# US 10,873,493 B2 · Carrier-phase recovery system and method

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- Number: US 10,873,493 B2
- Document ID: US10873493B2
- Status: Granted
- Kind: B2
- Application number: 16/412,104
- Filed: 2019-05-14
- Published: 2019-11-21
- Granted: 2020-12-22
- Earliest claimed: 2018-05-15
- Assignees: Cable Television Laboratories, Inc.
- Applicants: Cable Television Laboratories, Inc.
- Inventors: Mu Xu; Zhensheng Jia
- Web page: https://patentgrep.com/patent/US10873493B2

## CPC

- H04L 27/34: Amplitude- and phase-modulated carrier systems, e.g. quadrature-amplitude modulated carrier systems
- H04L 27/3455: {in order to facilitate carrier recovery at the receiver end, e.g. by transmitting a pilot or by using additional signal points to allow the detection of rotations}
- H04B 14/004: {Amplitude modulation}
- H04B 14/008: {Polarisation modulation}
- H04L 1/0054: {Maximum-likelihood or sequential decoding, e.g. Viterbi, Fano, ZJ algorithms}
- H04L 27/0014: {Carrier regulation (of chaotic carriers H04L27/001; for multicarrier receivers H04L27/2657)}
- H04L 27/361: {Modulation using a single or unspecified number of carriers, e.g. with separate stages of phase and amplitude modulation}
- H04L 27/3809: {Amplitude regulation arrangements}
- H04L 2027/0026: {Correction of carrier offset}
- H04L: TRANSMISSION OF DIGITAL INFORMATION, e.g. TELEGRAPHIC COMMUNICATION (arrangements common to telegraphic and telephonic communication H04M)
- H04B: TRANSMISSION

## Abstract

A carrier-phase recovery method includes: (i) applying a first carrier-phase recovery algorithm to complex-valued symbols of a signal received by a product detector, yielding coarse phase-estimates, the signal being modulated per an M-QAM scheme; (ii) modelling the coarse phase-estimates as a weighted sum of M probability-density functions of an M-component mixture model; (iii) optimizing the M probability-density functions with an expectation-maximization algorithm to yield M optimized probability-density functions; (iv) mapping, based on the M optimized probability-density functions, the coarse phase-estimates to one of M symbols corresponding to the QAM scheme, each coarse phase-estimate mapped to a same symbol belonging to a same one of M clusters; (v) applying a second carrier-phase recovery algorithm to each of the M clusters to generate refined phase-estimates each corresponding to a respective coarse phase-estimate; and (vi) mapping, based on the M optimized probability-density functions, each refined phase-estimate to one of the M symbols.

## Claims

### Claim 1

A carrier-phase recovery method comprising:
applying a first carrier-phase recovery algorithm to a plurality of complex-valued symbols of a signal received by a product detector to yield a plurality of coarse phase-estimates, the signal being modulated per an order-M quadrature-amplitude modulation (QAM) scheme;
modelling the plurality of coarse phase-estimates as a weighted sum of M probability density functions of an M-component mixture model;
optimizing parameters of each of the M probability density functions with an expectation-maximization algorithm to yield M optimized probability density functions;
mapping, based on the M optimized probability density functions, each of the plurality of coarse phase-estimates to one of M constellation symbols corresponding to the QAM scheme, each of the plurality of coarse phase-estimates mapped to a same constellation symbol belonging to a same one of M clusters;
applying a second carrier-phase recovery algorithm to each of the M clusters to generate a plurality of refined phase-estimates each corresponding to a respective one of the plurality of coarse phase-estimates; and
mapping, based on the M optimized probability density functions, each of the plurality of refined phase-estimates to one of the M constellation symbols.

### Claim 2 (depends on 1)

The method of claim 1, each of the plurality of coarse phase-estimates including a coordinate pair in a complex plane of a constellation diagram representing the signal, the method further comprising:
defining a plurality of regions in the complex plane based on intersections of adjacent optimized probability density functions of the M optimized probability density functions, each of the plurality of regions including a respective one of the M constellation symbols; and,
for each of the plurality of coarse phase-estimates, mapping the coarse phase-estimate to the one of the M constellation symbols corresponding to a region of the plurality of regions occupied by the coarse phase-estimate.

### Claim 3 (depends on 1)

The method of claim 1, further comprising, after applying a second carrier-phase recovery algorithm:
repeating steps of modelling, optimizing, mapping each of the plurality of coarse phase-estimates, and
applying the second carrier-phase recovery algorithm, wherein in the step of modelling, the refined phase-estimates generated by the second-carrier-phase recovery algorithm replace the coarse phase-estimates.

### Claim 4 (depends on 1)

The method of claim 1,
in the step of modeling, the mixture model being a Gaussian mixture model, each of the M probability density functions being a respective Gaussian distribution, the parameters of the mixture model including a mean, a covariance, and a weight of each of the Gaussian distributions; and
optimizing including employing an iterative expectation-maximization algorithm to obtain optimal values for each of the M means, covariances and weights.

### Claim 5 (depends on 1)

The method of claim 1, in the step of applying the first carrier-phase recovery algorithm, the first carrier-phase recovery algorithm using fewer than M symbols.

### Claim 6 (depends on 1)

The method of claim 1, in the step of applying, plurality of complex-valued symbols being less than ten thousand in number.

### Claim 7 (depends on 1)

The method of claim 1, in the steps of applying, the carrier-phase recovery algorithm being a Viterbi-Viterbi Fourth-Power estimator.

### Claim 8 (depends on 1)

The method of claim 1, the quadrature-amplitude modulation scheme being a dual-polarization QAM scheme.

### Claim 9

A carrier-phase recovery system:
a processor; and
memory adapted to store a plurality of complex-valued symbols of a signal and storing non-transitory computer-readable instructions that, when executed by the processor, control the processor to:
model the plurality of coarse phase-estimates as a weighted sum of M probability density functions of an M-component mixture model;
optimize parameters of each of the M probability density functions with an expectation-maximization algorithm to yield M optimized probability density functions;
map, based on the M optimized probability density functions, each of the plurality of coarse phase-estimates to one of M constellation symbols corresponding to the QAM scheme, each of the plurality of coarse phase-estimates mapped to a same constellation symbol belonging to a same one of M clusters;
apply a second carrier-phase recovery algorithm to each of the M clusters to generate a plurality of refined phase-estimates each corresponding to a respective one of the plurality of coarse phase-estimates; and
map, based on the M optimized probability density functions, each of the plurality of refined phase-estimates to one of the M constellation symbols.

### Claim 10 (depends on 9)

The carrier-phase recovery system of claim 9, each of the plurality of coarse phase-estimates including a coordinate pair in a complex plane of a constellation diagram representing the signal, the memory further storing non-transitory computer-readable instructions that, when executed by the processor, control the processor to:
define a plurality of regions in the complex plane based on intersections of adjacent optimized probability density functions of the M optimized probability density functions, each of the plurality of regions including a respective one of the M constellation symbols; and,
for each of the plurality of coarse phase-estimates, map the coarse phase-estimate to the one of the M constellation symbols corresponding to a region of the plurality of regions occupied by the coarse phase-estimate.

### Claim 11 (depends on 9)

The carrier-phase recovery system of claim 9, the memory further storing non-transitory computer-readable instructions that, when executed by the processor, control the processor to, after applying a second carrier-phase recovery algorithm:
repeat steps of modelling, optimizing, mapping each of the plurality of coarse phase-estimates, and
apply the second carrier-phase recovery algorithm, wherein in the step of modelling, the refined phase-estimates generated by the second-carrier-phase recovery algorithm replace the coarse phase-estimates.

### Claim 12 (depends on 9)

The carrier-phase recovery system of claim 9, the mixture model being a Gaussian mixture model, each of the M probability density functions being a respective Gaussian distribution, the parameters of the mixture model including a mean, a covariance, and a weight of each of the Gaussian distributions, and the memory further storing non-transitory computer-readable instructions that, when executed by the processor, control the processor to, when optimizing parameters:
employ an iterative expectation-maximization algorithm to obtain optimal values for each of the M means, covariances and weights.

### Claim 13 (depends on 9)

The carrier-phase recovery system of claim 9, the first carrier-phase recovery algorithm using fewer than M symbols.

### Claim 14 (depends on 9)

The carrier-phase recovery system of claim 9, plurality of complex-valued symbols being less than ten thousand in number.

### Claim 15 (depends on 9)

The carrier-phase recovery system of claim 9, the carrier-phase recovery algorithm being a Viterbi-Viterbi Fourth-Power estimator.

### Claim 16 (depends on 9)

The carrier-phase recovery system of claim 9, the quadrature-amplitude modulation scheme being a dual-polarization QAM scheme.