Estimating a transmission channel with pilot symbols distributed in lattice structure
First Claim
1. A method of estimating a transmission channel on the basis of a signal received after transmission through said transmission channel, said signal being a multicarrier signal constructed on a time/frequency lattice defined by a frequency axis and a time axis, and comprising frames having M×
- N symbols distributed over M subcarriers each of which is divided into N determined symbol times, each frame comprising P pilot symbols distributed timewise and frequencywise in such a way as to cover the frame according to a lattice structure, where the numbers M, N and P are nonzero integers, the pilot symbols comprising on the one hand symbols known as real pilot symbols, transmitted as symbols having a real value, and on the other hand symbols known as pure imaginary pilot symbols, transmitted as symbols having a pure imaginary value, the method comprising the steps of;
a) selecting one or more values zk of the signal received corresponding to one or more real pilot symbols of respective values ck on the one hand, and one or more values zl of the signal received corresponding respectively to one or more pure imaginary pilot symbols of respective values cl on the other hand, these pilot symbols being sufficiently close together both along the frequency axis and along the time axis for it to be possible to consider that the fading of the signal through the transmission channel has had a substantially identical (in modulus and in phase) complex value α
for these pilot symbols;
b) determining complex numbers u and v and a real number λ
by minimizing the following least squares expression;
where the sign Σ
denotes the summation operator, where ∥
x∥
denotes the absolute value operator for the real variable x or the modulus of the complex variable x, where λ
is a real number, where u and v are orthogonal (that is to say Re(u*.v)=0, where Re(w) denotes the real part operator for the complex number w, and where w* denotes the complex conjugate of the complex number w), such that ∥
u∥
=∥
v∥
, c) determining an estimated value {circumflex over (α
)} of the value α
of the fading of the signal through the transmission channel for the pilot symbols concerned, by calculating;
{circumflex over (α
)}=λ
/u.
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Accused Products
Abstract
A method for estimating a transmission channel from a multicarrier signal transmitted through said transmission channel, comprising real pilot symbols and so-called pure imaginary pilot symbols, consists in selecting one or several values zk of the received signal corresponding respectively to one or several real pilot symbols, and one or several values zl of the received signal corresponding respectively to one or several pure imaginary pilot symbols. The pilot symbols are sufficiently close both in frequency and in time such that it can be assumed that the fading of the signal through the transmission channel has a complex value α substantially identical for the symbols. An estimated value {circumflex over (α)} of α for the pilot symbols concerned is then determined by minimizing a least square equation involving the values zk and the values zl.
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Citations
13 Claims
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1. A method of estimating a transmission channel on the basis of a signal received after transmission through said transmission channel, said signal being a multicarrier signal constructed on a time/frequency lattice defined by a frequency axis and a time axis, and comprising frames having M×
- N symbols distributed over M subcarriers each of which is divided into N determined symbol times, each frame comprising P pilot symbols distributed timewise and frequencywise in such a way as to cover the frame according to a lattice structure, where the numbers M, N and P are nonzero integers, the pilot symbols comprising on the one hand symbols known as real pilot symbols, transmitted as symbols having a real value, and on the other hand symbols known as pure imaginary pilot symbols, transmitted as symbols having a pure imaginary value, the method comprising the steps of;
a) selecting one or more values zk of the signal received corresponding to one or more real pilot symbols of respective values ck on the one hand, and one or more values zl of the signal received corresponding respectively to one or more pure imaginary pilot symbols of respective values cl on the other hand, these pilot symbols being sufficiently close together both along the frequency axis and along the time axis for it to be possible to consider that the fading of the signal through the transmission channel has had a substantially identical (in modulus and in phase) complex value α
for these pilot symbols;
b) determining complex numbers u and v and a real number λ
by minimizing the following least squares expression;
where the sign Σ
denotes the summation operator,where ∥
x∥
denotes the absolute value operator for the real variable x or the modulus of the complex variable x,where λ
is a real number,where u and v are orthogonal (that is to say Re(u*.v)=0, where Re(w) denotes the real part operator for the complex number w, and where w* denotes the complex conjugate of the complex number w), such that ∥
u∥
=∥
v∥
,c) determining an estimated value {circumflex over (α
)} of the value α
of the fading of the signal through the transmission channel for the pilot symbols concerned, by calculating;
{circumflex over (α
)}=λ
/u. - View Dependent Claims (2, 3, 4, 5, 6, 7, 8, 9, 10)
- N symbols distributed over M subcarriers each of which is divided into N determined symbol times, each frame comprising P pilot symbols distributed timewise and frequencywise in such a way as to cover the frame according to a lattice structure, where the numbers M, N and P are nonzero integers, the pilot symbols comprising on the one hand symbols known as real pilot symbols, transmitted as symbols having a real value, and on the other hand symbols known as pure imaginary pilot symbols, transmitted as symbols having a pure imaginary value, the method comprising the steps of;
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11. A device for estimating a transmission channel on the basis of a signal received after transmission through said transmission channel, said signal being a multicarrier signal constructed on a time/frequency lattice defined by a frequency axis and a time axis, and comprising frames having M×
- N symbols distributed over M subcarriers each of which is divided into N determined symbol times, each frame comprising P pilot symbols distributed timewise and frequencywise in such a way as to cover the frame according to a lattice structure, where the numbers M, N and P are nonzero integers, the pilot symbols comprising on the one hand symbols known as real pilot symbols, transmitted as symbols having a real value, and on the other hand symbols known as pure imaginary pilot symbols, transmitted as symbols having a pure imaginary value, comprising;
means for selecting one or more values zk of the signal received corresponding to one or more real pilot symbols of respective values ck on the one hand, and one or more values zl of the signal received corresponding respectively to one or more pure imaginary pilot symbols of respective values cl on the other hand, these pilot symbols being sufficiently close together both along the frequency axis and along the time axis for it to be possible to consider that the fading of the signal through the transmission channel has had a substantially identical complex value α
for these pilot symbols;
means for determining complex numbers u and v and a real number λ
minimizing the following least squares expression;
where the sign Σ
denotes the summation operator,where ∥
x∥
denotes the absolute value operator for the real variable x or the modulus of the complex variable x,where λ
is a real number,where u and v are orthogonal (that is to say Re(u*.v)=0, where Re(w) denotes the real part operator for the complex number w, and where w* denotes the complex conjugate of the complex number w), such that ∥
u∥
=∥
v∥
,means for determining an estimated value {circumflex over (α
)} of the value α
of the fading of the signal through the transmission channel for the pilot symbols concerned, by calculating;
{circumflex over (α
)}=λ
/u.
- N symbols distributed over M subcarriers each of which is divided into N determined symbol times, each frame comprising P pilot symbols distributed timewise and frequencywise in such a way as to cover the frame according to a lattice structure, where the numbers M, N and P are nonzero integers, the pilot symbols comprising on the one hand symbols known as real pilot symbols, transmitted as symbols having a real value, and on the other hand symbols known as pure imaginary pilot symbols, transmitted as symbols having a pure imaginary value, comprising;
-
12. A device for estimating a transmission channel on the basis of a signal received after transmission through said transmission channel, said signal being a multicarrier signal constructed on a time/frequency lattice defined by a frequency axis and a time axis, and comprising frames having M×
- N symbols distributed over M subcarriers each of which is divided into N determined symbol times, each frame comprising P pilot symbols distributed timewise and frequencywise in such a way as to cover the frame according to a lattice structure, where the numbers M, N and P are nonzero integers, the pilot symbols comprising on the one hand symbols known as real pilot symbols, transmitted as symbols having a real value, and on the other hand symbols known as pure imaginary pilot symbols, transmitted as symbols having a pure imaginary value, comprising;
means for selecting one or more values zk of the signal received corresponding to one or more real pilot symbols of respective values ck on the one hand, and one or more values zl of the signal received corresponding respectively to one or more pure imaginary pilot symbols of respective values cl on the other hand, these pilot symbols being sufficiently close together both along the frequency axis and along the time axis for it to be possible to consider that the fading of the signal through the transmission channel has had a substantially identical complex value cc for these pilot symbols;
means for determining real numbers Re(β
) and Im(β
) minimizing the following least squares expression;
where the sign Σ
denotes the summation operator,where ∥
x∥
denotes the absolute value operator for the real variable xwhere Re(x) denotes the real part operator for the complex variable x, where Im(x) denotes the pure imaginary part operator for the complex variable x, and where β
denotes the inverse of α
; and
,means for determining an estimated value {circumflex over (α
)} of the fading of the signal through the transmission channel for the pilot symbols concerned, by inverting the complex number Re(β
)+i·
Im(β
).
- N symbols distributed over M subcarriers each of which is divided into N determined symbol times, each frame comprising P pilot symbols distributed timewise and frequencywise in such a way as to cover the frame according to a lattice structure, where the numbers M, N and P are nonzero integers, the pilot symbols comprising on the one hand symbols known as real pilot symbols, transmitted as symbols having a real value, and on the other hand symbols known as pure imaginary pilot symbols, transmitted as symbols having a pure imaginary value, comprising;
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13. A device for estimating a transmission channel on the basis of a signal received after transmission through said transmission channel, said signal being a multicarrier signal constructed on a time/frequency lattice defined by a frequency axis and a time axis, and comprising frames having M×
- N symbols distributed over M subcarriers each of which is divided into N determined symbol times, each frame comprising P pilot symbols distributed timewise and frequencywise in such a way as to cover the frame according to a lattice structure, where the numbers M, N and P are nonzero integers, the pilot symbols comprising on the one hand symbols known as real pilot symbols, transmitted as symbols having a real value, and on the other hand symbols known as pure imaginary pilot symbols, transmitted as symbols having a pure imaginary value, comprising;
means for selecting one or more values zk of the signal received corresponding to one or more real pilot symbols of respective values ck on the one hand, and one or more values zl of the signal received corresponding respectively to one or more pure imaginary pilot symbols of respective values cl on the other hand, these pilot symbols being sufficiently close together both along the frequency axis and along the time axis for it to be possible to consider that the fading of the signal through the transmission channel has had a substantially identical complex value α
for these pilot symbols; and
means for determining an estimated value {circumflex over (α
)} of the fading of the signal through the transmission channel for the pilot symbols concerned, which value is defined by {circumflex over (α
)}=ρ
·
ei·
φ
where ρ and
φ
are real numbers which minimize the following least squares expression;
where the sign Σ
denotes the summation operator,where ∥
x∥
denotes the absolute value operator for the real variable xwhere Re(x) denotes the real part operator for the complex variable x, and where Im(x) denotes the pure imaginary part operator for the complex variable x.
- N symbols distributed over M subcarriers each of which is divided into N determined symbol times, each frame comprising P pilot symbols distributed timewise and frequencywise in such a way as to cover the frame according to a lattice structure, where the numbers M, N and P are nonzero integers, the pilot symbols comprising on the one hand symbols known as real pilot symbols, transmitted as symbols having a real value, and on the other hand symbols known as pure imaginary pilot symbols, transmitted as symbols having a pure imaginary value, comprising;
Specification