Frequency offset estimation in orthogonal frequency division multiple access wireless networks
A method of wireless transmission for estimating the carrier frequency offset in a base station of a received transmission from a user equipment (UE) accessing a radio access network. The method time de-multiplexes selected symbols of a received sub-frame, computes the frequency-domain symbols received from each antenna through an FFT, de-maps the UEs selected sub-carriers for each antenna, computes metrics associated to a carrier frequency offset hypothesis spanning a searched frequency offset window, repeats these steps on subsequent received sub-frames from the UE over an estimation interval duration, non-coherently accumulates the computed metrics and selects the carrier frequency offset hypothesis with largest accumulated metric amplitude.
1. A method of wireless transmission for estimating the carrier frequency offset in a base station of a received Orthogonal Frequency Division Multiplexing (OFDM) transmission from a user equipment (UE) accessing an Orthogonal Frequency Division Multiplexing Access (OFDMA) radio access network, comprising:
receiving a transmission from the UE at one of a plurality of antennas at the base station;
extracting selected OFDM symbols from the OFDM symbol multiplex of a received sub-frame employing a-priori known sub-carrier modulation of the selected symbols;
computing the frequency-domain symbols received from each antenna through a Fast Fourier Transform (FFT);
de-mapping from the frequency-domain symbols the UEs selected sub-carriers of the OFDMA sub-carrier multiplex for each antenna;
computing from each de-mapped symbol from each antenna N metrics M i for i=1, . . . , N, each associated to a carrier frequency offset hypothesis δf i wherein a set of carrier frequency offset hypothesis spans a searched frequency offset window;
performing the steps of receiving, extracting, computing the frequency-domain symbols, de-mapping and computing metrics M i on subsequent received sub-frames from the UE over an estimation interval duration;
non-coherently accumulating across the estimation interval and all antennas the computed metrics M i,n associated to the carrier frequency offset hypothesis δf i for each carrier frequency offset hypothesis δf i ; and
selecting the carrier frequency offset hypothesis with largest accumulated metric amplitude as the estimated carrier frequency offset estimate.
2. The method of claim 1 , wherein:
the selected OFDM symbols are demodulation reference OFDM symbols (DMRS) provisioned in support of channel estimation.
3. The method of claim 1 , wherein:
the selected OFDM symbols are reconstructed demodulated OFDM symbols.
4. The method of claim 1 , wherein:
the OFDMA symbols are Single Carrier Frequency Division Multiple Access (SC-FDMA) symbols.
5. The method of claim 1 , wherein:
the OFDMA symbols are Discrete Fourier Transform Orthogonal Frequency Division Multiple Access (DFT-SOFDMA) symbols.
6. The method of claim 1 , wherein:
said step of computing the estimator metric M i corresponding to carrier frequency offset hypothesis δf i includes:
for each de-mapped sub-carrier k multiplying a transform of a de-mapped FFT output sub-carrier sample R S (k) and a transform of a frequency shifted replica S(k,δf i ) of the frequency-domain sequence symbol expected on sub-carrier k thereby producing a product;
summing the product across all de-mapped sub-carriers k thereby producing a sum; and
dividing the sum by a normalization factor.
7. The method of claim 6 , wherein:
the normalization factor is selected to provide a non-biased estimation.
8. The method of claim 6 , wherein:
the metric selected for addressing single UE in the OFDMA multiplex with Additive White Gaussian Noise (AWGN) channel wherein:
the transform of the received de-mapped FFT output sub-carrier sample R S (k) is the identity transform leaving R S (k) unchanged;
the transform of the frequency shifted replica S(k,δf i ) is the complex conjugate S(k,δf i )* of S(k,δf i ); and
the normalization factor is the square root of the sum of across de-mapped sub-carriers of the squared frequency shifted replica S(k,δf i )
∑
k
=
0
N
sc
-
1
S
(
k
,
δ
f
)
2
.
9. The method of claim 6 , wherein:
the metric selected for multiple UEs in the OFDMA multiplex with fading channel and slow varying frequency offset wherein:
the transform of the received de-mapped FFT output sub-carrier sample R S (k) is the square of the absolute value of R S (k) |R s (k)| 2 ;
the transform of the frequency shifted replica S(k,δf i ) is the square of the absolute value of S(k,δf i ) |S(k,δf)| 2 ; and
the normalization factor is the square root of the sum of across de-mapped sub-carriers of the fourth power frequency shifted replica S(k,δf i )
∑
k
=
0
N
sc
-
1
S
(
k
,
δ
f
)
4
.
10. The method of claim 6 , wherein:
the metric selected for addressing multiple UEs in the OFDMA multiplex with fading channel and fast varying frequency offset wherein:
the transform of the received de-mapped FFT output sub-carrier sample R S (k) is the square of the absolute value of R S (k) |R s (k)| 2 ;
the transform of the frequency shifted replica S(k,δf i ) is the square of the absolute value of S(k,δf i ) |S(k,δf)| 2 ; and
the normalization factor is the square root of the sum of across de-mapped sub-carriers of the squared frequency shifted replica S(k,δf i )
∑
k
=
0
N
sc
-
1
S
(
k
,
δ
f
)
4
.
11. The method of claim 6 , further comprising:
selecting a metric for addressing multiple UEs in the OFDMA multiplex with fading channel and fast varying frequency offset wherein:
the transform of the received de-mapped FFT output sub-carrier sample R S (k) is absolute value of R S (k) |R s (k)|;
the transform of the frequency shifted replica S(k,δf i ) is the absolute value of S(k,δf i ) |S(k,δf)|; and
the normalization factor is the square root of the sum of across de-mapped sub-carriers of the squared frequency shifted replica S(k,δf i )
∑
k
=
0
N
sc
-
1
S
(
k
,
δ
f
)
2
.
12. The method of claim 6 , wherein:
the frequency shifted replica S(k,δf i ) is constructed in frequency domain using an interpolation-based frequency-domain frequency offset generation technique defined as:
Z
i
(
k
,
ɛ
)
=
∑
l
=
0
N
sc
-
1
Z
(
l
)
C
(
l
-
k
,
ɛ
)
;
k
=
0
,
1
,
…
N
SC
-
1
where: N SC is the UE allocation size, in sub-carriers; ε is the normalized frequency shift: ε=δf/Δf sc ; Z(l) is the de-mapped frequency points of the UE corresponding to the N SC -point DFT of the original time-domain samples z(n); C(l−k,ε) is the interpolator coefficients; and Z i (k,ε) is the interpolated point from the Z(l) points, and:
C
(
k
,
ɛ
)
=
sin
(
π
(
k
+
ɛ
)
)
/
N
FFT
sin
(
π
(
k
+
ɛ
)
/
N
FFT
)
ⅇ
j
π
(
k
+
ɛ
)
N
FFT
-
1
N
FFT
≈
sin
c
[
π
(
k
+
ɛ
)
]
ⅇ
jπ
(
k
+
ɛ
)
N
FFT
-
1
N
FFT
for
k
=
-
N
SC
+
1
,
-
N
SC
+
2
,
…
0
,
1
,
…
N
SC
-
1
where: N FFT is the FFT size and
sin
c
(
x
)
=
sin
(
x
)
x
.
13. The method of claim 6 , wherein:
the frequency shifted replicas S(k,δf i ) are constructed from a frequency domain de-mapped samples Z(k) through a combined inverse discrete Fourier Transform (IDFT)/discrete Fourier Transform (DFT) as defined below:
Z ( k ,ε)= FFT 2N SC {z p ( n ) c ε ( n )}; k= 0,1 , . . . N SC −1 ; n= 0,1, . . . 2 N SC −1
where: FFT N is the N-point FFT; z p (n) is the 2N SC -point IDFT of Z p (k), reflecting a 2× time-domain over-sampling with respect to the original sampling rate of z(n); Z p (k) is a zero-padded extension of Z (k), the de-mapped frequency points of the UE, to get a 2N SC length vector:
Z
p
(
k
)
=
{
0
;
k
=
0
,
1
,
…
,
N
SC
-
1
Z
(
k
-
N
SC
)
;
k
=
N
SC
,
N
SC
+
1
,
…
,
2
N
SC
-
1
and c ε (n)=e j2πγn where the equivalent normalized frequency γ is given by
γ
=
1
2
(
1
+
ɛ
N
SC
)
.
14. The method of claim 1 , wherein:
the number N of frequency hypothesis is restricted to 3 in the searched frequency offset window [−f max 0 f max ] by using a parabolic interpolation to locate the position of the metric maximum where, given the three Cartesian points (x i , y i ), i=1, 2, 3 such that y i =a x i 2 +b x i +c, the abscissa x max of the maximum y max of the parabola is given by:
x
max
=
1
2
[
x
1
+
x
2
-
(
x
1
-
x
3
)
(
x
3
-
x
2
)
(
y
1
-
y
2
)
(
y
1
-
y
3
)
(
x
1
-
x
2
)
-
(
y
1
-
y
2
)
(
x
1
-
x
3
)
]
.
15. The method of claim 1 , wherein:
the estimated carrier frequency offset obtained during a previous estimation interval is removed from the received OFDM symbols after symbol de-mapping and before metric computation during a current estimation interval.
16. The method of claim 15 , wherein:
the estimated carrier frequency offset is removed from the received OFDM symbols using an interpolation-based frequency-domain frequency offset generation technique defined as:
Z
i
(
k
,
ɛ
)
=
∑
l
=
0
N
sc
-
1
Z
(
l
)
C
(
l
-
k
,
ɛ
)
;
k
=
0
,
1
,
…
N
SC
-
1
where: N SC is the UE allocation size, in sub-carriers; ε is the normalized frequency shift: ε=δf/Δf sc ; Z(l) is the de-mapped frequency points of the UE corresponding to the N SC -point DFT of the original time-domain samples z(n); C(l−k,ε) is the interpolator coefficients; and Z i (k,ε) is the interpolated point from the Z(l) points, and:
C
(
k
,
ɛ
)
=
sin
(
π
(
k
+
ɛ
)
)
/
N
FFT
sin
(
π
(
k
+
ɛ
)
/
N
FFT
)
ⅇ
j
π
(
k
+
ɛ
)
N
FFT
-
1
N
FFT
≈
sin
c
[
π
(
k
+
ɛ
)
]
ⅇ
j
π
(
k
+
ɛ
)
N
FFT
-
1
N
FFT
for
k
=
-
N
SC
+
1
,
-
N
SC
+
2
,
…
0
,
1
,
…
N
SC
-
1
where: N FFT is the FFT size and
sin
c
(
x
)
=
sin
(
x
)
x
.
17. The method of claim 15 , wherein:
the estimated carrier frequency offset is removed from the received OFDM symbols using a combined inverse discrete Fourier Transform (IDFT)/discrete Fourier Transform (DFT) as defined below:
Z ( k ,ε)= FFT 2N SC {z p ( n ) c ε ( n )}; k= 0,1 , . . . N SC −1 ; n= 0,1, . . . 2 N SC −1
where: FFT N is the N-point FFT; z p (n) is the 2N SC -point IDFT of Z p (k), reflecting a 2× time-domain over-sampling with respect to the original sampling rate of z(n); Z p (k) is a zero-padded extension of Z (k), the de-mapped frequency points of the UE, to get a 2N SC length vector:
Z
p
(
k
)
=
{
0
;
k
=
0
,
1
,
…
,
N
SC
-
1
Z
(
k
-
N
SC
)
;
k
=
N
SC
,
N
SC
+
1
,
…
2
N
SC
-
1
and c ε (n)=e j2πγn where the equivalent normalized frequency γ is given by
γ
=
1
2
(
1
+
ɛ
N
SC
)
.
18. The method of claim 1 , further comprising:
selecting a set of frequency bins each having a frequency range for each estimation interval, the frequency range covered by the frequency bins of an estimation interval being adjusted across estimation intervals with respect to a last obtained frequency estimation.
19. The method of claim 18 , wherein:
the frequency offset window is adapted as follows:
{
f
searched
∈
[
-
f
max
f
max
]
with
f
max
=
min
{
200
Hz
;
max
{
2000
Hz
;
3
δ
f
^
}
}
where: δf is the residual frequency estimate of the previous estimation interval.
20. The method of claim 1 , wherein:
the estimation intervals have a constant duration.
21. The method of claim 1 , wherein:
the duration of each estimation interval is controlled dynamically with a stopping criterion involving a measured standard deviation across elementary estimates of a sliding window at the end of the estimation interval.