Phase rotation estimation
View Patent ↗Apparatus, systems, and methods implementing techniques for estimating a relative rotation between a first complex signal and a second complex signal. The first complex signal is quantized to produce a quantized signal, and the quantized signal and an additional signal are combined, where the additional signal corresponds to the second complex signal. An estimate of a relative rotation between the first complex signal and the second complex signal is generated in accordance with the combined signal.
1. A method for estimating a relative rotation between a first complex signal and a second complex signal, the method comprising:
quantizing a first complex signal to produce a quantized signal;
combining the quantized signal and an additional signal to produce a combined signal, the additional signal corresponding to a second complex signal; and
generating an estimate of a relative rotation between the first complex signal and the second complex signal in accordance with the combined signal; wherein:
the first complex signal includes a first in-phase component and a first quadrature component, and the second complex signal includes a second in-phase component and a second quadrature component;
quantizing the first complex signal includes quantizing the first in-phase component and the first quadrature component; and
combining includes combining multiplicative products of any of the quantized first in-phase component, the quantized first quadrature component, the second in-phase component, and the second quadrature component.
2. The method of claim 1 further comprising:
quantizing the second complex signal to produce the additional signal.
3. The method of claim 1 wherein the additional signal is the second complex signal.
4. The method of claim 1 wherein generating an estimate includes filtering the combined signal.
5. The method of claim 4 wherein filtering the combined signal includes digitally filtering the combined signal.
6. The method of claim 5 wherein digitally filtering includes integrating.
7. The method of claim 4 wherein filtering the combined signal includes analog filtering of the combined signal.
8. The method of claim 4 wherein filtering the combined signal includes low-pass filtering of the combined signal.
9. The method of claim 8 wherein low-pass filtering includes integrating.
10. The method of claim 4 wherein filtering includes setting a filter to a predetermined state.
11. The method of claim 1 , further comprising:
quantizing the second in-phase component and the second quadrature component, wherein combining includes combining multiplicative products of any of the quantized first in-phase component, the quantized first quadrature component, the quantized second in-phase component, and the quantized second quadrature component.
12. The method of claim 1 wherein combining includes summing.
13. The method of claim 1 wherein combining includes differencing.
14. The method of claim 1 wherein quantizing includes multi-bit quantizing.
15. The method of claim 1 wherein quantizing includes one-bit quantizing.
16. The method of claim 15 wherein the first complex signal includes a first in-phase component and a first quadrature component, and one-bit quantizing includes quantizing any of the first in-phase component and the first quadrature component using one bit per component.
17. The method of claim 1 wherein at least one of the first complex signal and the second complex signal is a continuous-time signal.
18. The method of claim 1 wherein at least one of the first complex signal and the second complex signal is a discrete-time signal.
19. The method of claim 1 further comprising:
sampling at least one of the first complex signal and the second complex signal in time.
20. The method of claim 1 further comprising:
quantizing the estimate of the relative rotation between the first complex signal and the second complex signal.
21. The method of claim 1 wherein combining includes digitally combining.
22. The method of claim 1 further comprising:
filtering at least one of the first complex signal and the second complex signal.
23. The method of claim 22 wherein filtering includes high-pass filtering.
24. The method of claim 22 wherein filtering includes low-pass filtering.
25. The method of claim 22 wherein filtering includes band-pass filtering.
26. A method for estimating a relative rotation between a first complex signal and a second complex signal, the method comprising:
quantizing a first complex signal to produce a quantized signal;
combining the quantized signal and an additional signal to produce a combined signal, the additional signal corresponding to a second complex signal; and
generating an estimate of a relative rotation between the first complex signal and the second complex signal in accordance with the combined signal; wherein
the first complex signal and the second complex signal are substantially identical except for the relative rotation.
27. A method for estimating a relative rotation between a first complex signal and a second complex signal, the method comprising:
quantizing a first complex signal to produce a quantized signal;
combining the quantized signal and an additional signal to produce a combined signal, the additional signal corresponding to a second complex signal; and
generating an estimate of a relative rotation between the first complex signal and the second complex signal in accordance with the combined signal;
rotating at least one of the first complex signal and the second complex signal in accordance with the estimate of the relative rotation between the first complex signal and the second complex signal.
28. The method of claim 27 wherein rotating includes shifting the phase of the at least one of the first complex signal and the second complex signal.
29. The method of claim 27 wherein the first complex signal includes a first in-phase component and a first quadrature component, the second complex signal includes a second in-phase component and a second quadrature component, and rotating includes producing a weighted sum of any of the first in-phase component, the first quadrature component, the second in-phase component, and the second quadrature component.
30. A method for estimating a relative rotation between a first complex signal and a second complex signal, the method comprising:
quantizing a first complex signal to produce a quantized signal;
combining the quantized signal and an additional signal to produce a combined signal, the additional signal corresponding to a second complex signal; and
generating an estimate of a relative rotation between the first complex signal and the second complex signal in accordance with the combined signal;
wherein combining includes an analog combination.
31. A rotation-estimation circuit, comprising:
a quantizer operable to receive a first complex signal and produce a quantized signal;
a combiner operable to receive the quantized signal and an additional signal and produce a combined signal, the additional signal corresponding to a second complex signal; and
an estimate generator operable to receive the combined signal and produce an estimate of a relative rotation between the first complex signal and the second complex signal; wherein
the first complex signal includes a first in-phase component and a first quadrature component, and the second complex signal includes a second in-phase component and a second quadrature component;
the quantizer is operable to produce a quantized first in-phase component and a quantized first quadrature component; and
the combiner is operable to combine multiplicative products of any of the quantized first in-phase component, the quantized first quadrature component, the second in-phase component, and the second quadrature component to produce the combined signal.
32. The rotation-estimation circuit of claim 31 wherein the quantizer is further operable to receive the second complex signal and produce the additional signal.
33. The rotation-estimation circuit of claim 31 wherein the additional signal is the second complex signal.
34. The rotation-estimation circuit of claim 31 wherein the estimate generator includes a filter.
35. The rotation-estimation circuit of claim 34 wherein the filter includes an integrator.
36. The rotation-estimation circuit of claim 34 wherein the filter includes a low-pass filter.
37. The rotation-estimation circuit of claim 31 wherein the first complex signal and the second complex signal are substantially identical except for the relative rotation.
38. The rotation-estimation circuit of claim 31 , wherein:
the first complex signal includes a first in-phase component and a first quadrature component, and the second complex signal includes a second in-phase component and a second quadrature component;
the quantizer is operable to produce a quantized first in-phase component, a quantized first quadrature component, a quantized second in-phase component, and a quantized second quadrature component; and
the combiner is operable to combine multiplicative products of any of the quantized first in-phase component, the quantized first quadrature component, the quantized second in-phase component, and the quantized second quadrature component to produce the combined signal.
39. The rotation-estimation circuit of claim 31 wherein the combiner includes a summer.
40. The rotation-estimation circuit of claim 31 wherein the quantizer includes a one-bit quantizer.
41. The rotation-estimation circuit of claim 40 wherein the one-bit quantizer includes a comparator.
42. The rotation-estimation circuit of claim 40 wherein the first complex signal includes a first in-phase component and a first quadrature component, and the one-bit quantizer is operable to produce a quantized first in-phase component and a quantized first quadrature component.
43. The rotation-estimation circuit of claim 31 further comprising:
a sampler operable to sample at least one of the first complex signal and the second complex signal in time.
44. The rotation-estimation circuit of claim 31 further comprising:
a rotator operable to receive the estimate of the relative rotation and rotate at least one of the first complex signal and the second complex signal.
45. The rotation-estimation circuit of claim 44 wherein the first complex signal includes a first in-phase component and a first quadrature component, the second complex signal includes a second in-phase component and a second quadrature component, and the rotator is operable to produce a weighted sum of any of the first in-phase component, the first quadrature component, the second in-phase component, and the second quadrature component.
46. The rotation-estimation circuit of claim 31 further comprising:
a quantizer operable to receive the estimate of the relative rotation and produce a quantized estimate.
47. The rotation-estimation circuit of claim 31 further comprising:
a filter operable to receive at least one of the first complex signal and the second complex signal and produce a filtered signal.
48. A wireless transmitter operable to transmit a complex input signal, the wireless transmitter comprising:
a rotator operable to receive a first complex signal and adjust a phase of the first complex signal relative to a phase of a second complex signal to produce an adjusted signal, the rotator adjusting the phase of the first complex signal responsive to an estimate of a relative rotation between the first complex signal and the second complex signal; and
a rotation-estimation circuit, the rotation-estimation circuit including,
a quantizer operable to receive the first complex signal and produce a quantized signal;
a combiner operable to receive the quantized signal and an additional signal and produce a combined signal, the additional signal corresponding to the second complex signal; and
an estimate generator operable to receive the combined signal and produce the estimate of the relative rotation between the first complex signal and the second complex signal.
49. The wireless transmitter of claim 48 comprising:
a first mixer operable to mix the adjusted signal with a first local-oscillator signal to produce a modulated signal;
a second mixer operable to mix the modulated signal with a second local-oscillator signal to produce the second complex signal; and
a summer operable to combine the second complex signal and a complex input signal to produce the first complex signal.
50. The wireless transmitter of claim 48 comprising:
a filter operable to provide a gain to any of the first complex signal and the second complex signal.
51. The wireless transmitter of claim 48 wherein the rotator includes a mixer operable to mix the first complex signal with a local-oscillator signal to produce the adjusted signal, the rotator being operable to adjust a phase of the local-oscillator signal responsive to the estimate of the relative rotation between the first complex signal and the second complex signal.
52. The wireless transmitter of claim 48 wherein the quantizer is further operable to receive the second complex signal and produce the additional signal.
53. The wireless transmitter of claim 48 wherein the additional signal is the second complex signal.
54. The wireless transmitter of claim 48 wherein the estimate generator includes a filter.
55. The wireless transmitter of claim 48 wherein the first complex signal and the second complex signal are substantially identical except for the relative rotation.
56. The wireless transmitter of claim 48 wherein:
the first complex signal includes a first in-phase component and a first quadrature component, and the second complex signal includes a second in-phase component and a second quadrature component;
the quantizer is operable to produce a quantized first in-phase component and a quantized first quadrature component; and
the combiner is operable to combine multiplicative products of any of the quantized first in-phase component, the quantized first quadrature component, the second in-phase component, and the second quadrature component to produce the combined signal.
57. The wireless transmitter of claim 48 wherein:
the first complex signal includes a first in-phase component and a first quadrature component, and the second complex signal includes a second in-phase component and a second quadrature component;
the quantizer is operable to produce a quantized first in-phase component, a quantized first quadrature component, a quantized second in-phase component, and a quantized second quadrature component; and
the combiner is operable to combine multiplicative products of any of the quantized first in-phase component, the quantized first quadrature component, the quantized second in-phase component, and the quantized second quadrature component to produce the combined signal.
58. The wireless transmitter of claim 48 wherein the quantizer includes a one-bit quantizer.
59. The wireless transmitter of claim 58 wherein the one-bit quantizer includes a comparator.
60. The wireless transmitter of claim 58 wherein the first complex signal includes a first in-phase component and a first quadrature component, and the one-bit quantizer is operable to produce a quantized first in-phase component and a quantized first quadrature component.
61. The wireless transmitter of claim 48 wherein the first complex signal includes a first in-phase component and a first quadrature component, the second complex signal includes a second in-phase component and a second quadrature component, and the rotator is operable to produce a weighted sum of any of the first in-phase component, the first quadrature component, the second in-phase component, and the second quadrature component.