Method for estimating a received signal and corresponding device
A method and apparatus for estimating a transmission channel in a receiver of an OFDMA signal formed by a plurality of carriers modulated by data elements and distributed in the time-frequency domain in successive symbols, the plurality of carriers including pilot carriers, modulated by reference data elements known by receivers. The method includes: receiving a signal comprising a series of n symbols covering at least one resource block; making an initial channel estimation by identifying the pilot carriers included in the series of n symbols; determining diagonal entries of p frequency domain channel matrices G (x) for estimating the channel for at least x symbols among the n symbols, the x symbols being pilot symbols; determining, in the frequency domain, at least some non diagonal entries for each frequency domain channel matrix G of the n symbols from the determined diagonal entries of the x frequency domain channel matrices G (x) .
1. A method for estimating a transmission channel in a receiver of an OFDMA signal formed by a plurality of carriers being modulated by data elements and distributed in the time-frequency domain in successive symbols, said plurality of carriers including pilot carriers, modulated by reference data elements known by receivers, wherein said method comprises:
a step of receiving by the receiver a series of n symbols of the OFDMA signal, covering at least one resource block;
a step of making an initial channel estimation by identifying said pilot carriers included in said series of n symbols;
a step of determining diagonal entries of p frequency domain channel matrices G (x) for estimating said channel for at least some x symbols among said n symbols, said x symbols being pilot symbols; and
a step of determining, in the frequency domain, at least some non diagonal entries for each frequency domain channel matrix G of said n symbols from said determined diagonal entries of said x frequency domain channel matrices G (x) ,
wherein said step of determining diagonal entries comprises:
a step of transforming said signal from the time domain to the frequency domain, for delivering a corresponding frequency domain signal;
a step of estimating, from said frequency domain signal, a first channel estimation in the frequency domain;
a step of interpolating said first channel estimation in the frequency domain by employing a linear expression in order to determine diagonal entries of said matrices G (x) , wherein said linear expression comprises:
G
i
,
i
(
p
)
=
N
(
H
i
,
0
+
pT
0
E
i
+
(
pT
0
)
2
U
i
)
+
N
-
1
2
N
(
E
i
+
2
pT
0
U
i
)
+
(
N
-
1
)
(
2
N
-
1
)
6
N
N
U
i
where:
p is a symbol index of the (p+1) th received symbol;
N is a number of carriers of a symbol;
H is the Fourier transform of the channel impulse response for the entry i;
T 0 is equal to 1+L CP /N, where L CP is the length of the cyclic prefix;
E i and U i are the FFT transformation of basis coefficients for the variation of the channel of a certain time window:
U
i
=
[
(
4
/
7
)
(
G
i
,
i
(
7
)
-
G
i
,
i
(
0
)
)
-
(
G
i
,
i
(
4
)
-
G
i
,
i
(
0
)
)
]
12
N
T
0
2
E
i
=
(
G
i
,
i
(
4
)
-
G
i
,
i
(
0
)
)
4
N
T
0
-
U
i
(
N
-
1
N
+
4
T
0
)
.
2. The method according to claim 1 , wherein said step of determining diagonal entries is implemented for three pilot symbols.
3. The method according to claim 1 , wherein said step of determining at least some non diagonal entries employs a polynomial expression of any order, depending on a pilot distribution among said series of symbols.
4. The method according to claim 3 , wherein said polynomial expression is a second order polynomial expression.
5. The method according to claim 4 , wherein said second order polynomial expression is:
G i,k (p) =C e (mod(( k−i ), N )) E k +C u (mod(( k−i ), N )) U k +2pT 0 C e (mod(( k−i ), N )) U k
where C e and C u are constants defined as
C
e
(
n
)
=
-
1
N
.
1
1
-
exp
(
j2π
n
/
N
)
,
C
u
(
n
)
=
-
1
N
.
(
1
1
-
exp
(
j2π
n
/
N
)
+
2
N
·
exp
(
j2π
n
/
N
)
(
1
-
exp
(
j2π
n
/
N
)
)
2
)
,
with n≠0 and:
U
k
=
[
(
4
/
7
)
(
G
k
,
k
(
7
)
-
G
k
,
k
(
0
)
)
-
(
G
k
,
k
(
4
)
-
G
k
,
k
(
0
)
)
]
12
N
T
0
2
,
E
k
=
(
G
k
,
k
(
4
)
-
G
k
,
k
(
0
)
)
4
N
T
0
-
U
k
(
N
-
1
N
+
4
T
0
)
,
and
G( 7) , G( 4) and G (0) are matrices of the eighth, fifth and first symbols of said series of n symbols and
p is a (p+1) th received symbol;
N is a number of carriers of a symbol;
T 0 is equal to 1+L CP /N, where L CP is the length of the cyclic prefix.
6. A device for estimating a transmission channel in a receiver of an OFDMA signal formed by a plurality of carriers being modulated by data elements and distributed in the time-frequency domain in successive symbols, said plurality of carriers including pilot carriers, modulated by reference data elements known by receivers, wherein said device comprises:
means for receiving a series of n symbols of the OFDMA signal, covering at least one resource block;
means for making an initial channel estimation by identifying said pilot carriers included in said series of n symbols;
means for determining diagonal entries of x frequency domain channel matrices G (x) for estimating said channel for at least some x symbols among said n symbols, said x symbols being pilot symbols; and
means for determining, in the frequency domain, at least some non diagonal entries for each frequency domain channel matrix G of said n symbols from said determined diagonal entries of said x frequency domain channel matrices G (x) ,
wherein determining diagonal entries comprises:
transforming said signal from the time domain to the frequency domain, for delivering a corresponding frequency domain signal;
estimating, from said frequency domain signal, a first channel estimation in the frequency domain;
interpolating said first channel estimation in the frequency domain by employing a linear expression in order to determine diagonal entries of said matrices G (x) , wherein said linear expression comprises:
G
i
,
i
(
p
)
=
N
(
H
i
,
0
+
pT
0
E
i
+
(
pT
0
)
2
U
i
)
+
N
-
1
2
N
(
E
i
+
2
pT
0
U
i
)
+
(
N
-
1
)
(
2
N
-
1
)
6
N
N
U
i
where:
p is a symbol index of the (p+1) th received symbol;
N is a number of carriers of a symbol;
H is the Fourier transform of the channel impulse response for the entry i;
T 0 is equal to 1+L CP /N, where L CP is the length of the cyclic prefix;
E i and U i are the FFT transformation of basis coefficients for the variation of the channel of a certain time window:
U
i
=
[
(
4
/
7
)
(
G
i
,
i
(
7
)
-
G
i
,
i
(
0
)
)
-
(
G
i
,
i
(
4
)
-
G
i
,
i
(
0
)
)
]
12
N
T
0
2
E
i
=
(
G
i
,
i
(
4
)
-
G
i
,
i
(
0
)
)
4
N
T
0
-
U
i
(
N
-
1
N
+
4
T
0
)
.
7. A memory device comprising a computer program product stored thereon and comprising instructions of program code for implementing a method of estimating a transmission channel in a receiver of an OFDMA signal formed by a plurality of carriers being modulated by data elements and distributed in the time-frequency domain in successive symbols, said plurality of carriers including pilot carriers, modulated by reference data elements known by receivers, when the instructions are run on a computer, wherein said method comprises:
a step of receiving by the receiver a series of n symbols of the OFDMA signal, covering at least one resource block;
a step of making an initial channel estimation by the receiver by identifying said pilot carriers included in said series of n symbols;
a step of determining by the receiver diagonal entries of p frequency domain channel matrices G (x) for estimating said channel for at least some x symbols among said n symbols, said x symbols being pilot symbols; and
a step of determining by the receiver, in the frequency domain, at least some non diagonal entries for each frequency domain channel matrix G of said n symbols from said determined diagonal entries of said x frequency domain channel matrices G (x) ,
wherein said step of determining diagonal entries comprises:
a step of transforming said signal from the time domain to the frequency domain, for delivering a corresponding frequency domain signal;
a step of estimating, from said frequency domain signal, a first channel estimation in the frequency domain;
a step of interpolating said first channel estimation in the frequency domain by employing a linear expression in order to determine diagonal entries of said matrices G (x) , wherein said linear expression comprises:
G
i
,
i
(
p
)
=
N
(
H
i
,
0
+
pT
0
E
i
+
(
pT
0
)
2
U
i
)
+
N
-
1
2
N
(
E
i
+
2
pT
0
U
i
)
+
(
N
-
1
)
(
2
N
-
1
)
6
N
N
U
i
where:
p is a symbol index of the (p+1) th received symbol;
N is a number of carriers of a symbol;
H is the Fourier transform of the channel impulse response for the entry i;
T 0 is equal to 1+L CP /N, where L CP is the length of the cyclic prefix;
E i and U i are the FFT transformation of basis coefficients for the variation of the channel of a certain time window:
U
i
=
[
(
4
7
)
(
G
i
,
i
(
7
)
-
G
i
,
i
(
0
)
)
-
(
G
i
,
i
(
4
)
-
G
i
,
i
(
0
)
)
]
12
N
T
0
2
E
i
=
(
G
i
,
i
(
4
)
-
G
i
,
i
(
0
)
)
4
N
T
0
-
U
i
(
N
-
1
N
+
4
T
0
)
.