System and method for robust OFDM synchronization
Disclosed methods include transmitting an OFDM signal including a succession of frames spaced apart by a set of training symbols that are symmetric in time and each formed by a plurality of even-frequency sub-carriers, spaced by odd frequency zeros. The OFDM signal is received and sampled and timing metrics are determined. Local maximums, or peaks of the timing metrics are detected, and from the peaks a coarse time offset is determined. A correlation metric, at sample indexes within a region determined by the coarse time offset, is applied and, based on a peak, an estimated time offset is generated. A correlation metric of the estimated time offset is determined and, based on the correlation metric, an estimated frequency offset is generated.
1. A system for synchronizing a receiving of an orthogonal frequency division multiplexing (OFDM), the system comprising:
an input data interface configured to receive a sequence signal samples and associated indexes;
a processing unit; and
a memory configured to a store a plurality of instructions that when read and executed by the processing unit cause the processing unit to:
detect a timing metric at each of a succession of the indexes and determine, as a first peak, an index at which the timing metric is at a local maximum,
detect the timing metric at indexes within a first region of the indexes and determine, as a second peak, an index at which the timing metric is at another local maximum, the first region being based in part on the first peak,
select a coarse offset as the smaller of the first peak and the second peak,
detect a correlation metric at each of a plurality of indexes within a second region of the indexes, the second region being based at least in part on the coarse offset,
generate, as an estimated time offset, an index at which the detected correlation metric is at a local maximum, and
apply a synchronization correction to a recovery of symbols from the signal samples, based at least in part on the estimated time offset.
2. The system of claim 1 , wherein the input data interface is configured to receive the sequence signal samples and associated indexes for each frame among a succession of frames, and
wherein to detect the correlation metric at each of the plurality of indexes within the second region of the indexes includes, for each index, includes to:
calculate a single-frame correlation metric for each frame among multiple frames with the succession of frames, to form multiple single-frame correlation metrics for the index, and
combine the multiple single frame correlation metrics for the index into an accumulated correlation metric, and
detect the correlation metric for the index as the accumulated correlation metric.
3. The system of claim 2 , wherein to combine the multiple single frame correlation metrics for the index into the accumulated correlation metric includes to:
select, as a selected combining, between a coherent combining and a non-coherent combining, and
apply the selected combining.
4. The system of claim 1 , wherein the synchronization correction is a time correction and is based, at least in part, on the estimated time offset.
5. The system of claim 1 , wherein to detect the correlation metric includes to:
generate a cross-correlation data, based at least in part on a correlation window aligned with the index at which the correlation metric is at a local maximum,
generate an autocorrelation data, based at least in part on a region of the correlation window, and
determine the correlation metric, based at least in part on a ratio of the cross-correlation data to the autocorrelation data.
6. The system of claim 1 , wherein the instructions further include instructions that when read and executed by the processing unit cause the processing unit to:
generate an estimated frequency offset, based at least in part on the estimated time offset, wherein:
the synchronization correction is a frequency correction and is based, at least in part, on the estimated frequency offset.
7. The system of claim 6 , wherein:
the sequence of signal samples includes a window of integer N signal samples, aligned with a corresponding N time indexes, and
to generate the estimated frequency offset includes to:
detect a cross-correlation of signal samples within a region of the time indexes aligned with the estimated time offset and generate a corresponding first time offset cross-correlation data,
detect a cross-correlation of signal samples within a region spaced N time indexes from the region aligned with the estimated time offset, and generate a corresponding second time offset cross-correlation data,
generate, as a cross-correlation sum, a sum of the first time offset cross-correlation data and the second time offset cross-correlation data, and
determine the estimated frequency offset based, at least in part, on a scaling of the cross-correlation sum.
8. The system of claim 6 , wherein to apply the frequency correction includes to output, as a result, a frequency corrected signal sample stream, and wherein the instructions further include instructions that when read and executed by the processing unit cause the processing unit to:
apply a frequency domain demodulation to the frequency corrected signal sample stream and output a corresponding recovered frequency domain symbol stream;
determine a correlation between the recovered frequency domain symbol stream and a plurality of pre-stored frequency domain training symbols, and output a corresponding training symbol correlation data;
estimate a fine frequency offset, based at least in part on the training symbol correlation data; and
adjust the frequency correction, based at least in part on the estimated fine frequency offset.
9. The system of claim 8 , wherein to estimate the fine frequency offset includes to:
generate a discrete Fourier transform of the training symbol correlation data,
apply a Maximum Likelihood Estimation to the generated discrete Fourier transform based at least in part on the training symbol correlation data, and
generate the estimated fine frequency offset based, at least in part, on a result of the Maximum Likelihood Estimation.
10. A method for synchronizing a receiving of an orthogonal frequency division multiplexing (OFDM)communication, comprising:
receiving a sequence of signal samples and associated indexes;
detecting a timing metric at each of a succession of the indexes and determining, as a first peak, an index at which the timing metric is at a local maximum;
detecting the timing metric at indexes within a first region of the indexes and determining, as a second peak, an index at which the timing metric is at another local maximum, the first region being based in part on the first peak;
selecting a coarse offset as the smaller of the first peak and the second peak;
detecting a correlation metric at a plurality of indexes within a second region of the indexes, the second region being based at least in part on the coarse offset;
determining, as an estimated time offset, an index at which the correlation metric is a local maximum; and
applying a synchronization correction to a recovery of symbols from the signal samples, based at least in part on the estimated time offset.
11. The method of claim 10 , wherein the synchronization correction is a time correction and is based, at least in part, on the estimated time offset.
12. The method of claim 10 , the method further comprising:
generating an estimated frequency offset, based at least in part on the estimated time offset, wherein:
wherein the synchronization correction is a frequency correction, and the frequency correct is based, at least in part, on the estimated frequency offset.
13. The method of claim 12 , wherein:
the sequence of signal samples includes a window of integer N signal samples, aligned with a corresponding N time indexes, and
generating the estimated frequency offset includes:
detecting a cross-correlation of signal samples within a region of the time indexes aligned with the estimated time offset and generating a corresponding first time offset cross-correlation data,
detecting a cross-correlation of signal samples within a region spaced N time indexes from the region aligned with the estimated time offset, and generating a corresponding second time offset cross-correlation data,
generating, as a cross-correlation sum, a sum of the first time offset cross-correlation data and the second time offset cross-correlation data, and
determining the estimated frequency offset based, at least in part, on a scaling of the cross-correlation sum.
14. The method of claim 12 , wherein applying the frequency correction includes applying the frequency correction to the signal samples and outputting, as a result, a frequency corrected signal sample stream, and wherein the method further comprises:
applying a frequency domain demodulation to the frequency corrected signal sample stream and outputting a corresponding recovered frequency domain symbol stream;
determining a correlation between the recovered frequency domain symbol stream and a plurality of pre-stored frequency domain training symbols, and outputting a corresponding training symbol correlation data;
estimating a fine frequency offset, based at least in part on the training symbol correlation data; and
adjusting the frequency correction, based at least in part on the estimated fine frequency offset.
15. The method of claim 14 , wherein:
estimating the fine frequency offset includes:
generating a discrete Fourier transform of the training symbol correlation data,
applying a Maximum Likelihood Estimation to the generated discrete Fourier transform based at least in part on the training symbol correlation data, and
generating the estimated fine frequency offset based, at least in part, on a result of the Maximum Likelihood Estimation.