Method and system for modulation-independent carrier phase recovery

A system for carrier phase recovery, including a receiver for receiving one or more frames of L symbols. A phase estimator performs carrier phase estimation for the received frames of L symbols, and the resulting carrier phase estimates are stored in a non-transitory computer-readable storage medium. One or more rotators de-rotates the received frames of L symbols by one or more of the carrier phase estimates, and a data processor calculates a sum of the outputs of the L de-rotated signals raised to an nth power, and determines a real part of the sum. A minimum determination device determines a minimum of the real part of the sum with respect to the carrier phase estimates, and phase unwrapping and multiplier removal is performed if a minimum has been determined.

BACKGROUND OF THE INVENTION

1. Technical Field

The present invention relates generally to carrier phase recovery, and more particularly, to modulation-independent feed-forward carrier phase recovery with a multiplier free structure.

2. Description of the Related Art

Carrier phase recovery is an important problem in optical coherent detection schemes, because of the phase noise incurred from laser linewidth. As use of multimedia communications services over packet data networks (e.g., the Internet) continues to grow, the demand for higher capacity in core data transport networks also continues to grow. Core data networks may include optical networks based on fiber optic technology. To increase the capacity of optical networks, advanced signal modulation techniques, such as quadrature phase shift key (QPSK) and quadrature amplitude modulation (QAM) have been developed. In particular, M-ary QAM (M-QAM) (e.g., 16-QAM and 64-QAM) have the potential to realize high-speed optical transmission with high spectral efficiency.

Digital coherent detection has been employed for detecting and demodulating received optical signals, and a key step in digital coherent detection is carrier phase recovery. Carrier phase may be degraded by laser phase noise in a received optical signal, and laser phase noise is dependent on the linewidth of the optical carrier. For example, for high-order M-QAM modulation formats (e.g., M>4), the tolerance for laser phase noise becomes smaller as the modulation increases. As modulation formats become higher and higher, there is a need for a carrier phase recovery system and method to be universal to any modulation format (e.g., modulation independent characteristics).

Various carrier phase recovery systems and methods have been developed, but there are very few systems and methods available that are capable of performing modulation-independent carrier phase recovery. For example, one existing modulation-independent carrier phase recovery system employs a feedback structure with a cost function to remove the dependence on modulation formats. However, the cost function is not sensitive to phase errors, and requires feedback to adjust the phase estimation, which is not practical for use in a parallel architecture. Moreover, none of the existing systems and methods are capable of performing multiplier-free carrier phase recovery.

BRIEF SUMMARY OF THE INVENTION

A method for carrier phase recovery, including receiving one or more frames of L symbols using a receiver, performing carrier phase estimation for the one or more frames of L symbols using a phase estimator, and storing resulting carrier phase estimates in a non-transitory computer-readable storage medium. The one or more frames of L symbols are de-rotated by one or more of the carrier phase estimates, a sum of the outputs of the L de-rotated signals is calculated and raised to an nthpower, and a real part of the sum is determined. A minimum of the real part of the sum with respect to the carrier phase estimates is determined, and phase unwrapping and multiplier removal is performed if a minimum has been determined

A system for carrier phase recovery, including a receiver for receiving one or more frames of L symbols, and a phase estimator for performing carrier phase estimation for the one or more frames of L symbols, the resulting carrier phase estimates being stored in a non-transitory computer-readable storage medium. One or more rotators de-rotate the one or more frames of L symbols by one or more of the carrier phase estimates. A data processor calculates a sum of the outputs of the L de-rotated signals raised to an nthpower, and determines a real part of the sum. A minimum determination device determines a minimum of the real part of the sum with respect to the carrier phase estimates, and phase unwrapping and multiplier removal is performed if a minimum has been determined

A computer readable storage medium comprising a computer readable program, wherein the computer readable program when executed on a computer causes the computer to perform the steps of receiving one or more frames of L symbols using a receiver, performing carrier phase estimation for the one or more frames of L symbols using a phase estimator, and storing resulting carrier phase estimates in a non-transitory computer-readable storage medium. The one or more frames of L symbols are de-rotated by one or more of the carrier phase estimates, a sum of the outputs of the L de-rotated signals is calculated and raised to an nthpower, and a real part of the sum is determined. A minimum of the real part of the sum with respect to the carrier phase estimates is determined, and phase unwrapping and multiplier removal is performed if a minimum has been determined.

DETAILED DESCRIPTION

The present invention is directed to optimizing performance of communication systems by employing carrier phase estimation and recovery in accordance with the present principles. In one embodiment, the present principles provide a feed-forward, modulation-independent computer implemented method for carrier phase recovery. In accordance with particularly useful embodiments the present principles may provide a multiplier-free carrier phase recovery method to reduce complexity, thereby improving hardware efficiency and optimizing system performance. In some embodiments, the feed-forward structure enables parallel implementation of high-speed coherent receivers without performance degradation.

The carrier phase of a carrier wave modulated with, for example, information symbols may be recovered by carrier phase recovery according to an embodiment of the present principles. A new cost function which estimates a carrier phase with an ultra-high sensitivity method as compared with conventional carrier phase estimation techniques may be employed. The new cost function may be employed in a feed-forward blind-phase searching method to recover original signals without specifying modulation formats (e.g., modulation-independent). Feed-forward systems and methods may modify or control a process using anticipated results or effects rather than requiring the use of previous results or effects, as required by feedback systems and methods.

It should be understood that embodiments described herein may be entirely hardware or may include both hardware and software elements, which includes but is not limited to firmware, resident software, microcode, etc. In a preferred embodiment, the present invention is implemented in hardware.

Referring now to the drawings in which like numerals represent the same or similar elements and initially toFIG. 1, an exemplary system/method100for carrier phase recovery is illustratively depicted in accordance with an embodiment of the present principles. Carrier recovery systems may be a circuit which may be employed to estimate and compensate for frequency and phase differences between a received signal's carrier wave and the receiver's local oscillator. A constellation may be rotated by one or more effects (e.g., laser linewidth) through which a signal passes.

In an illustrative embodiment, to estimate the carrier phase of received signals that are phase rotated (e.g., by laser linewidth), a carrier phase may be estimated in a frame of, for example, L symbols102. The symbols in the frame of L symbols102may include, for example, r(k), r(k−1), etc., with r representing a receiver for a signal, and k representing the kth signal. Phase noise may change slowly over consecutive several symbols, and the frame length L (e.g., a frame of length L may include L symbols) may depend on the magnitude of the laser linewidth in the system. In an embodiment, a one symbol delay may be included in block103to unwrap the phase noise. The signal frame including L symbols102(e.g., received signals that have been phase rotated by the laser linewidth) may be rotated (e.g., de-rotated) in block104using one or more rotators by a current estimate for phase noise (θn) stored in, for example, a lookup table (LUT) for phase estimation. The phase rotation applied to each signal in block104may include ejθn, where e is an exponent, θnis a current estimate for phase noise, and j is an imaginary constellation point.

In an embodiment, the phase estimate θnmay include angles which range from, for example, −π/4 to +π/4. The signals may pass through signal splitters in block105, and the de-rotated signals may be raised to, for example, the fourth (4th) power in block108to mitigate the impact of phase modulation from the signals. The outputs of block108may then be summed up in block110, and the real part of that sum (e.g., real part of a symbol) may be determined in block112. It is noted that the above-mentioned angle range (−π/4 to +π/4), and the power to which the signals are raised (4th) are presented as such for simplicity of illustration, but any angles or powers may be employed according to various embodiments of the present principles.

In an embodiment, a minimum of the output of block112may be determined in block107with respect to the phase estimate θn. The minimum is determined because all signal points may include a maximum projection to the x-axis or y-axis when there is not any phase rotation. However, the presence of, for example, either 45 or 90 degree rotation of the constellation points (e.g., nπ/2+π/4, or nπ/2, respectively) may determine the sign of the projection (e.g., plus or minus). For example, in the case of Binary Phase Shift Keying (BPSK), with, for example, two constellation points (0, π), employing a projection of the 4thpower in block108may become the maximum. If the BPSK is rotated by 45 degrees (e.g., (π/4, 5π/4), then the projection would be the minimum after applying the 4thpower operation in block108. However, the continual rotation of the constellation by 45 degrees may cause increased phase ambiguity (e.g., phase noise), so the minimum may be employed to determine the phase estimate in block114.

In an embodiment, the carrier phase may be estimated using the following method:

arg⁢⁢minθ∈(-π/4,π/4)⁢real⁢{∑l=0L-1⁢(r⁡(k+l)·exp⁡(-j⁢⁢θn))4},(1)
where −π/4, +π/4 represents a range of angles, L represents a number of symbols, l represents an index, r(k+l) represents a symbol in the set of symbols represented by L, and the phase is represented by exp(−jθn). Because of the use of the 4thpower operation in this example, the phase estimate may be limited to −π/4 to +π/4, which may cause cycle slips if non-differential decoding were employed. Therefore, phase unwrapping may be applied in block116to unwrap the current phase estimate based on the previous phase estimate to prevent cycle slips according to the present principles.

In an embodiment, the phase unwrapping may be performed according to the following method:

θn⁢{θn-π2while⁢⁢θn-θn-1>π4θn+π2while⁢⁢θn-θn-1<-π4θnotherwise,(2)
where θnrepresents a current phase estimate, and θn−1represents a previous phase estimate. As shown above, during phase unwrapping, the phase estimate θnmay be adjusted by 0, or ±π/2, depending on the previous phase estimate θn−1. Accordingly, the output of block104may be multiplied by 1, or ±j in block116, and results may be output in block118in an embodiment of the present principles. In an embodiment, the output of block118may be applied during a next phase of digital coherent detection to improve transmission speed and/or to remove phase noise present in a communication medium. Furthermore, the output of block118may also be employed to remove dependence on a particular modulation format, as discussed in further detail hereinbelow.

In some embodiments, phase unwrapping may also be performed in block116to the minimum determined in block114. For example, phase unwrapping may be performed in block116by adding multiples of π/2, corresponding to 1 or ±j (e.g., because of the exp(jθn) operation described above in equation (1)). In an illustrative embodiment, the output signal of block104may be split by a signal splitter105, and the phase unwrapping may be performed by a phase unwrapper in block116.

Although the above method may be employed with any type of modulation format without prior knowledge, there may be many multipliers present inside the carrier phase estimator according to the present principles. Therefore, in some embodiments, the method may be simplified, and employed without multipliers (e.g., to reduce hardware complexity and improve processing speed) as follows:

Referring now toFIG. 2, a diagram200showing exemplary original201and recovered constellations203for carrier phase recovery is illustratively depicted in accordance with an embodiment of the present principles. For illustrative purposes, original constellations201(e.g., including carrier phase noise) are shown with respect to various constellation types, including BPSK202, Quadrature Phase Shift Keying (QPSK)204, 8 Quadrature Amplitude Modulation (8QAM)206, and 16 Quadrature Amplitude Modulation (16QAM)208.

In an embodiment, recovered constellations203which have been recovered according to the present principles are illustratively depicted, and correspond to the original constellations201. The recovered constellations203include BPSK210, QPSK212, 8QAM214, and 16QAM. It is noted that although the above constellation types are shown, it is contemplated that any constellation types may be employed according to the present principles. As shown in the recovered constellations203, carrier phase noise has been successfully removed. More symbols may be employed for estimating the carrier phase for higher-order QAM (e.g., 8QAM, 16QAM, etc.) because of the averaging effects of the method according to the present principles.

Referring now toFIG. 3, an exemplary processing system300to which the present principles may be applied, is illustratively depicted in accordance with an embodiment of the present principles. The processing system300includes at least one processor (CPU)304operatively coupled to other components via a system bus302. A cache306, a Read Only Memory (ROM)308, a Random Access Memory (RAM)310, an input/output (I/O) adapter320, a sound adapter330, a network adapter340, a user interface adapter350, and a display adapter360, are operatively coupled to the system bus302.

A first storage device322and a second storage device324are operatively coupled to system bus302by the I/O adapter320. The storage devices322and324can be any of a disk storage device (e.g., a magnetic or optical disk storage device), a solid state magnetic device, and so forth. The storage devices322and324can be the same type of storage device or different types of storage devices.

A speaker332is operatively coupled to system bus302by the sound adapter330. A transceiver342is operatively coupled to system bus302by network adapter340. A display device362is operatively coupled to system bus302by display adapter360.

A first user input device352, a second user input device354, and a third user input device356are operatively coupled to system bus302by user interface adapter350. The user input devices352,354, and356can be any of a keyboard, a mouse, a keypad, an image capture device, a motion sensing device, a microphone, a device incorporating the functionality of at least two of the preceding devices, and so forth. Of course, other types of input devices can also be used, while maintaining the spirit of the present principles. The user input devices352,354, and356can be the same type of user input device or different types of user input devices. The user input devices352,354, and356are used to input and output information to and from system300.

Moreover, it is to be appreciated that system400described below with respect toFIG. 4is a system for implementing respective embodiments of the present principles. Part or all of processing system300may be implemented in one or more of the elements of system400.

Further, it is to be appreciated that processing system300may perform at least part of the method described herein including, for example, at least part of method600ofFIG. 6. Similarly, part or all of system400may be used to perform at least part of method600ofFIG. 6.

Referring now toFIG. 4, with continued reference toFIG. 1, an exemplary system400for carrier phase recovery is illustratively depicted in accordance with an embodiment of the present principles. In one embodiment, data (e.g., a data transmission) may be received by a receiver418and a phase estimator402may be employed to estimate the carrier phase of received symbols102that have been phase rotated by, for example, phase noise caused by laser linewidth. A storage device404may be employed to store data in, for example, a LUT106, and a rotator device406may rotate (e.g., de-rotate) by the phase stored in the LUT106. A data processor408may raise de-rotated symbols to an nthpower to mitigate the impact of phase modulation from the signals, sum up the outputs (e.g., de-rotated symbols) of the rotator device406, and take the real part of the sum (e.g., real signals) according to the present principles. In various embodiments, all or some of the above-mentioned devices may be attached to a system bus401.

In an embodiment, a minimum determination device410may determine the minimum of the outputs of the data processor408(e.g., minimum of the real number in block112) with respect to a current carrier phase estimate θn. If a minimum is not reached, a controller device116may iterate the phase estimator402, rotator device406, data processor408, and minimum determination device410according to the present principles. A multiplier remover414may be employed to remove multipliers present in the system400to reduce hardware complexity and increase processing speed. A phase unwrapper412may unwrap a current phase estimate based on a previous phase estimate according to the present principles. The controller device416may control any aspect of the system and method according to the present principles, including data transmitting and receiving, and may be a global or local controller in various embodiments.

Referring now toFIG. 5, a diagram illustratively depicting a decision boundary500for removing multipliers during carrier phase recovery is illustratively depicted in accordance with an embodiment of the present principles. In one embodiment, to avoid (e.g., remove) multipliers, the received signals may be divided into a plurality of rings which may act as decision boundaries502,504for received signal points.

In an illustrative embodiment, the received signals (e.g., |r(k)|4) of the received points506are closer to the decision ring of 1 than to other rings, and as such, the 4thpower may be replaced by 1 to remove multipliers according to the approximation employed by the decision boundary500. The same rule may apply to points508, in which the power of |r(k)|4may be replaced by 1/16 (e.g., based on the closest decision ring), and to points510, in which the power of |r(k)|4may be replaced by 1/256 (e.g., based on the closest decision ring). For example, if r(k)=½, r(k) may be raised to the fourth power (e.g., (½)4), with the result being 1/16; and if r(k)=¼, r(k) may be raised to the fourth power (e.g., (¼)4), with the result being 1/256. In an embodiment, an advantage of using these numbers is that they are a power of two, and therefore the multiplication of 2nx is only right-shifting the value x by n bits in a register. The 4 times amplification may also be performed by left shifting the angle (e.g., (angle (r(k+l))−θn)) by 2 bits in some embodiments.

In an embodiment, the method for removing multipliers using the decision boundary500may be expressed as follows:

where << represents left-shifting and >> represents right shifting. The amount of right-shifting may depend on which boundary the received signal lies within. For example, right-shifting may be determined as follows:

Right⁢-⁢shifting⁢⁢n⁢⁢bits={8,if⁢⁢r⁡(k)⁢⁢is⁢⁢inside⁢⁢decision⁢⁢boundary⁢⁢5024,if⁢⁢r⁡(k)⁢⁢is⁢⁢between⁢⁢decision⁢⁢boundaries⁢⁢502⁢⁢and⁢⁢5040,if⁢⁢r⁡(k)⁢⁢is⁢⁢outside⁢⁢decision⁢⁢boundary⁢⁢504
This simplification (e.g., removal of multipliers) does not result in a significant impact on carrier phase recovery performance according to the present principles, but advantageously reduces hardware complexity and improves processing speed of the system according to various embodiments.

Referring now toFIG. 6, an exemplary method for carrier phase recovery is illustratively depicted in accordance with an embodiment of the present principles. In block602, a carrier phase estimate may be determined for a frame of L symbols by a phase estimator in accordance with an embodiment. In block604, the determined phase estimate may be stored in a storage device (e.g., LUT), and the signal frame of L symbols may be rotated (e.g., de-rotated) by the phase estimate stored in the LUT in block606. The phase rotation applied to each signal in block104may include ejθn, where, and e is an exponent, θnis a current estimate for phase noise, and j is an imaginary constellation point.

In an embodiment, the phase estimate θnmay include angles which range from, for example, −π/4 to +π/4. The signals may pass through signal splitters, and the de-rotated signals may be raised to, for example, the fourth (4th) power in block608to mitigate the impact of phase modulation from the signals. The outputs of block608may then be summed up in block610, and the real part of that sum (e.g., real part of a symbol) may also be determined in block610using a data processor. It is noted that the above-mentioned angle range (−π/4 to +π/4), and the power to which the signals are raised (4th) is presented as such for simplicity of illustration, but any angles or powers may be employed according to various embodiments of the present principles.

In an embodiment, a minimum of the output of block612may be determined in block614with respect to the phase estimate θn. The minimum is determined because all signal points may include a maximum projection to the x-axis or y-axis when there is not any phase rotation. However, the presence of, for example, either 45 or 90 degree rotation of the constellation points (e.g., nπ/2+π/4, or nπ/2, respectively) may determine the sign of the projection (e.g. plus or minus). For example, in the case of Binary Phase Shift Keying (BPSK), with, for example, two constellation points (0, π), employing a projection of the 4thpower in block108may become the maximum, and if the BPSK is rotated by 45 degrees (e.g., (π/4, 5π/4), then the projection would be the minimum after applying the 4thpower operation in block108. However, the continual rotation of the constellation by 45 degrees may cause increased phase ambiguity (e.g., phase noise), so the minimum may be employed to determine the current phase estimate.

In an embodiment, the carrier phase may be estimated using the following method:

arg⁢⁢minθ∈(-π/4,π/4)⁢real⁢{∑l=0L-1⁢(r⁡(k+l)·exp⁡(-j⁢⁢θn))4},(1)
where −π/4, +π/4 represents a range of angles, L represents a number of symbols, l represents an index, r(k+l) represents a symbol in the set of symbols represented by L, and the phase is represented by exp(−jθn). Because of the use of the 4thpower operation in this example, the phase estimate may be limited to −π/4 to +π/4, which may cause cycle slips if non-differential decoding were employed. Therefore, phase unwrapping may be applied in block616to unwrap the current phase estimate based on the previous phase estimate to prevent cycle slips according to the present principles.

In an embodiment, the phase unwrapping in block616may be performed according to the following method:

θn⁢{θn-π2while⁢⁢θn-θn-1>π4θn+π2while⁢⁢θn-θn-1<-π4θnotherwise,(2)
where θnrepresents a current phase estimate, and θn−1represents a previous phase estimate. As shown above, during phase unwrapping, the phase estimate θnmay be adjusted by 0, or ±π/2, depending on the previous phase estimate θn−1. Accordingly, the output of block606may be multiplied by 1, or ±j in block618, and results may be output in block620in an embodiment of the present principles. In some embodiments, phase unwrapping may also be performed in block616to the minimum determined in block614.

Although the above method may be employed with any type of modulation format without prior knowledge (e.g., feed-forward design), there may be many multipliers present inside the carrier phase estimator according to the present principles. Therefore, in some embodiments, the method may be simplified, and multipliers may be removed in block618(e.g., to reduce hardware implementation complexity and improve processing speed) according to the present principles as follows:

The foregoing is to be understood as being in every respect illustrative and exemplary, but not restrictive, and the scope of the invention disclosed herein is not to be determined from the Detailed Description, but rather from the claims as interpreted according to the full breadth permitted by the patent laws. Additional information is provided in an appendix to the application entitled, “Additional Information”. It is to be understood that the embodiments shown and described herein are only illustrative of the principles of the present invention and that those skilled in the art may implement various modifications without departing from the scope and spirit of the invention. Those skilled in the art could implement various other feature combinations without departing from the scope and spirit of the invention.