Iterative frequency offset estimation in wireless networks

1. An apparatus comprising:

radio frequency (“RF”) circuitry to down-convert a signal from a base station to generate in-phase and quadrature (“IQ”) components, wherein the signal includes a plurality of repeated extended coverage-synchronization channel (“EC-SCH”) bursts; and

a frequency offset estimator operatively coupled to the RF circuitry, the frequency offset estimator to estimate a frequency offset based on the IQ components and an iterative calculation of phase differences between different sets of bursts of the plurality of repeated EC-SCH bursts.

2. The apparatus of claim 1 , wherein the frequency offset estimator is further configured to calculate a first phasor (“R L1 ”) based on a distance between first and second bursts of the plurality of repeated EC-SCH bursts.

3. The apparatus of claim 1 , further comprising:

a frequency offset compensator operatively coupled with the frequency offset estimator to generate compensated IQ components based on the IQ components and the estimate of the frequency offset.

4. The apparatus of claim 1 , wherein the apparatus is a cellular Internet of things (“CIoT”) device.

5. An apparatus comprising:

radio frequency (“RF”) circuitry to down-convert a signal from a base station to generate in-phase and quadrature (“IQ”) components, wherein the signal includes one or more repeated bursts; and

a frequency offset estimator operatively coupled to the RF circuitry, the frequency offset estimator to estimate a frequency offset based on the IQ components and an iterative calculation of phase differences between different sets of bursts of the one or more repeated bursts,

wherein the frequency offset estimator is to determine a level-n phasor (“R Ln ”) carrying a phase difference with different distances based on:

R

Ln

=

1

M

⁢

∑

j

=

n

M

-

1

⁢

∑

k

=

0

N

-

1

⁢

x

⁡

(

j

,

k

)

*

conj

⁡

(

x

⁡

(

j

-

n

,

k

)

)

,

n

=

1

,

2

,

…

⁢

,

M

,

where x(j,k) is a k th sample of a j th burst, M is an assigned iteration number, and N is a number of data used for frequency offset estimation in one burst.

6. The apparatus of claim 5 , wherein, to estimate the frequency offset, the frequency offset estimator is to set a phasor (“R”) equal to a level-one phasor (“R L1 ”).

7. The apparatus of claim 6 , wherein, to estimate the frequency offset, the frequency offset estimator is to iteratively update the phasor until the assigned iteration number to determine a final phasor (“R M ”) based on

R

n

=

R

n

-

1

*

e

⁢

angle

(

R

Ln

*

conj

⁡

(

R

n

-

1

)

n

n

⁢

j

,

n

=

1

,

2

,

…

⁢

,

M

,

where angle(*) is an operation to calculate a phase of one complex value.

8. The apparatus of claim 7 , wherein the frequency offset estimator is to estimate the frequency offset (“Δf”) based on:

Δ

⁢

⁢

f

=

angle

⁡

(

R

M

)

2

⁢

π

*

1250

⁢

T

S

,

where T s is a basic time unit value.

9. One or more non-transitory, computer-readable media having instructions that, when executed, cause a device to:

calculate a level-one phasor based on in-phase and quadrature (“IQ”) components of adjacent bursts of a plurality of repeated extended coverage-synchronization channel (EC-SCH) bursts;

set a phasor equal to the level-one phasor;

iteratively update the phasor until an assigned iteration number to determine a final phasor; and

estimate a frequency offset based on the final phasor.

10. The one or more non-transitory, computer-readable media of claim 9 , wherein the phasor carries a phase difference based on distance between the adjacent bursts.

11. The one or more non-transitory, computer-readable media of claim 9 , wherein the instructions, when executed, further cause the device to determine a level-n phasor (“R Ln ”) carrying a phase difference with different distances between a plurality of repeated EC-SCH bursts given by:

R

Ln

=

1

M

⁢

∑

j

=

n

M

-

1

⁢

∑

k

=

0

N

-

1

⁢

x

⁡

(

j

,

k

)

*

conj

⁡

(

x

⁡

(

j

-

n

,

k

)

)

,

n

=

1

,

2

,

…

⁢

,

M

,

where x(j,k) is a k th sample of a j th burst, M is an assigned iteration number, and N is a number of data used for frequency offset estimation in one burst.

12. The one or more non-transitory, computer-readable media of claim 9 , wherein the instructions, when executed, further cause the device to iteratively update the phasor (“R”) to determine the final phasor (“R M ”) based on

R

n

=

R

n

-

1

*

e

⁢

angle

(

R

Ln

*

conj

⁡

(

R

n

-

1

)

n

n

⁢

j

,

n

=

1

,

2

,

…

⁢

,

M

,

where angle(*) is an operation to calculate a phase of one complex value.

13. The one or more non-transitory, computer-readable media of claim 12 , wherein the instructions, when executed, further cause the device to estimate the frequency offset (“Δf”) based on:

Δ

⁢

⁢

f

=

angle

⁡

(

R

M

)

2

⁢

π

*

1250

⁢

T

S

,

where T s is a basic time unit value.

14. An apparatus comprising:

means for receiving in-phase and quadrature (“IQ”) components of a plurality of repeated extended coverage-synchronization channel (“EC-SCH”) bursts and for estimating a frequency offset based on an iterative calculation of phase differences between different sets of bursts of the plurality of repeated EC-SCH bursts; and

means for compensating for the frequency offset to provide compensated IQ components.

15. The apparatus of claim 14 , wherein the means for estimating the frequency offset is to determine a level-n phasor (“R Ln ”) carrying a phase difference with different distances given by:

R

Ln

=

1

M

⁢

∑

j

=

n

M

-

1

⁢

∑

k

=

0

N

-

1

⁢

x

⁡

(

j

,

k

)

*

conj

⁡

(

x

⁡

(

j

-

n

,

k

)

)

,

n

=

1

,

2

,

…

⁢

,

M

,

where x(j,k) is a k th sample of a j th burst, M is an assigned iteration number, and N is a number of data used for frequency offset estimation in one burst.

16. The apparatus of claim 15 , wherein the means for estimating the frequency offset is to set a phasor (“R”) equal to a level-one phasor (“R L1 ”).

17. The apparatus of claim 16 , wherein the means for estimating the frequency offset is to iteratively update the phasor until an assigned iteration number to determine a final phasor (“R M ”) based on

R

n

=

R

n

-

1

*

e

⁢

angle

(

R

Ln

*

conj

⁡

(

R

n

-

1

)

n

n

⁢

j

,

n

=

1

,

2

,

…

⁢

,

M

,

where angle(*) is an operation to calculate a phase of one complex value.

18. The apparatus of claim 17 , wherein the means for estimating the frequency offset is to estimate the frequency offset (“Δf”) based on:

Δ

⁢

⁢

f

=

angle

⁡

(

R

M

)

2

⁢

π

*

1250

⁢

T

S

,

where T s is a basic time unit value.

19. The apparatus of claim 14 , wherein the apparatus is a cellular Internet of things (“CIoT”) device.