Blind estimation of frequency and phase offsets for received signals

1. A non-transitory memory medium storing program instructions, wherein the program instructions, if executed by a processor, cause the processor to:

receive samples of a first signal;

compute values of a cost function J over a two-dimensional (2D) grid that covers a portion of a 2D angle-frequency space, wherein said computing includes computing a cost function value J(θ,ω) for each point (θ,ω) in the 2D grid, wherein, for each point (θ,ω) in the 2D grid, said computing includes:

generating samples of a modified signal, wherein the modified signal is related to the first signal by a phase adjustment of angle θ and a frequency adjustment of frequency ω;

performing N iterations of the K-means clustering algorithm on the samples of the modified signal to determine a partition of the samples into K clusters and to determine K mean positions corresponding to the K clusters, wherein N is a positive integer, wherein K is an integer greater than one;

for each of the K clusters, computing a corresponding sum of distance measures over the cluster, wherein the distance measures are relative to the mean position of the cluster;

adding the sums to obtain the cost function value J(θ,ω);

determine a point (θ e ,ω e ) in the 2D angle-frequency space that minimizes the cost function J.

2. The memory medium of claim 1 , wherein the program instructions, if executed by a processor, further cause the processor to:

correct the samples of the first signal to obtain samples of a corrected signal, wherein said correcting includes applying a phase adjustment of angle θ e and a frequency adjustment of frequency ω e to the samples of the first signal.

3. The memory medium of claim 2 , wherein the program instructions, if executed by the processor, further cause the processor to:

recover a stream of information bits from the samples of the corrected signal.

4. The memory medium of claim 1 , wherein K is a power of two.

5. The memory medium of claim 1 , wherein the first signal is a complex baseband signal resulting from a demodulation of a modulated signal, wherein the modulated signal was modulated according to a quadrature amplitude modulation (QAM) having a K-point constellation.

6. The memory medium of claim 5 , wherein said performing N iterations of the K-means clustering algorithm includes supplying the K-means clustering algorithm with the K points of the constellation as an initial guess for the K mean positions.

7. The memory medium of claim 1 , wherein the 2D grid is a rectangular grid.

8. The memory medium of claim 1 , wherein said computing the values of the cost function J is organized in terms of a first iterative loop and a second iterative loop, wherein the second iterative loop is situated within the first iterative loop, wherein the first iterative loop is a loop on θ, wherein the second iterative loop is a loop on ω.

9. The memory medium of claim 1 , wherein the point (θ e , ω e ) is determined with a resolution finer than the resolution of the 2D grid.

10. The memory medium of claim 1 , wherein the program instructions, if executed by the processor, further cause the processor to:

adjust a frequency and a phase of a local carrier signal based on the angle θ e and the frequency ω e .

11. The memory medium of claim 1 , wherein the distance measures are squared norm values.

12. An apparatus comprising:

a processor; and

a memory storing program instructions, wherein the program instructions, if executed by the processor, cause the processor to:

receive samples of a first signal;

compute values of a cost function J over a two-dimensional (2D) grid that covers a portion of a 2D angle-frequency space, wherein said computing includes computing a cost function value J(θ,ω) for each point (θ,ω) in the 2D grid, wherein, for each point (θ,ω) in the 2D grid, said computing includes:

generating samples of a modified signal, wherein the modified signal is related to the first signal by a phase adjustment of angle θ and a frequency adjustment of frequency ω;

performing N iterations of the K-means clustering algorithm on the samples of the modified signal to determine a partition of the samples into K clusters and to determine K mean positions corresponding to the K clusters, wherein N is a positive integer, wherein K is an integer greater than one;

for each of the K clusters, computing a corresponding sum of distance measures over the cluster, wherein the distance measures are relative to the mean position of the cluster;

adding the sums to obtain the cost function value J(θ,ω); and

determine a point (θ e ,ω e ) in the 2D angle-frequency space that minimizes the cost function J.

13. The apparatus of claim 12 , wherein the program instructions, if executed by the processor, cause the processor to:

correct the samples of the first signal to obtain samples of a corrected signal, wherein said correcting includes applying a phase adjustment of angle θ e and a frequency adjustment of frequency ω e to the samples of the first signal.

14. The apparatus of claim 12 , further comprising:

a carrier signal generator configured to generate a carrier signal; and

a demodulator circuit configured to receive a modulated signal, and generate the first signal based on the modulated signal and the carrier signal;

wherein carrier signal generator is configured to adjust a phase and a frequency of the carrier signal based on the angle θ e and the frequency ω e .

15. A method comprising:

receiving samples of a first signal, wherein said receiving is performed by a processor;

computing a plurality of values of a cost function J for a respective plurality of points in a two-dimensional (2D) angle-frequency space, wherein said computing is performed by the processor, wherein said computing includes computing a cost function value J(θ,ω) for each point (θ,ω) of said plurality of points by:

applying a phase and frequency adjustment to the samples of the first signal to determine adjusted samples, wherein said phase and frequency adjustment is based on the angle θ and the frequency ω;

performing one or more iterations of the K-means clustering algorithm on the adjusted samples to determine a partition of the adjusted samples into K clusters and to determine K mean positions corresponding to the K clusters;

for each of the K clusters, computing a corresponding sum of distance measures over the cluster and relative to the mean position of the cluster;

adding the sums to obtain the cost function value J(θ,ω);

determining a point (θ e ,ω e ) in the 2D angle-frequency space that minimizes the cost function J, wherein said determining is performed by the processor.

16. The method of claim 15 , further comprising:

correct the samples of the first signal to obtain samples of a corrected signal, wherein said correcting includes applying a phase adjustment of angle θ e and a frequency adjustment of frequency ω e to the samples of the first signal.

17. The method of claim 16 , further comprising:

recover a stream of information bits from the samples of the corrected signal.

18. The method of claim 15 , wherein said computing the values of the cost function J is organized in terms of a first iterative loop and a second iterative loop, wherein the second iterative loop is situated within the first iterative loop, wherein the first iterative loop is a loop on θ, wherein the second iterative loop is a loop on ω.

19. The method of claim 15 , wherein the plurality of points belong to a 2D grid in the 2D angle-frequency space, wherein the point (θ e ,ω e ) is determined with a resolution that is finer than the resolution of the 2D grid.

20. The method of claim 15 , further comprising:

adjust a frequency and a phase of a local carrier signal based on the angle θ e and the frequency ω e .

21. The method of claim 15 , wherein the integer K is a power of two.