Methods and systems for diversity combining of synchronization statistics in OFDM systems
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 in an OFDM communications system implementing frequency hopping, comprising:
receiving a first pair of OFDM symbols on a first frequency band;
receiving a second pair of OFDM symbols on a second frequency band;
obtaining a first pair of frequency domain representations of the first pair of OFDM symbols at a pair of pilot tones;
obtaining a second pair of frequency domain representations of the second pair of OFDM symbols at the pair of pilot tones;
forming a first frequency domain statistic for the first frequency band by multiplying one of the first pair of frequency domain representations with the complex conjugate of the other of the first pair of frequency domain representations;
forming a second frequency domain statistic for the second frequency band by multiplying on of the second pair of frequency domain representations with the complex conjugate of the other of the second pair of frequency domain representations; and
combining the first frequency domain statistic with the second frequency domain statistic to form a combined frequency domain statistic.
2. The method of claim 1 , wherein the pair of pilot tones are pilot tones distributed symmetrically about 0.
3. The method of claim 1 , wherein the combined frequency domain statistic is [ χ l,k;γ χ l,k;γ ] T , where
χ
l
,
k
;
γ
•
∑
i
=
1
γ
x
l
,
k
❘
i
,
where the set {x l,k|i } i=1 γ is a set of frequency domain statistics on the pilot tone pair ±k, and includes the first frequency domain statistic and the second frequency domain statistic, l is a symbol time index, and i=1, . . . , γ is a sequence of frequency bands corresponding to the frequency hopping implemented by the OFDM communications system.
4. The method of claim 3 , further comprising computing a minimum variance unbiased estimator including the term
χ
l
,
k
;
γ
-
χ
l
,
k
;
γ
χ
l
,
k
;
γ
+
χ
l
,
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or
χ
l
,
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;
γ
+
χ
l
,
k
;
γ
χ
l
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k
;
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+
χ
l
,
k
;
γ
.
5. The method of claim 4 , wherein the minimum variance unbiased estimator comprises arctan
(
χ
l
,
k
;
γ
-
χ
l
,
k
;
γ
χ
l
,
k
;
γ
+
χ
l
,
k
;
γ
)
or arctan
(
χ
l
,
k
;
γ
+
χ
l
,
k
;
γ
χ
l
,
k
;
γ
+
χ
l
,
k
;
γ
)
.
6. The method of claim 1 , further comprising forming combined frequency domain statistics for the first and second pairs of OFDM symbols at a plurality of tone pairs.
7. The method of claim 1 , further comprising using the combined frequency domain statistic to generate a minimum variance unbiased estimator computation for carrier frequency offset or sampling frequency offset at the tone pair for the first and second pairs of OFDM symbols.
8. The method of claim 7 , further comprising forming a plurality of minimum variance unbiased estimator computations for carrier frequency offset or sampling frequency offset at a plurality of tone pairs for the first and second pairs of OFDM symbols.
9. The method of claim 8 , further comprising averaging the plurality of minimum variance unbiased estimator computations.
10. A system for use in an OFDM communications system implementing frequency hopping, comprising:
a transceiver;
a processor, coupled to the transceiver; and
a memory, coupled to the processor and configured to store instructions causing the processor to perform the steps of:
receiving a first pair of OFDM symbols on a first frequency band;
receiving a second pair of OFDM symbols on a second frequency band;
obtaining a first pair of frequency domain representations of the first pair of OFDM symbols at a pair of pilot tones;
obtaining a second pair of frequency domain representations of the second pair of OFDM symbols at the pair of pilot tones;
forming a first frequency domain statistic for the first frequency band by multiplying one of the first pair of frequency domain representations with the complex conjugate of the other of the first pair of frequency domain representations;
forming a second frequency domain statistic for the second frequency band by multiplying on of the second pair of frequency domain representations with the complex conjugate of the other of the second pair of frequency domain representations; and
combining the first frequency domain statistic with the second frequency domain statistic to form a combined frequency domain statistic.
11. The system of claim 10 , wherein the pair of pilot tones are pilot tones distributed symmetrically about 0.
12. The system of claim 10 , wherein the combined frequency domain statistic is [ χ l,k;γ χ l,k;γ ] T , where
χ
l
,
k
;
γ
•
∑
i
=
1
γ
x
l
,
k
❘
i
,
where the set {x l,k|i } i=1 γ is a set of frequency domain statistics on the pilot tone pair ±k, and includes the first frequency domain statistic and the second frequency domain statistic, l is a symbol time index, and i=1, . . . , γ is a sequence of frequency bands corresponding to the frequency hopping implemented by the OFDM communications system.
13. The system of claim 12 , wherein the steps further comprise computing a minimum variance unbiased estimator including the term
χ
l
,
k
;
γ
-
χ
l
,
k
;
γ
χ
l
,
k
;
γ
+
χ
l
,
k
;
γ
or
χ
l
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k
;
γ
+
χ
l
,
k
;
γ
χ
l
,
k
;
γ
+
χ
l
,
k
;
γ
.
14. The system of claim 13 , wherein the minimum variance unbiased estimator comprises arctan
(
χ
l
,
k
;
γ
-
χ
l
,
k
;
γ
χ
l
,
k
;
γ
+
χ
l
,
k
;
γ
)
or arctan
(
χ
l
,
k
;
γ
+
χ
l
,
k
;
γ
χ
l
,
k
;
γ
+
χ
l
,
k
;
γ
)
.
15. The system of claim 10 , wherein the steps further comprise forming combined frequency domain statistics for the first and second pairs of OFDM symbols at a plurality of tone pairs.
16. The system of claim 10 , wherein the steps further comprise using the combined frequency domain statistic to generate a minimum variance unbiased estimator computation for carrier frequency offset or sampling frequency offset at the tone pair for the first and second pairs of OFDM symbols.
17. The system of claim 16 , wherein the steps further comprise forming a plurality of minimum variance unbiased estimator computations for carrier frequency offset or sampling frequency offset at a plurality of tone pairs for the first and second pairs of OFDM symbols.
18. The system of claim 17 , wherein the steps further comprise averaging the plurality of minimum variance unbiased estimator computations.