Fast digital carrier frequency error estimation algorithm using synchronization sequence

1. A method for determining frequency error of a serial offset quadrature pulse shaped signal, the method comprising the steps of:

receiving, by a receiver, the serial offset quadrature pulse shaped signal having a synchronization sequence;

detecting, by the receiver, synchronization of the quadrature pulse shaped signal;

storing, in a memory, a baseband inphase (I) signal and a baseband quadrature (Q) signal of the synchronization sequence while detecting synchronization;

reading, from the memory, segments of the stored baseband I and Q signals after detecting synchronization;

correlating, by the receiver, the read segments with a spreading sequence;

determining, by the receiver, phase differences between each of the correlated segments; and

estimating, by the receiver, the frequency error based on the determined phase differences.

2. The method of claim 1 , wherein the determining step comprises the steps of:

developing, by the receiver, overlapping symbols from the correlated segments; and

calculating, by the receiver, differential phase measurements between the overlapping symbols to determine the phase differences between each of the correlated segments.

3. The method of claim 2 , wherein the developing step comprises:

correlating, by the receiver, the baseband I and Q signals over a plurality of symbols with a predetermined shift between each correlation.

4. The method of claim 3 , wherein the plurality of symbols is sixteen and the predetermined shift between each correlation is four symbols.

5. The method of claim 2 , wherein the estimating step comprises:

estimating, by the receiver, the frequency error based at least in part on the calculated differential phase measurements.

6. The method of claim 2 , wherein the estimating step, used in the receiver, comprises solving the equation:

f

est

=

1

2

⁢

π

⁢

⁢

T

offset

⁢

∑

k

=

0

N

-

1

⁢

w

k

⁢

Δθ

k

where f est is the estimated frequency error, T offset is the time offset between successive overlapping symbols, N is the number of overlapping symbols, W k is a weighting function, and Δθ k is the phase difference between successive overlapping symbols.

7. The method of claim 2 , wherein the received quadrature pulse shaped signal is received on a carrier having a carrier frequency, the overlapping symbols have a symbol rate, and the baseband I and Q signals are serially demodulated using a frequency that is one-quarter of the symbol rate below the carrier frequency.

8. The method of claim 1 , further comprising the step of:

phase rotating, by the receiver, the received quadrature pulse shaped signal to form the baseband I and Q signals.

9. The method of claim 8 , further comprising the step of:

serially demodulating the received quadrature pulse shaped signal.

10. The method of claim 9 , wherein the detecting synchronization step and the correlating step of the receiver operate against the same synchronization sequence for both the baseband I signal and the baseband Q signal.

11. The method of claim 1 , wherein after detecting synchronization the correlating step is started.

12. The method of claim 1 , wherein the detecting synchronization step comprises the following steps implemented in the receiver:

correlating the baseband I signal and correlating the baseband Q signal;

squaring the correlated baseband I signal and squaring the correlated baseband Q signal;

combining the squared baseband I signal and the squared baseband Q signal;

detecting a peak of the combined baseband I and Q signals; and

comparing the detected peak to an autocorrelation function to detect synchronization.

13. The method of claim 12 , wherein the combining step further comprises the step of:

determining the square root of the combined squared baseband I signal and squared baseband Q signal to develop the combined baseband I and Q signals.

14. The method of claim 1 , wherein the received quadrature pulse shaped signal is modulated in the receiver using one of Quadrature Phase Shift Keying (QPSK), Offset QPSK (OQPSK), Minimum Shift Keying (MSK), Gaussian MSK, Tamed Frequency Modulation (TFM), Intersymbol Jitter Free OQPSK (IJF-OQPSK), Raised Cosine Filtered OQPSK (RC-OQPSK), or bandwidth efficient Continuous Phase Modulation (CPM) schemes.

15. A receiver comprising:

a demodulator that receives a quadrature pulse shaped signal having a synchronization sequence and that develops a baseband inphase (I) signal and a baseband quadrature (Q) signal from the received quadrature pulse shaped signal;

a phase rotator coupled to the demodulator that rotates the baseband I and Q signals;

a synchronization detection module coupled to the phase rotator that detects synchronization of the received quadrature pulse shaped signal using the rotated baseband I and Q signals;

a memory coupled to the phase rotator and the synchronization detection module, the memory storing the rotated baseband I and Q signals during synchronization detection;

a correlator coupled to the synchronization detection module and the memory, the correlator correlating segments of the rotated baseband I and Q signals read from the memory after synchronization detection; and

a frequency error correction module coupled to the correlator that estimates carrier frequency errors for the received quadrature pulse shaped signal and that develops a carrier frequency error correction signal for use in correcting the carrier frequency errors.

16. The receiver of claim 15 , wherein the correlator develops overlapping symbols from the correlated segments and the frequency error correction module calculates differential phase measurements between the overlapping symbols to determine phase differences between the correlated segments to estimate the carrier frequency errors.

17. The receiver of claim 16 , wherein the frequency error correction module estimates the carrier frequency errors by solving the equation:

f

est

=

1

2

⁢

π

⁢

⁢

T

offset

⁢

∑

k

=

0

N

-

1

⁢

w

k

⁢

Δθ

k

where f est is the estimated frequency error, T offset is the time offset between successive overlapping symbols, N is the number of overlapping symbols, w k is a weighting function, and Δθ k is the phase difference between successive overlapping symbols.

18. The receiver of claim 15 , wherein the synchronization detection module controls the memory and the correlator such that, upon detection of synchronization, the memory stops storing the rotated baseband I and Q signals and the correlator starts correlating segments of the rotated baseband I and Q signals read from the memory.

19. The receiver of claim 15 , wherein the demodulator comprises:

downconverters that down-convert the received quadrature pulse shaped signal to the baseband I and Q signals;

low pass filters coupled to the downconverters that filter the baseband I and Q signals to remove undesirable terms introduced by the downconverters;

analog-to-digital (A/D) converters coupled to the low pass filters that digitize the filtered baseband I and Q signals; and

symbol matched filters coupled to the (A/D) converters to improve signal-to-noise ratios (SNR) of the digitized baseband I and Q signals.

20. The receiver of claim 15 wherein the correlator comprises:

a plurality of segments that include a predetermined number of symbols with a predetermined delay.

21. The receiver of claim 20 , wherein there are four correlator segments for each of the baseband I signal and the baseband Q signal, the predetermined number of symbols is sixteen, and the predetermined delay is four symbols.

22. The receiver of claim 15 , wherein the memory includes at least one circular buffer memory.

23. The receiver of claim 15 , wherein the synchronization detection module and the correlator operate against the same synchronization sequence for both the baseband I signal and the baseband Q signal.

24. The receiver of claim 15 , wherein the synchronization detection module comprises:

an inphase correlator that correlates the baseband I signal;

a quadrature correlator that correlates the baseband Q signal;

an inphase squaring component coupled to the inphase correlator that squares the correlated baseband I signal and a quadrature squaring component coupled to the quadrature correlator that squares the correlated baseband Q signal;

a combiner coupled to the inphase and quadrature phase squaring comnonent that combines the squared baseband I signal and the squared baseband Q signal;

a peak detection module coupled to the combiner that detects a peak of the combined baseband I and Q signals; and

a comparator coupled to the peak detection module that compares the detected peak to an autocorrelation function to detect synchronization.

25. The receiver of claim 24 , wherein the correlation detection module further comprises a square root calculator coupled between the combiner and the peak detection module, the square root calculator calculating the square root of the combined squared baseband I signal and squared baseband Q signal to develop the combined baseband I and Q signals.

26. The receiver of claim 15 , wherein the received quadrature pulse shaped signal is modulated using one of Quadrature Phase Shift Keying (QPSK), Offset QPSK (OQPSK), Minimum Shift Keying (MSK), Gaussian MSK, Tamed Frequency Modulation (TFM), Intersymbol Jitter Free OQPSK (IJF-OQPSK), Raised Cosine Filtered OQPSK (RC-OQPSK), or bandwidth efficient Continuous Phase Modulation (CPM) schemes.