# US 10,122,461 B2 · Method for selecting modes for transmission over multimode or multicore optical fibres

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- Number: US 10,122,461 B2
- Document ID: US10122461B2
- Status: Granted
- Kind: B2
- Application number: 15/508,775
- Filed: 2015-09-04
- Published: 2017-09-14
- Granted: 2018-11-06
- Earliest claimed: 2014-09-08
- Assignees: Institut Mines-Telecom
- Applicants: Institut Mines-Telecom
- Inventors: Elie Awwad; Ghaya Rekaya-Ben Othman; Yves Jaouen
- Web page: https://patentgrep.com/patent/US10122461B2

## CPC

- H04B 10/2581: Multimode transmission
- H04B 7/0413: MIMO systems
- H04B 10/0795: {Performance monitoring; Measurement of transmission parameters}
- H04J 14/052: {using multicore fibre (mode multiplex systems H04J14/04)}
- H04B: TRANSMISSION
- H04J: MULTIPLEX COMMUNICATION (transmission in general H04B; peculiar to transmission of digital information H04L5/00; systems for the simultaneous or sequential transmission of more than one television signal H04N7/08; in exchanges H04Q11/00; stereophonic systems H04S)

## Abstract

The invention relates to a mode selection method for a system for MIMO transmission on an optical fiber of multimode type. It comprises a step of measuring the transfer matrix of the transmission channel made up of a set of modes of the optical fiber (110), a step of transforming (120) the transfer matrix into a block diagonal matrix, each block being associated with a mode subset, a step of determining (130) the gain and/or the transmission capacity for each of the mode subsets, and a selection (140) of the mode subset corresponding to the highest gain and/or capacity, the MIMO transmission system then using only the modes of the subset thus selected to transmit on the optical fiber. The invention relates also to a core selection method for a system for MIMO transmission on optical fiber of multicore type.

## Claims

### Claim 1

A mode selection method for a system for MIMO transmission over a multimode optical fiber comprising:
measuring a transfer matrix of a transmission channel made up of a set of modes of said optical fiber;
transforming said transfer matrix into a block diagonal matrix, each block relating to a subset of modes of said optical fiber;
determining a gain and/or a transmission capacity for each of the mode subsets associated with said blocks;
selecting the mode subset corresponding to the highest gain and/or to the highest capacity, the MIMO transmission system then using only the modes of the subset thus selected to transmit over said optical fiber.

### Claim 2 (depends on 1)

The mode selection method as claimed in claim 1, wherein said step of transforming the transfer matrix comprises:
a thresholding step, said thresholding step comprising setting all the elements of the matrix below a predetermined threshold value to zero,
a step of reorganizing the transfer matrix thus obtained, by permutation of its rows and columns, the permutations on the rows and the permutations on the columns being identical.

### Claim 3 (depends on 1)

The mode selection method as claimed in claim 1, wherein the mode subset is selected according to the gain criterion
n
opt
=
arg
⁢
⁢
max
n
=
1
,
⁢
…
⁢
,
N
⁢
(
γ
n
)
in which γn=Tr(HnHnH), N being the number of mode subsets, Hn being the transfer matrix of the transmission channel reduced to the modes of the subset n, HnH being the conjugate transpose matrix of Hn and Tr(⋅) being the trace function.

### Claim 4 (depends on 1)

The mode selection method as claimed in claim 1, wherein the mode subset is selected according to a gain criterion
n
opt
=
arg
⁢
⁢
max
n
=
1
,
⁢
…
⁢
,
N
⁢
(
γ
n
M
n
)
in which γn=Tr(HnHnH), N being the number of mode subsets, Mn being the cardinal of the subset n, Hn being the transfer matrix of the transmission channel reduced to the modes of the subset n, HnH being the conjugate transpose matrix of Hn and Tr(⋅) being the trace function.

### Claim 5 (depends on 1)

The mode selection method as claimed in claim 1, wherein the mode subset is selected according to a capacity criterion
n
opt
=
arg
⁢
⁢
max
n
=
1
,
⁢
…
⁢
,
N
⁢
(
C
n
)
in which
C
n
=
∑
m
=
1
M
n
⁢
⁢
log
(
1
+
γ
n
m
⁢
P
e
M
n
⁢
N
0
)
,
Mn being the cardinal of the subset n, γnm being the gain of the transmission channel on the mode m of the subset n, Pe being the transmission power distributed over the Mn modes and N0 being the noise power on reception on a mode.

### Claim 6 (depends on 1)

The mode selection method as claimed in claim 1, wherein the mode subset is selected according to a hybrid gain and capacity criterion
n
opt
=
arg
⁢
⁢
max
n
=
1
,
⁢
…
⁢
,
N
⁢
(
Φ
⁡
(
C
n
,
γ
n
)
)
in which:
Cn is the capacity of the transmission channel reduced to the modes of the subset n,
γn is defined by γn=Tr(HnHnH), with Hn being the transfer matrix of the transmission channel reduced to the modes of the subset n, HnH being the conjugate transpose matrix of Hn and Tr(⋅) being the trace function, and
Φ(⋅,⋅) is an increasing function of Cn and γn.

### Claim 7 (depends on 1)

The mode selection method as claimed in claim 1, wherein in response to the selection of the mode subset, the degree of modulation of the symbols to be transmitted on the different modes is chosen to be equal to a value Q′ such that M′ log Q′=M log Q, in which M is the cardinal of the mode set before selection, M′ is the cardinal of the mode subset selected and Q is the degree of modulation of the symbols to be transmitted before the selection of the mode subset.

### Claim 8 (depends on 1)

The mode selection method as claimed in claim 1, wherein in response to the selection of the mode subset, the degree of modulation of the symbols to be transmitted on the different modes is chosen to be different for the different modes of the mode subset.

### Claim 9 (depends on 8)

The mode selection method as claimed in claim 8, wherein the symbols to be transmitted are subjected to a space-time coding, the elements of the space-time code being then transmitted only on the modes of said selected mode subset.

### Claim 10

A core selection method for a system for MIMO transmission over a multicore optical fiber comprising:
measuring a transfer matrix of a transmission channel made up of a set of cores of said optical fiber;
transforming said transfer matrix into a block diagonal matrix, each block relating to a subset of cores of said optical fiber;
determining a gain and/or a transmission capacity for each of the core subsets associated with said blocks;
selecting the core subset corresponding to the highest gain and/or the highest capacity, the MIMO transmission system then using only the cores of the subset thus selected to transmit over said optical fiber.

### Claim 11 (depends on 10)

The core selection method as claimed in claim 10, wherein said step of transforming the transfer matrix comprises:
a thresholding step, said thresholding step comprising setting all the elements of the matrix below a predetermined threshold value to zero,
a step of reorganizing the transfer matrix thus obtained, by permutation of its rows and columns, the permutations on the rows and those on the columns being identical.

### Claim 12 (depends on 10)

The core selection method as claimed in claim 10, wherein the core subset is selected according to the gain criterion
n
opt
=
arg
⁢
⁢
max
n
=
1
,
⁢
…
⁢
,
N
⁢
(
γ
n
)
in which γn=Tr(HnHnH), N being the number of core subsets, Hn being the transfer matrix of the transmission channel reduced to the cores of the subset n, HnH being the conjugate transpose matrix of Hn and Tr(⋅) being the trace function.

### Claim 13 (depends on 10)

The core selection method as claimed in claim 10, wherein the core subset is selected according to the gain criterion
n
opt
=
arg
⁢
⁢
max
n
=
1
,
⁢
…
⁢
,
N
⁢
(
γ
n
M
n
)
in which γn=Tr(HnHnH), N being the number of core subsets, Mn being the cardinal of the subset n, Hn being the transfer matrix of the transmission channel reduced to the cores of the subset n, HnH being the conjugate transpose matrix of Hn and Tr(⋅) being the trace function.

### Claim 14 (depends on 10)

The mode selection method as claimed in claim 10, wherein the core subset is selected according to a capacity criterion
n
opt
=
arg
⁢
⁢
max
n
=
1
,
⁢
…
⁢
,
N
⁢
(
C
n
)
in which
C
n
=
∑
m
=
1
M
n
⁢
⁢
log
(
1
+
γ
n
m
⁢
P
e
M
n
⁢
N
0
)
,
Mn being the cardinal of the subset n, γnm being the gain of the transmission channel on the core m of the subset n, Pe being the transmission power distributed over the Mn cores and N0 being the noise power on reception on a core.

### Claim 15 (depends on 11)

The core selection method as claimed in claim 11, wherein the core subset is selected according to a hybrid gain and capacity criterion
n
opt
=
arg
⁢
⁢
max
n
=
1
,
⁢
…
⁢
,
N
⁢
(
Φ
⁡
(
C
n
,
γ
n
)
)
in which:
Cn is the capacity of the transmission channel reduced to the cores of the subset n,
γn is defined by γn=Tr(HnHnH) with Hn being the transfer matrix of the transmission channel reduced to the cores of the subset n, HnH being the conjugate transpose matrix of Hn and Tr(⋅) being the trace function, and
Φ(⋅,⋅) is an increasing function of Cn and γn.

### Claim 16 (depends on 10)

The core selection method as claimed in claim 10, wherein in response to the selection of the core subset, the degree of modulation of the symbols to be transmitted on the different cores is chosen to be equal to a value Q′ such that M′ log Q′=M log Q in which M is the cardinal of the set of cores before selection, M′ is the cardinal of the core subset selected and Q is the degree of modulation of the symbols to be transmitted before the selection of the core subset.

### Claim 17 (depends on 15)

The core selection method as claimed in claim 15, wherein in response to the selection of the core subset, the degree of modulation of the symbols to be transmitted on the different cores is chosen to be different for the different cores of the subset.

### Claim 18 (depends on 17)

The core selection method as claimed in claim 17, wherein the symbols to be transmitted are subjected to a space-time coding, the elements of the space-time code being then transmitted only on the cores of said mode subset selected.