Method and apparatus for estimating lag in antenna feeder cable of wireless transmission system
View Patent ↗A method includes transmitting, at a first time, a first transmission vector signal towards an antenna via a feeder cable connected to the antenna; receiving a first reflected vector signal, the first reflected vector signal being a reflection of the first transmission vector signal reflected from a point in the feeder cable; determining a first transformed transmission vector signal by performing a first vector forward transform on the first transmission vector signal; determining a first transformed reflected vector signal by performing a first vector forward transform on the first reflected vector signal; determining a first complex conjugate vector signal based on the first transmission vector signal and the first reflected vector signal; determining a first computed vector signal by performing a first vector inverse transform on the first complex conjugate vector signal; and determining a first sub-vector by performing a windowing function based on the first computed vector signal.
1. A method comprising:
transmitting, at a first point in time, a first transmission vector signal towards an antenna via a feeder cable connected to the antenna;
receiving a first reflected vector signal, the first reflected vector signal being a reflection of the first transmission vector signal reflected from a point in the feeder cable;
determining a first transformed transmission vector signal by performing a first vector forward transform on the first transmission vector signal;
determining a first transformed reflected vector signal by performing a first vector forward transform on the first reflected vector signal;
determining a first complex conjugate vector signal based on the first transmission vector signal and the first reflected vector signal;
determining a first computed vector signal by performing a first vector inverse transform on the first complex conjugate vector signal; and
determining a first sub-vector by performing a windowing function based on the first computed vector signal.
2. The method of 1 , wherein the first vector forward transform is defined by the following equation,
X
(
k
)
=
1
N
[
∑
m
=
0
N
2
-
1
x
(
2
m
)
U
N
/
2
mk
+
U
N
k
∑
m
=
0
N
2
-
1
x
(
2
m
+
1
)
U
N
/
2
mk
]
,
wherein X(k) is an output vector signal of the first vector forward transform, x is an input vector signal of the first vector transform, U is a transform kernel, N is a length of the first vector forward transform, and m and k are index variables.
3. The method of 1 , wherein the first vector forward transform is defined by the following equation,
X
(
k
)
=
1
N
[
∑
m
=
0
N
2
-
1
x
(
2
m
)
U
N
2
mk
+
∑
m
=
0
N
2
-
1
x
(
2
m
+
1
)
U
N
(
2
m
+
1
)
k
]
,
wherein X(k) is an output vector signal of the first vector forward transform, x is an input signal of the first vector transform, U is a transform kernel, N is a length of the first vector forward transform, and m and k are index variables.
4. The method of 1 , wherein the first vector inverse transform is defined by the following equation,
x
(
m
)
=
1
N
[
∑
k
=
0
N
2
-
1
X
(
2
k
)
U
N
/
2
-
mk
+
U
N
-
k
∑
k
=
0
N
2
-
1
X
(
2
k
+
1
)
U
N
/
2
-
mk
]
,
wherein x(m) is an output vector signal of the first vector inverse transform, X is the first complex conjugate vector, U is a transform kernel, N is a length of the first vector inverse transform, and m and k are index variables.
5. The method of 1 , wherein the first vector inverse transform is defined by the following equation,
x
(
m
)
=
1
N
[
∑
k
=
0
N
2
-
1
X
(
2
k
)
U
N
-
2
mk
+
∑
k
=
0
N
2
-
1
X
(
2
k
+
1
)
U
N
-
m
(
2
k
+
1
)
]
,
wherein x(m) is an output vector of the first vector inverse transform, X is the first complex conjugate vector, U is a transform kernel, N is a length of the first vector inverse transform, and m and k are index variables.
6. The method of 1 , further comprising:
transmitting, at a second point in time, a second transmission vector signal towards an antenna via a feeder cable connected to the antenna;
receiving a second reflected vector signal, the second reflected vector signal being a reflection of the second transmission vector signal reflected from a point in the feeder cable;
determining a second transmission vector signal by performing a first vector forward transform on the second transmission vector signal;
determining a second reflected vector signal by performing a first vector forward transform on the second reflected vector signal;
determining a second complex conjugate vector signal based on the second transmission vector signal and the second reflected vector signal;
determining a second computed vector signal by performing a first vector inverse transform on the second complex conjugate vector signal; and
determining a second sub-vector signal by performing a windowing function based on the second computed vector signal.
7. The method of 6 , wherein the second vector forward transform is defined by the following equation,
X
(
k
)
=
1
N
[
∑
m
=
0
N
2
-
1
x
(
2
m
)
U
N
/
2
mk
+
U
N
k
∑
m
=
0
N
2
-
1
x
(
2
m
+
1
)
U
N
/
2
mk
]
,
wherein X(k) is an output vector of the second vector forward transform, x is an input signal of the second vector transform, U is a transform kernel, N is a length of second vector forward transform, and m and k are index variables.
8. The method of 6 , wherein the second vector forward transform is defined by the following equation,
X
(
k
)
=
1
N
[
∑
m
=
0
N
2
-
1
x
(
2
m
)
U
N
2
mk
+
∑
m
=
0
N
2
-
1
x
(
2
m
+
1
)
U
N
(
2
m
+
1
)
k
]
,
wherein X(k) is an output vector of the second vector forward transform, x is an input signal of the second vector transform, U is a transform kernel, N is a length of the second vector forward transform, and m and k are index variables.
9. The method of 6 , wherein the first vector inverse transform is defined by the following equation,
x
(
m
)
=
1
N
[
∑
k
=
0
N
2
-
1
X
(
2
k
)
U
N
/
2
-
mk
+
U
N
-
k
∑
k
=
0
N
2
-
1
X
(
2
k
+
1
)
U
N
/
2
-
mk
]
,
wherein x(m) is an output vector of the second vector inverse transform, X is the second complex conjugate vector, U is a transform kernel, N is a length of the second vector inverse transform, and m and k are index variables.
10. The method of 6 , wherein the first vector inverse transform is defined by the following equation,
x
(
m
)
=
1
N
[
∑
k
=
0
N
2
-
1
X
(
2
k
)
U
N
-
2
mk
+
∑
k
=
0
N
2
-
1
X
(
2
k
+
1
)
U
N
-
m
(
2
k
+
1
)
]
,
wherein x(m) is an output vector of the second vector inverse transform, X is the second complex conjugate vector, U is a transform kernel, N is a length of the second vector inverse transform, and m and k are index variables.
11. The method of claim 6 , further comprising:
determining a first transformed vector signal by performing a vector forward transform on the first sub-vector signal;
determining a first decomposition matrix based on the first transformed vector signal;
determining a second transformed vector signal by performing a vector forward transform on the second sub-vector signal; and
determining a second decomposition matrix based on the second transformed vector signal.
12. The method of claim 11 , further comprising:
determining a first vector of characteristic values d 1 , and first characteristic vectors V 1 based on the first decomposition matrix;
determining a first angular frequency of the first sub-vector signal based on the first characteristic vectors V 1 ;
determining a second vector of characteristic values d 2 , and second characteristic vectors V 2 based on the second decomposition matrix; and
determining a second angular frequency of the second sub-vector signal based on the second characteristic vectors V 2 .
13. The method of claim 12 , wherein,
the first angular frequency is defined as
F 1 (ω)= e H (ω) V 1N V 1N H e (ω),
the second angular frequency is defined as
F 2 (ω)= e H (ω) V 2N V 2N H e (ω),
e(ω) is a complex valued vector in which the angular frequency ω is treated as a variable over the closed interval [0,2π],
the Hermitian transpose of e(ω) is defined as
e H (ω)=[1, e jω , . . . e j(m-1)ω ],0≦ω≦2π,
N is the length of vector forward transforms performed on the first and second sub-vector signals, and
the method further comprises:
determining a vector
P
1
(
ω
)
=
1
F
1
(
ω
)
*
d
1
;
and
determining a vector
P
2
(
ω
)
=
1
F
2
(
ω
)
*
d
2
.
14. The method of claim 13 , further comprising:
determining a magnitude value of the matrix P 1 (ω);
searching for peaks in the vector P 2 (ω);
determining a plurality of lag values based on the searched peaks and the determined magnitude; and
selecting, as a valid lag value, at least one of the plurality of determined lag values.
15. A remote radio head comprising:
a feeder cable connected to an antenna, the feeder cable being configured to transmit, at a first point in time, a first transmission vector signal towards the antenna; and
a vector signal processor,
the vector signal processor being configured to,
receive the first transmission vector signal,
receive a first reflected signal, the first reflected signal being a reflection of the first transmission vector signal reflected from a point in the feeder cable,
determine a first transmission vector signal by performing a first vector forward transform on the first transmission vector signal,
determine a first reflected vector signal by performing a first vector forward transform on the first reflection signal,
determine a first complex conjugate vector based on the first transmission vector signal and the first reflected vector signal,
determine a first computed vector by performing a first vector inverse transform on the first complex conjugate vector, and
determine a first sub-vector by performing a windowing function based on the first computed vector signal.
16. The remote radio head of claim 15 , wherein the vector signal processor is further configured to,
transmit, at a second point in time, a second transmission vector signal towards an antenna via a feeder cable connected to the antenna,
receive a second reflected signal, the second reflected signal being a reflection of the second transmission reflected from a point in the feeder cable,
determine a second transmission vector signal by performing a first vector forward transform on the second transmission vector signal,
determine a second reflected vector signal by performing a first vector forward transform on the second reflection signal,
determine a second complex conjugate vector based on the second transmission vector signal and the second reflected vector signal,
determine a second computed vector signal by performing a first vector inverse transform on the second complex conjugate vector, and
determine a second sub-vector by performing a windowing function based on the second computed vector signal.
17. The remote radio head of claim 16 , wherein the vector signal processor is further configured to,
determine a first transformed vector signal by performing a vector forward transform on the first sub-vector signal,
determine a first decomposition matrix based on the first transformed vector signal,
determine a second transformed vector signal by performing a vector forward transform on the second sub-vector signal, and
determine a second decomposition matrix based on the second transformed vector signal.
18. The remote radio head of 17 , wherein the vector signal processor is further configured to,
determine a first vector of characteristic values d 1 , and first characteristic vectors V 1 based on the first decomposition matrix,
determine a first angular frequency of the first sub-vector signal based on the first characteristic vectors V 1 ,
determine a second vector of characteristic values d 2 , and second characteristic vectors V 2 , based on the second decomposition matrix, and
determine a second angular frequency of the second sub-vector signal based on the second characteristic vectors V 2 .
19. The remote radio head of claim 18 , wherein the vector signal processor is configured such that,
the first angular frequency is defined as
F 1 (ω)= e H (ω) V 1N V 1N H e (ω),
the second angular frequency is defined as
F 2 (ω)= e H (ω) V 2N V 2N H e (ω),
e(ω) is a complex valued vector in which the angular frequency ω is treated as a variable over the closed interval [0,2π],
the Hermitian transpose of e(ω) is defined as
e H (ω)=[1, e jω , . . . e j(m-1)ω ],0≦ω≦2π,
N is the length of vector forward transforms performed on the first and second sub-vector signals, and
the vector signal processor is further configured to:
determine a vector
P
1
(
ω
)
=
1
F
1
(
ω
)
*
d
1
,
and
determine a vector
P
2
(
ω
)
=
1
F
2
(
ω
)
*
d
2
.
20. The remote radio head of claim 19 , wherein the vector signal processor is further configured to,
determine a magnitude value of the matrix P 1 (ω)m
search for peaks in the vector P 2 (ω)m
determine a plurality of lag values based on the searched peaks and the determined magnitude, and
select, as a valid lag value, at least one of the plurality of determined lag values.