Detection of time-frequency hopping patterns
The present invention relates to a method for detecting a pilot pattern, comprising a pilot signal s p (t), in a received signal r(t) implemented in an Orthogonal Frequency Division Multiplexing (OFDM) system. The method comprises the steps: computing a value of a log-likelihood function (τ 0 ,ν 0 ) for a hypotheses space specified by the pilot signal s p (t) and an initial time frequency offset (τ 0 ,ν 0 ), and relating the computed value to a reference value to detect the pilot pattern.
1. A method for detecting a pilot pattern, comprising a pilot signal s p (t), t=time, in a received signal r(t) implemented in an Orthogonal Frequency Division Multiplexing (OFDM) system, said method comprising:
computing a value of a log-likelihood function Λ(τ 0 ,ν 0 ), τ=delay, ν=Doppler shift, for a hypotheses space specified by the pilot signal s p (t) and an initial time frequency offset (τ 0 ,ν 0 ), said log-likelihood function defined by:
Λ
(
τ
0
,
ν
0
)
=
∫
0
ν
max
∫
0
τ
max
I
(
τ
+
τ
0
,
ν
+
ν
0
)
2
ⅆ
τ
ⅆ
ν
where
I
(
τ
,
ν
)
=
Δ
∫
r
(
t
)
s
p
*
(
t
-
τ
)
ⅇ
-
j
2
π
ν
t
ⅆ
t
where I(τ,ν) is a delay-Doppler image, r(t) is the received signal including the pilot pattern, and s* p (t) is a hypothesized pilot signal, and
relating the computed value to a reference value to detect the pilot pattern.
2. The method according to claim 1 , wherein the reference value is a threshold value, and the act of relating the computed value comprises comparing the computed value against said threshold value.
3. The method according to claim 1 , wherein the act of relating the computed value comprises evaluating and comparing the computed value among possible hypotheses of the pilot signal s p (t) and initial time frequency offset (τ 0 ,ν 0 ).
4. The method according to claim 1 , wherein the act of computing a value is a direct evaluation of the log-likelihood function Λ(τ 0 ,ν 0 ), said evaluation comprises:
performing a delay-Doppler correlation, and
integrating an energy over the hypotheses space.
5. The method according to claim 1 , wherein the method further comprises sampling the received signal r(t) to obtain samples r τ0,ν0 [n,i] to compute the log-likelihood function, said samples has a time offset τ 0 and frequency offset ν 0 sampled at the chip rate of 1/T c , T c -chip duration, and that said method further comprises choosing the delay hypothesis τ 0 to be multiples of the chip duration T c .
6. The method according to claim 1 , wherein said log-likelihood function Λ(τ 0 ,ν 0 ) is approximated by discrete sums of its sampled version as
Λ
(
τ
0
,
ν
0
)
≈
∑
k
=
0
K
-
1
∑
l
=
0
Q
-
1
I
τ
0
,
ν
0
[
k
,
l
]
2
where
I
τ
0
,
ν
0
[
k
,
l
]
=
∑
n
=
0
Q
N
-
1
ⅇ
-
j
2
πln
Q
N
∑
i
=
0
N
fft
-
1
r
τ
0
,
ν
0
[
n
,
i
+
k
]
c
n
*
[
i
]
where Q=number of periods accumulated in time, K=N fft /M, N fft =number of subcarriers in an OFDM symbol, M=pilot insertion period and I τ0ν0 [k,i] is a sampled delay-Doppler image sampled at a chip rate 1/T C Hz in the delay domain and QNT S sec. in the Doppler domain.
7. The method according claim 5 , wherein the computed value of the log-likelihood function Λ(τ 0 ,ν 0 ) is evaluated in the frequency domain using Discrete Fourier Transform (DFT).
8. The method according to claim 7 , wherein the log-likelihood function is evaluated in the frequency domain by:
∑
k
=
0
K
-
1
∑
l
=
0
Q
-
1
I
τ
0
,
ν
0
[
k
,
l
]
2
=
∑
n
=
0
Q
N
-
1
∑
m
=
0
N
fft
-
1
R
τ
0
,
ν
0
[
n
.
m
]
C
*
[
n
,
m
]
2
which is the sum of received signal energy over the locations of the hypothesized pilot signal on a discrete time-frequency plane, where
R
τ
0
,
ν
0
[
n
,
m
]
=
∑
i
=
0
N
fft
-
1
r
τ
0
,
ν
0
[
n
,
i
]
ⅇ
-
j
2
π
m
i
N
fft
is a length—N fft DFT of the sampled receive signal corresponding to the n'th OFDM symbol and a time-frequency map:
C
[
n
,
m
]
=
∑
i
=
0
N
fft
-
1
c
n
[
i
]
ⅇ
-
j
2
π
m
i
N
fft
m
=
0
,
1
,
…
,
N
fft
-
1
is a discrete frequency domain representation of the pilot signal in the n'th OFDM symbol.
9. The method according to claim 5 , wherein the computed value of the log-likelihood function Λ(τ 0 ,ν 0 ) is evaluated in the time domain using Discrete Fourier Transform (DFT).
10. The method according to claim 9 , wherein the log-likelihood function is evaluated in the time domain by:
∑
k
=
0
K
-
1
∑
l
=
0
Q
-
1
I
τ
0
,
ν
0
[
k
,
l
]
2
=
K
∑
n
=
0
Q
N
-
1
∑
m
=
0
M
-
1
(
∑
i
=
0
N
fft
-
1
r
τ
0
,
ν
0
[
n
,
i
]
r
τ
0
,
ν
0
*
[
n
,
i
-
mK
]
)
ⅇ
-
j
2
πϕ
n
m
M
where Q=number of periods accumulated in time, K=N fft /M, N fft =number of subcarriers in an OFDM symbol, and M=pilot insertion period.
11. The method according to claim 1 , wherein said method for detecting a pilot pattern is used for synchronizing and/or identifying a multiple of devices in a communication network.
12. The method according to claim 11 , wherein, each device transmits time-frequency hopping pilot signals having a circularly shifted pattern assigned to each device.
13. A detector implemented in an OFDM system receiving at least one pilot signal generated in said OFDM system, wherein said detector comprises a memory unit and a processing device, and is configured to perform computing a value of a log-likelihood function Λ(τ 0 ,ν 0 ), τ=delay, ν=Doppler shift, for a hypotheses space specified by the pilot signal s p (t) and an initial time frequency offset (τ 0 ,ν 0 ), said log-likelihood function defined by:
Λ
(
τ
0
,
ν
0
)
=
∫
0
ν
max
∫
0
τ
max
I
(
τ
+
τ
0
,
ν
+
ν
0
)
2
ⅆ
τ
ⅆ
ν
where
I
(
τ
,
ν
)
=
Δ
∫
r
(
t
)
s
p
*
(
t
-
τ
)
ⅇ
-
j
2
π
ν
t
ⅆ
t
where I(τ,ν) is a delay-Doppler image, r(t) is the received signal including a pilot pattern, and s* p (t) is a hypothesized pilot signal, and
relating the computed value to a reference value to detect the pilot pattern.
14. An OFDM system comprising:
at least one base station and at least one mobile communication device,
a first node in the system adapted to transmit a pilot signal, and
a second node in the system adapted to receive said pilot signal, said second node further comprising a detector which is adapted to perform computing a value of a log-likelihood function Λ(τ 0 ,ν 0 ), τ=delay, ν=Doppler shift, for a hypotheses space specified by the pilot signal s p (t) and an initial time frequency offset (τ 0 ,ν 0 ), said log-likelihood function defined by:
Λ
(
τ
0
,
ν
0
)
=
∫
0
ν
max
∫
0
τ
max
I
(
τ
+
τ
0
,
ν
+
ν
0
)
2
ⅆ
τ
ⅆ
ν
where
I
(
τ
,
ν
)
=
Δ
∫
r
(
t
)
s
p
*
(
t
-
τ
)
ⅇ
-
j
2
π
ν
t
ⅆ
t
where I(τ,ν) is a delay-Doppler image, r(t) is the received signal including a pilot pattern, and s* p (t) is a hypothesized pilot signal, and
relating the computed value to a reference value to detect the pilot pattern.