Method for estimating and correcting a carrier frequency offset over dispersive but spectrally flat channels
View Patent ↗A method for estimating a carrier frequency offset over a dispersive but spectrally flat channel comprises determining an autocorrelation of a received oversampled complex baseband digital signal, and estimating the carrier frequency offset based on an angle of the determined autocorrelation.
1. A method of estimating a carrier frequency offset over a dispersive but spectrally flat channel, the method comprising:
determining an autocorrelation of a received oversampled complex baseband digital signal; and
estimating the carrier frequency offset in accordance with
Δ
f
=
f
s
2
π
k
α
angle
[
R
y
(
k
)
]
wherein f s is a sampling frequency, α is a constant, k is a constant associated with a capture range, and R y (k) is the determined autocorrelation of the received oversampled complex baseband digital signal.
2. The method of claim 1 , wherein α is determined based on a cutoff frequency of transmit and receive filters in a complex baseband representative of a communication system that includes the channel and a magnitude response of the channel.
3. The method of claim 1 , wherein the autocorrelation is determined in accordance with
R y ( k )=Σ n y ( n ) y *( n−k )
wherein y(n) is an nth sample of the received complex oversampled baseband signal sampled at frequency greater than f b , and k is an integer less than f s /f b , wherein f b is the baud rate of the received oversampled complex baseband digital signal.
4. The method of claim 1 , comprising generating a corrected carrier frequency offset based on the estimated carrier frequency offset.
5. The method of claim 4 , wherein generating a corrected carrier frequency offset comprises adjusting a local oscillator to compensate for the estimated carrier frequency offset.
6. The method of claim 4 , wherein generating a corrected carrier frequency offset comprises applying a direct digital frequency correction to the received oversampled complex baseband digital signal based on the estimated carrier frequency offset.
7. The method of claim 1 , wherein α is a constant having a value between 0.5 and 0.8.
8. The method of claim 1 , wherein α is a constant having a value of one.
9. The method of claim 1 , wherein k is determined in accordance with
k=└f s /(2 f cap )┘
wherein f cap is a capture range.
10. The method of claim 8 , further comprising in response to a determination that the carrier frequency offset is greater than a predetermined accuracy threshold, generating a corrected carrier frequency offset based on the estimated carrier frequency offset.
11. The method of claim 10 , further comprising repeating the determining and estimating until the determined carrier frequency offset is less than the predetermined accuracy threshold.
12. The method of claim 11 , wherein generating a corrected carrier frequency offset comprises adjusting a local oscillator to compensate for the estimated carrier frequency offset.
13. The method of claim 11 , wherein generating a corrected carrier frequency comprises applying a direct digital frequency correction to the received oversampled complex baseband digital signal based on the estimated carrier frequency offset.
14. A non-transitory computer-readable medium having computer-readable instructions executable by at least one processor of a receiver for:
determining an autocorrelation of a received oversampled complex baseband digital signal; and
estimating a carrier frequency offset over a dispersive but spectrally flat channel in accordance with
Δ
f
=
f
s
2
π
k
α
angle
[
R
y
(
k
)
]
wherein f s is a sampling frequency, α is a constant, k is a constant associated with a capture range, and R y (k) is the determined autocorrelation of the received oversampled complex baseband digital signal.
15. A receiver comprising:
operational components including a demodulator and analog-to-digital converters for converting a modulated passband signal received over a dispersive but spectrally flat channel to an oversampled complex baseband digital signal;
a processor operably coupled to the operational components and configured to:
determine an autocorrelation of the oversampled complex baseband digital signal; and
estimate a carrier frequency offset over the dispersive but spectrally flat channel in accordance with
Δ
f
=
f
s
2
π
k
α
angle
[
R
y
(
k
)
]
wherein f s is a sampling frequency, α is a constant, k is a constant associated with a capture range, and R y (k) is the determined autocorrelation of the received oversampled complex baseband digital signal.
16. The receiver of claim 15 , wherein α is determined based on a cutoff frequency of transmit and receive filters in a complex baseband representative of a communication system that includes the channel and a magnitude response of the channel.
17. The receiver of claim 15 , wherein the processor is further configured to determine the autocorrelation in accordance with
R y ( k )=Σ n y ( n ) y *( n−k )
wherein y(n) is an nth sample of the received complex oversampled baseband signal sampled at frequency greater than f b , and k is an integer less than f s /f b , where f b is the baud rate of the received oversampled complex baseband digital signal.
18. The receiver of claim 17 , wherein the processor is further configured to generate a corrected carrier frequency offset by adjusting a local oscillator to compensate for the estimated carrier frequency offset.
19. The receiver of claim 17 , wherein the processor is further configured to generate a corrected carrier frequency offset by applying a direct digital frequency correction to the received oversampled complex baseband digital signal based on the estimated carrier frequency offset.
20. The receiver of claim 17 , wherein processor is further configured to generate a corrected carrier frequency offset based on the estimated carrier frequency offset.
21. The receiver of claim 15 , wherein α is a constant having a value between 0.5 and 0.8.
22. The receiver of claim 15 , wherein α is a constant having a value of one.
23. The receiver of claim 15 , wherein the processor is further configured to determine k in accordance with
k=└f s /(2 f cap )┘
wherein f s is a sampling frequency and f cap is a capture range.
24. The receiver of claim 21 , wherein the processor is further configured to generate a corrected carrier frequency offset based on the estimated carrier frequency offset in response to a determination that the estimated carrier frequency offset is greater than a predetermined accuracy threshold.
25. The receiver of claim 23 , wherein the processor is further configured to repeat the determination and estimation until the estimated carrier frequency offset is less than the predetermined accuracy threshold.
26. The receiver of claim 24 , wherein the processor is further configured to generate a corrected carrier frequency offset by adjusting a local oscillator to compensate for the estimated carrier frequency offset.
27. The receiver of claim 24 , wherein the processor is further configured to generate a corrected carrier frequency offset by applying a direct digital frequency correction to the received oversampled complex baseband digital signal based on the estimated carrier frequency offset.