Method and receiver in a wireless communication system
View Patent ↗Receiver and method in a receiver, for estimating a normalised frequency offset between a transmitter and the receiver in a wireless communication system, based on Orthogonal Frequency Division Multiplexing, OFDM. The method comprises receiving a first pilot signal (y r 1) and a second pilot signal (y r 2) from the transmitter; computing a Karhunen-Loeve approximation λ K (φ), up to any finite order K of a log-likelihood function λ(φ), based on the received pilot signals (y r 1, y r 2); and estimating the frequency offset by calculating a maximum value of the computed Karhunen-Loeve approximation λ K (φ).
1. A method, implemented in a receiver, for estimating a normalised frequency offset between a transmitter and the receiver in a wireless communication system, based on Orthogonal Frequency Division Multiplexing, OFDM, the method comprising:
receiving a first pilot signal (y r1 ) and a second pilot signal (y r2 ) from the transmitter;
computing a Karhunen-Loeve approximation λ K (φ), up to any finite order K of a log-likelihood function λ(φ), based on the received first and second pilot signals (y r1 , y r2 ); and
estimating the frequency offset by calculating a maximum value of the computed Karhunen-Loeve approximation λ K (φ);
compensating the frequency offset by a frequency shift.
2. The method according to claim 1 , wherein K=3 and the representation λ 3 (φ) of the log-likelihood function λ(φ) comprises a set of three basis functions φ 1 (φ), φ 2 (φ), φ 3 (φ).
3. The method according to claim 2 , wherein the basis functions φ 1 (φ), φ 2 (φ), φ 3 (φ) are constructed of the form: φ(φ)=exp(−i2πφ[Δ+f k ]).
4. The method according to claim 3 , wherein the parameter f k is computed by:
f k =(k−2)·f Δ ; wherein 0.3≦fΔ≦0.7 and 1≦k≦3.
5. The method according to claim 4 , wherein f Δ =0.5.
6. The method according to claim 2 , wherein the log-likelihood function λhd 3 (φ) is constructed by:
λ
3
(
ϕ
)
=
Re
{
∑
k
=
1
3
α
k
·
φ
k
(
ϕ
)
}
,
7. The method according to claim 2 , wherein three values of the log-likelihood function λ 3 (φ) are evaluated at φ=−θ, 0, θ, wherein 0.3≦θ≦0.4.
8. The method according to claim 2 , wherein the log-likelihood function λ 3 (φ) is computed by finding coefficients α 1 , α 2 , α 3 , multiplying the coefficients α 1 , α 2 , α 3 with the corresponding basis functions φ 1 (φ), φ 2 (φ), φ 3 (φ), and then summing the terms.
9. The method according to claim 7 , wherein the coefficients a 1 , a 2 , a 3 are computed as:
[
α
1
α
2
α
3
]
=
[
φ
1
(
-
θ
)
φ
2
(
-
θ
)
φ
3
(
-
θ
)
φ
1
(
0
)
φ
2
(
0
)
φ
3
(
0
)
φ
1
(
θ
)
φ
2
(
θ
)
φ
3
(
θ
)
]
-
1
[
λ
(
-
θ
)
λ
(
0
)
λ
(
θ
)
]
.
10. The method according to claim 2 , wherein a maximum value of the computed function λ 3 (φ) is estimated by application of an optimisation algorithm.
11. The method according to claim 2 , wherein a maximum value of the computed function λ 3 (φ) is estimated by:
selecting P values φ such that φ ∈ {φ 1 , φ 2 , . . . , φ P }within [−0.5, 0.5];
computing P values of λ 3 (φ) at φ ∈ {φ 1 , φ 2 , . . . , φ P };
determining a biggest value of λ 3 (φ), denoted by λ max , as λ max =max λ 3 (φ m ), 1 ≦m≦P, and corresponding value of φ denoted φ max ; and
utilising the determined biggest value λ max and corresponding value φ max as a starting point in a line search algorithm to find the maximum of λ 3 (φ).
12. The method according to claim 11 , wherein, after having determined the biggest value λ max and corresponding value φ max , an assumption is made that the maximum value of λ 3 (φ) is within an interval:
ϕ
∈
2
ϕ
max
-
2
-
P
2
P
,
2
ϕ
max
-
P
2
P
.
13. The method according to claim 12 , wherein a golden section search with M iterations is performed for finding the maximum value of λ 3 (φ) within the interval.
14. The method according to claim 1 , wherein the receiver is included in a User Equipment, UE, and the transmitter is included in a radio network node.
15. A receiver, for estimating a normalised frequency offset between a transmitter and the receiver in a wireless communication system, based on Orthogonal Frequency Division Multiplexing, OFDM, said receiver comprising:
a receiving circuit, configured to receive a first pilot signal (y r1 ) and a second pilot signal (y r2 ) from the transmitter;
a processor, configured to compute a Karhunen-Loeve approximation λhd K(φ), up to any finite order K of a log-likelihood function λ(φ) based on the received first and second pilot signals (y r1 , y r2 ), and also configured to estimate the frequency offset by calculating a maximum value of the computed Karhunen-Loeve approximation λ K (φ);
the processor is further configured to compensate the frequency offset by a frequency shift.