CFR estimation method for multi-band OFDM-based UWB systems
A multi-stage CFR estimation method for multi-band OFDM-based UWB systems is provided. The method includes obtaining a CFR estimation ĥ r (1) by performing LS estimation using a channel estimation sequence from a received OFDM-UWB frame; obtaining a CFR estimation ĥ r (2) by applying a frequency-domain smoothing to the CFR estimation ĥ r (1) with a first smoothing factor; obtaining a frame header which contains OFDM symbols transmitted with frequency-domain spreading on each OFDM symbol, and detecting signal signs based on a combination of two spread signals of the same OFDM symbol in the frame header with a decision directed mode and the CFR estimation ĥ r (2) assisted; obtaining a CFR estimation ĥ r (3) by using the signs and a finite-alphabet feature of the detected transmitted signals; obtaining a CFR estimation ĥ r (4) by applying a frequency-domain smoothing to the CFR estimation ĥ r (3) with a second smoothing factor; and obtaining a CFR estimation ĥ r by averaging the CFR estimations ĥ r (2) and ĥ r (4) .
1. A channel frequency response (CFR) estimation method for a multi-band orthogonal frequency division multiplexing (OFDM)-based ultra-wideband (UWB) system to achieve a CFR estimation, ĥ r =[ĥ r (0),ĥ r (1), . . . , ĥ r (N−1)] T , on an rth sub-band, N indicating the number of subcarriers employed by one OFDM symbol, the superscript T denoting transpose, comprising:
receiving an OFDM-UWB frame in an OFDM-UWB receiver of the multi-band OFDM-based UWB system;
obtaining, by the OFDM-UWB receiver, a first CFR estimation ĥ r (1) =[ĥ r (1) (0),ĥ r (1) (1), . . . , ĥ r (1) (N−1)] T by performing least square estimation using a channel estimation sequence in the received OFDM-UWB frame;
obtaining a second CFR estimation ĥ r (2) =[ĥ r (2) (0),ĥ r (2) (1), . . . , ĥ r (2) (N−1)] T by applying frequency-domain smoothing to the first CFR estimation ĥ r (1) using a first smoothing factor;
obtaining, from the received OFDM-UWB frame, a frame header containing a plurality of OFDM symbols, each OFDM symbol being transmitted with frequency-domain spreading, and being divided into N transmitted signals for modulating corresponding subcarriers;
for each OFDM symbol, detecting signs of the N transmitted signals using two frequency-domain spread signals corresponding to each of the N transmitted signals and the second CFR estimation ĥ r (2) ;
obtaining a third CFR estimation ĥ r (3) =[ĥ r (3) (0),ĥ r (3) (1), . . . , ĥ r (3) (N−1)] T using the detected signs and a finite-alphabet feature of the N transmitted signals for each OFDM symbol;
obtaining a fourth CFR estimation ĥ r (4) =[ĥ r (4) (0), ĥ r (4) (1), . . . , ĥ r (4) (N−1)] T by applying frequency-domain smoothing to the third CFR estimation ĥ r (3) with a second smoothing factor; and
obtaining the CFR estimation ĥ r by averaging the second and fourth CFR estimations ĥ r (2) and ĥ r (4) .
2. The CFR estimation method according to claim 1 , wherein the step of obtaining the first CFR estimation ĥ r (1) , the first CFR estimation ĥ r (1) is determined by averaging two LS estimation results obtained from an identical sub-band.
3. The CFR estimation method according to claim 1 , wherein in the step of obtaining the second CFR estimation ĥ r (2) , the first CFR estimation ĥ r (1) on each of the subcarriers is smoothed using the first CFR estimations on its adjacent subcarriers.
4. The CFR estimation method according to claim 3 , wherein the second CFR estimation ĥ r (2) on one of the subcarriers k, ĥ r (2) (k), is given by
ĥ r (2) ( k )=α[ ĥ r (1) ( k− 1)+ĥ r (1) ( k+ 1)]+(1−2α)ĥ r (1) ( k ), kεZ Q/2 ∪Z N−Q/2 N−1 ,
where
α is the first smoothing factor satisfying the condition 0<α<0.5;
Q is the number of the subcarriers for actual tones;
Z P 1 P 2 denotes the finite integer set {P 1 , P 1 +1, . . . , P 2 }, and
ĥ r (1) (k−1), ĥ r (1) (k), and, ĥ r (1) (k+1) respectively indicate the first CFR estimations ĥ r (1) on the subcarriers k−1, k, and, k+1.
5. The CFR estimation method according to claim 1 , wherein in the step of obtaining the frame header, the frequency-domain spreading on each OFDM symbol is implemented by transmitting each signal of the OFDM symbol and its conjugated signal on two separate subcarriers.
6. The CFR estimation method according to claim 1 , wherein the step of detecting the signs of the N transmitted signals further includes:
dividing an output of one of the subcarriers, subcarrier k, of a discrete Fourier transform (DFT) processor, y m (i) (k), by the second CFR estimations ĥ r (2) on the subcarrier k, ĥ r (2) (k), determine a transmitted signal on the subcarrier k, ŝ m (i) (k);
dividing an output of the subcarriers, subcarrier N−k, of the DFT processor, y m (i) (N−k), by the second CFR estimations ĥ r (2) on the subcarrier N−k, ĥ r (2) (N−k), to determine a transmitted signal on the subcarrier N−k, ŝ m (i) (N−k);
multiplying the transmitted signal on the subcarrier k, ŝ m (i) (k), by the squared magnitude of the second CFR estimations ĥ r (2) on the subcarrier k, ĥ r (2) (k), to yield a weighted frequency-domain spread signal for subcarrier k, λ m (i) (k)=y m (i) (k)[ĥ r (2) (k)]*;
multiplying the transmitted signal on the subcarrier N−k, ŝ m (i) (N−k), by the squared magnitude of the second CFR estimations ĥ r (2) on the subcarrier N−k, ĥ r (2) (N−k), to yield a weighted frequency-domain spread signal for subcarrier N−k, λ m (i) (N−k)=y m (i) (N−k)[ĥ r 2 (N−k)]*; and
combining the two weighted frequency-domain spread signals, λ m (i) (k) and λ m (i) (N−k), to yield a pair of combinations of the two frequency-domain spread signals, λ m (i) (k)+λ m (i) (N−k) and λ m (i) (k)−λ m (i) (N−k); wherein
[.]* denotes conjugation;
the received OFDM-UWB frame includes a plurality of OFDM symbol groups, indexed with m, each of which has a certain number of OFDM symbols, indexed with i; and
the superscript (i) and the subscript m in y m (i) (k), ŝ m (i) (k) and λ m (i) (k) indicate that the step of detecting is performed by using the ith OFDM symbol in the mth OFDM symbol group.
7. The CFR estimation method according to claim 6 , wherein the sign of each transmitted signal include the signs of the real and imaginary parts of the transmitted signal, and using the pair of combinations of the two frequency-domain spread signals, λ m (i) (k)+λ m (i) (N−k) and λ m (i) (k)−λ m (i) (N−k), the signs of the real and imaginary parts of the transmitted signal on the subcarrier k are given by:
u
m
(
i
)
(
k
)
=
{
sgn
[
(
λ
m
(
i
)
(
k
)
+
λ
m
(
i
)
(
N
-
k
)
)
]
,
k
∈
ℤ
1
Q
/
2
and
k
∉
{
p
(
l
)
}
l
=
0
R
-
1
u
m
(
i
)
(
N
-
k
)
,
k
∈
ℤ
N
-
Q
/
2
N
-
1
and
k
∉
{
p
(
l
)
}
l
=
0
R
-
1
and
v
m
(
i
)
(
k
)
=
{
sgn
[
(
λ
m
(
i
)
(
k
)
-
λ
m
(
i
)
(
N
-
k
)
)
]
,
k
∈
ℤ
1
Q
/
2
and
k
∉
{
p
(
l
)
}
l
=
0
R
-
1
-
v
m
(
i
)
(
N
-
k
)
,
k
∈
ℤ
N
-
Q
/
2
N
-
1
and
k
∉
{
p
(
l
)
}
l
=
0
R
-
1
where
Z P 1 P 2 denotes a finite integer set {P 1 , P 1 +1, . . . , P 2 };
(x) and (x) denote the real and imaginary parts of x, respectively;
sgn(x) equals 1, if x≧0, and −1 otherwise;
Q is the number of the subcarriers for actual tones; and
{p(l)} l=0 R−1 index the R subcarriers assigned as pilot tones in each OFDM symbol.
8. The CFR estimation method according to claim 1 , wherein in the step of obtaining the third CFR estimation ĥ r (3) , the third CFR estimation ĥ r (3) on one of the subcarriers, subcarrier k, ĥ r (3) (k), with the finite-alphabet feature being {(+c,−c),(+c,+c),(−c,−c),(−c,+c)}, is obtained as:
h
^
r
(
3
)
(
k
)
=
{
c
4
∑
m
=
1
2
∑
q
=
r
-
1
q
=
r
+
2
(
y
m
(
q
)
(
k
)
[
u
m
(
q
)
(
k
)
-
jv
m
(
q
)
(
k
)
]
)
,
k
∈
ℤ
1
Q
/
2
⋃
ℤ
N
-
Q
/
2
N
-
1
and
k
∉
{
p
(
l
)
}
l
=
0
R
-
1
1
4
∑
m
=
1
2
∑
q
=
r
-
1
q
=
r
+
2
(
y
m
(
q
)
(
k
)
[
s
m
(
q
)
(
k
)
]
*
)
,
k
∈
{
p
(
l
)
}
l
=
0
R
-
1
where
y m (q) (k) is an output of the subcarrier k of a DFT processor;
s m (q) (k) is an input of an inverse discrete Fourier transform (IDFT) processor;
[.]* denotes conjugation;
u m (q) (k) and v m (q) (k) respectively indicate the signs of the real and imaginary parts of a transmitted signal on the subcarrier k; j=√{square root over (−1)};
the received OFDM-UWB frame includes a plurality of OFDM symbol groups, indexed with m, each of which has a certain number of OFDM symbols, indexed with q; and the superscript (q) and the subscript m indicate that the step of obtaining the third CFR estimation ĥ r (3) is performed by using the qth OFDM symbol in the mth OFDM symbol group;
Z P 1 P 2 denotes the finite integer set {P 1 , P 1 +1, . . . , P 2 }; and Q is the number of the subcarriers for actual tones; and
{p(l)} l=0 R−1 index the R subcarriers assigned as pilot tones in each OFDM symbol.
9. The CFR estimation method according to claim 1 , wherein the second smoothing factor on one of the subcarriers, subcarrier k, is obtained as:
α
r
(
k
)
-
min
(
α
,
Q
h
^
r
(
1
)
(
k
)
2
∑
l
∈
ℤ
1
Q
/
2
⋃
ℤ
N
-
Q
/
2
N
-
1
h
^
r
(
1
)
(
l
)
2
)
,
k
∈
ℤ
1
Q
/
2
⋃
ℤ
N
-
Q
/
2
N
-
1
where
min(x 1 , x 2 ) means selecting a smaller one between two values, x 1 and x 2 ;
α indicates the first smoothing factor;
ĥ r (1) (k) is the first CFR estimation ĥ r (1) on the subcarrier k;
ĥ r (1) (l) is the first CFR estimation ĥ r (1) on another of the subcarriers, subcarrier l;
Z P 1 P 2 denotes a finite integer set {P 1 , P 1 +1, . . . , P 2 }; and
Q is the number of the subcarriers for actual tones.
10. The CFR estimation method according to claim 1 , wherein the fourth CFR estimation ĥ r (4) on one of the subcarriers, subcarrier k, ĥ r 4 (k), is obtained as:
ĥ r 4 ( k )=α r ( k− 1) ĥ r (3) ( k− 1)+α r ( k+ 1) ĥ r (3) ( k+ 1)+(1−α r ( k− 1)−α r ( k+ 1) ĥ r (3) ( k ) kεZ 1 Q/2 ∪Z N−Q/2 N−1 ,
where
ĥ r (3) (k−1), ĥ r (3) (k), and ĥ r (3) (k+1) indicate the third CFR estimations ĥ r (3) on subcarriers k−1, k, and k+1, respectively;
α r (k−1), and α r (k+1) are the second smoothing factors corresponding to the subcarriers k−1, and, k+1, respectively;
Z P 1 P 2 denotes a finite integer set {P 1 , P 1 +1, . . . , P 2 }; and
Q is the number of the subcarriers for actual tones.
11. The CFR estimation method according to claim 1 , wherein in the step of obtaining the CFR estimation ĥ r by averaging the CFR second and fourth estimations ĥ r (2) and ĥ r (4) , the CFR estimation ĥ r is obtained as: ĥ r =(2ĥ r (2) +4ĥ r (4) )/6.