Full range offset correction for coherent optical OFDM systems
A method includes synchronizing a received signal with at least two orthogonal frequency division multiplexed OFDM training signals having only in-phase values and being real in the time domain and determining a frequency offset correction from the synchronization of the received signal and training symbols responsive to a cross-correlation between said training symbols to enable estimating all possible frequency offsets for correction for enabling OFDM demodulation of said received signal.
1. A method comprising the steps of:
synchronizing a received signal with at least two orthogonal frequency division multiplexed OFDM training signals having only in-phase values and being real in the time domain; and
determining a frequency offset correction from the synchronization of said received signal and training symbols responsive to a cross-correlation between said training symbols to enable estimating all possible frequency offsets for correction for enabling OFDM demodulation of said received signal,
wherein said frequency offsets across all possible frequencies are directly related to correction parameters r(NTs) and exp(j2πΔfNTs), where N is a training signal time frame, Ts is a time sampling frequency, r is a variable of the training signal, and Δf is a frequency offset.
2. The method of claim 1 , wherein said step of determining said frequency offset correction comprises, after said cross correlation, removing a phase shift from said received signal by applying a complex conjugate exp(j2πΔfNTs), where Nis a training signal time frame, Ts is a time sampling frequency, and Δf is a frequency offset.
3. The method of claim 2 , wherein said frequency offset correction {circumflex over (f)} n is responsive to a cross product relationship between said parameters:
{circumflex over (r)} n =r(NTs)×exp(j2πΔfNTs).
4. The method of claim 1 , wherein said cross correlation {circumflex over (R)}(D) is related to sequential variables r 1 n and r 2 n of respective said training signals
r 1 n =[R 1 e −j2πΔfTs R 2 e −j2πΔf×2Ts . . . R L e −j2πΔf×LTs ] n
r 2 n =[R 1 e −j2πΔf(N+1)Ts R 2 e −j2πΔf×(N+2)Ts . . . R L e −j2πΔf×(N+L)Ts ] n
where [R 1 R 2 . . . R L ] n are sequential training symbols, N is a training signal time frame, Ts is a time sampling frequency, and Δf is a frequency offset.
5. A method comprising the steps of:
synchronizing a received signal with at least two orthogonal frequency division multiplexed OFDM training signals having only in-phase values and being real in the time domain; and
determining a frequency offset correction from the synchronization of said received signal and training symbols responsive to a cross-correlation between said training symbols to enable estimating all possible frequency offsets for correction for enabling OFDM demodulation of said received signal,
wherein said cross correlation {circumflex over (R)}(D) is directly proportional to summation of sequential variables r 1 n and r 2 n of respective training signals according to the search relationship
R
^
(
D
)
=
∑
k
=
1
L
-
1
(
r
1
n
)
*
(
n
2
n
+
D
)
,
where D sets the searching range, k represents an OFDM symbol and L is an integer counter for a range of OFDM symbols.
6. A method comprising the steps of:
synchronizing a received signal with at least two orthogonal frequency division multiplexed OFDM training signals having only in-phase values and being real in the time domain; and
determining a frequency offset correction from the synchronization of said received signal and training symbols responsive to a cross-correlation between said training symbols to enable estimating all possible frequency offsets for correction for enabling OFDM demodulation of said received signal, wherein said frequency offset correction is responsive to a frequency estimation Δ{circumflex over (f)} based on
1
2
π
Ts
∠
〈
R
^
(
1
)
*
R
^
(
0
)
〉
where Ts is a time sampling frequency and {circumflex over (R)}(1) and {circumflex over (R)}(0) are respective first estimate training symbols of said training signals.