Carrier frequency offset and doppler frequency estimation and correction for OFDMA and SC-FDMA
View Patent ↗A system and method are provided for carrier frequency offset (CFO) and Doppler frequency estimation and correction for Orthogonal Frequency-Division Multiple Access (OFDMA) and Single Carrier-Frequency-Division Multiple Access (SC-FDMA) signals in a wireless communications receiver. The receiver is capable of accepting a plurality of multicarrier signals transmitted simultaneously from a plurality of transmitters, with overlapping carrier frequencies and orthogonal reference signals. For each multicarrier signal, a channel estimate is performed and the channel is equalized. Then, a frequency offset is estimated between the transmit carrier frequency of each multicarrier signal and a receiver local oscillator frequency using either the phase rotation of data constellations as a function of time or the phase rotation of channel estimates as a function of time. The receiver supplies the CFO/Doppler frequency estimates and corrects the equalized symbols prior to demodulation.
1. A method for carrier frequency offset (CFO) and Doppler frequency estimation and correction for Orthogonal Frequency-Division Multiple Access (OFDMA) and Single Carrier-Frequency-Division Multiple Access (SC-FDMA) signals, comprising:
accepting, at a receiver, a plurality of multicarrier signals transmitted simultaneously from a plurality of transmitters, the plurality of multicarrier signals having overlapping carrier frequencies, orthogonal reference signals, and one of intra-subframe hopping or inter-subframe hopping;
for each of the plurality of multicarrier signals, performing a channel estimate and equalizing a channel;
estimating frequency offset between a transmit carrier frequency of each of the plurality of multicarrier signals and a receiver local oscillator frequency using one of phase rotation of data constellations as a function of time or phase rotation of channel estimates as a function of time, wherein:
the estimating the frequency offset using the phase rotation of data constellations as a function of time comprises using a data-aided maximum-likelihood estimation (MLE) if the plurality of multicarrier signals have intra-subframe hopping or inter-subframe hopping, and
the estimating the frequency offset using the phase rotation of channel estimates as a function of time comprises using a time-domain demodulation reference signal (DM-RS) if the plurality of multicarrier signals have inter-frame hopping or intra-subframe hopping; and
determining a combined CFO and Doppler frequency estimate.
2. The method of claim 1 , wherein the estimating the frequency offset using the phase rotation of data constellations as a function of time comprises estimating using a differential estimation.
3. The method of claim 2 , wherein the estimating the frequency offset using the phase rotation of data constellations as a function of time comprises using the differential estimation comprises:
letting N denote a number of subcarriers allocated to a user;
letting z u,l (s) denote a N×1 vector of received equalized symbols for user u, symbol l, and slot s for l=−L1, . . . , L2 and s=0,1;
letting {circumflex over (x)} u,l (s) denote a N×1 vector of slicer outputs for user u, symbol l and slot s, assuming hard decisions are perfect; and
for l=0 and s=0,1, {circumflex over (x)} u,l (s) =z u,l (s) =[1 . . . 1] T , and solving for:
Δ
f
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=
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T
sym
arg
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4. The method of claim 1 , wherein the estimating the frequency offset using the phase rotation of channel estimates as a function of time comprises using one of frequency-domain demodulation reference signal (DM-RS) or Fourier kernel estimation.
5. The method of claim 4 , wherein the accepting the plurality of multicarrier signals comprises accepting multicarrier signals with inter-subframe frequency hopping; and
wherein the estimating the frequency offset using the phase rotation of channel estimates as a function of time includes using the frequency-domain DM-RS estimation.
6. The method of claim 5 , wherein using the frequency-domain DM-RS estimation comprises:
letting Ĥ k,u (s) denote a M r ×1 channel estimate obtained from a DM-RS symbol for slot s, subcarrier k, and user u for s=0,1 and k=0, . . . , N−1, where M r =a number of receive antennas and N is a number of subcarriers allocated;
computing the combined CFO and Doppler frequency estimate for user u given by:
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=
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2
π
T
slot
arg
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∑
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.
7. The method of claim 4 , wherein the accepting the plurality of multicarrier signals comprises accepting multicarrier signals from a single user; and
wherein estimating the frequency offset using the phase rotation of channel estimates as a function of time includes using the Fourier kernel estimation as follows:
letting N denote a number of subcarriers allocated to a user;
using only received reference signal symbols, defining:
r m (s) the received signal from attenna m in slot s on allocated tones
F Fourier kernel on allocated tones
G(Δf) diagonal matrix whose diagonal elements are e j2πΔfk (k=0, 1, . . . N−1)
X (s) Transmitted pilot in slot s
ĥ m (s) Given Δf, estimated frequency domain channel response of slot s on attenna m
using a grid search, minimizing the metric of:
arg
min
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m
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8. The method of claim 1 , wherein using the data-aided MLE comprises:
letting N denote a number of subcarriers allocated to a user, where N is an integer;
letting z u,l (s) denote a N×1 vector of received equalized symbols for user u, symbol l, and slot s for l=−L1 . . . , L2 and s=0,1;
letting {circumflex over (x)} u,l (s) denote a N×1 vector of slicer outputs for user u, symbol l, and slot s, assuming hard decisions are perfect;
for l=0 and s=0,1, {circumflex over (x)} u,l (s) =z u,l (s) =[1 . . . 1] T , finding the MLE for Δf u as follows:
Δ
f
^
u
=
1
2
π
T
sym
arg
min
Δ
f
u
∑
s
=
0
1
∑
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2
z
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j2π
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Δ
f
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T
sys
x
^
u
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l
(
s
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2
using a small angle approximation, such that
|2πmax( L 1 ,L 2 )Δ f u T sym |<<1; and
solving for
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=
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2
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T
sym
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9. The method of claim 1 ,
wherein the estimating the frequency offset using the time-domain DM-RS estimation comprises using the time-domain DM-RS estimation if the plurality of multicarrier signals has a frequency allocation of at least five times a channel coherence bandwidth.
10. The method of claim 9 , wherein using the time-domain DM-RS estimation comprises:
letting Ĥ k,u (s) denote a M r ×1 channel estimate obtained from a DM-RS symbol for slot s, subcarrier k, and user u for s=0,1 and k=0, . . . , N−1, where M r =a number of receive antennas; and N is a number of subcarriers allocated;
letting N FFT be an integer satisfying N FFT ≧N;
letting ĥ n,u (s) denote a M r ×1 time-domain channel estimate for slot s, index n for n=0, . . . , N−1, and user u, where the time-domain channel estimate is obtained by taking a N FFT -point inverse discrete Fourier transform of Ĥ k,u (s) ;
letting N dom denote a set of indices of dominant channel taps; and
finding the combined CFO and Doppler frequency estimate for user u given by:
Δ
f
^
u
=
1
2
π
T
slot
arg
[
∑
n
∈
N
dom
(
h
^
n
,
u
(
0
)
)
H
h
^
n
,
u
(
1
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]
.
11. The method of claim 1 further comprising:
subsequent to supplying the combined CFO and Doppler frequency estimate, phase rotating the equalized symbols as a function of the combined CFO and Doppler frequency estimates, slot index, and symbol index as follows:
letting T sym denote a duration of each symbol of the plurality of multicarrier signals;
letting z u,l (s) denote a N×1 vector of received equalized symbols for user u, symbol l and slot s for l=−L 1 , . . . , L 2 and s=0,1; and
finding:
{tilde over (z)} u,l (s) =e −j2πlΔ{circumflex over (f)} u T sym z u,l (s) ;l=−L 1 , . . . ,L 2 ;s= 0,1.
12. The method of claim 11 , further comprising:
cascading corrected equalized symbols with a frequency offset estimation process comprising one of the phase rotation of data constellations as a function of time or the phase rotation of channel estimates as a function of time;
supplying an updated combined CFO and Doppler frequency estimate;
phase rotating the corrected equalized symbols as a function of the updated combined CFO and Doppler frequency estimate, slot index, and symbol index; and
determining updated corrected equalized symbols.
13. A system for carrier frequency offset (CFO) and Doppler frequency estimation and correction for Orthogonal Frequency-Division Multiple Access (OFDMA) and Single Carrier-Frequency-Division Multiple Access (SC-FDMA) signals, comprising:
a plurality of receive antennas configured for accepting a plurality of multicarrier signals transmitted simultaneously from a plurality of transmitters, the plurality of multicarrier signals having overlapping carrier frequencies and orthogonal reference signals;
a local oscillator configured to supply a down-conversion frequency;
a channel estimator module having a plurality of inputs configured to accept the plurality of multicarrier signals and an output configured to supply respective channel estimates for the plurality of multicarrier signals;
an equalizer having an input configured to accept the channel estimates and a plurality of outputs configured to supply a plurality of equalized symbols;
a plurality of CFO/Doppler estimation and correction modules configured to accept a plurality of equalized channel estimates, each of the plurality of CFO/Doppler estimation and correction modules having an output configured to supply combined CFO and Doppler frequency estimates for a frequency offset between a transmit carrier frequency of a corresponding multicarrier signal and a receiver local oscillator frequency using one of a phase rotation of data constellations as a function of time or a phase rotation of channel estimates as a function of time, wherein the phase rotation of data constellations as a function of time comprises a data-aided maximum-likelihood estimation (MLE) if the plurality of multicarrier signals have intra-subframe hopping or inter-subframe hopping, and wherein the phase rotation of channel estimates as a function of time comprises a time-domain demodulation reference signal (DM-RS) if the plurality of multicarrier signals have inter-frame hopping or intra-subframe hopping.
14. The system of claim 13 , wherein each of the plurality of CFO/Doppler estimation and correction module estimates the phase rotation of data constellations as a function of time using a differential estimation.
15. The system of claim 14 , wherein a first CFO/Doppler estimation and correction module estimates the phase rotation of data constellations as a function of time comprises using the differential estimation as follows:
letting N denote a number of subcarriers allocated to a user;
letting z u,l (s) denote a N×1 vector of received equalized symbols for user u, symbol l and slot s for l=−L 1 , . . . , L 2 and s=0,1;
letting {circumflex over (x)} u,l (s) denote a N×1 vector of slicer outputs for user u, symbol l and slot s, assuming hard decisions are perfect; and
for l=0 and s=0,1, {circumflex over (x)} u,l (s) =z u,l (s) =[1 . . . 1] T , and solving for:
Δ
f
^
u
=
1
2
π
T
sym
arg
{
∑
s
=
0
1
∑
l
=
-
L
1
L
2
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1
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.
16. The system of claim 13 , wherein each of the plurality of CFO/Doppler estimation and correction module estimates using the phase rotation of channel estimates as a function of time uses one of frequency-domain demodulation reference signal (DM-RS) or Fourier kernel estimation.
17. The system of claim 16 , wherein the plurality of receive antennas accept a first multicarrier signal with inter-subframe frequency hopping; and
wherein a first CFO/Doppler estimation and correction module associated with the first multicarrier signal estimates the phase rotation of channel estimates as a function of time using the frequency-domain DM-RS estimation as follows:
letting Ĥ k,u (s) denote a M r ×1 channel estimate obtained from the DM-RS symbol for slot s, subcarrier k and user u for s=0,1 and k=0, . . . , N−1, where M r =a number of receive antennas and N is a number of subcarriers allocated; and
computing a combined CFO and Doppler frequency estimate for user u given by:
Δ
f
^
u
=
1
2
π
T
slot
arg
[
∑
k
=
0
N
-
1
(
H
^
k
,
u
(
0
)
)
H
H
^
k
,
u
(
1
)
]
.
18. The system of claim 16 , wherein the plurality of receive antennas accept a first multicarrier signal from a first user; and
wherein a first CFO/Doppler estimation and correction module associated with the first multicarrier signal estimates the phase rotation of channel estimates as a function of time using the Fourier kernel estimation as follows:
letting N denote a number of subcarriers allocated to a user;
using only received reference signal symbols, defining:
r m (s) the received signal from attenna m in slot s on allocated tones
F Fourier kernel on allocated tones
G(Δf) diagonal matrix whose diagonal elements are e j2πΔfk (k=0, 1, . . . N−1)
X (s) Transmitted pilot in slot s
ĥ m (s) Given Δf, estimated frequency domain channel response of slot s on attenna m
using a grid search, minimizing the metric of:
arg
min
Δ
f
∑
s
,
m
r
m
(
s
)
-
F
H
G
(
Δ
f
)
FX
h
^
m
(
s
)
2
.
19. The system of claim 13 ,
wherein a first CFO/Doppler estimation and correction module associated with a first multicarrier signal estimates the phase rotation of data constellations as a function of time using the data-aided MLE as follows:
letting N denote a number of subcarriers allocated to a user;
letting z u,l (s) denote a N×1 vector of received equalized symbols for user u, symbol l and slot s for l=−L 1 , . . . , L 2 and s=0,1;
letting {circumflex over (x)} u,l (s) denote a N×1 vector of slicer outputs for user u, symbol l and slot s, assuming hard decisions are perfect;
for l=0 and s=0,1, {circumflex over (x)} u,l (s) =z u,l (s) =[1 . . . 1] T , finding an MLE for Δf u as follows:
Δ
f
^
u
=
1
2
π
T
sym
arg
min
Δ
f
u
∑
s
=
0
1
∑
l
=
-
L
1
L
2
z
u
,
l
(
s
)
-
ⅇ
j2π
l
Δ
f
u
T
sys
x
^
u
,
l
(
s
)
2
using a small angle approximation, such that
|2πmax( L 1 ,L 2 )Δ f u T sym <<1; and
solving for
Δ
f
^
u
=
1
2
π
T
sym
∑
s
=
0
1
∑
l
=
-
L
1
L
2
l
Im
[
(
x
^
u
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l
(
s
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z
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l
=
-
L
1
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2
l
2
Re
[
(
x
^
u
,
l
(
s
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)
H
z
u
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l
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s
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]
.
20. The system of claim 13 , wherein the plurality of receive antennas accept a first multicarrier signal with frequency hopping comprising one of intra-subframe hopping or inter-subframe hopping, wherein the first multicarrier signal has a frequency allocation of at least five times a channel coherence bandwidth; and
wherein a first CFO/Doppler estimation and correction module associated with the first multicarrier signal estimates the phase rotation of channel estimates as a function of time using the time-domain DM-RS estimation as follows:
letting Ĥ k,u (s) denote Mr×1 channel estimate obtained from the DM-RS symbol for slot s, subcarrier k, and user u for s=0,1 and k=0, . . . , N−1, where Mr=a number of receive antennas and N is a number of subcarriers allocated;
letting N FFT be an integer satisfying N FFT >=N;
letting ĥ n,u (s) denote a Mr×1 time-domain channel estimate for slot s, index n and user u for s=0,1 and n=0, . . . , N−1, where the time-domain channel estimate is obtained by taking a N FFT -point inverse discrete Fourier transform of Ĥ k,u (s) ;
letting N dom denote a set of indices of dominant channel taps; and
finding a combined CFO and Doppler frequency estimate for user u given by:
Δ
f
^
u
=
1
2
π
T
slot
arg
[
∑
n
∈
N
dom
(
h
^
n
,
u
(
0
)
)
H
h
^
n
,
u
(
1
)
]
.
21. The system of claim 13 , wherein a first CFO/Doppler estimation and correction module, subsequent to supplying the combined CFO and Doppler frequency estimates, supplies corrected equalized symbols by phase rotating the plurality of equalized symbols as a function of the combined CFO and Doppler frequency estimates, slot index, and symbol index as follows:
letting T sym denote a duration of each multicarrier signal symbol;
letting z u,l (s) denote a N×1 vector of received equalized symbols for user u, symbol l and slot s for l=−L1, . . . , L2 and s=0,1; and
finding:
{tilde over (z)} u,l (s) =e −j2πlΔ{circumflex over (f)} u T sym z u,l (s) ;−L 1 , . . . ,L 2 ;s= 0,1.
22. The system of claim 21 , wherein a second CFO/Doppler estimation and correction module accepts the corrected equalized symbols from the first CFO/Doppler estimation and correction module, estimates a frequency offset between a transmit carrier frequency of the first multicarrier signal and the receiver local oscillator, and supplies updated combined CFO and Doppler frequency estimates; and
wherein the second CFO/Doppler estimation and correction module supplies updated corrected equalized symbols by phase rotating the corrected equalized symbols as a function of the updated combined CFO and Doppler frequency estimates, the slot index, and the symbol index.