Methods and systems for computing a minimum variance unbiased estimator of carrier and sampling clock frequency
Various embodiments of the systems and methods described herein may be used to compute a minimum variance unbiased estimator by receiving a first OFDM signal at a pilot tone, receiving a second OFDM signal sent in the same frequency band and determining a differential phase metric between the first OFDM signal and the second OFDM signal. In some embodiments, the differential phase metric may be used to diversity combine synchronization statistics. In various embodiments, the differential phase metric may be used to detect a narrow-band interference.
1. A method of computing a minimum variance unbiased estimator comprising:
receiving a first OFDM symbol on a frequency band;
obtaining a first frequency domain representation of the first OFDM symbol, z l,k , at a pair of pilot tones ±k, where l is a symbol time index associated with the first OFDM symbol;
receiving a second OFDM symbol sent in the frequency band;
obtaining a second frequency domain representation of the second OFDM symbol, z l′,±k , at the pair of pilot tones ±k, where l′ is a symbol time index associated with the second OFDM symbol;
determining a differential phase metric associated with the first OFDM symbol and the second OFDM symbol, by multiplying the first frequency domain representation by a complex conjugate of the second frequency domain representation to form the frequency domain statistic x l,±k =z l,±k z l′,±k *; and
computing the minimum variance unbiased estimator using the frequency domain statistic, the minimum variance unbiased estimator comprising
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2. The method of claim 1 , wherein the unique minimum variance unbiased estimator is applied for a carrier relative frequency offset.
3. The method of claim 1 , wherein the unique minimum variance unbiased estimator is applied for a sampling clock relative frequency offset.
4. The method of claim 1 , wherein the unique minimum variance unbiased estimator is applied using a symmetric representation of the first and second OFDM symbols.
5. The method of claim 4 , wherein the symmetric representation comprises a conjugate symmetric component.
6. The method of claim 1 , wherein the unique minimum variance unbiased estimator is applied using an asymmetric representation of the first and second OFDM symbols.
7. The method of claim 1 , wherein the the first OFDM symbol and the second OFDM symbol are two consecutive symbols.
8. The method of claim 1 , further comprising calculating a differential phase metric at all pilot tones used to estimate the carrier and sampling clock frequency.
9. A system for computing a minimum variance unbiased estimator comprising:
an antenna;
a processor, coupled to the antenna; and
a memory, coupled to the processor and configured to store instructions causing the processor to:
receive a first OFDM symbol on a frequency band;
obtain a first frequency domain representation of the first OFDM symbol, z l,k , at a pair of pilot tones ±k, where l is a symbol time index associated with the first OFDM symbol
receive a second OFDM symbol sent in the same frequency band;
obtain a second frequency domain representation of the second OFDM symbol, z l′,±k , the tones ±k, where l′ is a symbol time index associated with the second OFDM symbol;
determine a differential phase metric associated with the first OFDM symbol and the second OFDM symbol, by multiplying the first frequency domain representation by a complex conjugate of the second frequency domain representation to form the frequency domain statistic x l,±k =z l′,±k z l′,±k *; and
compute the minimum variance unbiased estimator using the frequency domain statistic, the minimum variance unbiased estimator comprising
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10. The system of claim 9 , wherein the instructions are further configured to cause the processor to apply the unique minimum variance unbiased estimator for a carrier relative frequency offset.
11. The system of claim 9 , wherein the instructions are further configured to cause the processor to apply the unique minimum variance unbiased estimator for a sampling clock relative frequency offset.
12. The system of claim 9 , wherein the instructions are further configured to cause the processor to apply the unique minimum variance unbiased estimator using a symmetric representation of the first and second OFDM symbols.
13. The system of claim 12 , wherein the symmetric representation of comprises a conjugate symmetric component.
14. The system of claim 9 , wherein the instructions are further configured to cause the processor to apply the unique minimum variance unbiased estimator using an asymmetric representation of the first and second OFDM symbols.
15. The system of claim 9 , wherein the first OFDM symbol and the second OFDM symbol are two consecutive symbols.
16. The system of claim 9 , wherein the instructions are further configured to cause the processor to calculate a differential phase metric at all pilot tones used to estimate the carrier and sampling clock frequency.
17. The method of claim 1 , wherein the minimum variance unbiased estimator further comprises arctan
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18. The method of claim 1 , further comprising computing a plurality of minimum variance unbiased estimators using frequency domain representations of the first and second OFDM symbols on a plurality of tone pairs.
19. The method of claim 18 , further comprising averaging the plurality of minimum variance unbiased estimator computations.
20. The system of claim 9 , wherein the minimum variance unbiased estimator further comprises arctan
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21. The system of claim 9 , further comprising computing a plurality of minimum variance unbiased estimators using frequency domain representations of the first and second OFDM symbols on a plurality of tone pairs.
22. The system of claim 21 , further comprising averaging the plurality of minimum variance unbiased estimator computations.