(1)-330(6), the symbols in each group, the symbol that is selected for subsequent Maximum-Likelihood stage operations, and the selected symbol ring classification.

The sub-sampling selection logic325comprises one or more hardware elements (e.g., switches, multiplexers, etc.) that use the ring partitioning segment information to select the appropriate symbols. In essence, the sub-sampling selection logic325is configured to perform a two-stage analysis of the symbols within a group330(1)-330(6). First, the sub-sampling selection logic325eliminates any symbols for which a precursor of the symbols was used in the Viterbi-Viterbi stage245. Second, the sub-sampling selection logic325selects, from any remaining symbols, the symbol that have the highest ratio between the measured signal phase error and additive noise.

FIG. 5illustrates an example in which the groups330(1)-330(6) each have two members and where one symbol is selected from each group. It is to be appreciated that these examples are merely illustrative and that other group sizes (e.g., groups of 4 symbols) are possible.

In the example ofFIG. 5, as a result of the sub-sampling selection logic325, six symbols are selected for processing by the sub-sampled Maximum-Likelihood phase estimation block326. In general, the sub-sampled Maximum-Likelihood phase estimation block326is configured to perform Maximum-Likelihood operations using the six selected symbols (symbols R2′, R3′, R5′, R7′, R9′, and R11′) to generate a Maximum-Likelihood phase estimates (offset)332(1)-332(6) for each group.

At the symbol rotation segment334, the Maximum-Likelihood phase estimates332(1)-332(6) are then applied to the Viterbi-Viterbi phase error corrected symbols R1′ though R12′ in the respective group. More specifically, at the symbol rotation segment334, each of the Viterbi-Viterbi phase error corrected symbols R1′ though R12′ are provided to an associated processing block335(1)-335(12). Each block335(1)-335(12) also receives a Maximum-Likelihood phase estimate for the corresponding group. For example, blocks335(1) and335(2) receive the Viterbi-Viterbi phase error corrected symbols R1′ and R2′, respectively. The blocks335(1) and335(2) also receive the Maximum-Likelihood phase estimate332(1) corresponding to group330(1) to which symbols R1′ and R2′ belong. That is, the Maximum-Likelihood phase estimate332(1) generated from R2′ is used for the phase error correction of both symbols R1′ and R2′ at the symbol rotation segment334. Table 9, below, illustrates the Maximum-Likelihood phase estimate that is used to correct each of the symbols R1′ through R12′ at the symbol rotation segment335.

The symbol rotation segment334is configured to output a plurality of complete phase error corrected signals, shown inFIG. 5as symbols R1″ though R12″. These symbols R1″ through R12″ represent fully phase recovered symbols.

FIG. 6is a schematic diagram of another two-stage carrier phase estimation with sub-sampled Viterbi-Viterbi and Maximum-Likelihood carrier phase estimation stages in accordance with examples presented herein. More specifically,FIG. 6illustrates an arrangement where the Viterbi-Viterbi phase estimate is only applied to symbols that will be considered in the Maximum-Likelihood stage behind the Viterbi-Viterbi stage. After the Maximum-Likelihood phase error estimation, the sum of the Viterbi-Viterbi estimate and the Maximum-Likelihood estimate is applied to all corresponding uncorrected symbols (R1-R12).

FIG. 6illustrates a Viterbi-Viterbi stage445that is substantially similar to the Viterbi-Viterbi stage245ofFIG. 4. That is, the Viterbi-Viterbi stage445operates as described above to generate the plurality of Viterbi-Viterbi estimated phase corrections from the symbols selected through the sub-sampling techniques, in this case symbols R1, R6, and R10. The generated Viterbi-Viterbi estimated phase corrections generated from R1, R6, and R10are shown inFIG. 6as Viterbi-Viterbi estimated phase corrections432(1),432(6), and432(10), respectively.

Unlike in the above example ofFIG. 4, the Viterbi-Viterbi stage445does not apply the Viterbi-Viterbi estimated phase corrections432(1),432(6), and432(10) to the original symbols R1-R12. Instead, the Viterbi-Viterbi estimated phase corrections432(1),432(6), and432(10) are provided to a rotation segment434coupled to sub-sampling logic455. The symbols R1-R12are grouped in six (6) pairs. The sub-sampling logic455operates to select the symbol from each pair that, as detailed above, has highest ratio between the measured signal phase error and additive noise (outmost ring). Only the six symbols selected by the sub-sampling logic455receive Viterbi-Viterbi phase correction at rotation segment434.

The rotation segment434generates six Viterbi-Viterbi phase error corrected symbols, namely R1′, R3′, R5′, R7′, R10′, and R11′ that correspond to the symbols selected by the sub-sampling logic455. These Viterbi-Viterbi phase error corrected symbols are provided to Maximum-Likelihood stage450that comprises a decision segment481, multiplication segment482, an adder tree segment483, and a vector-to-angle conversion segment484. The segments481,482,483, and484collectively operate to generate six Maximum-Likelihood estimated phase corrections, shown inFIG. 6as470(1),470(3),470(5),470(7),470(10), and470(11) that correspond to Viterbi-Viterbi phase error corrected symbols, namely R1′, R3′, R5′, R7′, R10′, and R11′, respectively.

Also shown inFIG. 6is a correction block485that comprises an estimate addition segment486, an angle-to-vector conversion segment488, and a rotation segment490. The estimate addition segment484sums the Viterbi-Viterbi estimated phase corrections432(1),432(6), and432(10) and the corresponding Maximum-Likelihood estimated phase corrections470(1),470(3),470(5),470(7),470(10), and470(11) (i.e., generates combined estimated phase corrections). After angle-to-vector conversion segment488, the combined estimated phase corrections are applied to all corresponding uncorrected symbols (R1-R12) at rotation segment490to generate fully phase recovered symbols R1″-R12″.

FIG. 7is a flowchart of a method600in accordance with examples presented. Method600begins at605where a plurality of consecutive symbols associated with an optical signal received at an optical receiver is obtained. For example, the optical signal was transmitted over an optical fiber span by a transmitter and received at the optical receiver. At610, carrier phase recovery of the optical signal is performed using one or more carrier phase estimation stages. At615, a subset of the plurality of consecutive symbols is selected for use in carrier phase estimation. The subset of symbols selected for use in carrier phase estimation at each of the one or more stages comprises symbols that provide the most phase information about the optical signal that is relevant for phase error estimation in each of the one or more stages.

In certain examples, the one or more carrier phase estimation stages include a Viterbi-Viterbi carrier phase estimation stage that generates Viterbi-Viterbi phase error corrected symbols. In such embodiments, the selection of the subset of the plurality of consecutive symbols for carrier phase estimation may include performing ring partitioning of the symbols to determine within which of a first, second, or third constellation radius ring each of the symbols falls, organizing the plurality of consecutive symbols into a plurality of groups, and selecting, from each of the plurality of groups, a symbol that has the highest ratio between the measured signal phase error and additive noise and is useable in a given phase error estimation stage.

The above description is intended by way of example only.