# US 10,122,442 B2 · Determination of constellation impairment parameters via error-vector magnitude minimization

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- Number: US 10,122,442 B2
- Document ID: US10122442B2
- Status: Granted
- Kind: B2
- Application number: 15/614,394
- Filed: 2017-06-05
- Published: 2017-12-14
- Granted: 2018-11-06
- Earliest claimed: 2016-06-09
- Assignees: Tektronix, Inc.
- Applicants: Tektronix, Inc.
- Inventors: Steven A. Jacobs; Robert A. Marsland, Jr.
- Web page: https://patentgrep.com/patent/US10122442B2

## CPC

- H04B 10/0795: {Performance monitoring; Measurement of transmission parameters}
- H04B 10/079: using measurements of the data signal
- H04B 10/616: {Details of the electronic signal processing in coherent optical receivers}
- H04B 17/11: for calibration
- H04L 1/00: Arrangements for detecting or preventing errors in the information received {(correcting synchronisation H04L7/00)}
- H04B: TRANSMISSION
- H04L: TRANSMISSION OF DIGITAL INFORMATION, e.g. TELEGRAPHIC COMMUNICATION (arrangements common to telegraphic and telephonic communication H04M)

## Abstract

A test and measurement system is disclosed. The system includes a data store with a data description of a received in-phase (I) quadrature (Q) symbol. The received IQ symbol is received from a transmitter associated with impairments, and the received IQ symbol is modified from a corresponding ideal IQ symbol by the impairments. A computer processor is coupled to the data store and generates an Error-Vector Magnitude (EVM) function that describes a difference between the received IQ symbol and the ideal IQ symbol in terms of a plurality of impairment parameters indicating the impairments. The processor then determines values for the impairment parameters that quantify the impairments. The values are determined by selection of values for the impairment parameters that minimize the EVM function.

## Claims

### Claim 1

A test and measurement system comprising:
a data store including a data description of at least one received in-phase (I) quadrature (Q) symbol, the received IQ symbol received from a transmitter associated with impairments and the received IQ symbol modified from a corresponding ideal IQ symbol by the impairments; and
a computer processor coupled to the data store and configured to:
generate an Error-Vector Magnitude (EVM) function that describes a difference between the received IQ symbol and the ideal IQ symbol in terms of a plurality of impairment parameters indicating the impairments; and
determine values for the impairment parameters that quantify the impairments, the values determined by selection of values for the impairment parameters that minimize the EVM function.

### Claim 2 (depends on 1)

The test and measurement system of claim 1, wherein the EVM function is generated as a blind EVM function without information indicating values of the ideal IQ symbol.

### Claim 3 (depends on 2)

The test and measurement system of claim 2, wherein at least one impairment value is determined via an analytical computation to simplify minimization of the EVM function via a numerical computation.

### Claim 4 (depends on 2)

The test and measurement system of claim 2, wherein the EVM function is generated according to:
EVM
B
(
x
,
y
)
=
{
1
N
⁢
∑
k
=
1
N
⁢
[
min
1
≤
j
≤
M
R
⁢
(

I
k
(
x
,
y
)

-
a
j
)
2
+
min
1
≤
m
≤
M
R
⁢
(

Q
k
(
x
,
y
)

-
a
m
)
2
]
}
1
/
2
,
where EVMB(x,y) indicates the difference between the received IQ symbol and the ideal IQ symbol for x polarizations and y polarizations, N indicates a number of IQ symbols considered, k indicates a time slot of the received IQ symbol, aj is a possible value for an I portion of a constellation, Qk(x,y) is a Q portion of the ideal IQ symbol for x polarizations and y polarizations, and am is a possible value for a Q portion of a constellation.

### Claim 5 (depends on 4)

The test and measurement system of claim 4, wherein the I portion of the ideal IQ symbol for x polarizations and y polarizations is further determined according to:
Ik(x,y)=μI(x,y)−(Ak(x,y) cos τ+Bk(x,y) sin τ)/(SI(x,y) sin θ(x,y)),
where μI(x,y) is a direct current (DC) offset of an I portion of the received IQ symbol for x polarizations and y polarizations, Ak(x,y) and Bk(x,y) describe correlations between the impairment parameters, τ indicates a polarization rotation impairment caused by a communication medium, SI(x,y) indicates I gain of the received IQ symbol, and θ indicates an IQ phase angle of the received IQ symbol.

### Claim 6 (depends on 5)

The test and measurement system of claim 5, wherein the correlations between the impairment parameters are further described according to:
Ak(x,y)=Zkr(x,y) sin {(k−1)ψ+ϕmη1−θ(x,y)}+Zki(x,y) cos {(k−1)ψ+ϕmη1−θ(x,y)},and
Bk(x,y)=±Zkr(y,x) sin {(k−1)ψ+ϕ±η2−θ(x,y)}±Zki(y,x) cos {(k−1)ψ+ϕ±η2−θ(x,y)},
where Zkr(x,y) indicates a real part of received symbol data, Zki(x,y) indicates an imaginary part of the received symbol data, ψ indicates a heterodyne frequency parameter employed to determine a heterodyne frequency impairment (ν), ϕ indicates an optical phase impairment, and η1 and η2 indicate polarization rotation impairments caused by the communication medium.

### Claim 7 (depends on 4)

The test and measurement system of claim 4, wherein the Q portion of the ideal IQ symbol for x polarizations and y polarizations is further determined according to:
Qk(x,y)=μQ(x,y)+(Ck(x,y) cos τ+Dk(x,y) sin τ)/(SQ(x,y) sin θ(x,y)),
where μQ(x,y) is a direct current (DC)offset of a Q portion of the received IQ symbol for x polarizations and y polarizations, Ck(x,y) and Dk(x,y) describe correlations between the impairment parameters, τ indicates polarization rotation impairment caused by a communication medium, SQ(x,y) indicates Q gain of the received IQ symbol, and θ indicates an IQ phase angle of the received IQ symbol.

### Claim 8 (depends on 7)

The test and measurement system of claim 7, wherein the correlations between the impairment parameters are further described according to:
Ck(x,y)=Zkr(x,y) sin {(k−1)ψ+ϕmη1}+Zki(x,y) cos {(k−1)ψ+ϕmη1},and
Dk(x,y)=±Zkr(y,x) sin {(k−1)ψ+ϕ±η2}±Zki(y,x) cos {(k−1)ψ+ϕ±η2},
where Zkr(x,y) indicates a real part of received symbol data, Zki(x,y) indicates an imaginary part of the received symbol data, ψ indicates a heterodyne frequency parameter employed to determine a heterodyne frequency impairment (ν), ϕ indicates an optical phase impairment, and η1 and η2 indicate polarization rotation impairments caused by the medium.

### Claim 9 (depends on 1)

The test and measurement system of claim 1, wherein the received IQ symbol is further received via a communication medium including an optical fiber, and wherein the impairments determined by minimization of the EVM function are further associated with the communication medium.

### Claim 10 (depends on 1)

The test and measurement system of claim 1, wherein selecting values for the impairment parameters that minimize the EVM function includes employing a minimization procedure that minimizes the EVM function while avoiding local minima.

### Claim 11

A method comprising:
obtaining at least one received in-phase (I) quadrature (Q) symbol, the received IQ symbol received from a transmitter associated with impairments and the received IQ symbol modified from a corresponding ideal IQ symbol by the impairments;
generating an Error-Vector Magnitude (EVM) function that describes a difference between the received IQ symbol and the ideal IQ symbol in terms of a plurality of impairment parameters indicating the impairments; and
determining values for the impairment parameters that quantify the impairments, the values determined by selecting values for the impairment parameters that minimize the EVM function.

### Claim 12 (depends on 11)

The method of claim 11, wherein the EVM function is generated as a blind EVM function without information indicating values of the ideal IQ symbol.

### Claim 13 (depends on 11)

The method of claim 11, wherein values for the impairment parameters are determined concurrently and not sequentially.

### Claim 14 (depends on 11)

The method of claim 11, wherein at least one impairment value is determined via an analytical computation to simplify the EVM function prior to minimizing the EVM function via a numerical computation.

### Claim 15 (depends on 11)

The method of claim 11, wherein selecting values for the impairment parameters that minimize the EVM function includes employing a generalized simulated annealing (GSA) minimization procedure to minimize the EVM function while avoiding local minima.

### Claim 16

A non-transitory computer readable storage medium having instructions stored thereon that, when executed by a processor of a test and measurement system, cause the test and measurement system to perform the steps of:
obtaining at least one received in-phase (I) quadrature (Q) symbol, the received IQ symbol received from a transmitter associated with impairments and the received IQ symbol modified from a corresponding ideal IQ symbol by the impairments;
generating an Error-Vector Magnitude (EVM) function that describes a difference between the received IQ symbol and the ideal IQ symbol in terms of a plurality of impairment parameters indicating the impairments; and
determining values for the impairment parameters that quantify the impairments, the values determined by selecting values for the impairment parameters that minimize the EVM function.

### Claim 17 (depends on 16)

The non-transitory computer readable storage medium of claim 16, wherein the EVM function is generated as a blind EVM function without information indicating values of the ideal IQ symbol.

### Claim 18 (depends on 16)

The non-transitory computer readable storage medium of claim 16, wherein values for the impairment parameters are determined concurrently and not sequentially.

### Claim 19 (depends on 16)

The non-transitory computer readable storage medium of claim 16, wherein at least one impairment value is determined via an analytical computation to simplify the EVM function prior to minimizing the EVM function via a numerical computation.

### Claim 20 (depends on 16)

The non-transitory computer readable storage medium of claim 16, wherein selecting values for the impairment parameters that minimize the EVM function includes employing a generalized simulated annealing (GSA) minimization procedure to minimize the EVM function while avoiding local minima.