US 11,108,615 B2Granted

Method for receiving an image signal and method for transmitting an image signal

AssigneeRadius Inc.

InventorTohru Kohda

Life of this patent

Estimating the term…

Abstract

In accordance with an embodiment of the present invention, a method for receiving a signal, comprising the estimation step for estimating time and frequency shifts that are embedded in the received signal, to cancel-out shifts, wherein the method refers to the non-commutative shift parameter space of co-dimension 2.

Claims8

Dependent claims

A method for receiving a signal with a high

-phase-shift keying (PSK) modulated symbol (signal)
{
d
p
,
p
′
=
exp
⁡
(
i
⁢
⁢
2
⁢
π
⁢
k
ℳ
)
∈
ℂ
}
p
,
p
′
=
1
P
,
P
′
,
(
0
≤
k
≤
ℳ
-
1
)
on a lattice
TsZ×FsZ
of a time-frequency plane (TFP), with address
{right arrow over (p)}=(p,p′),0≤p≤P−1,0≤p′≤P′−1
at a receiver apparatus, that convey a set of coefficients
{ai}i=1n
in a space domain (SD) and
{a′i}i=1n
in a spatial frequency domain (SFD) with a conjoint 2D spatial/spatial frequency (S/SF) representation
H
⁡
[
x
]
=
∑
i
=
1
n
⁢
⁢
a
i
⁢
g
⁡
[
x
;
θ
→
i
]
,
H
^
⁡
[
u
]
=
F
(
2
)
⁡
[
H
⁡
[
x
]
]
=
∑
i
=
1
n
⁢
⁢
a
i
′
⁢
g
^
⁡
[
u
;
θ
→
i
]
in terms of a set of templates and their Fourier transform (FT)s
{g[x;{right arrow over (θ)}i],ĝ[u;{right arrow over (θ)}i]}i=1n,
with parameters
{right arrow over (θ)}i=(x0i,u0i,{right arrow over (a)}i),x0i=(x0i,y0i),u0i=(u0i,v0i),{right arrow over (a)}i=(ai,βi),
in place of an original SD-image I(x) with 2D space (S) variable vector
x=(x,y)
and its FT SFD-image
Î[u]=F(2)[I[x]]
with 2D spatial frequency (SF) variable vector
u(u,v)
, of a plurality of bits,
comprising performing
a decoding step at the receiver apparatus for decoding a symbol sequence
dji
into two sets of received SD- and SFD-expansion coefficients, respectively denoted by
{ãi}t=1n,{ã′i}i=1n
and
a reconstructing step at the receiver apparatus, using a 2D elementary function (template)
g[x;{right arrow over (θ)}i]
and its
FTĝ[u;{right arrow over (θ)}i]
, for reconstructing an associated image and its FT, denoted as
{tilde over (H)}(x) and {circumflex over ({tilde over (H)})}(u)
, corresponding to
H
⁡
[
x
]
=
∑
i
=
1
n
⁢
⁢
a
i
⁢
g
⁡
[
x
;
θ
→
i
]
,
H
^
⁡
[
u
]
=
∑
i
=
1
n
⁢
⁢
a
i
′
⁢
g
^
⁡
[
u
;
θ
→
i
]
.
and given as respectively
H
~
⁡
[
u
]
=
∑
i
=
1
n
⁢
⁢
a
~
′
⁢
g
⁡
[
x
;
θ
→
i
]
,
H
^
~
⁡
[
u
]
=
∑
i
=
1
n
⁢
⁢
a
~
′
⁢
g
^
⁡
[
u
;
θ
→
i
]
.

255 more elements

A method for transmitting a signal with a high

-phase-shift-keying (PSK) symbol (signal)
d
q
→
=
exp
⁡
(
i
⁢
⁢
2
⁢
πk
ℳ
)
∈
ℂ
,
(
0
≤
k
≤
ℳ
-
1
)
on a lattice
Tx×Ts
of a time-frequency plane (TFP), with address
{right arrow over (q)}=(q,q′)
at a transmitter apparatus, that conveys a conjoint two dimensional spatial/spatial frequency (2D S/SF) image representation as a set of coefficients
{ai}i=1n
in a space-domain two dimensional (SD 2D) Gabor representation
H
⁡
[
x
]
=
∑
i
=
1
n
⁢
⁢
a
i
⁢
g
⁡
[
x
;
θ
i
→
]
,
respectively as a set of coefficients,
{a′i}i=1n
in a spatial frequency-domain two dimensional (SFD 2D) Gabor representation
H
⁡
[
u
]
=
∑
i
=
1
n
⁢
⁢
a
i
⁢
g
^
⁡
[
u
;
θ
i
→
]
)
,
as compressed data, in place of an original space-domain (SD)-image I(x) (respectively, its Fourier transform (FT), spatial frequency-domain (SFD)-image
Î(u)=F(2)[I[x]]),
of a plurality of bits,
comprising performing
a representation step at the transmitter apparatus for representing an original image I(x),
respectively its (Fourier transform (FT) image
Î(u),
either exactly or by projecting it onto a chosen set of two dimensional space-domain (2D SD)-templates
{g[x;{right arrow over (θ)}i]}i=1n,
respectively their FT SFD-templates
{ĝ[u;{right arrow over (θ)}i]}i=1n,
such that a resultant vector
H
⁡
[
x
]
=
∑
i
=
1
n
⁢
⁢
a
i
⁢
g
⁡
[
x
;
θ
i
→
]
,
(
resp
.
,
H
^
⁡
[
u
]
=
ℱ
(
2
)
⁡
[
H
⁡
[
x
]
]
=
∑
i
=
1
n
⁢
⁢
a
i
′
⁢
g
^
⁡
[
u
;
θ
i
→
]
)
minimizes squared norms of errors
|I[x]−H[x]∥2,(resp.,∥Î[u]−Ĥ[u]∥2)
and
an encoding step at the transmitter apparatus for encoding two sets of n expansion coefficients
{ai}i=1n and {a′i}i=1n
into an
-ary PSK symbol sequence
d{right arrow over (q)}
with data address
{right arrow over (q)}=(q,q′)
to be transmitted, and then transmitting a signal with
d{right arrow over (q)}
at the transmitter apparatus via an optional doubly dispersive channel for mobile communication.

186 more elements

A transmitter-receiver system for an original image and its Fourier transform (FT) image signals via a doubly dispersive channel for mobile communication, comprising:

a transmitter apparatus;
and
a receiver apparatus,
the transmitter apparatus including
a representation part for representing an image and its FT image as a set of expansion coefficients, regarded as compressed data of an image and its FT image by projecting it onto a set of two dimensional spatial-spatial frequency (2D S-SF) shifted functions, together with use of a spatial-spatial frequency shift operator (SSFSO) representing spatial-spatial frequency (S-SF) shifts and a phase term due to a half shift of a S shift, and a frequency dual of the SSFSO representing S-SF shifts and a phase term due to a half shift of the SF shift, with reference to a non-commutative shift parameter space of co-dimension 4 and
an encoding part for encoding a resultant projection coefficient to an
-ary symbol sequence to be transmitted, in place of an original SD-image I(x), respectively its Fourier transform (FT), spatial frequency-domain (SFD)-image
Î(u),
of a plurality of bits, and while
an optimization part for optimizing expansion coefficients by applying von Neumann's alternating projection theorem (APT) to a 4D symmetrical localization operator (LO), which is a concatenation of a space domain-projection operator (SD-PO) and a spatial frequency domain-projection operator (SFD-PO), and by a repetition of two such 4D LOs, with use of a symmetrical SSFSO and its frequency dual, and
a transmitting part at the transmitter apparatus for transmitting the signal with encoded data sequence,
the receiver apparatus including
a receiving part for receiving a signal with
-PSK symbol sequence at a receiver apparatus,
a decoding part at the receiver apparatus for decoding the received
-ary symbol sequence to two sets of SD-SFD projection coefficients of an image and its FT image, and
a reconstruction part at the receiver apparatus for reconstructing image and FT image using received expansion coefficients of the image and its FT image, in conjunction with 2D S-SF shifted functions, together with the use of a SSFSO representing S-SF shifts and a phase term due to a half shift of the S shift, and a frequency dual of the SSFSO representing S-SF shifts, and a phase term due to a half shift of the SF shift, with reference to two non-commutative shift parameter spaces of co-dimension 4.

14 more elements

Dependencies are inferred from the claim text.

Facts

Application: 16/803,266Filed 27 Feb 2020 · continuation
Priority: WO PCT/JP2018/00173522 Jan 2018
Published: US 2020/0204426 A125 Jun 2020
Granted: 31 Aug 2021
Term ends: Not estimatedThe source records don’t support an estimate.

Classification11 codes

H04L 27/2669
Details of algorithms: characterised by the domain of operation
H04B 1/70757
With code phase acquisition: with increased resolution, i.e. higher than half a chip
H04B 1/7093
Correlator structure: matched filter type
H04L 27/2602
Multicarrier modulation systems: signal structure

Family

PCT/JP2018/024592Parent of this continuation · filed 28 Jun 2018
Application16/369,053Parent of this continuation · filed 29 Mar 2019
US 2020/0204426 A1Pre-grant publication · published 25 Jun 2020
US 10,666,486 B2Parent of this continuation
US 2019/0229972 A1Published application
US 11,108,615 B2This patent

From the US filing history. Foreign family members aren’t listed.

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Abstract

A method for receiving a signal with a high

-phase-shift keying (PSK) modulated symbol (signal)
{
d
p
,
p
′
=
exp
⁡
(
i
⁢
⁢
2
⁢
π
⁢
k
ℳ
)
∈
ℂ
}
p
,
p
′
=
1
P
,
P
′
,
(
0
≤
k
≤
ℳ
-
1
)
on a lattice
TsZ×FsZ
of a time-frequency plane (TFP), with address
{right arrow over (p)}=(p,p′),0≤p≤P−1,0≤p′≤P′−1
at a receiver apparatus, that convey a set of coefficients
{ai}i=1n
in a space domain (SD) and
{a′i}i=1n
in a spatial frequency domain (SFD) with a conjoint 2D spatial/spatial frequency (S/SF) representation
H
⁡
[
x
]
=
∑
i
=
1
n
⁢
⁢
a
i
⁢
g
⁡
[
x
;
θ
→
i
]
,
H
^
⁡
[
u
]
=
F
(
2
)
⁡
[
H
⁡
[
x
]
]
=
∑
i
=
1
n
⁢
⁢
a
i
′
⁢
g
^
⁡
[
u
;
θ
→
i
]
in terms of a set of templates and their Fourier transform (FT)s
{g[x;{right arrow over (θ)}i],ĝ[u;{right arrow over (θ)}i]}i=1n,
with parameters
{right arrow over (θ)}i=(x0i,u0i,{right arrow over (a)}i),x0i=(x0i,y0i),u0i=(u0i,v0i),{right arrow over (a)}i=(ai,βi),
in place of an original SD-image I(x) with 2D space (S) variable vector
x=(x,y)
and its FT SFD-image
Î[u]=F(2)[I[x]]
with 2D spatial frequency (SF) variable vector
u(u,v)
, of a plurality of bits,
comprising performing
a decoding step at the receiver apparatus for decoding a symbol sequence
dji
into two sets of received SD- and SFD-expansion coefficients, respectively denoted by
{ãi}t=1n,{ã′i}i=1n
and
a reconstructing step at the receiver apparatus, using a 2D elementary function (template)
g[x;{right arrow over (θ)}i]
and its
FTĝ[u;{right arrow over (θ)}i]
, for reconstructing an associated image and its FT, denoted as
{tilde over (H)}(x) and {circumflex over ({tilde over (H)})}(u)
, corresponding to
H
⁡
[
x
]
=
∑
i
=
1
n
⁢
⁢
a
i
⁢
g
⁡
[
x
;
θ
→
i
]
,
H
^
⁡
[
u
]
=
∑
i
=
1
n
⁢
⁢
a
i
′
⁢
g
^
⁡
[
u
;
θ
→
i
]
.
and given as respectively
H
~
⁡
[
u
]
=
∑
i
=
1
n
⁢
⁢
a
~
′
⁢
g
⁡
[
x
;
θ
→
i
]
,
H
^
~
⁡
[
u
]
=
∑
i
=
1
n
⁢
⁢
a
~
′
⁢
g
^
⁡
[
u
;
θ
→
i
]
.

255 more elements

Facts

Application

16/803,266Filed 27 Feb 2020 · continuation

Priority

WO PCT/JP2018/00173522 Jan 2018

Published

US 2020/0204426 A125 Jun 2020

Granted

31 Aug 2021

Term ends

Not estimatedThe source records don’t support an estimate.

Classification11 codes

H04L 27/2669
Details of algorithms: characterised by the domain of operation
H04B 1/70757
With code phase acquisition: with increased resolution, i.e. higher than half a chip
H04B 1/7093
Correlator structure: matched filter type
H04L 27/2602
Multicarrier modulation systems: signal structure

Family

PCT/JP2018/024592Parent of this continuation · filed 28 Jun 2018

Application16/369,053Parent of this continuation · filed 29 Mar 2019

US 2020/0204426 A1Pre-grant publication · published 25 Jun 2020

US 10,666,486 B2Parent of this continuation

US 2019/0229972 A1Published application

US 11,108,615 B2This patent

From the US filing history. Foreign family members aren’t listed.